Lecture 4 - Costs

How does a firm determine how its cost vary with output?

- A firm determines the cost-minimizing production process for any given level of output, by; 1. determining the isoquant curve for that level of output 2. determining the isocost LINE that is tangent to the isoquant curve. Cost minimisation occurs when using the inputs specified by the isoquant curve, at the point at which it intersects the isocost curve. - Determining the cost-minimizing production process, when output increases: 1. Repeat the above analysis for the different levels of output, this allows the firm to determine how its cost varies with output. The points at which the 2 curves intersect make up the firms expansion curve.

Discuss the difference between sunk costs, and avoidable costs for short-run and long-run.

- In the short-run, some of the firms fixed cost may be considered "sunk" costs, in that a firm must pay for its rent, even if does not operate (contract driven) - In the long-term firms may incur fixed costs, however these fixed costs are AVOIDABLE (rather than SUNK, as in the short-run). As such it resembles an OPPORTUNITY COST. Example: The rent of F per month that a restaurant pays is a fixed cost because it does not vary with the number of meals (output) served. In the short run, this fixed cost is sunk: The firm must pay F even if the restaurant does not operate. In the long run, this fixed cost is avoidable: The firm does not have to pay this rent if it shuts down/or terminates the lease. >> The long-run is in this case therefore determined by the legnth of the rental contract during which time the firm is obligated to pay rent.

What is the marginal cost, for a production function where: q = f(L, K with line on top)

- It is one variable input variable costs. - MC =ΔVC/Δq

Discuss the price assosciated with fixed and variable inputs when calculating costs of production.

- The COST assosciated with inputs that cannot be adjusted (FIXED INPUTS) is FIXED. - The COST from inputs that can be ADJUSTED (VARIABLE INPUTS) is VARIABLE

Summarise the 4 most important concepts of short-run production costs.

- The COST assosciated with inputs that cannot be adjusted (FIXED INPUTS) is FIXED. While the COST from inputs that can be ADJUSTED (VARIABLE INPUTS) is VARIABLE. - Given that INPUT PRICES ARE CONSTANT, the shape of the VARIABLE COST and COST CURVES are determined by the production function. - Where there are diminishing marginal returns to a variable input, the variable cost and cost curves become relatively steep as output increases, so the AVERAGE COST, AVERAGE VARIABLE COST, & MARGINAL COST RISE WITH OUPUT. -Because of the relationship between marginals and averages, both the average cost and average variable cost curves fall when marginal cost is below them and rise when marginal cost is above them, so THE MARGINAL COST CUTS BOTH THESE AVERAGE COST CURVES AT THEIR MINIMUM POINTS.

What are the long-run marginal cost and average cost determined by?

- The long-run cost curve.

Draw the variable cost curve for a produciton function: q= f(K with line on top, L) Discuss what it is determined by and its shape

- The production function determines the shape of the variable cost curve, provided that the price of inputs are fixed. - The graph shows the firm's short-run production function relationship between output and labor when capital is held fixed. SHAPE: As labor increases, the total product of labor curve increases less than in proportion. This flattening of the total product of labor curve at higher levels of labor reflects the DIMINISHING MARGINAL RETURNS ON LABOR (variable costs rise more than in proportion as output increases). This graph is the same as the ones with all 4 cost curves, but the output and cost axes are reversed.

Where does the maringal cost curve cut the average cost curve and average variable cost curve?

-Because of the relationship between marginals and averages, both the average cost and average variable cost curves fall when marginal cost is below them and rise when marginal cost is above them, so THE MARGINAL COST CUTS BOTH THESE AVERAGE COST CURVES AT THEIR MINIMUM POINTS.

What are the 3 important properties of isocost lines?

1. AXIS-INTERSECTION: Isocost line hits y-axis at C/r. Isocost line hits x-axis at C/w 2. ISOCOSTS THAT ARE FARTHER FROM THE ORIGIN HAVE HIGHER COSTS >> Because the isocost lines INTERSECT THE CAPITAL axis at C/r and the LABOR axis at C/w, an increase in the cost shifts these intersections with the axes proportionately outward. 3. GRADIENT OF ALL ISOCOSTS LINES for the same production process are the same (depends on the cost of inputs, w/r).

How does a firm minimize costs? What are the two pre-requisites?

1. The firm must product at a technologically efficient level (e.g. a firm cannot use fewer inputs to produce same level of ouput, such that all inputs are used optimally). 2. The firm cannot produce the same level of output for a lower cost (usually you take the long-run cost curve, because the firm is interested in minimizing cost in the long-run).

What are the 3 equivalent approaches a firm can choose to minimize costs?

1.) Lowest-isocost rule: Pick the bundle of inputs where the lowest isocost line touches the isoquant. 2.) Tangency rule: Pick the bundle of inputs where the isoquant is tangent to the isocost line. 3.) Last-dollar rule: Pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input.

What are the 4 measures, that indicate how costs vary with different levels of ouput? List them.

1.) Marginal cost (MC ): the amount by which a firm's TOTAL cost changes if the firm produces one more unit of output. >> (as the fixed costs stay they same, this is a measure of how variable costs change when producing one more unit) MC = change in C / change in q or MC = change in VC / q 2.) Average fixed costs (AFC): the fixed cost divided by the units of ouput produced AFC = FC/Q 3.) Average variable costs (AVC): the variable cost divided by the units of ouput produced. AVC = VC/q 4.) Average cost (AC): the total cost divided by the units of output produced. AC = C/q.

List the 3 short-run cost-level curves and 4 cost per-unit curves discussed so far.

3 cost-level curves: total cost, fixed cost, and variable cost 4 cost-per-unit curves: average cost, average fixed cost, average variable cost, and marginal cost

What is the two-step process a firm uses to choose how to produce its output efficiently?

A firm uses a two-step procedure in determining how to produce a certain amount of output efficiently (assumed that firms maximize profit, and so produce efficently) 1. It first determines which production processes are technologically efficient so that it can produce the desired level of output with the least amount of inputs. 2. The firm's second step is to pick from these technologically efficient production processes the one that is also economically efficient, minimizing the cost of producing a specified amount of output. >> To determine this the firm combines information from the ISOQUANT (level of ouput stays the same, but combinations of input change) and cost of each variable (ISOCOST) By reducing its cost of producing a given level of output, a firm can increase its profit. > PROFIT MAXIMISING. (WE WILL SEE HOW A FIRM CAN USE AN ISOQUANT AND A ISOCOST LINE TO PICK THE ECONOMICALLY EFFICIENT COMBINATION OF INPUTS)

What is the 2-step process for a firm to determine how it will produce its product?

A firm uses a two-step procedure in determining how to produce a certain amount of output efficiently (assumed that firms maximize profit, and so produce efficently) 1. It first determines which production processes are technologically efficient so that it can produce the desired level of output with the least amount of inputs. 2. The firm's second step is to pick from these technologically efficient production processes the one that is also economically efficient, minimizing the cost of producing a specified amount of output. >> To determine which process minimizes its cost of production, the firm uses information about the production function and the cost of inputs. By reducing its cost of producing a given level of output, a firm can increase its profit.

Define short-run variable costs NB it is not the same as variable inputs but they are directly related.

A firm's variable cost (VC) is the production expense that CHANGES WITH OUTPUT PRODUCED. The variable cost is the cost of the variable inputs (their OPPORTUNITY COSTS)—the inputs the firm can adjust to alter its output level, such as labor and materials. The firm's variable cost changes with output.

Discuss how a franchise tax would affect a firm´s short-term cost curves.

A franchise tax— also called a business license fee—is a lump sum that a firm pays for the right to operate a business. An $800-per-year tax is levied "for the privilege of doing business in California." These taxes do not vary with output, so they affect firms' fixed costs only—not their variable costs. > By affecting the average fixed costs, the tax also affects average (total) costs.

Define durable good

A product that is usable for years.

Why is it important that firms accuralty meausre the economic cost of their factors of production? What are the two problems with determing the economic cost of durable goods, such as capital and land?

Economic cost = opportunity cost IMPORTANT: To maximize profit, a firm must properly measure the opportunity cost of a piece of capital even if its value rises or decreases over time. 1. How to allocate the initial purchase cost over time? 2. What to do if the value of the capital changes over time?

Draw and discuss the relationiship between long-run cost curve, longrun MC and long-run AC curves.

AC = the slope of the line from the origin to the point of given output level on the long-run cost curve. MC = slope of the line tangent to the long-run cost curve at the particular level of output. AC = MC at point q, where the slope of a line from the origin to point q equals the AC, and the line is also tangent to the long-run cost curve, so that the slope also equals the MC. The long-run average cost curve falls when the long-run marginal cost curve is below it and rises when the long-run marginal cost curve is above it. Thus, the marginal cost crosses the average cost curve at the lowest point on the average cost curve.

What is the relationship between AVC and Average product of labor for a one variable in-put production function?

AVC = w / APL With a constant wage, the average variable cost moves in the opposite direction of the average product of labor. As we discussed in Chapter 6, the average product of labor tends to rise and then fall (according to the rise in MPL that then begins to diminish), so the average cost tends to fall and then rise, as in panel b of Figure 7.1.

Discuss the short-run cost curves graph showing the 4 measures of AVERAGE costs. What are its axis, what does it show? Explain the trends of the 4 cost curves.

AVERAGE FIXED COSTS: - The curve decreases, and approached zero, as output increases, and the costs are spread over many units of output. AVERAGE TOTAL COST: Vertical sum of the average variable cost and average fixed cost curves. For example at 6 units, AVC = 20 and AFC =8, so the AC=28. AVERAGE COST: For any output, it is the slope of the line from a point on the total cost curve to the origin. Average costs initially decrease, as the fixed costs are spread over more units, and AVC decrease. Begins to increase when marginal costs are higher than ac (similar to graphs with total output and units of labor input). MARGINAL COST: Curve which represents the slope of the total cost curve, at any given point.

What is the difference between opportunity costs and sunk costs when determining the most economical production process?

An opportunity cost is not always easy to observe but should always be taken into account when deciding how much to produce. In contrast, a sunk cost—a past expenditure that cannot be recovered— easy to observe, is not relevant to a manager when deciding how much to produce now. If an expenditure is sunk, you cannot be used on an alternative, and so its OPPORTUNITY COST IS ZERO. >> Sunk costs do not represent costs of your production process, rather expenditurs of the past that should not influence the production process.

Discuss average cost (AC). Gives its fomula(s). How do you determine the price of a product, for a firm to make a profit, given its average cost (AC).

Average cost (AC): the total cost divided by the units of output produced. The average cost is also the sum of the average fixed cost and the average variable cost: AC = C/q. AC = AFC + AVC. The firm makes a profit if its average cost is below its price, which is the firm's average revenue

Discuss average fixed cost (AFC). Gives its fomula(s). How does the AFC change as ouput increaseS?

Average fixed costs (AFC): the fixed cost divided by the units of ouput produced AFC = FC/Q The average fixed cost falls as output rises because the fixed cost is spread over more units.

Discuss average variable cost (AVC). Gives its fomula(s) What do firms use this measure for?

Average variable costs (AVC): the variable cost (cost of all variable inputs) divided by the units of ouput produced. AVC = VC/q Because the variable cost increases with output, the average variable cost may either increase or decrease as output rises. A firm uses the average variable cost to determine whether to shut down operations when demand is low.

What determines the shape of the other cost curves, i.e. marginal cost, average cost, fixed cost?

Because the production function determines the shape of the variable cost curve, it also determines the shape of the marginal, average variable, and average cost curves.

When firms rent or buy durabl goods, how does the opportunity cost of them change over time?

Because the values of trucks, machines, and other equipment decline over time, their rental rates fall, so the firm's opportunity costs decline. In contrast, the value of some land, buildings, and other forms of capital may rise over time (so the rent of them will rise, and opporunity rise therefore also will)

How do firms calculate the opportunity cost of durable goods, if there are no rental markets for the bought durabl good? For example a truck that costs 20,000 dollars.

But what if there is no rental market for trucks available to the firm? It is still important to determine an appropriate opportunity cost. Suppose that the firm has two choices: It can choose not to buy the truck and keep the truck's purchase price of $20,000, or it can use the truck for a year and sell it for $17,000 at the end of the year. a.) If the firm does NOT purchase the truck, it will deposit the $20,000 in a bank account that pays 5% per year, so the firm will have $21,000 at the end of the year. Thus, the opportunity cost of capital of using the truck for a year (is NOT using the truck for a year) is 21,000-17,000 = 4,000. This $4,000 opportunity cost equals the $3,000 depreciation of the truck plus the $1,000 in forgone interest that the firm could have earned over the year if the firm had invested the $20,000.

How does a firm choose the lowest-cost way to produce a given level of output?

By COMBINING the information about COST CONTAINED IN THE ISOCOST LINES with information about EFFICIENT PRODUCTION summarized by an ISOQUANT, a firm chooses the lowest-cost way to produce a given level of output. ** LOWEST-ISOCOST RULE** Pick the bundle of inputs where the LOWEST ISOCOST LINE TOUCHES THE ISOQUANT.

From an equation of an isocost line, can you determine how many units of an input a firm is able to buy? How? Calculate how many units of K, a firm can buy if it only have K and L inputs, w=5, r=10, and total costs must equal 100.

C (with line) = wL + rK. Using algebra, we can rewrite this equation to show how much capital the firm can buy if it spends a total of C (with line on top) and purchases L units of labor: K = (C/r) - (w/r)*(L) From isocost line you find, that you need 2L for every K, so by substituting in, we find that the 100 dollar isocost line is: K = (100/10)-(5/10)*(2) K = 10- L (From the graph, or substituting in values of L, you can determine tha value of K).

What are the two forms of equations for isocost lines?

C(with line on top) = wL + rK K = (C with line /r) - (w/r)*(L)

What occurs at the point at which, MRTS = - w/r

Cost minimisation occurs when the isocost line is tangent to the isoquant curve. At this point the slope of the isocost line equals the slope of the isoquant line. The slope of the isocost line is the negative of: w/r. The slope of the isoquant curve is the marginal rate of technical substitutioN MRTS Thus, when MRTS = -w/r COST MINIMISATION for the given level of output with given costs of inputs occurs. When the slopes are not equal at y, the firm can produce the same output at lower cost.

Discuss the short-run cost curves graph showing the 4 measures of ABSOLUTE costs. What are its axis, what does it show? Explain the trends of the 4 cost curves.

FIXED COSTS: costs which do not vary with output, and are therefore represented as a horizontal line, at y= 48. VARIABLE COSTS: shows the costs that change as ouput changes, e.g. costs of variable inputs. >> The curve is zero at zero units of output and rises with output. TOTAL COSTS: The sum of the variable and fixed costs. Has the same slope as the variable costs curve, but shifted upward, because of the added fixed costs. >> Variable cost curve shifted up by 48 dollars = fixed costs. MARGINAL COSTS: For any level of output, is equal to the slope of the cost curve, which is also equal to the slop of the variable cost curve.

Define short-run fixed cost. Nb it is different from fixed variable, but they are directly related.

Fixed cost (F ): a production expense that DOES NOT VARY WITH OUTPUT PRODUCED (cost of fixed inputs). The short-run fixed cost includes the cost of inputs that the firm cannot practically adjust in the short run, such as land, a plant, large machines, and other capital goods. The fixed cost for a capital good a firm owns and uses is the OPPORTUNITY of renting it to someone else. Fixed variable: A production variable that cannot practically be changed/altered within the given time considered. E.g. number of production plants over the next month cannot usually be increased.

What is the slope of a family of isocost lines, as total cost increases?

From the equation: K = - (w/r)*(L) + (C with line/r) Has the same form as, y = -mx + b So gradient = w/r As the wage and rent stay the same per unit, regardless of output level, the GRADIENT OF ALL ISOCOSTS LINE are the same. >> THE SLOPE OF THE ISOCOST LINE DEPENDS ON THE RELATIVE PRICES OF THE INPUT. >> THE ISOCOST LINES ARE PARALLEL.

When are the variable cost and cost curves determined by the production function?

Given that INPUT PRICES ARE CONSTANT, the shape of the VARIABLE COST and COST CURVES are determined by the production function.

Where do isocost lines hit the x and y-axis, representing the two variable inputs of the production function?

ISOCOST HITS Y-AXIS AT: K = (C with line/r) - (w/r)*(L) K = - (w/r)*(L) + (C with line/r) Has the same form as, y = -mx + b Line hits y-axis at b, in this case C/r.***** ISOCOST HITS W-AXIS AT: L = C/w - rK/w L = - rK/w + C/w Has the same form as, y = -mx + b Line hits y-axis at b, in this case C/w.*****

Draw 2 isocost lines where one has higher costs than the other.

ISOCOSTS THAT ARE FARTHER FROM THE ORIGIN HAVE HIGHER COSTS, than those that are closer to the origin. Because the isocost lines INTERSECT THE CAPITAL axis at C/r and the LABOR axis at C/w, an increase in the cost shifts these intersections with the axes proportionately outward.

Define an ISOQUANT and ISOCOST LINE. What are the differences?

ISOQUANT: is a line showing the different combinations of inputs that produce the SAME (iso) LEVEL (quant) OF OUTPUT, at a technologically efficient leve. (3 Broad types: perfect substitutes, perfect proportion and imperfect substitutes). >>> They show how easy it is for a firm to switch from one input to another. The slope is the diminishing marginal rate of technological substitution (MRTS), which changes as input levels increases, giving rise to the CURVED shape. q = f(L, K) 100 = xL, yK ISOCOST LINE; line showing all the COMBINATIONS OF INPUTS that require the same (iso) total EXPENDITURE (COST) >> ISOCOST line is NOT curved because the slope shows the rate at which the firm can substitute capital for labor HOLDING COSTS CONSTANT. This does not change as input levels increase. C(with line on top) = wL + rK, where w = wage per hour r = rent per hour

What is the opportunity cost of a firm buying a forklift for 25,000 dollars? What implications does this have on the firms production costs?

If a firm buys a forklift for $25,000 and can resells it for the same price immediatley, it is not a sunk expenditure, as it can have an alternative use or be resod, and the opportunity cost of the forklift is $25,000. If the firm decides to keep the forklift, the opportunity cost could be calculated by determining how much the forklift could be rented for per month. As it is an opportunity cost it SHOULD be included in the firms production costs.

How do firms calculate the opportunity cost of durable goods, if they are bought? For example a truck that costs 20,000 dollars.

If the firm buys the durable good (truck), calculating the relevant opportunity cost is more complex, as you have to consider 1.) cost allocation over time (there is only 1 explicit cost, how do you spread it over time) and 2.) changes in value of the durable good The true opportunity cost of using a truck that the firm owns is the amount that the firm could earn if it rented the truck to others. 1.) That is, regardless of whether the firm rents or buys the truck, the manager views the opportunity cost of this capital good as the rental rate for a given period of time. 2.) If the value of an older truck is less than that of a newer one, the rental rate for the truck falls over time.

How do firms calculate the opportunity cost of durabl goods, if they are rented? For example a truck that it rents for 400 dollars a month.

If the firm can rent capital for short periods of time, it calculates the cost of this capital in the same way that it calculates the cost of nondurable inputs such as labor services or materials (just summing the implicit and explicit costs). ____________________________ If the firm rents the durable good (truck), the rental payment is the relevant opportunity cost per month, in this case 400 dollars per month. CALCULATING COST OF DURABLE GOOD: 1.) ALLOCATIN THE COST OVER TIME The truck is rented month to month, so the firm does not have to worry about how to allocate the purchase cost of a truck over time. 2.) WHAT TO DO IF VALUE INCREASES/DECREASES the rental rate will adjust if the cost of trucks changes over time.

Why must the isocost line be tangent to the isoquant for cost to be minimised? Show that costs of producing a specified output are not minimised at other input levels.

If the firm spent less than $2,000, it could not produce 100 units of output. Each combination of inputs on the $1,000 isocost line lies below the isoquant, so the firm cannot produce 100 units of output for $1,000. The firm can produce 100 units of output using other combinations of inputs beside x; however, using these other bundles of inputs is more expensive. For example, the firm can produce 100 units of output using the combinations y (L = 24, K = 303) or z (L= 116, K = 28). Both these combinations, however, cost the firm $3,000. >> If an isocost line crosses the isoquant twice, as the $3,000 isocost line does, there must be another lower isocost line that also touches the isoquant ***** THE FIRM CHOOSES THE INPUT BUNDLE WHERE THE RELEVANT ISOQUANT IS TANGENT TO AN ISOCOST LINE to produce A GIVEN LEVEL OF OUPUT AT THE LOWEST COST.****

Which of the 3 equivalent methods of determining the lowest-cost combination of inputs to produce a given level of output is MOST ROBUST?

If the isoquant is not smooth, the lowest-cost method of production cannot be determined by using the tangency rule or the last-dollar rule. The LOWEST-ISOCOST rule always works—even when isoquants are not smooth.

What are the short-term variable costs and marginal costs for a one variable input produciton function? E.g. q= f(L, K with line on top)

If the wage rate, w, is fixed, and the variable input is L: ΔVC = wΔL MC = wΔL/Δq so marginal costs are equal to the increase in wages paid for a small (one unit) increase in output.

Why are short-run and long-run costs important for a profit-optimizing firm?

To make profit-maximizing decisions, a firm needs to know how its cost varies with output (and over time) A firm's cost rises as it increases its output. A firm cannot vary some of its inputs, such as capital, in the short run (Chapter 6). As a result, it is usually more costly for a firm to increase output in the short run than in the long run, when all inputs can be varied

What costs must firms consider when deciding on their produciton process?

To produce a particular amount of output, a firm incures BOTH EXPLICIT AND IMPLICIT COSTS of its FACTORS OF PRODUCTION EXPLICIT COSTS: The manager can easily calculate these explicit costs, which are its direct, out-of-pocket payments for inputs to its production process within a given time period. IMPLICIT COSTS: difficult to calculate, in that they reflect only a forgone opportunity rather than an explicit, current expenditure. (This is especially important when dealing with durable capital goods)

What are the two formulas for calculating average costs of a one variable input function? E.g. q= f(L, K with line on top)

What determines variable costs in the short-run, with one variable input? can only be changes in this one variable input. if the wage rate, w, is fixed, and the variable input is L: APL = q/L and AVC = wL/q Mathematically rearranging: AVC = VC/q = wL/q = w/APL

Illustrate why a sunk cost should not influence a manager's current decisions, by considering a firm that paid $300,000 for a piece of land for which the market value has fallen to $200,000. The land is worth $240,000 to the firm if it builds a plant on this parcel. Is it worth carrying out production on this land or should the land be sold for its market value of $200,000?

Now, the land's true opportunity cost is $200,000. The $100,000 difference between the $300,000 purchase price and the current market value of $200,000 is a sunk cost that has already been incurred and cannot be recovered. IF SUNK COSTS ARE INCLUDED - FALSE: - If the firm uses the original purchase price in its decision-making process, the firm will falsely conclude that using the land for production will result in a $60,000 loss: the $240,000 value of using the land minus the purchase price of $300,000. IF SUNK COSTS ARE NOT INCLUDED - CORRECT: Instead, the firm should use the land because it is worth $40,000 more as a production facility than if the firm sells the land for $200,000, its next best alternative. Thus, the firm should use the land's opportunity cost to make its decisions and ignore the land's sunk cost

Define short-run total costs

TOTAL COSTS/ COSTS (total cost, C ) are the sum of a firm's variable cost and fixed cost: C = VC + F.

Discuss how a tax on per unit out-put would affect a firm´s short-term cost curves.

Taxes applied to a firm shift some or all of the marginal and average cost curves. For example, suppose that the government collects a specific tax of $10 per unit of output from the firm. This tax, which varies with output, affects the firm's variable cost but not its fixed cost. As a result, it affects the firm's average cost, average variable cost, and marginal cost curves but NOT its average FIXED COST CURVE. At every quantity, the average variable cost and the average cost rise by the full amount of the tax. The average cost equals the average variable cost plus the average fixed cost. Because the tax increases average variable cost by $10 and does not affect the average fixed cost, the tax increases average cost by $10. The tax also increases the firm's marginal cost> It adds 10 dollars to the marginal cost before tax.

What is the difference between technological efficiency/efficient production and economical efficiency? How do they relate.

Technological (or technical) efficiency: when a firm produces the maximum output possible, from the given inputs (as shown by pdf) Economic efficiency: When a firm produces its output at the lowest possible cost. Economic efficiency requires technological efficiency (must be producing the maximum output with given goods, e.g. there is no unused factors of production, for the firm to be producing at the lowest cost).

Define economic cost or opportunity cost.

The ECONOMIC or OPPORTUNITY COST is the value of the best alternative use of a resource. This includes BOTH explicit and implicit costs. If a firm purchases and uses an input immediately, that input's opportunity cost is the amount the firm pays for it. However, if the firm does not use the input in its production process, its best alternative would be to sell it to someone else at the market price

Define the average (total) cost. Why is a firms average (total) costs U-shaped?

The average cost (AC) curve is the vertical sum of the average variable cost (AVC) and average fixed cost curves. Because the average fixed cost curve falls with output and the average variable cost curve rises with output, the average cost curve is U-shaped. The firm's average fixed cost (AFC) falls as output increases. The firm's average variable cost curve is strictly increasing.

How can you deduce average total cost from the short-run cost curves graph showing the 4 measures of ABSOLUTE costs.

The average cost at a particular output level is the slope of a line from the origin to the corresponding point on THE TOTAL COST CURVE.. >>The slope of that line is the rise—the cost at that output level—divided by the run—the output level—which is the definition of the average cost. EXAMPLE: In panel a, the slope of the line from the origin to point A is the average cost for 8 units of output. The height of the cost curve at A is 216, so the slope is which is the height of the average cost curve at the corresponding point a in panel b.

Define AVC curve and discuss the shape of the average cost curve

The average cost curve is the vertical sum of the average variable cost curve and the average fixed cost curve, as in panel b. AT LOW OUPUT LEVELS: If the average variable cost (AVC) curve is U-shaped, adding the strictly falling average fixed cost (FC fall because the cost of fixed variables are spread over larrger output) makes the average cost fall more steeply than the average variable cost curve at low output levels. AT HIGH OUTPUT LEVELS: At high output levels, the average cost and average variable cost curves differ by ever smaller amounts, as the average fixed cost, F/q, approaches zero. Thus, the average cost curve is also U-shaped.

How can you deduce average VARIABLE cost from the short-run cost curves graph showing the 4 measures of ABSOLUTE costs.

The average variable cost is the slope of a line from the origin to a point on the variable cost curve. The slope of the dashed line from the origin to B in panel a is 20—the height of the variable cost curve, 120, divided by the number of units of output, 6—which is the height of the average variable cost at 6 units of output, point b in panel b.

Give the formula for an ISOCOST LINE, in which the production process only has 2 inputs, labor and capital, and cost equals 100.

The cost of producing a given level of output depends on the price of labor and capital. Labor: The firm hires L hours of labor services at a wage of w per hour, so its labor cost is wL. Capital: The firm rents K hours of machine services at a rental rate of r per hour, so its capital cost is rK. (If the firm owns the capital, r is the implicit rental rate, ie. the cost of renting the capital elsewhere.) The firm's total cost is the sum of its labor and capital costs: C(with line on top) = wL + rK, where w = wage per hour r = rent per hour An isocost line, shows all the combinations of inputs that require the same total cost plotted on a line. Thus, 100 = wL + rK

Define expansion path

The curve through the tangency points between isocost lines and isoquants, such as x, y, and z, is called the expansion path. ***The points on the expansion path (THE CURVE SHOWS) are the COST-MINIMIZING COMBINAITONS OF LABOR & CAPITAL FOR EACH LEVEL OF OUTPUT.

What does the lowest-isocost rule state?

The firm minimizes its cost by using the combination of inputs on the isoquant that is on the lowest isocost line that touches the isoquant. For example: This isocost line touches the isoquant at the bundle of inputs x, where the firm uses L=50 and K=100 units of capital.

Once the furniture manufacturer determines the lowestcost combination of inputs to produce a given level of output, it uses that method as long as the input prices remain constant. How should the firm change its behavior if the cost of one of the factors changes? Suppose that the wage falls from $24 To $8 but the rental rate of capital stays constant at $8.

The firm minimizes its new cost by substituting away from the now relatively more expensive input, capital, toward the now relatively less expensive input, labor. The change in the wage does not affect technological efficiency, so it DOES NOT AFFECT THE ISOQUANT. Because of the wage decrease, the new ISOCOST LINES HAVE A FLATTER SLOPE. The new, flatter isocost line is tangent to the isoquant at Bundle where the firm uses less capital, but more labor, and the firms cost of production falls. >> This example illustrates that a CHANGE IN THE RELATIVE PRICES OF INPUTS AFFECTS THE MIX OF INPUTS THAT A FIRM USES.

What happens to the slope of an isocost line if one of the variable inputs become more expensive per unit?

K = - (w/r)*(L) + (C with line/r) Has the same form as, y = -mx + b If there is a change in either w, or r, the slope of the isocost line changes.

What does the last dollar rule state? What is the mathematical expression for this?

LAST DOLLAR RULE: Cost is minimized if inputs are chosen so that the last dollar spent on labor adds as much extra output as the last dollar spent on capital. (MPL/w) = (MPk/r)

What is the relationship between MC and Marginal product of labor for a one variable in-put production function?

MC = w / MPL The formula shows that the marginal cost moves in the direction opposite that of the marginal product of labor. At low levels of labor: the marginal product of labor commonly rises with additional labor because extra workers help the original workers and they can collectively make better use of the firm's equipment. >>> As the marginal product of labor rises, the marginal cost falls. At higher levels of labor: Now workers must share the fixed amount of equipment and may get in each other's way, marginal product of labor increases less. As a result the marginal cost curve slopes upward because of diminishing marginal returns to labor. Thus, the marginal cost first falls and then rises.

What are the two formulas for calculating marginal costs of a one variable input function? E.g. q= f(L, K with line on top)

MC = wΔL/Δq so marginal costs are equal to the increase in wages paid for a small (one unit) increase in output. We also know MPL =Δq/ΔL Mathematically (from rearranging the two equations), this means: MC = w/MPL

State the equation for the TANGENCY RULE (The firm chooses the input bundle where the relevant isoquant is tangent to an isocost line to produce a given level of output at the lowest cost).

MRTS = -w/r

Discuss marginal cost (MC). Gives its fomula(s), and state what firms use it for.

Marginal cost (MC ): the amount by which a firm's TOTAL cost changes if the firm produces one more unit of output. >> (as the fixed costs stay they same, this is a measure of how variable costs change when producing one more unit) MC = change in C / change in q or MC = change in VC / q *** A firm uses marginal cost in deciding whether it pays to change its output level.****

What is the general difference in cost of production in terms of short-run and long-run?

More likely to be more profit-maximizing in the long-term, because: When a firms ouput increases, its costs rise (higher variable inputs) . A firm cannot vary some of its (fixed) inputs, such as capital, in the short run . >> As a result, it is usually more costly for a firm to increase output in the short run than in the long run, when all inputs can be varied.... IN THE LONG-RUN, THE FIRM ADJUSTS ALL ITS INPUTS SO THAT ITS COST OF PRODUCTION IS AS LOW AS POSSIBLE.

Should sunk costs be considered by a manager, trying to identify the most economically efficient production process?

NO. When calculating the costs of production you sum the opportunity costs of each of your factors of production. The opportunity cost of sunk goods is zero, and they should therefore not be included.

Are long-run cost curves always straight?

No. It depends on economies of scale. For example if the firm experiences economies of scale at lower ouputs, then as output level increases, the cost will increase, but less than in proportion to the output level, giving rise to a non-straight long-run cost curve. In the example graph provided: the long-run cost curve of this firm rises less than in proportion to output at outputs below and then rises more rapidly.

What are the firms fixed cost in the long-run?

The long-run is determined by the length of time, in which a firm is able to change all its inputs, such that all inputs are variable. - This means that there is NO LONG-RUN FIXED COSTS (F=0).

Where does the marginal cost curve cross the AVC and the AC curves, and why?

The marginal cost curve, MC, cuts the average variable cost, AVC, and average cost, AC, curves at their minimums. It crosses the minimun of the AC curve, because when the MC is greater than the AC curve, then the AC is increasing, and when the MC curve is less than the AC curve, then the AC is decreasing. Therefore the crossing point, occurs before AC begins to increase, which is also the minimum point. AVC follows a similar pattern to the AC, because the total cost cuve and variable cost curves have the same slopes (AC is just shifted upwards by the fixed costs). The MC crosses the AVC at a lower output/cost level, than the AC, because the average cost is higher, as it also includes the fixed costs of production.

Define marginal cost Give the formula for calulating MC in the short-run for the production function: q = f (L, K with line on top)

The marginal cost is the change in variable cost as output increases by one unit MC = ΔVC/Δq. In the short-run, capital is constant, so the only way q can increase is by changing L. The extra labor required to produce one more unit of output is: = ΔL/Δq. The extra labor costs the firm, w per unit. So the firsms cost rises by w(ΔL/Δq). As a result, the firm's marginal cost is MC = (ΔVC/Δq) = w(ΔL /Δq) . We also know MPL =Δq/ΔL Mathematically (from rearranging the two equations), this means: MC = w/MPL

How can you deduce MARGINAL cost from the short-run cost curves graph showing the 4 measures of ABSOLUTE costs.

The marginal cost is the slope of EITHER the TOTAL cost curve or the VARIABLE cost curve at a given output level. >> As the cost and variable cost curves are parallel, they have the same slope at any given output. The difference between cost and variable cost is fixed cost, which does not affect marginal cost. The dashed line from the origin is tangent to the cost curve at A in panel a. Thus, the slope of the dashed line equals both the average cost and the marginal cost at 8 units of output.

What is the opportunity cost of a specialized piece of equipment for 25,000 dollars that cannot be resold? What implications does this have on the firms production costs?

The original expenditure is a sunk cost, as the equipment cannot be used for another alternative, rented, or re-sold. The opportunity cost = zero. Because this equipment has no alternative use and cannot be resold, its opportunity cost is zero, and it should not be included in the firm's current cost calculations.

At what point does a firm minimize its costs of production? Represent it on a graph

The point at which the ISOCOST (economically efficient) IS TANGENT TO THE ISOQUANT (technological efficiency/efficient production), At which point the SLOPE OF THE ISOCOST, EQUALS THE SLOPE OF THE ISOQUANT, which is the negative of the marginal rate of technical substitution. >>>MRTS = the rate at which the firm can trade capital for labor in the input markets equals the rate at which it can substitute capital for labor in the production process.

What determines the shaps of a firms´s cost curves

The production function determines the shape of a firm's cost curves. The production function shows the amount of inputs needed to produce a given level of output.

How does a firm use the production function to calculate its costs?

The production function shows the amount of inputs needed to produce a given level of output. The firm calculates its cost by multiplying the quantity of each input by its price and summing the costs of the inputs.

Describe the relationship between marginal cost and average cost on the short-run cost curves graph.

Where the marginal cost curve is below the average cost, the average cost curve declines with output. Because the average cost of 47 for 2 units is greater than the marginal cost of the third unit, 20, the average cost for 3 units falls to 38. Where the marginal cost is above the average cost, the average cost curve rises with output. At 8 units, the marginal cost equals the average cost, so the average is unchanging, which is the minimum point, a, of the average cost curve. We can show the same results using the graph. Because the dashed line from the origin is tangent to the variable cost curve at B in panel a, the marginal cost equals the average variable cost at the corresponding point b in panel b. Again, where marginal cost is above average variable cost, the average variable cost curve rises with output; where marginal cost is below average variable cost, the average variable cost curve falls with output.

Why does average cost, average variabl cost, and marginal cost eventually rise with output?

Where there are DIMINISHING MARGINAL RETURNS to a VARIABLE INPUT, the variable cost and cost curves become relatively steep as output increases, so the AVERAGE COST, AVERAGE VARIABLE COST, & MARGINAL COST RISE WITH OUPUT.

How do you illustrate the relationship between the various cost measures and output?

You make 2 graphs with x-axis = output, and y-axis = cost. 1.) 4 measures of TOTAL costs 2.) 4 measures of AVERAGE costs

What are the 3 types of cost of production?

Sunk costs are fixed costs which cannot be reclaimed by e.g. selling the item that was purchased. An example of a sunk cost = advertising Many types of fixed costs are not sunk: as we have seen, if the firm buys a machine and no longer wants to use it, it can sell it afterwards.

Discuss the difference in considerations for a firm profit maximising with the following production function, in the short-run and long-run: Short run: q = f (L, K with line on top) Long run: q = f (L, K)

In the LONGRUN the FIRM CAN CHOOSE TO PRODUCE USING THE PROCESS/METHOD WITH LOWEST PRODUCTION COSTS. The firm chooses how much labor and capital to use in the long run, whereas the firm chooses only how much labor to use in the short run when capital is fixed. >> As a consequence, the firm's LONG-RUN COST IS LOWER than its short-run cost of production if it has to use the "wrong" level of capital in the short run.

In the long-run how does increasing all inputs affect the level of output?

Increasing all inputs in proportion may cause output to: 1. increase MORE THAN IN PROPORTION (increasing returns to scale) at low levels of output, 2. increase IN PRPORTION (constant returns to scale) at intermediate levels of output, 3. LESS THAN IN PROPORTION (decreasing returns to scale) at high levels of output. If a production function has this returns-to-scale pattern and the prices of inputs are constant, long-run average cost must be U-shaped.

Meredith's firm sends her to a conference for managers and has paid her registration fee. Included in the registration fee is free admission to a class on how to price derivative securities such as options. She is considering attending, but her most attractive alternative opportunity is to attend a talk by Warren Buffett about his investment strategies, which is scheduled at the same time. Although she would be willing to pay $100 to hear his talk, the cost of a ticket is only $40. Given that there are no other costs involved in attending either event, what is Meredith's opportunity cost of attending the derivatives talk?

Oppotunity cost is the value of the next best alternative foregone when an economic decision is made. Opportunity cost = explicit costs (price of alternative event) + implicit costs (benefits of alternative event) Explicit cost of attending WB = 0 Implicit (benefit/value) of attending WB = 100-40 = 60 Therefore the opportunity cost of attending the derivatives talk is the value of the next best alternative, which in this case Meredith values at 60 dollars. __________________________________________ To calculate her opportunity cost, determine the benefit that Meredith would forgo by attending the derivatives class. Because she incurs no additional fee to attend the derivatives talk, Meredith's opportunity cost is the forgone benefit of hearing the Buffett speech. Because she values hearing the Buffett speech at $100, but only has to pay $40, her net benefit from hearing that talk is 60 (100-40) Thus, her opportunity cost of attending the derivatives talk is $60.

Define sunk costs

Sunk costs are fixed costs which cannot be reclaimed by e.g. selling the item that was purchased. An example of a sunk cost = advertising

Define implicit and explicit costs

Recap: direct, out-of-pocket payments for inputs to its production process within a given time period. Implicit costs are less obvious: they derive from foregone opportunities (the value of forgone opportunities)

In the short-run and long-run, what does total costs equal to, and what cost curves are you interested in?

SHORT-RUN: - Total costs = variable costs + fixed costs 3 cost-level curves: total cost, fixed cost, and variable cost 4 cost-per-unit curves: average cost, average fixed cost, average variable cost, and marginal cost LONG-RUN: Total costs = variable costs 1 cost-level curve: total cost 2 cost-per-unit curves: average cost and marginal cost.

Explain why the (total) cost curve first falls and then rises, for SHORT-RUN and LONG-RUN. Why are the reasons different?

SHORT-RUN: First FALLS: key reason why the short-run average cost is initially downward sloping is that the AVERAGE FIXED COST curve is downward sloping: Spreading the fixed cost over more units of output lowers the average fixed cost per unit. Then RISES: A major reason why the short-run average cost curve slopes upward at higher levels of output is diminishing marginal returns. LONG-RUN: - Does not fall because of fixed costs, because in the long-run all factors of production can be varied. - Does not rise because of diminishing marginal returns, because all factors can be varied in the long-run. Instead, RETURNS TO SCALE at different levels of output, play a major role in determining the shape of the average cost curve and other cost curves.

What are the axis on a short-term and long-term cost curve?

SHORT-TERM: X-axis = quantity per unit Y-axis = cost per unit LONG-TERM: You have choice for all inputs X-axis = quantity/units of labor Y-axis = quantity/units of capital

What is the difference between long-run and short-run production?

Short-run is defined as a time frame so short, that at least one input is fixed and cannot be change to (increase output, and reduce costs) Long-run is define as a time frame, long enough, such that all factors of production are variable.

What determines variable costs in the short-run, with one variable input?

Short-run means that at least one variable is fixed, and cannot practically be changed within the considered time period. So to change ouput, you can only change in the input that is variable input (not the fixed inputs). So for a production function: q = f(L, K with line on top), only changes in L will change output level.

Define long-run cost curve

Shows how costs vary with different levels of output in the long run, when the firm operates at a technologically efficient and economically efficient leve. C = f (q) It is derived from the expansion curve, but instead of having labor and capital as its x- and y-axis, it has costs on the y-axis and output level on the x-axis. LONG-RUN cost = bottom graph.