Daniel l. Rubinfeld

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278 Part 2 Producers, Consumers, and Competitive Markets .. Dollars per unit of output :vIC per unit of output P, P, 51 5, P 1 P1 SL In (b), the long-run supply curve in a constant-cost indushy is a horizontal line SL' When demand increases, initiaI1y'~ causing a price rise (represented by a move from point A to point C), the firm initially increases its output from ql to~ Q2' as shO'wn in (a). But the enhy of new firms causes a shift to the right in industry supply. Because input prices are unaffected by the increased output of the industry, entry occurs until the original price is obtained (at point B). market demand CLUYe 0 1 and short-run market supply curve 51- Point A at the intersection of demand and supply is on the long-run supply curve 5L because it tells us that the industry will produce Ql units of output 'when the long-run equilibrium price is Pl' Io obtain other points on the long-run supply Cllr\'e, suppose the market demand for the product lmexpectedly increases (say, because of a reduction in personal income taxes). A typical firm is initially producing at an output of 1]1' where PI is equal to long-run marginal cost and long-run average cost. But because the firm is also in short-run equilibrium, price also equals short-run marginal cost Suppose that the tax cut shifts the market demand curve from 0 1 to O2, Demand cun'e O 2 intersects supply CLUTe 51 at C As a result, price increases from P1 to Pz· Part (a) of Figure 8.16 shows how this price increase affects a typical firm in the industry. When the price increases to P 2 , the firm follo'ws its short-nm marginal cost c'urve and increases output to lh- This output choice maxim.izes profit because it satisfies the condition that price equal short-run m.arginal cost. If e\'ery firm responds this 'way, each will be earning a positive profit in short-run equilibrium. This profit 'will be attractive to investors and v,rill cause existing firms to expand operations and ne,'" firms to enter the market. As a result, in Figure 8.16(b) the short-run supply curve shifts to the right from 51 to 52' This shift causes the market to move to a ne,'" long-run equilibrium at the intersection of O 2 and 52' For this intersection to be a long-run equilibrium, output must expand enough so that firms are earning zero profit and the incentiYe to enter or exit the industry disappears. In a constant-cost industry, the additional inputs necessary to produce higher output can be purchased without an increase in per-unit price. This might happen, for example, if unskilled labor is a rnajor input in production, and the market 'wage of unskilled labor is unaffected by the increase in the demand for labor. Because the prices of inputs have not changed, firms' cost curves are also unchanged; the ne\v equilibrium must be at a point such as B in Figure 8.16(b), at which price is equal to P 1 , the original price before the unexpected increase in demand occurred. The long-rull supply curve for a constant-cost illdustry is, therefore, a izorizolltallille ot a price that is e1]ual to the long-nln minimulIl average cost oj production. At any higher price, there would be positive profit, increased entry, increased short-run supply, and thus downward pressure on price. Remember that in a constant-cost industry, input pri~es do r:ot change when conditions change in the output market. Constant-cost mdustnes can have horizontallong-nm average cost curves. Increasing-Cost 8 Profit Maximization and Competitive Supply increasing-cost industry In an increasi~g-cost industry, the prices of some or all inputs to production P 1 P 1 increase a~ the mustry expands and the demand for the inputs grows. This situation 11llght anse, for example, if the industry uses skilled labor, which Industry whose long-run supply curve is upward sloping. becomes in short supply as the demand for it increases. If a firm requires mineral resources that are available only on certain types of land, the cost of land as an input ll:cre.ase.s v:ith output. Figure 8.17 shows the derivation of long-run supply, w~ICh IS ~~rru~ar to the ~revious constant-cost derivation. The industry is initia!ly 111 eqLUlIbnum at A. m part (b). When the demand curve unexpectedly shifts from 0 1 to O 2 , the pnce of the product increases in the short run to Po, and ~ndustry utput increases from Q1 to Q2- A typical firm, as shown in pa;t (a), :ncreases Its output. from 1]1 to 1]2 in response to the higher price by moving along Its short-run margmal cost curve. The higher profit earned by this and other firms induces new firms to enter the industry . Dollars per Firm Dollars per Industry unit of unit of output output 51 52 P2 P 2 SL Po .' P 3 : (b), the. l~g-run s~pply c:rrve. in an i~crea~ing-cost industry is an upward-sloping curve SLo When demand ~eases, ll11tially. causmg a pnc~ nse, the firms mcrease their output from q1 to qz in (a). In that case, the entry of new s causes. a shift ~o the nght m supply. Because input prices increase as a result, the new lona-run equilibrium ,!curs at a higher pnce than the initial equilibrium. 0
280 Part 2 Producers, Consumers, and Competitive Markets Chapter 8 Profit Maximization and Competitive Supply 281 decreasing-cost industry Industry whose long-run supply curve is downward sloping. As new firms enter and output expands, increased demand for inputs causes some or all input prices to increase" The short-run market supply curve shifts to the right as before, though not as much, and the new equilibrium at B results in a price P 3 that is higher than the initial price P 1 . Because the higher input prices raise the finns' short-run and long-run cost curves, the higher market price is needed to ensure that firms earn zero profit in long-run equilibrium" Figure 8.17(a) illustrates this" The average cost curve shifts up from AC I to AC 2 , "while the marginal cost curve shifts to the left from MC 1 to MC 2 . The new long-run equilibrium price P 3 is equal to the new minimum average cost As in the constant-cost case, the higher short-run profit caused by the initial increase in demand disappears in the long run as firms increase output and input costs rise. The new equilibrium at B in Figure 8.17(b) is, therefore, on the long-run supply curve for the industry. III [Ill illcre[lsillg-cost illdustry, the IOllg-rull industry supply curve is lIpw[lrd sloping. The industry produces more output, but only at the higher price needed to compensate for the increase in input costs. The term "increasing cost" refers to the upward shift in the firms' long-run a\'erage cost curves, not to the positive slope of the cost curve itself. Decreasing-Cost Industry The industry supply curve can also be dmvmvard sloping. In this case, the unexpected increase in demand causes industry output to expand as before. But as the industry gro"WS larger, it can take advantage of its size to obtain some of its inputs more cheaply. For example, a larger industry may allow for an improved transportation system or for a better, less expensive financial network. In this case, firms' average cost curves shift dovvnward (even though they do not enjoy econornies of scale), and the market price of the product falls. The lower market price and lo"vver average cost of production induce a new long-run equilibrium with more finns, more output, and a lower price. Therefore, in a decreasing-cost industry, the long-run supply curve for the industry is dmvnward sloping. The Effects of a Tax In Chapter 6, we saw that a tax on one of a firm's inputs (in the form of an effluent fee) creates an incentive for the fum to change the way it uses inputs in its production process. Now we consider ways in which a firm responds to a tax on its output. To simplify the analysis, assume that the fum uses a fixed-proportions production technology. If the fu-m is a pollutel~ the output tax might encomage the firm to reduce its output, and therefore its effluent, or it might be imposed merely to raise revenue. First, suppose the output tax is imposed only on this finn and thus does not affect the market price of the product. We will see that the tax on output encourages the finn to reduce its output. Figure 8.18 shows the relevant short-nm cost curves for a firm enjoying positive economic profit by producing an output of q! and selling its product at the market price Pl' Because the tax is assessed for every unit of output, it raises the firm's marginal cost curve from Me 1 to MC 2 = MC I + t, where t is the tax per unit of the firm's output. The tax also raises the average variable cost curve by the amount t. The output tax can have h'\'o possible effects. If the fum can still earn a positive or zero economic profit after the imposition of the tax, it will maximize its profit by choosing an output level at which marginal cost plus the tax is equal to the price of the product. Its output falls from 1]1 to (]2, and the implicit effect of the tax is to shift its supply curve upward (by the amOLmt of the tax). If the fum can no longer eam an economic profit after the tax has been imposed, the fu'm will choose to exit the market. An output tax raises the firm's marginal cost curve by the amount of the tax. The firm will reduce its output to the point at which the marginal cost plus the tax is to the of the product. Now suppose that all finns in the industry are taxed and so have increasing marginal costs. Because each firm reduces its output at the current market price, the total output supplied by the industry will also fall, causing the price of the product to increase. Figure 8.19 illustrates this. An upward shift in the supply curve, from 5) to S2 = 5) + t, causes the market price of the product to increase (by less than the amount of the tax) from PI to P 2 . This increase in price diminishes some of the effects that we described previously. Firms will reduce their output less than they would without a price increase. Finally, output taxes may also encourage some finns (those whose costs are somewhat higher than others) to exit the industry. In the process, the tax raises the long-run average cost curve for each firm. Long-Run Elasticity of Supply The long-run elasticity of industry supply is defined in the same way as the short-run elasticity: It is the percentage change in output (tlQ IQ) that results from a percentage change in price (::lPIP). In a constant-cost industry, the longrun supply curve is horizontal, and the long-run supply elasticity is infinitely large. (A small increase in price will induce an extremely large increase in output.) In an increasing-cost industry, however, the long-run supply elasticity will be positive but finite. Because industries can adjust and expand in the long run, We would generally expect long-run elasticities of supply to be larger than shortrun elasticities. 9 The magnitude of the elasticity will depend on the extent to c , In Some cases the opposite is true Consider the elasticity of supply of scrap metal from a durable good like copper Recall from Chapter 2 that because there is an existing stock of scrap, the long-run elasticity of supply will be smaller than the short-run elasticity
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Daniel l. Rubinfeld

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