MICRO Week 8, MICRO Week 13 & 14, Week 11 Micro, MICRO Week 9, MICRO week 10, Week 10 Micro

The Optimality Condition for a Monopolist

*Why Interest in the Marginal Revenue Curve?* [8.2 slide 10] The vertical distance between the short-run total cost and total revenue curves is greatest when the two curves are parallel *MR(Q)=MC(Q)* Suppose this were not the case. For example, suppose that at the maximum-profit point the total cost curve were steeper than the total revenue curve. It would then be possible to earn higher profits by producing less output, because costs would go down by more than the corresponding reduction in total revenue. Conversely, if the total cost curve were less steep than the total revenue curve, the monopolist could earn higher profits by expanding output, because total revenue would go up by more than total cost.

CONCEPT CHECK

4.1, Slide 10-11

a. TC = 5,000 + 900q b. ATC = (5000 + 900q) / q c. very large because the average total cost of production falls with output.

A firm has a fixed production cost of ​$5,000 and a constant marginal cost of production of ​$900 per unit produced. a. What is the​ firm's total cost​ function? b. The​ firm's average total cost​ (ATC) of production is c. If the firm wanted to minimize the average total​ cost, would it choose to be very large or very​ small? Explain.

use more labor and less capital

A firm uses 80 hours of labor and 6 units of capital to produce​ 10,000 gadgets per day.​ Labor's marginal product is 4 gadgets per hour and the marginal product of capital is 20 gadgets per unit. Each unit of labor costs​ $8 per hour and each unit of capital costs​ $50 per unit. If the firm wants to continue producing​ 10,000 gadgets per day at the lowest possible​ cost, it should

decrease output until marginal revenue equals marginal cost.

A monopolist is producing at a point at which marginal cost exceeds marginal revenue. How should it adjust its output to increase​ profit? The monopolist should

Total Cost (TC)

All costs of production: the sum of variable cost and fixed cost.

How to Obtain the Demand Curve for Clean Air

Although there is no actual market for clean air, people do pay more for houses where the air is clean than for comparable houses in areas with dirtier air. Using data on house prices in neighborhoods of Boston and Los Angeles, researchers obtain an estimated demand curve for clean air that looks approximately like the one shown in the next figure. Air pollution here is measured by the level of nitrogen oxides (NOX), and the unit is parts per hundred million (pphm). The demand curve shows the household's willingness to pay for each additional unit of reduction in NOX level.

The Long Run

An amount of time needed to make all production inputs variable.

Long-Run Marginal Cost (LMC)

Analogously to the short-run case, long-run marginal cost (LMC) is the slope of the long-run total cost curve: LMC=ΔLTC/ΔQ. In words, LMC is the cost to the firm, in the long run, of expanding its output by 1 unit.

Economies of Scale

As output increases, the firm's average cost of producing that output is likely to decline, at least to a point. *Economies of scale:* Situation in which the LAC declines as output increases. Economies of scale can happen for the following reasons: 1. If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive. 2. The firm may be able to acquire some production inputs at lower cost because it is buying them in large quantities and can therefore negotiate better prices.

Regardless of whether MC is decreasing​, AVC could be increasing or decreasing depending on whether MC is greater than or less than AVC.

Assume that the marginal cost​ (MC) of production is decreasing. Can you determine whether the average variable cost​ (AVC) is increasing or​ decreasing? Explain.

there are at least as many possibilities for substitution between factors of production in the long run as in the short run.

At every output​ level, a​ firm's short-run average cost​ (SAC) equals or exceeds its​ long-run average cost​ (LAC) because

average variable cost equals marginal cost.

At the point where average variable cost reaches its minimum value

Monopoly

Average revenue equals price. The​ profit-maximizing output is the one at which marginal revenue and marginal cost are equal. The​ monopolist's demand curve is the same as the market demand curve. The​ profit-maximizing output is the one at which the difference between total revenue and total cost is largest.

Production

Can be described as a process that transforms inputs into outputs.

higher; smaller

Compared to the equilibrium price and quantity sold in a competitive​ market, a monopolist will charge a​ ____________ price and sell a​ ___________ quantity.

Fixed Cost (FC)

Cost that does not vary with the level of output in the short run (the cost of all fixed factors of production). Equipment rental payment, property taxes, insurance payments, interest on loans

Variable Cost (VC)

Cost that varies with the level of output in the short run (the cost of all variable factors of production). Labor cost

The Importance of Marginal Product Concept

Decisions about running an enterprise most naturally arise in the form of decisions about *marginal changes.* - Should we hire another engineer or accountant? Should we install another copier? Should we lease another delivery truck? To answer such questions intelligently, we must compare the benefit of the change in question with its cost. The marginal product concept plays a pivotal role in the calculation of the benefits when we alter the level of a productive input.

Aggregate Individual Demand Curves Algebraically

Derive the market demand for shelter in three steps: 1. Find the kink point price - The kink point price is the lower vertical intercept of the two demands. Set Q_A=8-0.5P=0, get P=16. Set Q_B=4-0.5P=0, get P=8. 8<16, so the kink point price is 8. 2. Find the aggregated demand for P≤8. - Within this rage for price, both demands are represented by their demand functions. Hence, the market demand for P≤8 is Q=Q_A+Q_B=(8-0.5P)+(4-0.5P)=12-P 3. Find the aggregate demand for 𝑃 > 8. - Within this price range, Bob's demand is 0. (not 𝑄_𝐵=4−0.5𝑃!). Andy's demand is still 𝑄_𝐴=8−0.5𝑃. Hence, the market demand for 𝑃>8 is 𝑄=𝑄_𝐴+𝑄_𝐵=(8−0.5𝑃)+0=8−0.5𝑃 [4.3 Slide 8]

decreases

Economies of scale happen when the​ firm's long run average total cost​ ________ as output increases.

The Monopolist's Total Revenue Curve

Facing the entire market demand curve, the monopolist must cut its price - not only for the marginal unit but for all preceding units as well - to sell a larger amount of output. Total revenue for the monopolist does not rise linearly with output. [8.2 slide 6] As an example, consider market demand P=80-1/5 Q For the monopolist to increase sales, it is necessary to cut price (top panel). Total revenue (π=PQ=80Q-1/5 Q^2) rises with quantity, reaches a maximum value, and then declines (middle panel). Price elasticity: ϵ=-5 P/Q=-400/Q+1 The quantity level for which the price elasticity of demand is unity corresponds to the midpoint of the demand curve, and at that value total revenue is maximized.

Engel curves always slope upward. This statement is

False because Engel curves slope downward for Giffen goods.

The Profit-Maximization Condition for a Monopolist

For any firm, when the firm produces, the profit-maximization condition is MR(Q)=MC(Q) For a monopolist, MR(Q)=ΔTR(Q)/ΔQ=P(Q)+(ΔP(Q))/ΔQ Q In particular, for a linear market demand P=t-kQ *MR(Q)=t-2kQ*

Marginal Revenue for a Monopolist: Any P(Q)

Generally, for any inverse demand function P(Q), when a monopolist raises output from Q_0 to (Q_0+ΔQ), the price drops from P_0 to (P_0+ΔP). (Note that ΔP is negative.) Two effects on his revenue 1. gain in revenue from new sales =(P_0+ΔP)ΔQ 2. loss in revenue from selling the previous output level at the new, lower price =ΔP ∙Q_0 The change in revenue at Q_0 due to this change ΔQ is ΔTR(Q_0)=(P_0+ΔP)ΔQ+ΔP ∙Q_0 The marginal revenue is MR(Q_0 ) = (ΔTR(Q_0))/ΔQ = ((P_0+ΔP)ΔQ+ΔP ∙Q_0)/ΔQ = (P_0+ΔP)+ΔP/ΔQ Q_0≈P_0+ΔP/ΔQ Q_0 The argument above holds for any Q_0 and P_0 on the demand curve, so we can drop the subscript 0 and write MR(Q) = P(Q)+(ΔP(Q))/ΔQ Q where P(Q) emphasizes that it is a function of Q. (ΔP(Q)) / ΔQ<0. Hence, the monopolist's marginal revenue at any output level is always less than the corresponding price

The Long-Run Expansion Path

Given sufficient time to adjust, the firm can always buy the cost-minimizing input bundle that corresponds to any particular output level and relative input prices. To see how the firm's costs vary with output in the long run (i.e. the long-run total cost curve), we need only compare the costs of the respective optimal input bundles. *Output expansion path* the locus of tangencies (minimum-cost input combinations) traced out by an isocost curve of given slope as it shifts outward into the isoquant map for a production process. This definition for output expansion path can be extended to allow changes in input prices. Such an extension reflects the possible changes in input prices due to increased bargaining power in the input markets as scale increases. [6.2 Slide 25] With fixed input prices r and w, bundles S,T, U, and others along the locus EE represent the least costly ways of producing the corresponding levels of output

Five Sources of Monopoly

How does a firm come to be the only one that serves its market? Economists discuss five factors, any one or combination of which can enable a firm to become a monopoly. 1. Exclusive Control over Important Inputs 2. Economies of Scale 3. Patents 4. Network Economies 5. Government Licenses or Franchises

The​ income-consumption curve

Illustrates the​ utility-maximizing combinations of goods associated with every income level.

MRTS as Ratio of Marginal Products

Imagine adding some labor (ΔL) and reducing the amount of capital just sufficient to keep output constant (ΔK; note that it is negative). - The gain in output is MP_L ΔL. (MP_L: the marginal product of labor.) - The reduction is MP_K ΔK. (MP_K: the marginal product of capital.) The reduction in output from having less K is exactly offset by the gain in output from having more L *MP_K ΔK+MP_L ΔL=0* Rearranging terms: *|ΔK/ΔL|=(MP_L)/(MP_K )* which says the MRTS is the ratio of the marginal product of labor to the marginal production of capital.

there will eventually be diminishing marginal products for the​ firm's variable inputs.

In the short run when some inputs are​ fixed, marginal cost must eventually rise as a​ firm's output increases because

Income-Consumption Curve (ICC)

Income: $40, 60, 100, 120 / wk. Py = $1 / unit, Ps = $10 / sq. yd. Holding the prices of X and Y constant, the ICC for a good X is the set of optimal bundles traced on an indifference map as income varies. The budget line shifts parallelly. For this given consumer, the quantity of each good consumed increases. But it does not have to be like this. For the consumer whose indifference map is shown, the ICC happens to be a straight line, but this need not always be the case.

Disagree: the student confused diminishing​ returns, which refers to the behavior of costs in the short​ run, with diseconomies of scale.

In​ 2019, an article in the Wall Street Journal noted that the federal​ government's Office of the Comptroller of the Currency had said about Wells Fargo​ bank, "We continue to be disappointed with...its inability to execute effective corporate governance and a successful risk management​ program." According to the​ article, a senior member of Congress​ "suggested the bank should be downsized because it was too large to​ manage." ​Source: Rachel Louise Ensign and Andrew​ Ackerman, "Regulator Slams Wells Fargo after CEO Testifies to​ Congress," Wall Street Journal​, March​ 12, 2019. After reading this​ article, a student​ remarks: "It seems that Wells Fargo is suffering from diminishing​ returns." Briefly explain whether you agree with this remark.

will not be a straight line if the ratio of inputs used changes with output.

Is the​ firm's expansion path always a straight​ line? A​ firm's expansion path

Inputs, or Factors of Production

Land, labor, capital, and entrepreneurship.

The Substitution and Income Effects of a Price Change for an Inferior Good

M=$24. P_H=$1/lb initially, then rises to $2/lb. To be as satisfied as before the price increase, need M′=$34. B′ is the corresponding imaginary budget line - parallel to B_1 and tangent to l_0. C is the imaginary intermediate optimal bundle. SE: A to C. IE: C to D. For an inferior good such as hamburger, the income effects works in the opposite direction from the substitution effect.

Inferior Good

One whose quantity demanded falls as income rises. Ex: Hamburger

Compare to a Competitive Firm's Total Revenue Curve

Recall that a competitive firm is facing a horizontal demand curve for its products. P(Q)=P^∗ Hence, TR(Q)=P(Q)∙Q =P^∗ Q

Isoquants

Such curves are called *isoquants,*and are defined as the set of all input combinations that yield a given level of output. Consider Q=F(K,L)=2KL. Suppose we want to describe all possible combinations of K and L that give rise to a particular level of output—say, Q=16. Solving Q=2KL=16 for K in terms of L yields *K=8/L* The (L, K) pairs that satisfy the above equation are shown by the curve labeled Q=16 in next figure. The curves labeled Q=32 and Q=64 are similarly obtained.

The Value of Clean Air

Suppose the government is interested in a Clean Air Program. The key question: Are the benefits of cleaning up the air sufficient to outweigh the costs? The benefits of cleaning up the air can be measured by consumer surplus.

Choosing Inputs to Minimize Total Cost

Suppose we wish to produce q_1. Given the isoquant curve q_1, there are many different bundles of (K,L) to produce q_1. How can we do so at minimum cost? Look at the firm's production isoquant, labeled q_1, in the graph on the next slide. The problem is to choose the point on this isoquant that minimizes total cost. The point of tangency of the isoquant q1 and the isocost line C1 at point A gives us the cost-minimizing choice of inputs, L1 and K1

Income Effect

That component of the total effect of a price change that results from the associated change in real purchasing power The direction of the income effect depends on whether the good is normal or inferior. - For normal goods, the same direction as the substitution effect - For inferior goods, the opposite direction

Example: A Competitive Firm's Marginal Revenue

The demand curve facing a competitive firm is horizontal: • P(Q)=P^∗ • (ΔP(Q))/ΔQ=0 Hence, MR(Q) = P(Q)+ΔP(Q)/ΔQ Q = P^∗+0×Q = P^∗

The Key Feature that Differentiates the Monopoly from the Competitive Firm

The feature is the price elasticity of demand facing the firm For the perfectly competitive firm, price elasticity is infinite: each firm faces a horizontal demand curve for its products. A monopoly faces the market demand curve and thus has significant control over the price it charges.

An Engel curve is​ backward-bending when

The good is inferior after a certain level of income.

Short Run

The period of time during which at least one of the inputs used in a production process cannot be varied. In the short run, assume labor input is variable but the capital input is fixed, say, at the value K=K_0=1. Then F(K,L)=2K_0 L=2L

Long Run

The period of time required to alter the amounts of all inputs used in a production process. In the long run, both K and L are variable, so F(K,L)=2KL

Long-Run Average Cost

The ratio of long-run total cost to output: LAC=LTC/Q

Marginal Revenue

The slope of the total revenue curve is the definition of marginal revenue. It is the change in total revenue when the sale of output changes by 1 unit. MR(Q)=(ΔTR(Q))/ΔQ Recall that for perfectly competitive firms, MR(Q)=P^∗, where P^∗ is the constant market equilibrium price taken as given by the firms. - Implied by TR(Q)=P^∗ Q. For a monopolist, will show that MR(Q)=P(Q)+(ΔP(Q))/ΔQ Q, where P(Q) is the market inverse demand function - Implied by TR(Q)=P(Q)∙Q

does not exist

The supply curve for a monopolist

Linear Isoquant

The​ slope, or the​ MRTS, is constant. This means that the same number of units of one input can always be exchanged for a unit of the other input and output can be maintained. The inputs are perfect substitutes.

Horizontal Summation

To get the market demand curve, we begin by calling out a price—say, $4/sq yd—and adding the quantities demanded by each consumer at that price. This sum, 6 sq yd/wk + 2 sq yd/wk = 8 sq yd/wk, is the total quantity of shelter demanded at the price $4/sq yd. We then plot the point (8, 4) as one of the quantity-price pairs on the market demand curve D. To generate additional points on the market demand curve, we simply repeat this process for other prices. The procedure of announcing a price and adding the individual quantities demanded at that price is called horizontal summation.

The level of utility increases as an individual moves downward along the demand curve. This statement is

True because price decreases pivot the budget line outward.

Perfect Complements

Typing: typists and typewriters MRTS not defined

will lose money if it remains in business.

What is likely to happen in the long run to firms that do not reach minimum efficient​ scale? A firm that does not reach its minimum efficient scale

the level of output at which the long−run average cost of production no longer decreases with output.

What is minimum efficient​ scale? Minimum efficient scale is

The Nature of a Good may Change as Income Changes

[4.1 Slide 25] Whether a good is normal or inferior can change as income changes. Hamburger, though a normal good between A and B, becomes an inferior good when the income-consumption curve bends backward between B and C.

Concept Check

[4.2 Slide 11]

A giffen good

is the special subset of inferior goods in which the income effect dominates the substitution effect.

When the price of good X increases and all goods​ (including X) are normal​ goods, the income effect leads consumers to buy

less of all goods

Isoquants

"Iso" comes from the Greek word for "same" Similarity of an isoquant map to an indifference map: movements towards northeast means increasing levels of output. Difference: outputs are cardinal, whereas utilities are ordinal.

a. increase; remain unchanged; increase b. remain unchanged; increase; increase

*Suppose a firm must pay an annual​ tax, which is a fixed​ sum, independent of whether it produces any output. How does this tax affect the​ firm's fixed,​ marginal, and average​ costs?* a. With a​ lump-sum tax, the fixed cost of production will ________ the marginal cost of production will ______ _________ and the average cost of production will ________. *Now suppose the firm is charged a tax that is proportional to the number of items it produces.​ Again, how does this tax affect the​ firm's fixed,​ marginal, and average​ costs?* b. With a proportional​ tax, the fixed cost of production will ______ _________ the marginal cost of production will ________ and the average cost of production will ________.

Effect of Changes in Input Prices

Changes in relative price alters the slope of isocost lines, causing the lowest workable isocost line to rotate around the given isoquant. Consequence: the firm uses more of the cheaper input.

Isoquant Curve

A curve that shows all the combinations of inputs that yield the same total output

total costs to increase by more than double when output doubles.

If input prices are constant in the long​ run, a firm with decreasing returns to scale can expect

Giffen Goods

[4.2 Slide 13] For certain inferior goods, the magnitude of the income effect is large enough to overwhelm the substitution effect. Upward sloping demand curve Income effect would be so large that it offsets substitution effect - IE: C to D - SE: A to C

Perfect Substitutes

[5.3 Slide 17] Car wash: workers vs automatic wash systems. MRTS is some constant.

Consumer Surplus

*Surplus:* Net benefits; net of expenditures When exchange takes place *voluntarily,* economists generally assume it makes all participants better off. Otherwise they would not have engaged in the exchange. *Consumer Surplus*: a dollar measure of the extent to which a consumer benefits from participating in a transaction. Useful for evaluating potential government programs. - Costs and benefits of building a road

Total Product Curve

A curve relates the total amount of output to the quantity of the variable input.

What is a production​ function? How does a​ long-run production function differ from a​ short-run production​ function?

A function showing the highest output that a firm can produce for every specified combination of inputs. In the​ long-run production​ function, all inputs are​ variable, whereas the​ short-run production function has at least one fixed input.

Monopoly

A market structure in which a single seller of a product with no close substitutes serves the entire market. A simply definition; but exceedingly difficult to apply in practice Is a local movie theater a monopoly? Depends on what we mean by a close substitute: - To casual moviegoers, a theater showing Halloween Part 8 is likely to have a rich variety of close substitutes (the market of low-grade blood-and-gore movies) - To Spiderman fans, a theater that is in the midst of an exclusive 6-month, first-run engagement of the latest Spiderman film has no close substitute

Variable Input

A production input that can be varied in both the short run and the long run is called a

In tracing out a​ price-consumption curve​ (PCC) for good​ X, which of the following variables is held​ constant? A. Consumer satisfaction​ (utility). B. Consumer income. C. Consumption of all other goods. D. The price of good X.

Consumer Income

The Monopolist's Total Revenue Curve

Mathematically, for any form of P(Q) TR(Q)=P(Q)∙Q where ∙ denotes multiplication. For the example P(Q)=80-1/5 Q, TR(Q)=(80-1/5 Q)Q =80Q-1/5 Q^2 For the parabola y=ax^2+bx+c, the axis of symmetry is -b/2a. Apply the result here, the axis of symmetry is -b/2a=-80/2(-1/5) =200.

Normal Good

One whose quantity demanded rises as income rises. When income rises, many consumers switch from low-priced ground beef with high fat content to leaner, more expensive, cuts of meat Ex: Tenderloin

No Supply Curve For The Monopolist

Reason: the monopolist is not a price taker - There is no unique correspondence between price and marginal revenue when the market demand curve shifts - As a result, it is possible to observe the monopolist producing Q1* and selling at P*, and then selling Q2* at P* in another period - No unique correspondence between P and Q and thus no supply curve exists for the monopolist.

Substitution Effect

That component of the total effect of a price change that results from the associated change in the relative attractiveness of other goods. Always causes the quantity purchased to move in the opposite direction from the change in price.

L- Shaped Isoquant

The inputs are perfect​ complements, or that the firm is producing under a fixed proportions type of technology. In this​ case, the firm cannot give up one input in exchange for the other and still maintain the same level of output.

LAC and Industry Structure

The shape of LAC is important because of its effect on the structure of industry. Downward sloping throughout (U-shaped LAC, with Q_0 greater than the whole industry output): *a single firm* *natural monopoly:* an industry whose market output is produced at the lowest cost when production is concentrated in the hands of a single firm. U-shaped LAC, with Q_0 constituting a substantial share of industry output: *a small handful of big firms* U-shaped LAC, with Q_0 constituting a small fraction of industry output: *numerous small firms*

Keep price and output the same.

What would a​ profit-maximizing monopoly do in the short run if its fixed costs​ increased?

net loss in consumer and producer surplus due to a​ monopolist's pricing​ strategy/policy.

With respect to​ monopolies, deadweight loss refers to the

Marginal Cost

is the change in total cost that results from producing an additional unit of output. MC=ΔTC/ΔQ=ΔVC/ΔQ. The second equality holds since ΔFC/ΔQ is zero. MC Curve: [6.1 Slide 26] MC at any level of output Q is the slope of the TC (or VC) curve at that Q. The MC curve is downward sloping up to the inflection point of the TC curve at Q_1 and upward sloping thereafter. The MC curve intersects the ATC and AVC curves at their respective minimum points. When MC < average cost (either ATC or AVC), MC drags down the average cost curve; when MC > average cost, MC pulls up the average cost curve. (slope) Geometrically, marginal cost at any level of output may be interpreted as the slope of the total cost curve at that level of output. And since the total cost and variable cost curves are parallel, marginal cost is also equal to the slope of the variable cost curve. (Recall that the variable cost component is all that varies when total cost varies, which means that the change in total cost per unit of output must be the same as the change in variable cost per unit of output.) (minimum) Notice in the top panel in Figure 9.5 that the slope of the total cost curve decreases with output up to Q1, and rises with output thereafter. This tells us that the marginal cost curve, labeled MC in the bottom panel, will be downward sloping up to Q1 and upward sloping thereafter. Q1 is the point at which diminishing returns set in for this production function, and diminishing returns are what ac-count for the upward slope of the short-run marginal cost curve. (intersection) At the output level Q3, the slope of the total cost curve is exactly the same as the slope of the ray to the total cost curve (the ray labeled R1 in the top panel in Figure 9.5). This tells us that marginal cost and average total cost will take precisely the same value at Q3. To the left of Q3, the slope of the total cost curve is smaller than the slope of the corresponding ray, which means that marginal cost will be smaller than average total cost in that region. For output levels in excess of Q3, the slope of the total cost curve is larger than the slope of the corresponding ray, so marginal cost will be larger than average total cost for output levels larger than Q3. These relationships are reflected in the average total cost and marginal cost curves shown in the bottom panel in Figure 9.5. Notice that the relationship between the MC and AVC curves is qualitatively similar to the relationship be-tween the MC and ATC curves. One common feature is that MC intersects each curve at its minimum point. Both average cost curves have the additional property that when MC is less than average cost (either ATC or AVC), the average cost curve must be decreasing with output; and when MC is greater than average cost, average cost must be increasing with output.

The horizontal summation of the demands of each consumer at different price levels is called

the market demand curve.

The monopolist is not maximizing profit and should decrease output.

Which of the following is true at the output level where P​ = MC?

the long-run average cost curve

Which of the following terms refers to the lowest cost at which a firm is able to produce a given level of output in the long​ run, when no inputs are​ fixed?

Two Properties of The Individual Demand Curve

The level of utility that can be attained changes as we move along the curve. At every point on the demand curve, the consumer is maximizing utility.

the isoquant line is tangent to the isocost line.

When the cost minimizing combination of inputs is being used and there is no corner​ solution,

The Conditions for Cost Minimization

*Condition 1:* tangency of the isoquant and isocost curves - slope of the isoquant =-MRTS - slope of the isocost =-w/r It follows that the tangency rule can be written as MRTS=w/r For example, for the production function f(L,K)=LK, MP_L=K and MP_K=L, which implies MRTS=〖MP〗_L∕〖MP〗_K =K/L. If w=$10 per hour and r=$20 per hour, the tangency condition is K/L=10/20. Two equivalent ways to get MRTS: 1. By definition: set q ̅=LK. Then K=q ̅/L. Differentiate K w.r.t. L yields dK/dL=-q ̅/L^2 =-K/L, where the last equality follows from K=q ̅/L. 2. Use the ratio of MP's: (MP_L)/(MP_K )=K/L *Condition 2:* the combination is on the given isoquant. If Q=f(L,K) is the known production function, and q ̅ is the output the firm wants, then the cost minimizing combination (L,K) must produce q ̅, f(L,K)=q ̅ For example, for f(L,K)=LK and a given output level 100, the condition is simply LK=100. Combine conditions 1 and 2 allows us to solve for the cost minimizing bundle.

a. when a​ firm's long-run average costs increase with output. b. Firms have difficulty coordinating production

*What are diseconomies of scale?* a. Diseconomies of scale is *What is the main reason that firms eventually encounter diseconomies of scale as they keep increasing the size of their store or​ factory?*

Income and Substitution Effects

A change in the price of a good affects purchase decisions for two reasons. For example, if the price of a good *increase:* - Its close substitutes become more attractive than before. - The consumer's purchasing power decreases. For example, when the price of rice increases, wheat becomes more attractive. For a normal good, the loss in purchasing power will further reduce the amount purchased. But for an inferior good, the effect is just the opposite.

constant but otherwise unknown without information about the marginal product of each input.

A firm has a production process in which the inputs to production are perfectly substitutable in the long run. Can you tell whether the marginal rate of technical substitution is high or​ low, or is further information​ necessary? Discuss. *In this​ example, the marginal rate of technical substitution​ (MRTS) is*

a. not minimizing the cost of production because MPK/r < MPL/w b. The firm could decrease the cost of production holding output constant by using more labor and less capital

A firm produces output with capital and labor. Suppose currently the marginal product of labor is 29 and the marginal product of capital is 5. Each unit of labor costs ​$6 and each unit of capital costs ​$2. Is the firm minimizing the cost of​ production? Explain. Let MPK be the marginal product of​ capital, MPL be the marginal product of​ labor, r be the price of​ capital, w be the cost of​ labor, and MRTS be the marginal rate of technical substitution. a. The firm is b. If​ not, how could the firm decrease the cost of production holding output​ constant?

Patents

A patent typically confers the right to exclusive benefit from all exchanges involving the invention to which it applies. - Cost: higher price to consumers - Benefit: encourages inventions that would not otherwise occur US: 17 years. A compromise figure that is too long for many inventions, too short for many others. For prescription drug, for example, the testing and approval process often consumes all but a few years of the current patent period.

Fixed Input

A production input that can only be varied in the long run is called a

a. that​ aren't producing at minimum efficient scale will have higher costs than their competitors. b. fewer firms in the industry and the remaining firms will likely be larger.

An article in the Wall Street Journal described the Chinese automobile industry as​ "a hodgepodge of​ companies," most of which produce fewer than​ 100,000 cars per year. Ford Chief Executive Alan Mulally commented on the situation by​ saying, "If you​ don't have​ scale, you just​ won't be able to be​ competitive." ​Source: Colum​ Murphy, "Chinese Car Makers Struggle to Lure​ Buyers," Wall Street Journal​, April​ 19, 2014. a. Mulally meant that Chinese firms b. We can predict​ that, as the Chinese automobile industry develops over the next 10​ years, there should be

Example 7.4 The Effect of Effluent Fees on Input Choices

An effluent fee is a per-unit fee that a steel firm must pay for the effluent that goes into the river. What is the effect of an effluent fee on the amount of wastewater dumped by the steel firm? [6.2 Slide 22] When the firm is not charged for dumping its wastewater in a river, it chooses to produce a given output using 10,000 gallons of wastewater and 2000 machine-hours of capital at A. However, an effluent fee raises the cost of wastewater, rotates the isocost curve from FC to DE, and causes the firm to produce at B—a process that results in much less effluent. The manager estimates that a machine-hour costs $40 and that dumping each gallon of wastewater in the river costs $10. The total cost of production is therefore $180,000: $80,000 for capital and $100,000 for wastewater.

The Isocost Curve

An isocost curve shows all possible combinations of labor and capital that can be purchased for a given total cost. The total cost C of producing any particular output is given by the sum of the firm's labor cost wL and its capital cost rK: *C=wL+rK* For each different level of total cost, the equation above describes a different isocost line. If we rewrite the total cost equation as an equation for a straight line, we get K= (C / r) - (w / r)L. It follows that the isocost line has a slope of ΔK/ΔL = -w∕r, the ratio of the wage rate to the rental rate of capital.

Diseconomies of Scale

At some point, however, it is likely that the average cost of production will begin to increase with output. *Diseconomies of scale:* Situation in which the LAC increase as output increases. Diseconomies of scale can happen for the following reasons: 1. Managing a larger firm may become more complex and inefficient as the number of tasks increases 2. The advantages of buying in bulk may have disappeared once certain quantities are reached. At some point, available supplies of key inputs may be limited, pushing their costs up.

Conclusion

Bundle D shows that if consumers got exactly the same amount of gas tax back as a rebate, they would buy less gasoline. Since gasoline is a normal good in the graph, the effect of the rebate is to offset only partially the income effect of the price increase. It does nothing to alter the substitution effect. The critics were wrong! The Carter administration's tax-and-rebate proposal was never implemented, largely because of the objections of critics who lacked the economic knowledge to understand it. The policy is an even more compelling idea today with global demand for oil growing at record rates, with heightened political instability in the Middle East, and with the approaching threat imposed by global climate change. If gasoline is inferior, there is no need to do this analysis, because a rebate would for sure decrease the consumption of gasoline.

Curvature of the VC Curve

Concave production function for L<4 → convex VC for Q<43 Increasing returns to labor for L<4: increments in L produce successively larger increments in Q in that region. Put another way, a given increase in output Q requires successively smaller increments in the variable input, L, i.e. VC=wL grows at a diminishing rate for output levels less than 43. Convex production function for L<4 → convave VC for Q<43 Diminishing returns to labor for L>4: ... Successively larger increments in L are required to produce a given increment in Q, i.e., VC grows at an increasing rate for output levels greater than 43. We can also describe the curvature of VC more rigorously using the following result: MC=ΔVC/ΔQ=wΔL/ΔQ=w/(ΔQ/ΔL)=w/(MP_L ) where the last equality holds because ΔQ/ΔL=MP_L, the marginal product of labor. The first "=": the marginal cost (MC) is the change in variable cost (VC) for a 1-unit change in output (q), i.e., MC=ΔVC/Δq. The second "=": the change in variable cost is the per unit cost of the extra labor, the wage rate w, times the amount of extra labor needed to produce the extra output, ΔL. That is, ΔVC=wΔL. The last "=": the marginal product of labor MP_L is the change in output resulting form a 1-unit change in labor input, or MP_L=Δq/ΔL. Therefore, the extra labor needed to obtain an extra unit of output is ΔL/Δq=1/MP_L.

Production Function

Consider a production process that employs two inputs, capital (K) and labor (L), to produce meals (Q) *Q=F(K,L)* where F is a mathematical function that summarizes the production process. For example, F(K,L)=2KL, where K is measured in equipment-hours per week, L is measured in person-hours per week, and output is measured in meals per week. (That is, both inputs and outputs are flows.) The function from of F can be used to reflect the technology of production. For example, the coefficient 2 in F(K,L)=2KL can be used to reflect a certain level of technology of production. If it increases to 3, the technology of production advances.

Concept Check

Consider a short-run production process for which AP_(L=10)=7 and MP_(L=10)=12. If we increase the labor input by a sufficiently small amount, will AP_L increases or decreases at L=10 for this process? APL increases

Production in the Short Run

Consider again Q=F(K,L)=2KL, where K is measured in equipment-hours per week, L is measured in person-hours per week, and output is measured in meals per week. Suppose in the short run, the labor input is variable but the capital input is fixed, say, at the value K=K_0=1. Then the short-run production function is Q=F(K_0,L)=2L We can plot this production function in a two-dimensional diagram, as in (a). Generally, for F(K_0,L)=2K_0 L, the graph is a straight line through the origin whose slope is ΔQ/ΔL=2K_0 for any fixed K_0.

a. Diminishing marginal​ returns, where additional cooks produce less additional output. b. Yes, restaurant owners can vary the​ size, or​ number, of kitchens.

Devra​ Gartenstein, a restaurant​ owner, made the following observation about preparing​ food: "Cooks become increasingly less productive as a kitchen becomes increasingly​ crowded." a. *What do economists call the problem she is​ describing? What are its implications for the marginal product of labor for​ cooks?* b. *Do restaurant owners have a solution to this problem in the long​ run? Briefly explain.*

Does Monopoly Profits Persist?

Economic profit sometimes tend to vanish in the long run for a monopolist. - To the extent that the factors that gave rise to the firm's monopoly position come under attack in the long run, there will be downward pressure on its profits. But in other cases there may be a tendency for monopoly profits to persist. - Natural monopoly due to declining LAC. As we saw in Chapter 10, economic profits tend to vanish in the long run in perfectly competitive industries. This tendency will sometimes be present for monopoly. To the extent that the factors that gave rise to the firm's monopoly position come under attack in the long run, there will be downward pressure on its profits. For example, competing firms may develop substitutes for important inputs that were previously under the control of the monopolist. Or in the case of patented products, competitors may develop close substitutes that do not infringe on existing patents, which are in any event only temporary. But in other cases there may be a tendency for monopoly profits to persist. The firm shown in Figure 11.12, for example, has a declining long-run average cost curve, which means that it may enjoy a persistent cost advantage over potential rivals. In such natural monopolies, economic profits may be highly stable over time. And the same, of course, may be true for a firm whose monopoly comes from having a government license.

Exclusive Control over Important Inputs

Examples: - Perrier bottled mineral water: exclusive control over a spring - DeBeers Diamond Mines' exclusive control over most of the world's supply of raw diamonds Not a guarantee of permanent monopoly: New ways are constantly being devised of producing existing products. The Perrier Corporation of France spends millions of dollars each year advertising the unique properties of this water. The commercials says the water is of a once-in-eternity confluence of geological factors that created their mineral spring. A similar monopoly position has resulted from the deBeers Diamond Mines' exclusive control over most of the world's supply of raw diamonds. Exclusive control of key inputs is not a guarantee of permanent monopoly power. The preference for having a real diamond, for example, is based largely on the fact that mined diamonds have historically been genuinely superior to synthetic ones. But assuming that synthetic diamonds eventually do become completely in-distinguishable from real ones, there will no longer be any basis for this preference. And as a result, deBeers' control over the supply of mined diamonds will cease to confer monopoly power. New ways are constantly being devised of producing existing products, and the exclusive input that generates today's monopoly is likely to become obsolete tomorrow.

The MRTS gives the amount by which the quantity of one input can be reduced when one extra unit of another input is​ used, so that output remains constant.

Explain the term​ "marginal rate of technical​ substitution." ​(Assume a​ two-input production function.​) What does a MRTS​ = 3 mean? It means that if the input on the horizontal axis is increased by one​ unit, then the input on the vertical axis *decreases* by 3 units and output will *not change.*

Fixed Cost Curve

FC is flat. The vertical distance between TC and VC is everywhere FC: TC=FC+VC Note that the TC of producing zero output is equal to FC. (FC) Because fixed costs do not vary with the level of output, their graph is simply a horizontal line. (TC) Because TC=FC+VC, the TC curve can be obtained by parallelly shifting the VC curve upward by the amount of the FC. Put another way, the vertical distance between the VC and TC curves is everywhere equal to FC. The total cost curve is parallel to the variable cost curve and lies FC units above it. Note in particular that the total cost of producing zero output is equal to fixed costs, FC. This means that the FC is there no matter you produce or not. It also means that if you are given a TC function, which is a function of Q, you can find the FC by setting Q=0.

slope of the isocost lines will​ change, and the firm will substitute toward the relatively cheaper input​, pivoting the expansion path toward the axis of the relatively cheaper input.

How does a change in the price of one input change the​ firm's long-run expansion​ path? If the price of an input​ changes, then the

Government Licenses or Franchises

In many markets, the law prevents any-one but a government-licensed firm from doing business. - At rest areas on the Massachusetts Turnpike, the Turnpike Authority negotiates with several fast-food companies, chooses one, and then grants it an exclusive license to serve a particular area. (A scale economy acting in another form.) - Some airport authorities auction their terminal counter space to the highest bidders. The Turnpike's purpose in restricting access in the first place is that there is simply not room for more than one establishment in these locations. Price and government licenses Government licenses are sometimes accompanied by strict regulations that spell out what the licensee can and cannot do. Where the government gives a chain restaurant an exclusive license, for example, the restaurant will often be required to charge prices no more than, say, 10 percent higher than it charges in its unregulated outlets. •In other cases, the government simply charges an extremely high fee for the license, virtually forcing the licensee to charge premium prices. This is the practice of some airport authorities, who essentially auction their terminal counter space to the highest bidders. Your annoyance at having to pay $5 for a hot dog in LaGuardia Airport is thus more properly focused on the Port Authority of New York than on the vendor.

Short Run vs. Long Run

In practice, there are many production processes in which the quantities of at least some inputs cannot be altered quickly, making it useful to distinguish between: - *Long Run:* the period of time required to alter the amounts of all inputs used in a production process. - *Short Run:* the period of time during which at least one of the inputs used in a production process cannot be varied. This gives rise to the distinction between: - *Variable Input:* an input that can be varied in the short run - *Fixed Input:* an input that cannot vary in the short run In the long run, all inputs are variable inputs, by definition. *Transit:* The production function tells us how output will vary if some or all of the inputs are varied. In practice, there are many production processes in which the quantities of at least some inputs cannot be altered quickly. (Example) The FM radio broadcast of classical music is one such process. To carry it out, complex electronic equipment is needed, and also a music library and a large transmission tower. Records and compact discs can be purchased in a matter of hours. But it may take weeks to acquire the needed equipment to launch a new station, and months or even years to purchase a suitable location and construct a new transmission tower. (transit) This difference in the times needed to adjust the amount of various inputs makes it useful to distinguish between the short run and the long run in production. (Concepts) Formally, the long run is defined as the period of time required to alter the amounts of all inputs used in a production process, whereas the short run is defined as the period of time during which at least one of the inputs used in a production process cannot be varied. This divide between the short run and the long run also gives rise to the distinction between two types of inputs, namely the variable input and the fixed input. By definition, a variable input is an input that can be varied in the short run to change the output level. A fixed input on the other hand is defined as an input that cannot vary in the short run. Note that in the long run, all inputs are variable inputs by definition. (Example) In the classical music broadcast example, compact discs are variable inputs in the short run, but the broadcast tower is a fixed input. If sufficient time passes, however, even the broadcast tower becomes a variable input. (Specific length) Note that short run or long run is not associated with a specific period of time. In the FM radio example, the long run is months or years. In some production activities, like those of a street-corner hot dog stand, the long run may be just a few days.

Since firms can reach minimum efficient scale at a relatively low output​ rate, there will continue to be a large number of firms drilling for oil in the United States

In recent​ years, the United States has experienced large increases in oil production. The increases in oil production are due in large part to a new​ technology, hydraulic fracturing​ ("fracking"). Fracking involves injecting a mixture of​ water, sand, and chemicals into rock formations at high pressure to release oil and natural gas. A news story indicates that economies of scale in fracking may be considerably smaller than in conventional oil drilling. ​ Source: Russell Gold and Theo​ Francis, "The New Winners and Losers in​ America's Shale​ Boom," Wall Street Journal​, April​ 20, 2014. If this view is​ correct, what would the likely consequences be for the number of firms drilling for oil in the United​ States?

The Importance of MC

In terms of its role in the firm's decision of how much output to produce, by far the most important of the seven cost curves is the marginal cost curve. The firm's typical operating decision involves the question of whether to expand or contract its current level of output. To make this decision intelligently, the firm must compare the relevant costs and benefits. The cost of expanding output (or the savings from contracting) is by definition equal to marginal cost. In terms of its role in the firm's decision of how much output to produce, by far the most important of the seven cost curves is the marginal cost curve. The reason, as we will see in the coming chapters, is that the firm's typical operating decision involves the question of whether to expand or contract its current level of output. To make this decision intelligently, the firm must compare the relevant costs and benefits. The cost of expanding output (or the savings from contracting) is by definition equal to marginal cost.

Flexibility in Long-Run Production

In the long run, a firm has much more flexibility. It can expand its capacity by expanding existing factories or building new ones; it can expand or contract its labor force, and in some cases, it can change the design of its products or introduce new products. Such flexibility gives rise to a cost minimization problem: how a firm can choose its combination of inputs to minimize its cost of producing a given output. For simplicity, we will work with two variable inputs: labor (L) and capital (K). It is useful to have an object that can describe all the input combinations that produces the same output level. That object is the isocost curve.

Too Many Dimensions

In the long run, all factors of production are by definition variable. This creates a problem for graphical representation: - For Q=F(K,L) with both K and L variable, we need a three-dimensional diagram to deprescribe the production function. - When there are more than two variable inputs, we require even more dimensions. Solution: *isoquants.* The idea is similar to using indifference curves to describe utility functions of two goods.

Adjustments in the Long Run

In the long run, the monopolist is of course free to adjust all inputs, just as the competitive firm is. What is the optimal quantity in the long run for a monopolist with a given technology? The best the monopolist can do is to produce the quantity for which long-run marginal cost is equal to marginal revenue.

Network Economies

On the demand side of many markets, a product becomes more valuable as greater numbers of consumers use it. - Ecosystem; - Microsoft's Windows operating system on personal computers: the inventory of available software and games is vastly larger than for any competing operating system. The more people who own the product, the higher its effective quality level. - Put different, any given quality level can be produced at lower cost as sales volume increases. - Thus can be viewed as another form of economies of scale

Giffen Good

One for which the quantity demanded rises as its price rises. Examples are rare. Often associated with extremely low income levels. - Potato during the Irish potato famine A much-cited example of a Giffen good was the potato during the Irish potato famine of the nineteenth century. The idea was that potatoes were such a large part of poor people's diets to begin with that an increase in their price had a severe adverse effect on the real value of purchasing power. Having less real income, many families responded by cutting back on meat and other more expensive foods and buying even more potatoes. Food is an inferior, as well as a Giffen good (concept check solution)

Common Properties of Short-Run Production Functions

Passes through the origin Output initially grows at an increasing rate. - The benefits of division of tasks and specialization of labor Beyond some point, output grows at a diminishing rate with increases in the variable input — *the law of diminishing returns.* Eventually, the limitation of fixed capital emerges, and employees starts to get in each other's way. The property that output initially grows at an increasing rate may stem from the benefits of division of tasks and specialization of labor. With one employee, all tasks must be done by the same person, while with two or more employees, tasks may be divided and employees may better perform their dedicated tasks. (Example) To understand the benefits of division of tasks and specialization of labor, imagine you manages a kitchen in a restaurant. When you have only one chef working in the kitchen, he needs to do everything by himself, and when he switches from preparing vegetables to cooking them, he needs to move around, he may also need to change his equipment, all of which takes times. Also, he may not be good at every step. When you add one more chef to the kitchen, then each can specialization in one task. You will save the transition time, and each chef can specialize in his own task to further improve his skills in that task. Overall, having one more chef more than doubles the productivity, and you will see the output increases at an increasing rate. The final property noted about the short-run production function —that beyond some point, output grows at a diminishing rate with increases in the variable input—is known as the law of diminishing returns. And although it too is not a universal property of short-run production functions, it is extremely common. (Example) This law of diminishing returns can also be understood with the help of the restaurant kitchen example. After all, the size of the kitchen and the number of stoves are fixed at least in the short run. If you keep hiring more chefs to work for you, at some point, the benefits from division of labor and specialization will be exhausted, and they may started to get in each other's because of the limited space and equipment. The result is that output will start to increase at a slower and slower rate.

Motivation

Recall that the market demand curve tells how much of a good the market as a whole wants to purchase at various prices. Suppose we want to generate a demand schedule for a good—say, shelter—not for the market as a whole but for only a single consumer Holding income, preferences, and the prices of all other goods constant, how will a change in the price of shelter affect the amount of shelter the consumer buys?

Does Monopoly Result in Efficiency?

Recall the claim that perfect competition led to an efficient allocation of resources. - In a perfectly competitive equilibrium, there are no possibilities for additional gains from exchange. - The value to buyers of the last unit of output is exactly the same as the market value of the resources required to produce it. - The total surplus (consumer surplus + producer surplus) is maximized. How does the equilibrium under monopoly measure up by the same criteria?

Marginal Revenue and Elasticity

Recall the price elasticity of demand ϵ = ΔQ / ΔP P/Q Implies: ΔP/ΔQ = 1/ϵ P/Q Hence MR(Q) = (1+1/ϵ)P(Q)

Production Function in the Short Run vs. The Long Run

Recall: Q=F(K,L)=2KL In the long run, both K and L are variable, so *F(K,L)=2KL* In the short run, assume labor input is variable but the capital input is fixed, say, at the value K=K_0=1. Then *F(K,L)=2K_0 L=2L* (transit) What about the production equation Q=F(K,L) we mentioned? How does this differentiation between the short run and the long run affect it? Consider again the production process described by 2KL. In the long run, both K and L are variable, the period of time is long enough to change both of them, so, the long-run production function is just 2KL itself. In the short run, things are different. Suppose we are concerned with production in the short run—here, a period of time in which the labor input is variable but the capital input is fixed, say, at the value K=K_0=1. With capital held constant, output becomes, in effect, a function of only the variable input, labor: F(K,L)=2K_0 L=2L. The short-run production function Q=2L corresponds to the first row of the previous table. (Implication) What's the implication? Well, obviously, the short-run production function is easier to analyze because it is a function of only one variable. Graphically, it means we can plot the production function in a two-dimensional diagram. For the long-run production function, things are a little more complicated and we need to use some other tools to represent the production function graphically in a two-dimensional diagram.

Sally's GPA for this semester is lower than her cumulative GPA.

Sally looks at her college transcript and says to​ you, ​ "How is this​ possible? My grade point average​ (GPA) for this​ semester's courses is higher than my GPA for last​ semester's courses, but my cumulative GPA still went down from last semester to this​ semester." *Explain to Sally how this is possible.*

a. 35 pizzas ( 28 + 40 + 37 = 105 / 3 = 35 ) b. Decrease

Suppose Anna hires workers to cook pizzas. If the first​ worker's marginal product is 28 pizzas​, the second​ worker's marginal product is 40​, and the third​ worker's marginal product is 37​, then the average product of labor is __ pizzas. ​(Enter a numeric response using a real number rounded to one decimal​ place.) Now suppose Anna hires a fourth worker whose marginal product is below the average. If​ so, then the average product of labor will _______.

a. 4 b. 5 (9 - 4 = 5) c. 7 (16 - 9 = 7) d. Specialization

Suppose Charles owns a​ lawn-mowing company. Assume that without​ workers, no yards are mowed. When he hires one​ worker, he is able to mow 4 yards per day. With two​ workers, he can mow 9 yards per​ day, and with three​ workers, he can mow 16 yards per day. a. *The marginal product of the first worker is __ yards per day.* b. *The marginal product of the second worker is __ yards per day.* c. *Last, the marginal product of the third worker is __ yards per day.* d. *The marginal product of labor potentially increases​ (from one to three​ workers) due to ___*

a. No since MPL/w does not equal MPC / c b. Yes, they need to increase L which would cause MPL to decrease and MPc to increase

Suppose that a paving company produces paved parking spaces​ (q) using a fixed quantity of land​ (T) and variable quantities of cement​ (C) and labor​ (L). The firm is currently paving​ 1,000 parking spaces. The​ firm's cost of cement is ​$4,200.00 per acre covered​ (c) and its cost of labor is ​$35.00​/hour ​(w). For the quantities of C and L that the firm has​ chosen, MPC=70 and MPL=7. a. Is this firm minimizing its cost of producing parking​ spaces? b. Does the firm need to alter its choices of C and L to decrease​ cost?

Two Facts and Their Conclusions

The ICC traces out how the consumer's consumption will vary as a function of the size of the rebate. For any given quantity of gasoline consumed, the vertical distance between budget constraints B1 and B2 corresponds to the total amount of tax paid on that amount of gasoline. The two facts above implies: the rebate size needed to consume bundle D is exactly equal to the tax on gasoline at bundle D (Sketch of the proof is on the last slide of this section.) Fact 1 is a result of the setup that the price of the composite good is $1 per unit.

A Gasoline Tax-and-Rebate Policy

The administration of President Jimmy Carter proposed to use gasoline taxes to help limit the quantity demanded of gasoline, thereby making the United States less dependent on foreign sources of oil. One immediate objection to this proposal was that the resulting rise in gasoline prices would impose economic hardship on the poor. Anticipating this objection, the Carter administration proposed to ease the burden on the poor by using the proceeds of the gasoline tax to reduce the payroll tax (the tax used to finance Social Security). Critics: to return the proceeds of the tax in this fashion would defeat its purpose. If consumers got the gas tax back in the form of paychecks, they would go on buying just as much gasoline as before. Are the critics correct? *Suppose that the price of gasoline is $1 per gallon (about what it was when President Carter made his proposal); and suppose that a tax of $0.50/gal is imposed that results in a $0.50 rise in the price of gasoline (note that this is a specific tax). Suppose also that a representative consumer is then given a lump-sum payroll tax rebate that happens to be exactly equal to the amount of gasoline tax he pays. The question is: will this policy have any effect on the amount of gasoline this consumer buys? Consider a consumer whose income is $150/wk. Suppose his optimal bundles under $1 per gallon and $1.5 per gallon are given by C and A, respectively, on the next graph.* *[4.5 SLIDE 6-8]*

The Marginal Rate of Technical Substitution

The analogous concept in production theory to the marginal rate of substitution is called the marginal rate of technical substitution, or MRTS. It is the rate at which one input can be exchanged for another without altering output. Geometrically, the MRTS at a point is the absolute value of the slope of the isoquant at that point. For example, if L is on the horizontal axis, *MRTS=|ΔK / ΔL|* Diminishing MRTS for most production processes.

Example: Tesla's Battery Costs

The average battery production cost was about $400 per kWh in 2016. The battery for Tesla's Model 3 has a 50 kWh capacity, which at $400 per kWh implies a cost of $20,000 per battery. However, that cost can be reduced substantially by producing batteries in large volumes. A high volume of production is the objective of Tesla's Gigafactory. Tesla's electric cars, with prices around $85,000 have been unaffordable for most people. However, in 2017, Tesla will be producing a new "mass market" car, with a starting price of about $35,000. To achieve such a dramatic reduction in price, the company will rely on scale economies in battery production in its new $5 billion "Gigafactory" in Nevada. Battery costs are expected to decrease by one-third (to about $250 per kWh of energy storage), and fall further as production rises. A kilowatt hour (kWh)

Average Product

The average product of a variable input is defined as the total product divided by the quantity of that input. The average product of labor, denoted AP_L, it is given by *AP_L=Q/L* When the variable input is labor, the average product is also called labor productivity. Geometrically, the average product is the slope of the line joining the origin to the corresponding point on the total product curve. [5.2 slide 23 graphs] Three such lines, R_1, R_2, and R_3, are drawn to the total product curve shown in the top panel in the figure. The average product at L=2 is the slope of R_1, which is 14/2=7. Note that R_2 intersects the total product curve in two places—first, directly above L=4, and then directly above L=8. Accordingly, the average products for these two values of L will be the same—namely, the slope of R_2, which is 43/4=86/8=10.75. R_3 intersects the total product curve at only one point, directly above L=6. The average product for L=6 is thus the slope of R_3, 72/6=12. Also, since R_3 is the steepest ray we can get, the AP_L curve peaks at L=6.

Marginal Product

The change in the total product that occurs in response to a unit change in the variable input (all other inputs held fixed). Formally, if ΔL denotes a small change in labor, and ΔQ denotes the resulting change in output, then the marginal product of L, denoted MP_L, is defined as *MP_L=ΔQ/ΔL* Geometrically, the marginal product at any point is simply the slope of the total product curve at that point, as shown in the top panel of next figure. A business manager trying to decide whether to hire or fire another worker has an obvious interest in knowing what the marginal product of labor is.

Review: Supply Curves of Competitive Firms

The competitive firm has a well-defined supply curve. It takes market price as given and responds by choosing the output level for which marginal cost and price are equal. At the industry level, a shifting demand curve will trace out a well-defined industry supply curve, which is the horizontal summation of the individual firm supply curves Can we derive a supply curve for a monopolist? (8.3 video)

Law of Diminishing Returns

The law of diminishing returns is a short-run phenomenon. Formally, it may be stated as follows: as *equal amounts of a variable input* are sequentially added while *all other inputs are held fixed,* the resulting increments to output will eventually diminish. Why can't all the world's people be fed from the amount of grain grown in a single flowerpot? The law of diminishing returns perfectly explains why can't all the world's people be fed from the amount of grain grown in a single flowerpot: No matter how much labor, fertilizer, water, seed, capital equipment, and other inputs were used, only a limited amount of grain could be grown in a single flower-pot. With the land input fixed at such a low level, increases in other inputs would quickly cease to have any effect on total output. It is worth mentioned once more that the law of diminishing returns is a short-run phenomenon, that is, you need to fix all other inputs when increasing the variable inputs in consideration. If you overlooked the requirement of fixing all other inputs, you will make a mistake by applying the law of diminishing returns.

a U​ shape, initially falling when the marginal product of labor is rising and then eventually rising when the marginal product of labor is falling.

The marginal cost of production shows the change in a​ firm's total cost from producing one more unit of a good or service. What is the shape of the marginal cost​ curve? ​ Graphically, the marginal cost curve is

Concept Check

The market demand for a local movie theater tickets is Q=100-1/2 P. Suppose the market is a monopoly. What is the theater's marginal revenue function? P=200-2Q MR(Q)=200-4Q * Q = 100 - 1/2P 1/2P = 100-Q P = 200 - 2Q

they may get in each other's way​, and output will increase at a diminishing rate.

The menu at ​Joe's coffee shop consists of a variety of coffee​ drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers that can be served by that worker in a given time period. Joe has been employing one​ worker, but is considering hiring a second and a third. Explain why the marginal product of the second and third workers might be higher than the first. *Why might you expect the marginal product of additional workers to diminish​ eventually? ​ Eventually, as successive workers continue to be added to the production​ process,*

workers can specialize at a separate task​, and output will increase at an increasing rate.

The menu at ​Joe's coffee shop consists of a variety of coffee​ drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers that can be served by that worker in a given time period. Joe has been employing one​ worker, but is considering hiring a second and a third. Explain why the marginal product of the second and third workers might be higher than the first. The marginal product of the second and third workers might be increasing because

The Most Important Factor

The most important of the five factors: economies of scale Exclusive control over important inputs and patents are transitory sources of monopoly Network economies and government licenses can both be persistent. But network economies can be viewed as another form of economies of scale; the same is true for many of the government licenses. Production processes change over time, which makes exclusive control over important inputs only a transitory source of monopoly Patents too are inherently transitory. One way to view network economies is that the product of any given quality level can be produced at lower costs as sales volume increases. many of these licenses are themselves merely an implicit recognition of scale economies that would lead to monopoly in any event.

An Analogy

The relationship between the marginal and average product curves is analogous to the relationship between the grade of an additional student and the class average grade. If the class average is 85 points, and the grade of the additional student is 90 (or anything greater than 85), then the class average will increase. If the class average is 85 points, and the grade of the additional student is 80 (or anything below 85), then the class average will decrease.

The Relationship between the Marginal and Average Product Curves

The relationship between the marginal product curve and the average product curve: When the marginal product curve lies above the average product curve, the average product curve must be rising; and when the marginal product curve lies below the average product curve, the average product curve must be falling. The two curves intersect at the maximum value of the average product curve Because of the way the marginal and average products are defined, systematic relationships exist between them. In words, their relationship can be summarized as follows: (read the slides) [5.2 slide 25 graphs] (L=6, intersection) The steepest of the three rays, R_3, is tangent to the total product curve at L=6. Its slope, 72/6=12, is the average product of labor at L=6. The marginal product of labor at L=6 is defined as the slope of the total product curve at L=6, which happens to be exactly the slope of R_3, since R_3 is tangent to the total product curve. Thus AP_(L=6)=MP_(L=6), as shown in the bottom panel by the fact that the AP_L curve intersects the MP_L curve for L=6. (L<6, MPL>APL) For values of L less than 6, note in the top panel that the slope of the total product curve is larger than the slope of the ray to the corresponding point. Thus, for L<6, MP_L>AP_L, as reflected in the bottom panel. (L>6, MPL<APL) Note also in the top panel that for values of L greater than 6, the slope of the total product curve is smaller than the slope of the ray to the corresponding point. This means that for L>6, we have MP_L>AP_L, as shown in the bottom panel. (transit) Using their geometric meaning, we have proved that (i) The two curves intersect at the maximum value of the average product curve and (ii) When the marginal product curve lies above the average product curve, the average product curve must be rising; and when the marginal product curve lies below the average product curve, the average product curve must be falling. (intuition) A moment's reflection on the definitions of the two curves akes the intuitive basis for this relationship clear. If the contribution to output of an additional unit of the variable input exceeds the average contribution of the variable inputs used thus far, the average contribution must rise.

Production Function

The relationship by which inputs are combined to produce output. (Intro) Many people think of production as a highly structured, often mechanical process whereby raw materials are transformed into finished goods. And without doubt, a great deal of production—like Tesla manufacturing a Model 3 sedan, or Apple designing and assembling an iPhone —is this sort. In Economics, however, we emphasize that production is a much more general concept, and it can include many activities that are not ordinarily thought of as production. (Production examples) For example, for a stand-up comedian, the simple act of telling a joke constitutes production. Similarly, the postal worker who delivers my tax return to the IRS is engaged in production, the young lady who gives me a haircut every few weeks is engaged in production, and a 7-year old kid selling drinks behind his/her lemonade stand is also engaged in production. Even I myself is engaged in production by giving a lecture on economics. (goods and services) From these examples, you can see that production is not only about physical goods, it could also be about services, and the process does not have to sophisticated to be called production. (Concepts) Formally, production can be described as a process that transforms inputs (factors of production) into outputs. Here inputs, or factors of production, could be land, labor capital, entrepreneurship, and so on, and outputs could be cards, smartphones, haircuts, lectures and so forth. In economics, at least in the classical theory of firms in microeconomics, we are not interested in the details of the production process, like how a smartphone is assembled step by step on an assembly line from hundreds of parts. Rather, we treat the production process as a black box as shown on the slide. All that we are interested in is the relationship by which inputs are combined to produce output. So, by hiring 10 people and renting 2 pieces of assembly equipment, how many smartphones I can make in one day, that input and output quantity relationship is what we are interested in here. And this relationship is called a production function. (technology) As you can imagine, this production function, this black box of the production process, depends on the existing state of technology which has been improving steadily over time.

Two Extreme cases for Input Subsitution

The shape of the isoquant tells us how a firm is "willing" wo substitute one input for another. The extreme cases of inputs are *perfect substitutes* and *perfect complements.* Just as the shape of the indifference curve tells us how the consumer is willing to substitute one good for another, In production theory, the shape of the isoquant tells us how a firm is willing wo substitute one input for another A production function with perfect complementary input is also called a fixed-proportions production function or Leonitief production function.

Recast the Tangency Condition: Equal Marginal Product per Dollar

The tangency condition can be written as (MP_L)/w=(MP_K)/r. - MP_L/w, *the marginal product of labor per dollar,* is the additional output that results from spending an additional dollar for labor. - MP_K/r, *the marginal product of capital per dollar,* is the additional output that results from spending an additional dollar for capital. MRTS = w/r mPl/mPk = w/r Therefore, a cost-minimizing firm should choose its quantities of inputs so that the last dollar's worth of any input yields the same amount of extra output. If the wage rate is $10 and adding a worker will increase output by 20 units, then the additional output per dollar spent on an additional worker will be 20/10=2 units of output per dollar

Long-Run Total Cost (LTC)

To go from the long-run expansion path to the *long-run total cost (LTC)* curve, we simply plot the relevant quantity-cost pairs from the last figure. LTC=LTC(Q)

a horizontal line

To model the input decisions for a production​ system, we plot labor on the horizontal axis and capital on the vertical axis. In the short​ run, labor is a variable input and capital is fixed. The​ short-run expansion path for this production system is

The marginal rate of substitution​ (MRS) diminishes as an individual moves downward along the demand curve. Assume the statement refers to good X with price PX​, where good X is measured on the horizontal axis of an indifference map and good Y is measured on the vertical axis. This statement is

True because the MRS equals PX / PY​, which decreases as an individual moves downward along the demand curve.

Holding capital​ constant, when the amount of labor increases from 5 to​ 6, output increases from 20 to 25. Then when labor increases from 6 to​ 7, output increases from 25 to 28.

Which of the following is an example of the law of diminishing marginal​ returns?

Preview [8.1]

Virtually every movie theater charges different admission prices to moviegoers who belong to different groups: - students, adults, senior citizens; - "ten-packs" at a discount, Tuesday discount, dinner hour discount. None of these practices would be expected under our model of perfect competition, which holds that all buyers pay a single price for a completely standardized product. The same movie theater charges everyone the same prices for items like popcorns, soft drinks and candy. But theses prices are usually much higher than those of the same items sold in grocery stores, certainly far greater than any reasonable measure of the marginal cost of providing them. Both behaviors—charging differential admission prices on the one hand and uniformly high concession prices on the other—are, as we will see, perfectly consistent with what the economic model predicts about the single seller of a good or service. This chapter examines the market structure that least resembles perfect competition—namely, monopoly, a market served by a single seller of a product with no close substitutes. Five factors that lead to this market structure. Monopolist's rule for maximizing profits in the short run is the same as the one used by perfectly competitive firms.

The Inflexibility of Short-Run Production

When a firm operates in the short run, its cost of production may not be minimized because of inflexibility in the use of fixed inputs. - The firm is unable to substitute the relatively inefficient inputs (i.e. the inputs with low marginal products per dollar) for more efficient ones. In the long run, the firm has the flexibility to adjust all inputs to produce any given input in a cost-efficient way. - Equal marginal products per dollar for all inputs. [6.3 Slide 6] Suppose output is initially at level q1, (using L1, K1). In the short run, output q2 can be produced only by increasing labor from L1 to L3 because capital is fixed at K1. In the long run, q_2 can be produced cost efficiently by increasing labor from L1 to L2 and capital from K1 to K2. Why is the cost of production higher when capital is fixed? Because the firm is unable to substitute relatively inexpensive capital for more costly labor when it expands production. This inflexibility is reflected in the short-run expansion path, which begins as a line from the origin and then becomes a horizontal line when the capital input reaches K1. The laundry shop example: In the short run, Kelly can only use the exiting washer and dryers. In the long run, she can consider buying more washers and dryers.

Equals the negative of the slope of the isoquant, equals the marginal product of labor divided by the marginal product of capital, and declines as more and more labor is used.

When capital is plotted on the vertical axis and labor is plotted along the horizontal​ axis, the marginal rate of technical substitution​ (MRTS) of labor for capital along a convex isoquant

less than price

When the demand curve is downward​ sloping, marginal revenue is

The draftsman since the lowest point on each SAC curve will have a horizontal tangent line which only occurs at the lowest point on the LAC.

Whose argument is stronger regarding the SAC curves and the LAC​ curve?

Equals the ratio of input​ prices, and this ratio is fixed

Why are isocost lines straight​ lines? Isocost lines are straight because the slope of such line

Since at least one factor of production is fixed in the short​ run, as more and more workers must share the fixed​ factors, the marginal product of each additional worker will eventually decrease.

Why does production eventually experience diminishing marginal returns to labor in the short​ run?

Output decisions depend not only on marginal cost but also on the demand curve. Shifts in demand lead to changes in​ price, output, or both.​ Thus, there is no​ one-to-one correspondence between price and the​ seller's quantity.

Why is there no market supply curve under conditions of​ monopoly?

Equal Marginal Products per Dollar

Why must the rule of equal marginal products per dollar hold for cost minimization? If the rule does not hold, the firm can produce more without increasing cost. - E.g., suppose w=$10, r=$2, and MP_L=MP_K=20 bags of laundry. (MP_L)/w=2<5=(MP_K)/r - Reallocate the last dollar to produce more: reduce one dollar's worth of labor input (output drops by 2 bags) and use that dollar to add one dollar's worth of capital input (output increases by 5 bags) Keep doing the reallocation until (MP_L)/w=(MP_K)/r, which will occur due to diminishing marginal returns. Intuitively, labor and capital are equally productive, but capital is cheaper, so the firm wants to use more capital and less labor. If the firm reduces labor and increases capital, its marginal product of labor will rise and its marginal product of capital will fall. Eventually, the point will be reached at which the production of an additional unit of output costs the same regardless of which additional input is used. At that point, the firm is minimizing its cost.

will not always result in a higher price because the​ monopolist's output decision depends on marginal cost and the shape of the demand curve.

Will an increase in the demand for a​ monopolist's product always result in a higher​ price? Explain. An increase in the demand for a​ monopolist's product

Convex Isoquant

Within some​ range, a declining number of units of one input can be substituted for a unit of the other​ input, and output can be maintained at the same level. In this​ case, the MRTS is diminishing as we move down along the isoquant.

The Engel Curve

[4.1 Slide 14 & 15] A curve that plots the relationship between the quantity of X consumed and income. Can make a schedule before drawing the curve as well. It is named after the German statistician Ernst Engel (1821-1896), who was the first to investigate this relationship between goods expenditure and income systematically in 1857. The best-known single result from the article is Engel's law, which states that as income rises, the proportion of income spent on food falls. (That is, the "Engel coefficient" falls.) One application of the statistic is treating it as a reflection of the living standard of a country. A high Engel coefficient indicates a low standard of living 1: (2,40) 2: (3,60) 3: (5,100) 4: (6, 120) *Properties of Points:* Utility maximizing Higher income, higher utility. -- more shelter consumption

Example: Consumer Expenditures In The United States

[4.1 Slide 27 & 28] Consider three commodities (or services): - Health care - Entertainment - Rented dwelling Which of the three can have a downward-sloping Engel curve (at least for certain range of income)? We can derive Engel curves for groups of consumers. This information is particularly useful if we want to see how consumer spending varies among different income groups. Health care and entertainment are normal goods, as expenditures increase with income. Rental housing, however, is an inferior good for incomes above $40,000.

Price-Consumption Curve (PCC)

[4.1 Slide 6] Y: Composite good, $1 per unit. Income: $120. Ps = $24, 12, 6, 4 /sq. yd. *Calculate end points:* Income / Ps - ->120 / Ps Holding income and the price of Y constant, the PCC for a good X is the set of optimal bundles traced on an indifference map as the price of X varies. As Ps decreases, the budget line rotate outwards. Each time the price of shelter falls, this consumer chooses a bundle that contains more shelter than in the bundle chosen previously. The amount of money spent on the composite good may either rise or fall when the price of shelter falls As price of shelter decreases, then the budget line rotates around the vertical intercept outwards - Quantity of shelter consumed increases

Shift of the Individual Demand Curve

[4.1, Slide 17 & 18] 1: (2,10) 2: (3,10) 3: (5,10) 4: (6,10)

The Total Effect of a Price Increase

[4.2 Slide 7] With price increase, less shelter for same amount of income. - Price increase reduces budget set that is a smaller triangle; worse off

The Substitution and Income Effects of a Price Change

[4.2 Slide 8] To decompose the total effect, we begin by asking: How much income would the consumer need to reach his original indifference curve (I_0) after the increase in the price of shelter? $240. B′ is the corresponding imaginary budget line - parallel to B_1 and tangent to l_0. C is the imaginary intermediate optimal bundle. SE: A to C. IE: C to D. SE: the hypothetical compensation of (240-120)=$120 helps to make the consumer as satisfied as before the price increase, thereby isolates the substitution effect. IE: the hypothetical movement of the consumer's income from $240/wk to $120/wk accentuates the reduction of his consumption of shelter, causing it to fall from 6 sq yd/wk to 2 sq yd/wk. Shelter happens to be a normal good in this example. So is the composite good.

Measure the Value of Clean Air by Consumer Surplus

[4.4 Slide 12] The yellow-shaded triangle gives the consumer surplus generated when NOX pollution is reduced by 5 pphm at a price of $1000 per pphm of reduction. A 5-pphm reduction in NOX pollution is worth $2500 to this representative household. Q: how come NOX pollution becomes a good? A: We are looking at NOX pollution reduction. NOX pollution is a "bad" and thus NOX pollution reduction is a "good". If we know the number of household, we can multiple $2500 by that number to estimate the total benefits of cleanup.

A More Practical Short-Run Production Function

[5.2 Slide 10] As you saw in the last Concept Check, the graphs of short-run production functions will not always be straight lines. The short-run production function shown in the current Figure has several properties that are commonly found in production functions observed in practice. First, it passes through the origin, which is to say that we get no output if we use no variable input. Second, initially the addition of variable inputs augments output at an increasing rate: moving from 1 to 2 units of labor yields 10 extra units of output, while moving from 2 to 3 units of labor gives 13 additional units. Finally, the function has the property that beyond some point (L > 4 in the diagram), additional units of the variable input give rise to smaller and smaller increments in output. Thus, the move from 5 to 6 units of labor yields 14 extra units of output, while the move from 6 to 7 units of labor yields only 9. For some production functions, the level of output may actually decline with additional units of the variable input beyond some point, as happens here for L > 8. With a limited amount of capital to work with, additional workers may eventually begin to get in one another's way The curvilinear shape shown here is common to many short-run production functions. Output initially grows at an increasing rate as labor increases. Beyond L > 4, output grows at a diminishing rate with increases in labor.

Inevitable Starvation for Human Race?

[5.2 Slide 14] Employing the logic based on fixed agricultural land and the law of diminishing returns, the British economist Thomas Malthus argued in 1798 that population growth will drive average food consumption down to the starvation level. Reality so far: food production per capita grew more than twenty-fold in the last 200 years. Is the law of diminishing returns wrong? In fact, even famous scholars can overlook the importance of this requirement for diminishing returns to labor. For example, in 1798, the British economist Thomas Malthus, employing the same logic of in the example of growing grain in a flowerpot, argued that the law of diminishing returns would imply eventual misery for the human race. His logic is that agricultural land is fixed and, beyond some point, the application of additional labor will yield ever smaller increases in food production. The inevitable result is that population growth will drive average food consumption down to the starvation level. Is Malthus correct? We do not know for sure what will happen in a thousand years from now, but we do know that at least in the past 200 years, food production per capita has grown more than twenty-fold. In the last 70 years alone, food production per capita grew more than 50%. What's happening here? Is the law of diminishing returns wrong? Apparently, the law of diminishing returns is still valid. What changed in the last 200 years is the state of agricultural technology. With the same amount of land, we are able to produce much more. Since we are not fixing the state of technology, it is possible for the returns to labor to increase at an increasing rate as output increases.

Technological Improvements in Production

[5.2 Slide 15] Technological improvements in production are represented graphically by an upward shift in the production function. The law of diminishing returns applies to each of these curves, and yet the growth in food production has kept pace with the increase in labor input during the period shown. To see the effect of technological improvements on returns to labor, we can look at this graph shown on the slide. Here technological improvements in production are represented graphically by an upward shift in the production function. The law of diminishing returns applies to each of these curves, and yet the growth in food production has kept pace with the increase in labor input during the period shown. Thomas Malthus failed to anticipate the capacity of productivity growth to keep pace with population growth. Of course, his basic insight—that a planet with fixed resources can support only so many people—remains valid. But he apparently overlooked or underestimated the power of technological advancement.

Short Run to MPL graph

[5.2 Slide 19 graphs] MPL reaches maximum at inflection point (Top panel: How to compute MPL from TP) For example, the marginal product of labor when L=2 is MP_(L=2)=12. Likewise, MP_(L=4)=16 and MP_(L=7)=6 for the total product curve shown in the figure. Note, finally, that MP_L is negative for values of L greater than 8. (Inflection, concave and convex) inflection point on the total product curve, the point where its curvature switches from convex (increasing at an increasing rate) to concave (increasing at a decreasing rate). (Bottom panel) The marginal product curve itself is plotted in the bottom panel in the figure. Note that it rises at first, reaches a maximum at L=4, and then declines, finally becoming negative for values of L greater than 8. Note also that the maximum point on the marginal product curve corresponds to the inflection point on the total product curve.

Isoquant Map

[5.3 slide 7 graph] "Iso" comes from the Greek word for "same," The isoquant map describes the properties of a production process in much the same way as an indifference map describes a consumer's preferences. (The similarity) On an indifference map, movements to the northeast correspond to increasing levels of satisfaction. Similar movements on an isoquant map correspond to in-creasing levels of output. A point on an indifference curve is preferred to any point that lies below that indifference curve, and less preferred than any point that lies above it. Likewise, any input bundle on an isoquant yields more output than any input bundle that lies below that isoquant, and less output than any input bundle that lies above it. Thus, bundle C in the figure yields more output than bundle A, but less output than bundle D. (The difference) The only substantial difference between an isoquant map and an indifference map lies in the the significance of the labels attached to the two types of curves. From our discussion on utility, remember we said that utilities are ordinal, that is, the actual numbers assigned to each indifference curve were used to indicate only the relative rankings of the bundles on different indifference curves. This is to say that, with indifference curves, we are free to relabel the indifference curves in any way that preserves the original ranking of bundles. By contrast, the number assigned to an isoquant corresponds to the actual level of output we get from an input bundle along that isoquant. So, with isoquant maps, the labels are determined uniquely by the production function, and we are not allowed to scale them up or down.

The Long-Run Total, Average, and Marginal Cost Curves

[6.2 Slide 27] The long-run total cost curve will always pass through the origin. The long-run average and long-run marginal cost curves are derived from the long-run total cost curve in a manner completely analogous to the short-run case. The relationship between average and marginal quantities still apply. In the long run, the firm always has the option of ceasing operations and ridding itself of all its inputs. This means that the long-run total cost curve (top panel) will always pass through the origin.

Producing A Given Output at Minimum Cost

[6.2 slide 11] Isocost curve C_1 is tangent to isoquant q1 at A: (L_1,K_1) Hence, C_1 is the minimum cost to produce q1: - Some input combinations other than A - e.g., (L_2,K_2) and (L_3,K_3) - can yield the same output but at higher cost. - Input combinations that cost less C_1 -- e.g., any combination on isocost C_0 -- will not allow the firm to achieve output q1.

Input Substitution When an Input Price Changes

[6.2 slide 20] When the price of labor increases, the isocost curves become steeper. Output q1 is now produced at point B on isocost curve C2 by using L2 units of labor and K2 units of capital.

The Isocost Line

[6.2 slide 7] The isocost line C_0 describes all possible combinations of labor and capital that cost a total of C0 to hire. A higher level of total cost C_1 corresponds to a higher isocost line. Given w and r, all the isocost lines are parallel. The slope ΔK/ΔL = -w∕r means that if the firm reduces capital input by w/r units (which saves (w/r)r=w dollars) and hires an additional unit of labor input (which costs w), its total cost of production would remain the same (move down along a given isocost curve).

The Relationship between Short-Run and Long-Run Cost Curves

[6.3 Slide 16] The long-run average cost (LAC) curve is the envelope of the short-run average cost curves (SAC). For the output level at which a given SAC is tangent to the LAC, the long-run marginal cost (LMC) of producing that level of output is the same as the short-run marginal cost (SMC) Each point along a given SAC curve, except for the tangency point, lies above the corresponding point on the LAC curve. - Too much capital to the left of the tangency, and too little capital to the right of the tangency. At the minimum point on the LAC curve (q_2), the long-run and short-run marginal and average costs all take exactly the same value

The Shape of LAC

[6.3 slide 9] As output level increases, a firm's long-run average cost can increase, remain constant, or increase. minimum efficient scale: the level of production required for LAC to reach its minimum level

Economies of Scale

[8.1 slide 12] When the long-run average cost curve is downward sloping, the least costly way to serve the market is to concentrate production in the hands of a single firm. A market that is most cheaply served by a single firm is called a *natural monopoly.* Often the case for industries with large fixed cost. - local telephone landlines

Marginal Revenue for a Monopolist (Calculus)*

[8.2 Slide 12] The chain rule in calculus: if f(x)=g(x)h(x), then f^′ (x)=g(x) h^′ (x)+g^′ (x)h(x) The chain rule in calculus implies MR(Q)=ΔTR(Q)/ΔQ=P(Q)+(ΔP(Q))/ΔQ Q

Marginal Revenue for a Monopolist: A Linear Demand Curve Example

[8.2 slide 13-14] Consider the example P=80-1/5 Q. Start with Q_0=100 and P_0=60. If the monopolist wishes to increase the output from Q_0=100 to 150 so that ΔQ=50, correspondingly he must cut the price from P_0=60 to 50 so that ΔP=-10. (Note the negative sign.) The change in his revenue results from two effects 1. The gain in revenue from the 50 units of new sales (B in next figure). (P+ΔP)ΔQ=50×50=250 2. The loss in revenue from selling the previous output level 100 units at the new, lower price (A in next figure). ΔP ∙Q_0=(-10)×100=-1000 The change in the revenue is ΔTR(Q_0)=2500-1000=1500 The marginal revenue at Q_0=100 associates with this particular change ΔQ=50 is MR(Q_0 )=(ΔTR(Q_0))/ΔQ=1500/(50 )=30

Example: The Monopolist's Marginal Revenue with Linear Demand Functions

[8.2 slide 18-19] Consider again P=80-1/5 Q. Then (ΔP(Q))/ΔQ=-1/5. Hence, MR(Q)=P(Q)+ΔP(Q)/ΔQ Q = (80-1/5 Q)+(-1/5)Q = 80-2/5 Q Generalize: for any P=t-kQ, the monopolist's marginal revenue is MR(Q)=t-2kQ The monopolist's marginal revenue curve is a straight line

Marginal Revenue and Elasticity for Linear Demand Curves

[8.2 slide 23-24] Elasticity changes along a linear demand curve ϵ<-1 for prices higher than the middle point of the linear demand curve ϵ=-1 at the middle point ϵ>-1 for prices higher than the middle point Hence, the marginal revenue is positive only on the upper half of the linear demand curve.

The Profit-Maximizing Price and Quantity for a Monopolist

[8.3 slide 6] Maximum profit occurs at the output level Q*, where MR=MC At Q*, the firm charges P* and earns an economic profit of Π.

Numerical Example

[8.3 slide 7] A monopolist faces a demand curve of P=100 -2Q and a short-run total cost curve of TC=640+20Q. The associated marginal cost curve is MC=20. What is the profit-maximizing price? How much will the monopolist sell, and how much economic profit will it earn at that price? MR = 100-4Q Q* = 20 P* = 60 ATC(Q*) = 52 Profit per unit = 8 Π = (P* - ATC(Q*)) * Q* = 160 *Demand: P*=100-2Q = 100-2*20=60 *Change in TC(Q*) = 640/Q + 20 =52

The Monopolist's Shutdown Condition

[8.3 slide 9-10] The shutdown condition for a monopolist: there exists no quantity for which the demand curve lies above the average variable cost curve. Mathematically: Π=TR-TC =TR-VC-FC =(P-AVC) Q^∗-FC Hence, produce at Q^∗ as long as (P-AVC)>0 at Q^∗. No positive level of output for which price exceeds AVC, and so the monopolist does best by ceasing production in the short run.

Long-Run Equilibrium for a Profit-Maximizing Monopolist

[8.4 slide 6] LMC = MR determines Q^∗. The optimal capital stock in the long run gives rise to the short-run marginal cost curve SMC^∗, which passes through the intersection of LMC and MR. For the conditions pictured, the long-run economic profit level, Π, is positive.

The Individual Consumer's Demand Curve

[Slide 7 & 8, 4.1] Like the market demand curve, the individual demand curve is a relationship that tells how much the consumer wants to purchase at different prices. Make the demand schedule table before drawing the demand curve Note the change of the vertical axis 1: (2.5, 24) 2: (7,12) 3: (15,6) 4: (20,4) Consumers utility increases down the individual demand curve

Average Fixed Cost (AFC)

is fixed cost divided by the quantity of output: AFC=FC/Q AFC Curve: [6.1 slide 23] AFC falls with output: "spreading overhead costs." Geometrically, AFC at any level of output Q is the slope of the ray to the FC curve at Q. As output shrinks toward zero, AFC grows without bounds, and it falls ever closer to zero as output increases. Like all other AFC curves, it takes the form of a rectangular hyperbola.

Average Total Cost (ATC)

is total cost divided by the quantity of output: ATC=TC/Q=AFC+AVC ATC Curve: [6.1 slide 25] Still similarly, ATC at any level of output Q is the slope of the ray to the TC curve at Q. Top panel: The slope of a ray to the TC curve declines with output up to the output level Q_3; thereafter it begins to increase. Bottom panel: ATC reaches its minimum value at Q_3, the output level at which the ray R_3 is tangent to the TC curve. ATC=AFC+AVC Q_2, the output level at which the ray R_2 is tangent to the variable cost curve (ATC=AFC+AVC) so the vertical distance between the ATC and AVC curves at any level of output will always be the corresponding level of AFC.

Average Variable Cost (AVC)

is variable cost divided by the quantity of output: AVC=VC/Q AVC Curve [6.1 slide 24] Similarly, AVC at any level of output Q is the slope of the ray to the VC curve at Q. Top panel: The slope of a ray to the VC curve declines with output up to the output level Q_2; thereafter it begins to increase. Bottom panel: AVC reaches its minimum value at Q_2, the output level at which the ray R_2 is tangent to the VC curve. Q_2, the output level at which the ray R_2 is tangent to the variable cost curve