Econ 311 Final Exam

Three conditions characterizing perfect condition

1. Number of Firms: there need to be a large number of firms so that no one firm has any impact on the market equilibrium price by itself. Thus, any one firm can change its behavior without changing the overall market equilibrium. 2. Types of Products Sold: All firms produce an identical product. By identical, we don't just mean that all the firms make televisions or all the firms make smoothies. We mean the consumers view the output of the different producers as perfect substitutes and do not care who made it. 3. Barriers to Entry: There cannot be any barriers to entry. That is, if someone decides she wants to start selling nails tomorrow, there is nothing that prevents her from doing it.

9 Simplifying Assumptions about Firms' Production Behavior (1-3)

1. The firm produces a single good 2. The firm has already chosen which product to produce 3. For whatever quantity it makes, the firm's goal is to minimize the cost of producing it

Measuring a firm's profit

π = TR - TC = (P - ATC) × Q - profit is positive only when P > ATC*. If P = ATC*, profit is zero, and when P < ATC*, profit is negative.

Total Cost (TC)

Total Cost (TC) = Fixed Costs (FC) + Variable Costs (VC)

Equilibrium conditions for Bertrand duopoly

- But suppose the customers in this market have a simple demand rule: Buy the PS4 from the store that sells it at the lowest price. If both stores charge the same price, consumers flip a coin to determine where they buy. - Each store chooses its price to maximize its profit, realizing that it will sell the number of units according to the demand curves above. - Remember that in a Nash equilibrium, each firm is doing the best it can given whatever the other firm is doing. - In fact, the market outcome of Bertrand competition with identical goods is the same as that in a perfectly competitive market: Price equals marginal cost. - The equilibrium of this Bertrand oligopoly occurs when each store charges a price equal to its marginal cost - So the outcome isn't the most preferable outcome for the firms, but neither firm can do better by unilaterally changing its price. -all firms change the same price

Model assumptions for Stackelberg competition with identical goods

- Firms sell identical products. - Firms compete by choosing a quantity to produce. - All goods sell for the same price (which is determined by the sum total of quantities produced by all the firms combined). - Firms do not choose quantities simultaneously. One firm chooses its quantity first. The next firm observes this and then chooses its quantity.

Model Assumptions for Cournot competition

- Firms sell identical products. - Firms compete by choosing a quantity to produce. - All goods sell for the same price—the market price, which is determined by the sum of the quantities produced by all the firms in the market. - Firms choose quantities simultaneously.

Model Assumptions for Bertrand Competition

- Firms sell identical products. - The firms compete by choosing the price at which they sell their products. - The firms set their prices simultaneously.

Putting the relationships of economies to scale together

- Putting together these relationships, we can see what the typical U-shaped long-run average total cost curve implies about economies of scale. At low output levels (the left, downward-sloping part of the ATC curve), total cost rises more slowly than output does. As a result, average total cost falls, and the firm has economies of scale. - At the very bottom of the average total cost curve where it is flat, average cost does not change, total cost rises proportionally with output, and marginal cost equals ATC. Here, therefore, average total cost increases at the same rate that output increases, and there are constant economies of scale. - At higher output levels (the right upward-sloping part of the ATC curve where ATC is rising), marginal cost is above average total cost, causing total cost to rise more quickly than output does. As a result, there are diseconomies of scale.

Producer surplus for a competitive firm graphically from marginal cost

- producer surplus is the vertical difference between the market price and the supply curve, which we now know reflects firms' marginal costs - If we add up all these price-marginal cost markups across every unit of output the firm makes, we get the firm's producer surplus, the shaded area in panel a of Figure 8.10 .If this isn't clear, imagine slicing the shaded area into many tiny vertical slices, one for each unit of output. Each slice equals the difference between the price the unit sells for and the marginal cost of producing it. If we add up all the slices—that is, the price-cost gaps for all the units of output—we get the firm's producer surplus.

Long-run cost curves

Long-run cost curves assume that a firm's capital inputs can change just as its labor inputs may.

9 Simplifying Assumptions about Firms' Production Behavior (4-6)

4. The firm uses only two inputs to make its product: capital and labor 5. In the short run, a firm can choose to employ as much or as little labor as it wants, but it cannot rapidly change how much capital it uses. In the long run, the firm can freely choose the amounts of both labor and of capital it employs. 6. The more inputs the firm uses, the more output it takes

9 Simplifying Assumptions about Firms' Production Behavior (7-9)

7. A firm's production exhibits diminishing marginal returns to labor and capital 8. The firm can buy as many capital or labor inputs as it wants at fixed prices 9. If there is a well-functioning capital market, the firms does not have a budget constraint.

Isoquants

A curve showing all the different combinations of inputs that allow a firm to make a particular quantity of output. Isoquants further from the origin correspond to higher output levels (because more capital and labor lead to higher output), isoquants cannot cross, and isoquants are convex to the origin. The slope of the isoquant plays a key role in analyzing production decisions because it captures the tradeoff in the productive abilities of capital and labor. Steep slope = the firm can reduce the amount of capital it uses by a lot while increasing labor only a small amount, and still maintain the same level of output. Flatter slope = if the firm wants to reduce capital just a bit it will have to increase labor a lot to keep output at the same level

When a firm should increase production and decrease production

A firm should increase production as long as revenue increases by more than cost (i.e., when MR = P > MC). Conversely, a firm should decrease production if cost increases by more than revenue (i.e., when MR = P < MC)

Firms Cost minimization problem

A firm's goal is to produce its desired quantity of output at the minimum possible cost. In deciding how to achieve this goal, a firm must solve a cost-minimization problem: It must achieve an objective given a constraint. The objective is the firm's total cost of inputs, RK + WL. The firm chooses capital and labor inputs K and L to minimize these expenditures under the constraint. Constraint faced: The quantity of output the firm has chosen to produce. - The firm must hire enough capital and labor to produce certain levels of output.

Marginal Revenue

A firm's marginal revenue is the additional revenue it gets from selling one additional unit of output: Marginal revenue (MR) = change in total revenue / change in Q

Short-run total cost curve

A firm's short-run total cost curve shows the firm's total cost of producing different quantities of output when it is stuck at a particular level of capital . Just as there is a different short-run production function for every possible level of capital, so too is there a different short-run total cost curve for each capital level.

Perfectly competitive firm

A perfectly competitive firm is a price taker. It must sell its output at whatever price is determined by supply and demand forces in the market as a whole. The small size of each firm relative to the size of the total market means the perfectly competitive firm can sell as much output as it wants to at the market price.

Constant returns to scale

A production function has constant returns to scale if changing the amount of capital and labor by some multiple changes the quantity of output by exactly the same multiple. (For example, doubling capital and doubling labor results in a doubling of output.)

Increasing Returns to Scale

A production function has increasing returns to scale if changing all inputs by some multiple changes output more than proportionately. (Doubling capital and labor more than doubles output.)

Average Fixed Cost

AFC = FC/Q Fixed cost per unit of output

Profit maximizing monopolist Response to change in demand

Again, we follow the three-step method. Because the demand curve has shifted in this case, the marginal revenue curve changes as well. The new demand curve is linear, so we know how to derive the marginal revenue curve; we double the number in front of the quantity in the inverse demand curve Step 1: Derive the marginal revenue curve. Step 2: Find the quantity at which MR = MC Step 3: Determine the profit-maximizing price using the optimal quantity and the demand curve. - An outward demand shift leads to an increase in both quantity and price in a market where the seller has market power, the same direction as in perfect competition. But again, the size of the changes differs. - with market power, the rotation in demand also moves the marginal revenue curve as shown in panel b of Figure 9.5.

Long-run Marginal cost

Long-run marginal cost is the additional cost of producing another unit when inputs are fully flexible.

Fixed Costs (FC)

An input cost that does not vary with the amount of output

Equilibrium conditions for Stackelber duopoly

An oligopoly model in which firms move sequentially—first one, then another, then (if there are more than two firms) another, and so on, is called Stackelberg competition.

Average Product

Average product is the total quantity of output divided by the number of units used to produce it. For example the average product of labor (AP sub L) = Q/L Where: Q = quantity produced L = amount of labor used to produce it

Average Cost Curves

Average total cost first falls as output rises because the dominant influence on average total cost is the rapidly declining average fixed cost. But as output continues to rise, average variable cost keeps increasing, first slowing the rate at which average total cost is falling and eventually causing average total cost to increase with output. These changes create a U-shaped average total cost curve.

Average Total Cost (ATC)

Average total cost is total cost TC per unit of output Q: ATC = TC/Q = AFC + AVC

Sources of Market Power

Barriers to entry are the factors that keep entrants out of a market despite the existence of a large producer surplus that comes from market power. 1. Natural Monopoly: A natural monopoly refers to a situation in which the cost curve of a firm in an industry exhibits economies of scale at any output level. In other words, the firm's long-run average total cost curve is always downward-sloping—the bigger the firm gets, the lower is its average total cost, even if it sells the entire market quantity itself. In markets with cost curves like this (high fixed cost and constant or slowly rising marginal cost), one firm will tend to become very large and dominate the industry with its low cost. 2. A second common type of barrier to entry is the presence of consumer switching costs. If customers must give something up to switch to a competing product, this will tend to generate market power for the incumbent and make entry difficult. 3. Product differentiation: That means firms can price slightly above their competition without losing all of their sales to their competitors. There is a segment of consumers who have a particular preference for one firm's product and will be willing to pay a premium for it (a limited premium, but a premium nonetheless). This imperfect substitutability across varieties of a product is called product differentiation, and it is another source of market power. 4. government regulation

Relationship between Average and Marginal cost

Because average cost and marginal cost are both derived from total cost, they are directly related. If the marginal cost of output is less than the average cost at a particular quantity, producing an additional unit will reduce the average cost because the extra unit's cost is less than the average cost of making all the units before it. - This means that if the marginal cost curve is below an average cost curve at some quantity, average cost must be falling—that is, the average cost curve is downward-sloping. - When the marginal cost of the additional unit is above average cost, then producing it increases the average cost. Therefore, if the marginal cost curve is above an average cost curve at a quantity level, average cost is rising, and the average cost curve slopes up at that quantity.

Application of economies to scale

Because economies of scale imply that total cost increases less than proportionately with output, they also imply that long-run average total cost falls as output grows. That is, the long-run average total cost curve is downward-sloping when there are economies of scale because total cost rises at a slower rate than quantity (remember, ATC = TC/Q). - Similarly, diseconomies of scale imply an upward-sloping long-run average total cost curve because total cost rises more quickly than output. - Constant economies of scale make the long-run average total cost curve flat.

shifts of short-run supply curve

Because of this relationship between marginal cost and the firm's short-run supply curve, anything that changes marginal cost will shift supply. As you may recall from Chapter 7, factors that shift the marginal cost curve include changes in input prices and technology. Note, however, that fixed cost does not affect a firm's marginal cost, and therefore changes in fixed cost do not shift the short-run supply curve. In the long run, as we know, no costs are fixed.

Derivation of a firm's short run supply curve

Because the supply curve shows the quantity supplied at any given price, and the firm chooses to produce where P = MC, the short-run marginal cost curve is the firm's short-run supply curve. There is one caveat: Only the portion of the marginal cost curve above the minimum average variable cost will be on the firm's supply curve, because at any price below the minimum average variable cost, the firm would shut down and quantity supplied would be zero - Figure 8.6 shows that the firm's short-run supply curve is the portion of its marginal cost curve MC that is at or above its average variable cost AVC, including the portion that is below its average total cost ATC. For prices below AVC, supply is zero, as shown in the figure. Keep in mind that we hold everything else constant except price and output when deriving the firm's supply curve.

Expansion path and Total Cost Curve

Both the total cost curve and the expansion path show how, when the firm is minimizing its costs of producing any given quantity, the firm's minimized costs change when its output changes

Production in Short-run

Capital Stock is fixed but the firm can choose how much labor to hire to minimize its cost of making the output quantity

Isocost lines and Input Price Changes: When capital becomes more expensive

Changes in the price of capital also rotate the isocost line. When the price of capital (R) becomes more expensive and wage stays the same. If the firm hired only capital the slope would flatten becomes it can afford less than before. A drop in the capital price would rotate thhe isocosts counter clockwise (to the right) like in example 6.9 and vice versa.

How to sum up a firm's cost minimization problem

Choose K and L to minimize total costs, subject to the constraint that enough K and L must be chosen to produce a given quantity of output. (Remember that at this point in our analysis, quantity has already been chosen. Now it's the firm's task to figure out how to optimally produce that quantity.)

Short-Run Production function Example

Cobbs-Douglas Production Function Example: Q = f(K bar, L)= (K bar)^.5 L^.5 = 4^.5 * L^.5 = 2L^.5 Where: Q = Output (K bar) = Fixed Capital L = Labor

Long-Run and Short-run total expansion path

Cost of input usage along expansion path. - Whether Ivor's Engines wants to make more or fewer than 20 engines (the output level at which short- and long-run costs are the same), its total costs are higher in the short run than in the long run.

Variable cost (VC)

Costs that change as the firm changes its quantity of outputs. When a firm needs more of an input to make more output, the payment for that input counts as a variable cost.

Decreasing Return to scale

Decreasing returns to scale exist if adjusting all inputs by the same multiple changes output by less than that multiple. (Output does not fully double when inputs are doubled.)

Economic Profit

Economic Profit = total revenue - Economic Costs

Economies of scale

Economies of scale are the cost-based flip-side of returns to scale. Economies of scale look at the way cost changes in proportion to output. * If doubling output causes cost to less than double a firm has economies of scale

Returns to scale

Economists use the term returns to scale to describe what happens to the amount of output in response to a proportional increase in all of the inputs.

Short-run marginal cost

Every short-run average total cost curve has a corresponding short-run marginal cost curve that shows how costly it is to build another unit of output when capital is fixed at some particular level. A short-run marginal cost curve always crosses its corresponding short-run average total cost curve at the minimum of the average total cost curve.

Long-run market supply curve with free entry/exit and constant costs

Figure 8.14 shows the current market price and long-run cost curves for a typical firm in this industry. Because firms in this industry are earning positive profits, new firms—whether started anew by entrepreneurs or new divisions of companies already operating in different industries—will want to take advantage of this opportunity by entering the industry. With free entry into the industry—which doesn't have to mean "free" in the monetary sense (there can be startup costs), but rather, indicates that entry is not blocked by any special legal or technical barriers—the market price will fall until it equals the minimum average total cost. - In other words, entry shifts the short-run industry supply curve out from S1 to S2 (Figure 8.15). This outward shift lowers the market price from P1 to P2.

increasing cost industries

Firms in increasing-cost industries see their cost curves shift up when industry output increases. This might occur because the price of an input rises in response to the industry's higher demand for that input. This means that, the higher industry output, the greater firms' average total costs, even in the long run. For this reason, the long-run supply curves of increasing-cost industries are upward-sloping. They're not as steeply sloped as the short-run supply curve for the industry because they account for entry and exit, but they're not horizontal either.

Fixed Cost Curve

Fixed cost does not vary with output, so it is constant and the fixed cost curve is horizontal. And because fixed cost must be paid in the short run even if the firm chooses to not produce anything, fixed cost is the same at Q = 0 as it is at every other level of output.

Graphical analysis of perfect complements in Production

For perfect complements the curves are L shaped right angles. Explanation of graph: Cabs K and drivers L are perfect complements. The isoquants are L-shaped, and the optimal quantity (K, L) for each output Q is the corner of the isoquant. In this case, 1 cab with 1 driver produces Q = 1, while 2 cabs with 2 drivers produce Q = 2.

Graphical analysis of perfect substitutes in Production

For perfect substitutes in production the curves are straight lines. Explanation of graph: Robots K and labor L are perfect substitutes. The isoquants are straight lines, and the MRTS sub LK does not change along the isoquant. In this case 2 humans can substitute for 1 robot.

long-run and short-run average total cost curve

From total cost curves we can construct long-run and short-run average total cost curves. The long-run average total cost curve is (ATC sub LR). The short-run average total cost curve is ATC sub SR, 20 - We add the "20" subscript to denote that the curve shows the firm's average total cost when its capital is fixed at a level that minimizes the costs of producing 20 units of output.) - As with the total cost curves, the short- and long-run average total cost curves overlap at Q = 20 engines, because that's where the firm's fixed capital level of 6 units is also cost-minimizing. Here, long-run and short-run average total costs are $180/20 = $9. - For all other output quantities, short-run average total cost is higher than long-run average total cost. Short-run total cost is higher than long-run total cost at every other quantity. Because average total cost divides these different total costs by the same quantity, average total cost must be higher in the short run, too. - The long-run total and average total cost curves don't change, because the firm will still choose the same capital inputs (resulting in the same costs) given its flexibility in the long run. However, the short-run cost curves change because the fixed level of capital has changed. By the same logic as above, the short-run total and average total cost curves will be above the corresponding long-run curves at every quantity except one. - long-run average total cost curve is the envelope of all the short-run average total cost curves,

Shape of Isoquants indicates the substitutability of Inputs

Highly curved isoquants, such as those shown in panel b of Figure 6.5, mean that the MRTS sub (LK) changes a lot along the isoquant. In this case, the two inputs are poor substitutes. The relative usefulness of substituting one input for another in production depends a great deal on the amount of the input the firm is already using.

Long-run Production function

In the long-run production function all inputs can be adjusted. First, in the long run, a firm might be able to lessen the sting of diminishing marginal products. As we saw above, when capital is fixed, the diminishing marginal product limits a firm's ability to produce additional output by using more and more labor. If additional capital can make each unit of labor more productive, then a firm can expand its output more by increasing capital and labor inputs jointly. Long-Run production function: Q= K^.5 L^.5

Entry of New Firms increases supply and lowers equilibrium price

If P2 is still above the minimum average total cost, an incentive remains for more firms to enter because they would make a profit. Entering firms would be making less profit than earlier entrants, but they're still better off entering the market than staying out. New entrants will shift the industry supply curve further out, lowering the market price even further. - This process continues until the last set of entrants drives down the market price to the minimum average total cost and there are no profits to be made by entering the industry. At this point, any potential entrant would be indifferent between entering the industry and staying out. Entry ceases, and the market is in long-run competitive equilibrium. The bottom line is that if there is free entry, the price in a perfectly competitive industry will be driven down toward the minimum average total cost of the industry's firms, and no firms will be making a profit.

Constant economies of scale

If doubling output causes cost to double, a firm has constant economies of scale

diseconomies of scale

If doubling output causes cost to more than double, a firm has diseconomies of scale

Perfect Complements in Production

If inputs are perfect complements, isoquants have an "L" shape. This implies that using inputs in any ratio outside of a particular fixed proportion—that at the isoquants' corners—yields no additional output. Cabs and drivers on a given shift are fairly close to perfect complements in the production of cab rides. Anything other than a 1 to 1 ratio of cabs to drivers is unlikely to produce any additional cab rides. If a cab company has, say, 30 drivers and 1 cab, it will not be able to offer any more rides than if it had 1 driver and 1 cab. Nor could it offer more rides if it had 1 driver and 30 cabs. Of course, the cab company could offer more rides if it had 30 drivers and 30 cabs, because this would preserve the 1 to 1 driver-to-cab ratio

Perfect Substitutes in Production

If inputs are perfect substitutes the MRTS doesn't change at all with the amounts of the inputs used, and the isoquants are perfectly straight lines. This characteristic means the firm can freely substitute between inputs without suffering diminishing marginal returns. Example of a Production Function Formula where labor and capital are perfect substitutes: Q= f(K, L) = 10K + 5L; 2 units of labor can wlays be substituted for 1 unit of capital without changing output, no matter how many units of either input the firm is already using

Mathematically deriving producer surplus

If we add up the firm's marginal cost for all the units of output it produces, we have its variable cost. And if we add up the firm's revenue for every unit of output it produces, we have its total revenue. That means the firm's total revenue minus its variable cost equals the sum of the price-marginal cost markups it earns on every unit it sells—that is, its producer surplus: PS = TR - VC

Deriving short-run and long-run total cost

If we plot the total cost curves that correspond to these short- and long-run expansion paths, we arrive at Figure 7.6. The long-run total cost curve TCLR is the same as when we assumed the firm was free to adjust all inputs to minimize costs. At Q = 20 engines, this curve and the short-run total cost curve TCSR overlap because we assumed that capital was at the cost-minimizing capital level at this quantity. (We've labeled this point Y because it corresponds to the quantity and total cost combination at point Y in Figure 7.5.) For every other quantity, however, the short-run (fixed-capital) total cost curve is higher than the long-run (flexible-capital) total cost curve. Note that short-run total costs are positive when Q = 0 but zero in the long run. In other words, there are fixed costs in the short run but not in the long run when all inputs are flexible.

Total cost curve

If we plot the total cost from the isocost line and the output quantity from the isoquants located along the expansion path, we have a total cost curve that shows the cost of producing particular quantities.

Graphical approach to deriving of short-run market supply curve from individual supply curve

If we use a graphical approach to the short-run industry supply curve, the firms' supply curves would look as they do on the left-hand side of Figure 8.8. To build the industry short-run supply curve, we horizontally add the firm's short-run supply curves: At any given price, we find the individual firms' outputs, add them up, and plot their sum to get the industry quantity supplied. These values yield the industry short-run supply curve on the right-hand side of the figure.

Marginal revenue for a perfectly competitive firm

In a perfectly competitive market, marginal revenue equals the market price; that is, MR = P. This fact means that a perfectly competitive firm's total revenue is proportional to its output. If output increases by 1 unit, total revenue increases by the price of the product. For this reason, a perfectly competitive firm's total revenue curve is a straight line from the origin

Cournot Equilibrium: A Mathematical Approach

In addition to finding the Cournot equilibrium graphically, we can solve for it algebraically by solving for the output levels that equate the two reaction curves. One way to do this is to substitute one equation into the other to get rid of one quantity variable and solve for the remaining one.

Decreasing-cost industries

In decreasing-cost industries, firms' cost levels decline with increases in industry output. This might be because there are some increasing returns to scale at the industry level, or in the production of one or more of the industry's inputs. The long-run supply curves for these industries are downward-sloping.

Marginal Product in the short-run

In the short-run, the marginal product that is most relevant is the marginal product of labor because we are assuming its capital is fixed

Determining the level of output that maximizes profit mathematically

In mathematical terms, the profit-maximizing level of output occurs where marginal revenue (here, price) equals marginal cost: MR = MC or Market Price = Marginal Cost or Change in total revenue / change in quantity produced = Change in total cost/ change in quantity

Producer surplus for a competitive firm graphically from average variable cost cost

In panel b of Figure 8.10 , the firm's total revenue is the area of the rectangle with a height of P and a base of Q*. Variable cost is output multiplied by average variable cost, so the firm's variable cost is the area of the rectangle with a base of Q* and a height of AVC* (AVC at the profit-maximizing level of output). The difference between these two areas is the shaded rectangle with base Q* and height (P - AVC*). The area of this rectangle also equals the firm's producer surplus.

Long-run market supply curve

In the long run, though, firms can enter or leave the industry in response to changes in profitability. Entry: Firms decide to enter or exit a market depending on whether they expect their action will be profitable.

Marginal Rate of Technical Substitution (MRTS)

MRTS is the negative slope of the marginal rate of technical substitution of one inout (on the x-axis) for another (on the y-axis), or MRTS sub XY. It is the quantity change in input Y necessary to keep output constant if the quantity of input X changes by 1 unit. The MRTS is about a firm's ability to trade one input for another while still producing the same quantity of output. The shape of the curves in both cases tells you about the rate at which one good/input can be substituted for the other

Mathematical definition of isocost line

Mathematically, the isocost line corresponding to a total expenditure level of C is given by: C = RK + WL Where: C = Total expenditure level R = Price (rental rate) per unit of capital W = is the price (the wage) per unit of labor K = # of units of capital L = # of labor that the firm hire We can rewrite this expression in slope intercept form: K = (C/R) - (W/R)L

Calculus of Marginal Product of Capital

Mathematically, the marginal product of capital is the partial derivative of the production function with respect to capital. It's a partial derivative because we are holding the amount of labor constant. Positive whenever capital is greater than zero. In other words the marginal product of labor and marginal product of capital of the Cobb-Douglas production function satisfy the condition of production, that output increases as the firm uses more inputs.

Minimum average total cost

Minimum Average total cost occurs when ATC = MC

Minimum Average Variable Cost

Minimum Average variable cost occurs where AVC = MC

Relationship between price elasticity of demand & MR for profit maximizing monopolist

One more important point about the implications of market power concerns how the slope of the demand curve influences the relative size of consumer and producer surplus in the market. Consider two different markets: one with a relatively steep (inelastic) demand curve and one with a flatter (elastic) one. Each is served by a monopolist. To keep things easy to follow, imagine that both firms have the same constant marginal cost curves, and that it just so happens each firm's profit-maximizing output is the same. - Firms with market power love to operate in markets in which consumers are relatively price-insensitive. If you're a consumer in that market, though, look out: Prices are going to be high.

Opportunity Costs

Opportunity costs are what the producer gives up by using an input, whether that use is associated with an accounting cost or not.

Producer surplus for an industry

Producer surplus for an entire industry is the same idea as producer surplus for a firm. It is the area below the market price but above the short-run supply curve—now, however, it is the industry supply curve rather than the firm's (Figure 8.11). This surplus reflects the industry's gain from producing units at a lower cost than the price at which they are sold.

Short-Run Production function formula in Cobb-Douglas Functional Form

Q = AK^(α)L^(1-α) Where: α = 0< α < 1 A = parameter for total factor productivity K = amount of input Capital L = amount of input Labor Q = output The exponents on K and L (α, 1-α) sum to 1, which means the production function exhibits constant returns to scale.

Perfect Complements Production formula

Q = min(L, K) where min indicates that output is determined by the minimum level of either labor (L) or capital (K).

Equilibrium conditions for cournot duopoly

Q = q sub 1 + q sub 2 Step 1: we start by writing the inverse demand curve equation in terms of the quantity choices of each firm Step 2: Because the slope of the marginal revenue curve is twice the slope of the inverse demand function.

Short-run cost curves

Short-run cost curves relate a firm's production cost to its quantity of output when its level of capital is fixed.

graphical approach: Monopoly Profit maximization

Step 1: Derive the marginal revenue curve from the demand curve. For a linear demand curve, this will be another straight line with the same vertical intercept that is twice as steep. Step 2: Find the output quantity at which marginal revenue equals marginal cost. This is the firm's profit-maximizing quantity of output. Step 3: Determine the profit-maximizing price by locating the point on the demand curve at that optimal quantity level. - That's all there is to it. Once we have the firm's MR curve, we can use the profit-maximization rule MR = MC to find the firm's optimal level of output and price.

Marginal Rate of Technical Substitution of Labor for Capital (MRTS sub LK)

The amount of capital needed to hold output constant if the quantity of labor used by the firm changes. The MRTS sub (LK) at any point on an isoquant tells you the relative marginal products of capital and labor at any point.

Determining when a firm should shut down

The answer (continue to operate at a loss or shut down) depends on the firm's costs and revenues under each scenario. Table 8.2 shows the information the firm needs to make its decision. - The operate-or-shut-down decision can be summed up as follows: Operate if TR ≥ VC. Shut down if TR < VC

Economic Costs

The costs that economists pay attention to—include accounting cost and something else: the producer's opportunity costs - The recognition that a firm's decisions about production must be based on economic cost (which takes into account a firm's opportunity costs) underlies everything we discuss about costs in the rest of this chapter and throughout the remaining chapters of this book.

Perceived Demand of perfectly competitive firm

The demand curve facing a firm in a perfectly competitive market is perfectly elastic at the market equilibrium price. Meaning, the demand curve for a firm in a perfectly competitive market is horizontal

Accounting Costs

The direct costs of operating a business, including costs for raw materials, wages paid to workers, rent paid for office or retail space, and the like

Marginal Product

The incremental output that a firm can produce by using an additional unit of an input (holding use of the other input constant) is called the marginal product. Ex: If a firm with this production function (in which capital is fixed at 4 units) uses 0 units of labor, it produces 0 units of output. (Perhaps the firm can't make any output without anyone to run the machines.) If it hires 1 unit of labor to combine with the 4 units of capital, it can produce 2 units of output. Therefore, the marginal product of that first unit of labor is 2.00. With 2 units of labor (and the same 4 units of capital), the firm can produce 2.83 units of output, making the marginal product of the second unit of labor the change in output or 2.83 - 2.00 = 0.83.

Isocost Line

The key concept that brings cost into the firm's decision. An isocost line connects all the combinations of capital and labor that the firm can purchase for a given total expenditure.

Difference between marginal products and returns to scale

The key difference between the two concepts is that marginal products refer to changes in only one input while holding the other input constant, but returns to scale is about changes in all inputs at the same time. In other words, diminishing marginal returns refers to short-run changes, while returns to scale is a long-run phenomenon because we are changing all inputs simultaneously.

Expansion Path

The line connecting all the firms cost-minimizing isoquant-isocost kine tangencies for outputs levels is the firms expansion path. It illustrates how the optimal mix of labor and capital varies with total output. The expansion path shows the optimal input combinations at each output quantity.

Marginal Product of labor (MP sub L)

The marginal product of labor (MPL) is the change in quantity (ΔQ) resulting from a 1-unit change in labor inputs (ΔL): Formula: MP sub L = Change in Q/ Change in L

Graphical analysis of the marginal product of labor

The marginal product of labor is the slope of the production function. As the quantity of labor increases, the marginal product decreases. To graph marginal product of labor graph the decrease in slope of the production function starting from labor 1.

Diminishing marginal returns of capital and labor

The marginal products of capital and labor decrease as the amount of that input increases, all else equal.

Marginal Cost

The other key cost concept is marginal cost, a measure of how much it costs a firm to produce one more unit of output: MC = change in TC/change in Q = change in variable cost(VC) / change in Q

Profit function

The profit function is total revenue TR minus total cost TC (each of which is determined by the firm's output quantity): π = TR - TC where: π = profit a firm makes TR = total revenue TC = total cost

Variable Cost Curve

The relationship between the amount of variable inputs a firm must buy and its output means the slope of the VC curve is always positive. The variable cost curve rises with output: At lower outputs, it increases with output at a diminishing rate, while at higher outputs, it begins to rise at an increasing rate.

Total Cost Curve

The total cost curve shows how a firm's total production cost changes with its level of output. Because all costs can be classified as either fixed or variable, the sum of these two components equals total cost. The total cost curve is the sum of the fixed and variable cost curves. It runs parallel to the variable cost curve and is greater than the variable cost curve by the amount of the fixed cost.

Graphical & Mathematical approach to cost-minimization

The total costs of producing a given quantity are minimized where the isocost line is tangent to the isoquant. The tangency implies that at the combination of inputs that minimizes the cost of producing a given quantity of output, the ratio of input equals the MRTS. Meaning cost is minimized where: -(W/R) = - (MP sub L / MP sub K) or (W/R) = (MP sub L)/(MP sub K) or (W/R) = MRTS sub LK

Profit maximization for perfectly competitive firms

There are two basic elements to profit: revenue and cost. In general, these are both affected by a firm's decisions about how much output to produce and the price it will charge for its output. Because perfectly competitive firms take the market price as given, we only need to focus on the choice of output. * If the market price (marginal revenue) is greater than the marginal cost of making another unit of output, then the firm can increase its profit by making and selling another unit, because revenues will go up more than costs. If the market price is less than the marginal cost, the firm should not make the extra unit. The firm will reduce its profit by doing so because while its revenues will rise, they won't rise as much as its costs. * The quantity at which the marginal revenue (price) from selling one more unit of output just equals the marginal cost of making another unit of output is the point at which a firm maximizes its profit.

Measuring a firms profit graphically

Therefore, the firm's profit can be seen in Figure 8.4 as the rectangle with height (P - ATC*) and base equal to the profit-maximizing quantity Q*. - Panel a of Figure 8.4 shows the firm's average total cost curve, its marginal cost curve, and its demand (marginal revenue) curve. The firm's total revenue equals the area of the rectangle with height P and base Q*. Its total cost is the area of the rectangle with height ATC* (ATC at the profit-maximizing level of output Q*) and base Q*. Because total revenue is greater than total cost at Q*, the firm is earning a positive level of profit.

Relationship between economies of scale and returns to scale

They are related—cost and the level of inputs move closely together—but there is a difference. the measure of economies of scale, which is about how total costs change with output, does not impose constant input ratios the way returns to scale do. - Because a firm can only reduce its cost more if it is able to change its input ratios when output changes, it can have economies of scale if it has constant or even decreasing returns to scale. That is, even though the firm might have a production function in which doubling inputs would exactly double output, it might be able to double output without doubling its total cost by changing the proportion in which it uses inputs. * Therefore, increasing returns to scale imply economies of scale, but not necessarily the reverse.

Graphical Representation: Short-run production function

This figure graphs the firms continuous short-run production function using the values from table 6.1. The production function's positive slope means that an increase in labor increases output. A firm hires more labor, however, output increases at a decreasing rate and the slope flattens.

Profit maximizing monopolist Response to change in marginal cost

To determine the market impact of this increase in marginal cost, we follow the three-step method but with the new marginal cost curve: Step 1: Derive the marginal revenue curve. Step 2: Find the quantity at which MR = MC Step 3: Determine the profit-maximizing price using the optimal quantity and the demand curve. - A firm with market power responds to a cost shock in a way that is similar to a competitive firm's response. When marginal cost rises, price rises, and output falls. When marginal cost falls, price falls, and output rises.

Determining the level of output that maximizes profit graphically

To figure out the level of output that maximizes profit, think about what happens to total cost and total revenue if the firm decides to produce one additional unit of output. Or, put differently, determine the firm's marginal cost and marginal revenue. - This point occurs at Q* in Figure 8.2. There, the slope of the total revenue curve (the marginal revenue—here, the market price) equals the slope of the total cost curve (the marginal cost at Q*).

Monopoly Profit Maximization

To maximize its profit, a firm should choose its quantity where its marginal revenue equals its marginal cost: MR = MC - Setting MR = MC gives us the quantity, Q*, that maximizes the firm's profit, and from that we figure out the profit-maximizing price. The height of the demand curve at that profit-maximizing quantity Q* tells us the market price for the firm's output. - The monopolist can either produce the profit-maximizing quantity of output and let the market determine the price (which will be the profit-maximizing price), or it can set the profit-maximizing price and let the market determine the quantity (which will be the profit-maximizing quantity).

Accounting Profit

Total Revenue - accounting costs

Mathematical approach: Monopoly Profit maximization

We can also solve for the profit-maximizing quantity and price mathematically, given equations for the firm's demand and marginal cost curves. Step 1: Derive the marginal revenue curve from the demand curve. Let's start by obtaining the inverse demand curve by rearranging the demand curve so that price is a function of quantity rather than the other way around: which gives you a linear inverse demand curve of the form P = a - bQ and MR curve= a -2bQ Step 2: Find the output quantity at which marginal revenue equals marginal cost. Therefore, we just set the marginal revenue curve equal to this value and solve for Q: which is the profit maximizing quantity Step 3: Determine the profit-maximizing price by locating the point on the demand curve at that optimal quantity level. Find the profit-maximizing price by plugging the optimal quantity into the demand curve.

Measuring consumer surplus, producer surplus & deadweight loss in monopoly & perfect competition

We can compute the consumer and producer surplus when a firm has market power in the same way we computed these surpluses in a competitive market. The consumer surplus is the area under the demand curve and above the price. The producer surplus is the area below the price and above the marginal cost curve. Remember that the supply curve in a perfectly competitive market is actually part of its marginal cost curve, so there is no difference in the case of market power. - CS: The consumer surplus triangle has a base equal to the quantity sold and a height equal to the difference between the demand choke price and the market price. The demand choke price is especially easy to calculate from an inverse demand curve; you just plug in Q = 0 and solve for the price. - PS: The producer surplus is a rectangle with a base equal to the quantity sold and a height equal to the difference between the monopoly price and marginal cost. - DEAD WEIGHT LOSS: The deadweight loss of market power can be seen in Figure 9.6. It is the area of triangle C whose base is the difference between the firm's output with market power and its output under perfect competition and whose height is the difference between the prices under market power (Pm) and competition (Pc).

Determining when a profit maximizing firm should shut down

We can now rewrite the rules above in terms of the market price P facing the firm and its average variable cost AVC* at the profit-maximizing (or in this case loss-minimizing) quantity: Operate if P ≥ AVC*. Shut down if P < AVC*.

Graphical Approach: Equilibrium conditions for cournot duopoly

We can show this graphically in Figure 11.4. Saudi Arabia's output is on the vertical axis and Iran's output is on the horizontal axis. The curves illustrated are reaction curves. A reaction curve shows the best production response a country (or firm, in a more general oligopoly context) can make given the other country's/firm's action. Because both reaction curves are downward-sloping, a firm's optimal output falls as the other producer's output rises. - Solve simutaneously What Cournot's approach does is maximise both market share and profitability by defining optimum prices. This price will be the same for both companies, as otherwise the one with the lower price will obtain full market share, which makes this a Nash equilibrium, also known for this model the Cournot-Nash equilibrium. - he outcome is below that of perfect competition and therefore is not socially optimal, but it is better than the monopoly outcome.

Long-run and short-run marginal costs

We know that in the short run with capital fixed, there is only one output level at which a firm would choose that same level of capital: the output at which the short-run average total cost curve touches the long-run average total cost curve.

Deriving Long-Run marginal cost from short run marginal cost

We know that in the short run with capital fixed, there is only one output level at which a firm would choose that same level of capital: the output at which the short-run average total cost curve touches the long-run average total cost curve. - So, for example, if Q = 10, Ivor's Engines would choose a level of capital in the long run (K = 4) that is the same as that corresponding to short-run average total cost curve ATC sub SR,10. Because the short- and long-run average total cost curves coincide at this quantity (but only at this quantity), so too do the short- and long-run marginal cost curves. In other words, because the firm would choose the same level of capital even if it were totally flexible, the long-run marginal cost at this quantity is the same as the short-run marginal cost on MC sub SR,10. Therefore, to find the long-run marginal cost of producing 10 units, we can go up to the short-run marginal cost curve at Q = 10. This is point A in Figure 7.9 and represents the long-run marginal cost at an output level of 10 engines. Page 272 - Likewise, the long-run marginal cost at Q = 20 is the value of MC sub SR,20 when Ivor's Engines is making 20 engines. Therefore, the long-run marginal cost at Q = 20 can be found at point Y in Figure 7.9 (this is the same point Y as in Figures 7.7 and 7.8). Repeating the logic, Ivor's long-run marginal cost for producing 30 engines equals the value of MCSR,30 when output Q = 30, which is point B in the figure. - When we connect these long-run marginal cost points A, Y, and B, along with the similar points corresponding to every other output quantity, we trace out the long-run marginal cost curve MCLR.

Derivation of market supply from individual firm supplies

What does determine the price in a perfectly competitive market? The combined output decisions of all the firms in the market: the industry supply curve. In this section, we look at how this combined output response is determined. - We assume that firms' combined output responses do not have any notable impact on input prices, so the industry short-run supply curve is the sum of firm-level short-run supply curves. - To derive the industry short-run supply curve from these firm supply curves, we add up the individual firm outputs at each possible market price.

Isocost lines and Input Price Changes: When labor becomes more expensive

When relative prices change, the isocost line rotates. When, labor's price (W) becomes more expensive and the firm only invests in labor the isocost line becomes steeper and rotates clockwise (to the left) like in figure 6.8 and vice versa.

Derivation of MR and profit maximization under price regulation

When there is a concern that firms in an industry have too much market power, governments sometimes directly regulate prices. Often, this occurs in markets considered to be natural monopolies. If it appears that there is no way to prevent the existence of a natural monopoly because of the nature of the industry's cost structure, the government will often allow only a single firm to operate but will limit its pricing behavior to prevent it from fully exploiting its market power. - To understand the logic behind these actions, consider a typical natural monopoly case as shown in Figure 9.8. Let's suppose it is the market for electricity distribution, which we argued earlier may, in fact, be a natural monopoly. With a demand curve of D, an unregulated electric company would produce at the point where marginal revenue equals marginal cost. This would lead to a price of Pm, substantially higher than the firm's marginal cost. The consumer surplus in this situation will be only the area A, rather than the area A + B + C, as would be the case if prices were instead set at Pc, a level equal to the firm's marginal cost.

Isocost line graphically

Y-intercept of isocost line = C/R Slope of isocost line = - price of labor/ price of capital or -W/R Here, the slope reflects the cost consequences of trading off or substituting one input for another. - If the isocost line's slope is steep, labor is relatively expensive compared to capital. If the firm wants to hire more labor without increasing its overall expenditure on inputs, it is going to have to use a lot less capital. (Or if you'd rather, if it chose to use less labor, it could hire a lot more capital without spending more on inputs overall.) If the price of labor is relatively cheap compared to capital, the isocost line will be relatively flat. The firm could hire a lot more labor and not have to give up much capital to do so without changing expenditures.

Constant-cost industry

an industry whose firms' total costs do not change with total industry output

Long-run marginal cost and long-run average total cost.

long-run marginal cost is below long-run average total cost when average total cost is falling (such as at point A), above long-run average total cost when average total cost is rising (such as at point B), and equal to long-run average total cost when average total cost is at its minimum (point Y)

Average variable Cost

measures the per-unit variable cost of production. It is calculated by dividing variable cost by the quantity of output: AVC = VC/Q

Long Run Total Cost Curve for a firm

n the long run, however, a firm produces where its long-run marginal cost equals the market price. Moreover, because all inputs and costs are variable in the long run, the firm's long-run supply curve is the part of its long-run marginal cost curve above its long-run average total cost curve (LATC = LAVC because there are no fixed costs in the long run).