Daniel l. Rubinfeld

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~- 262 Part 2 Producers, Consumers, and Competitive Markets Chapter 8 Profit Maximization and Competitive Supply 263 First, except under limited circumstances, nL'emge -unrinble cost sizol!ld /lot be used ns n substitute for mnrgillnl cost. When marginal and ave~age cost are nearly constant, there is little difference between them. Hmyever, it both marginal and average cost are increasing sharply, the use of average variable cost can be mis. leading in deciding hm\' much to produce. Suppose for example, that a com. pany has the foUovA/ing cost information: Current output Materials cost Labor cost 100 units per day, 80 of v-vhich are produced during the regular shift and 20 of which are produced during overtime $8 per unit for all output $30 per unit for the regular shift; 550 per unit for the overtime shift Let's calculate average variable cost and marginal cost for the first 80 units of output and then see how both cost measures change when we include the additional 20 lmits produced with overtime labor. For the first 80 units, average variable cost is simply the labor cost ($2400 $30 per unit X 80 units) plus the materials cost ($640 = $8 per unit X 80 units) divided by the 80 units-($2400 + $640)/80 = $38 per unit. Because the average variable cost is the same for each unit of output, the marginal cost is also equal to 538 per unit. When output increases to 100 units per day, both average variable cost and marginal cost change. The variable cost has now increased; it includes the additional materials cost of $160 (20 units X $8 per urut) and the additional labor cost of $1000 (20 units X $50 per unit). Average variable cost is therefore the total labor cost plus the materials cost ($2400 + $1000 + $640 + $160) divided by the 100 lmitS of output, or $42 per urut. What about marginal cost While the materials cost per unit has remained unchanged at $8 per unit, the marginal cost of labor has nov\' increased to $50 per unit, so that the marginal cost of each unit of overtime output is $58 per day. Because the marginal cost is higher than the average variable cost, a manager who relies on average variable cost will produce too much output. Second, n sillgle item 011 n firm's nccolllztillg ledger IIlny hnve two cOlllpollellts, only olle of which illvolves mnrgillnl cost. Suppose, for example, that a manager is trying to cut back production. She reduces the number of hours that some employees work and lays off others. But the salary of an employee who is laid off may not be an accurate measure of the marginal cost of production when cuts are made. Union contracts, for example, often require the firm to pay laidoff employees part of their salary. In this case, the marginal cost of increasing production is not the same as the savings in marginal cost when production is decreased. The savings is the labor cost after the required layoff salary has been subtracted. Third, nil opportllllity costs shollid be il1clllded ill deterlllilling IIlnrgillnl cost. Suppose a department store wants to sell children's furniture. Instead of b~ding a new selling area, the manager decides to use part of the third floor, which had been used for appliances, for the furruhlre. The marginal cost of this space is the $90 per square foot per day in profit that would have been earned had the store continued to sell appliances there. This opportwl.ity cost measure may be much greater than what the store achlally paid for that part of the building. These three guidelines can help a manager to measure marginal cost correctly. Failure to do so can cause production to be too high or too low and thereby reduce profit. 8.5 ASllpply Cll/'ve for a firm tells us how much output it will produce at every possible price. We have seen that competitive firms will increase output to the point at which price is equal to marginal cost but will shut down if price is below average economic cost. We have also seen that average economic cost is equal to average total cost when there are no sunk costs but equal to average variable cost when costs treated as fixed are actually amortized sunk costs. Therefore, the firm's supply curve is the portiol1 of the mnrginnl cost CIIi've thnt lies nbove the nvernge economic cost Cllrve. Figure 8.6 illustrates the short-nm supply curve for the case in wruch all fixed costs are achlally amortized sunk costs. In Hus case, for any P greater than minimum AVC, the profit-maximizing output can be read directly from the graph. At Price (dollars per unit) P2 --------------------------------------------- P=AVC - - I o q2 MC Output In the short nm, the firm chooses its output so that marginal cost Me is equal to price a.s long as the firm covers its average economic cost. When all fixed costs are amortized sunk costs, the short-run supply curve is given by the crosshatched portion of the In §7.1, we explain that economic cost is the cost associated with forgone opportunities.
264 Part 2 Producers, Consumers, and Competitive Markets Chapter 8 Profit Maximization and Competitive Supply 265 In §6.3, we explain that diminishing marginal returns occurs when each additional increase in an input results in a smaller and smaller increase in output. a price P]t for example, the quantity supplied will be £71; and at P2, it will be q For P less than (or equal to) minimum AVe, the profit-maximizing output i~ equal to zero. In Figure 8.6 the entire short-run supply curve consists of the crosshatched portion of the vertical axis plus the marginal cost ClUTe above the point of minimum average variable cost. Short-run supply curves for competitive finns slope upward for the same reason that marginal cost increases-the presence of diminishing marginal returns to one or more factors of production. As a result, an increase in the market price will induce those firms already in the market to increase the quantities they produce. The higher price makes the additional production profitable and also increases the firm's total profit because it applies to all units that the firm produces. an Price When the price of its product changes, the firm changes its output level to ensure that marginal cost of production remains equal to price. Often, however! the product price changes at the same time that the prices of inputs change. In this section we show how the firm's output decision changes in response to a change in the price of one of its inputs. Figure 8.7 shows a firm!s marginal cost curve that is initially given by Me! when the firm faces a price of $5 for its product. The firm maximizes profit by producing an output of £h. Now suppose the price of one input increases. Because it now costs more to produce each unit of output, this increase causes the marginal cost curve to shift upward from MC l to MC2· The new profitmaximizing output is q2! at which P = MC 2 . Thus, the higher input price causes the firm to reduce its output. If the finn had continued to produce q1! it would have incurred a loss on the last unit of production. In fact! all production beyond q2 reduces profit. The shaded area in the figure gives the total savings to the firm (or equivalently! the reduction in lost profit) associated with the reduction in output from '71 to '72' Suppose you are managing an oil refinery that converts crude oil into a particular mix of products, including gasoline! jet fuel, and residual fuel oil for home heating. Although plenty of crude oil is available, the amount that you refine depends on the capacity of the refinery and the cost of production. How much should you produce each day3 Information about the refineris marginal cost of production is essential for this decision. Figure 8.8 shows the short-run marginal cost curve (SMC). Marginal cost increases with output, but in a series of uneven segments rather than as a smooth curve. 111e increase occurs in segments because the refinery uses different processing lU1its to turn crude oil into finished products. When a particular processing unit reaches capacity, output can be increased only by substihlting a more expensive process. For example, gasoline can be produced from light crude oils rather inexpensively in a processing unit called a "thermal cracker,!' When this unit becomes full, additional gasoline can still be produced (from heavy as well as light crude oil)! but only at a higher cost. In the case Cost 27 (dollars per barrel) 26 Price, Cost (dollars per unit) #&5 24 23~ __________ J-______ -L ____ ~ ______ ~ ____ ~_ 8,000 9,000 10,000 11,000 Output (barrels per day) The marginal cost of producing petrolewn products from crude oil increases sharply at several levels of output as the refinery shifts from one processing unit to another. ~ a result! the output level can be insensitive to some changes in price but very sen Sltiveto When the marginal cost of production for a firm increases (from MC 1 to MCz)! level of output that maximizes profit falls (from '71 to '72)' 3J1; F I~ example is based on James M. Griffin, "The Process Analysis Alternative to Statistical Cost n~::ons: A,n Application to Petroleum Refining/' Americall Ecollomic Review 62 (1972): 46-56, The ers ha\ e been updated and applIed to a particular refinery.
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Daniel l. Rubinfeld

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