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38

Fig. XI The Fquihbrium of the Industry and Firm

INDUSTRY

FIRM

MR=AR

MR = MC. Tfierefore profit maximization occurs at tfie output at which marginal revenue just equals marginal cost. Moreover, so long as the change in profit, exceeds zero, MR exceeds MC and the firm should expand. In addidon, when - is less than 0, MR is less than MC, and the firm should cut back. For these reasons we say that the profit maximking output occurs when MR = MC. However, we emphasize one crucial qualificadon: All of the above analysis presumes the firm should operate at all. In some cases, which we explain below, it should shut down.

In order to show the equilibrium of the com-peddve firm graphically, we need to impose the firms demand curve graph of Figure VIII onto the cost curve graphs of Figure VII.

This is done in Figure XI. Opdmum production in this situadon is the quandty q, MR = MC. The general rule for demonstratuig any opdmum is to show that all alternatives are inferior. In this situation, consider two units less, at q - 2. At that output MR exceeds MC. For instance MR might be S4 and MC \$2. Then the firm can gain \$2 (\$4 - \$2) b)- expanding its output one unit to q - 1. At this point. .MR is still \$4, but MC has now risen to, say, \$3. Cleari\. the firm gains \$1 by producing this added unit (S4 - \$3). Stepping up production to q on the other hand brings in a MR of \$4 and a MC of the same amount. Therefore the firm will just be indifferent to producing this last unit.

So much for points to the left of q. A similar analysis applies at all ouipuu to the right of q. At such outputs MC exceeds MR. Therefore, cutting back in the direction of q reduces total cost more than total revenue, causing profit to rise until the output q is

reached. For example, if at q -t 1 units MC = \$5 and MR = \$4, the firms profit will rise by \$1 (\$5 - \$4) if it cuts back a unit to q. In summary, if the firm produces ] at all, it should pick the output at which marginal cost; equals marginal revenue (MR = MC).

Now what about profits? In Figure XI they are j non-existent To see this, note that Jt = TR - TC. In the \ graph, TR (Pq) equals the area enclosed by the axes,* the demand curve, and the dashed vertical line at q.i Total cost, (ATC)q, is exacdy the same area. Hence i profit is zero. This is not surprising: Remember that! all costs to an economist are opportunity costs - thej value of the next best alternative is included in costi When profits are zero, the firm is doing just as well; it could in any alternative use ofits resources, and corij sequendy has no incentive to change its behavic Thus, in Figure XI, both the firm and industr) are short run equilibrium.

PROFITS, SHUT DOWNS, AND OPERATING AT \ LOSS IN IHE SHORT RUN

Next consider a profit situation in Figur XII caused by an industry demand increase. In thii case, the perfecdy elastic demand curve faced the price-taking firm will shift upward from its posi tion in Figure XI. As before, die firm will produce di output at which marginal revenue equals marginal cc (MR - MC). Total cost, (ATC)q, equals area I in th situation. But total revenue (Pq) equals areas 1 + 2 iu the graph. The difference between them, area 2, profit. Of course, the firm will want to stay in busines after all, the presence of profit means it is doing bctf than in alternative.

Two typ>es of short run loss situations can occijj

and die first is shown in Figure XIII. The firm again selects the output at which MR = MC. But here total cost, (ATC)q, equals areas 3 + 4 -f 5, while total levemie (Pq) equals areas 3 + 4 only. In other words, ihe shaded area 5 is a loss. Nonetheless, in this case the firm should not shut down: shutting down would cause an even greater loss. Consider the firms alternadves. Even ifit shuts down, the firm must continue to pay a total fixed cost, (AFC)q, equal to areas 5 + 4. On the other hand, if it remains open, it can cover not only all of its total variable cost, but a portion of its total fixed cost, area 4, as well. For this reason, it can do no better than to stay open and experience the lo.ss of area 5 rather than close and take that of area 4 as well. Note that as long as P exceeds minimum AVC, the firm will stay open and produce an output along its MC curve in order to set MR = MC. Hence, - and this is crucial -the MC curve above minimum AVC is the short run supply curve for the pricetaking firm.

A situation in which the firm should shut down is displayed in Figure XTV. By staying open and producing the q at which MC = MR, the firm gains a total revenue (Pq) equal to area 6. Total cost, (ATC)q, at this output is the sum of areas 6 + 7 + 8. In other words, by producing, the firm not only loses all its total fixed cost, (AFC)q, area 8, but a portion of its total variable cost as well, area 7. The loss from completely shutting down, area 8, is less than that of staying open 7 + 8, so the firm will shut down. The firm will supply nothing if price lies below minimum average variable cost, i.e., ifP<AVC.

As a final borderline case, the firm will be indifferent to operating if P just equals its minimum AVC. When that happens, the firm will lose its total fixed

cost if it produces. Since it loses this cost if it shuts down, the firm will be indifferent. In summary:

(1) If the firm produces at all, it does so where marginal revenue equals marginal costs, i.e. where MR = MC.

(2) The short run supply curve of the price-taking firm is the portion of its marginal cost (MC) curve which lies above minimum average variable cost (AVC).

(3) For the price-taking firm, MR = P = AR, so that if the firm produces, it picks the output at which P = MC.

(4) In the short run, the firm will operate at a loss if price lies between its minimum AVC and its minimum . If P less than minimum AVC, it will shut down.

(5) TT = [P - (ATC)]q

We can tie all this together through a numerical example. Consider Table II below where weve calculated all average and marginal cost schedules associated with the total cost schedule of column 2. For example, looking at the first entry in column 2 and seeing that TC = \$50 when q = 0, we know that TFC = \$50. Total variable cost in column 4 is obtained by subtracting \$50 from the appropriate total cost entry. Weve defined marginal cost (MC) as the change in total cost from producing another , i.e., the sldpedflEe total cost curve. But since the slope of the TC curve at any particular output equals the slope of the TVC curve, we can also get MC directiy as the change in total variable cost TVC from producing another unit. Finally, average total cost ( ) and average variable cost (AVC) are obtained simply by dividing total cost (TC) and total x-ariable cost (TVC) by the various levels of output, q.

Fig. Xll

Fig. XIll

Fig. XIV

\$/4

PROFITS

OPERATING AT A LOSS

SHUT DOWN

/

AVC

MR=AR

Table II Costs of Maxiwidget Production

 Total Total Average Average Total Fixed Variable Marginal Total Variable Quantity Cost Cost Cost Cost Cost Cost (TC) (TFC) (TVC) (MC) ( ) (AVC) \$0 - 11:== \$50 undef undef \$100 \$50- \$100..00 \$50.00 \$120 \$70 < ----- :r=»"\$3o ::r=\$5o \$150 \$100-= \$50.00 \$3333 \$190 \$140- \$4750 \$35.00 \$240 \$190-=: \$48.00 \$38.00 \$300 \$250 <: - Con \$50.00 \$41.67 \$370 \$320-= \$5Z86 \$45.71 \$450 \$400< - ---\$90 \$5625 \$50.00 \$540 \$490 . \$60.00 \$54.44

The graph of these cost curves is presented as Figure XV below. (You can ignore the price lines in the figure for now.) To put this all through its paces, lets imagine that the firm is a price-taker facing a price P=\$20. What should it do? Since P=MR=AR for a price-taker, we know that if the firm operates, it will pick the output at which marginal revenue equals marginal cost. From the table and graph that output is 2 units. However, since P<AVC at q=2, the fmn would not operate; it would shut down losing its TFC=\$50 instead. Note, however, that if the firm were to operate and produce two units, it would lose even more, its total revenue (Pq) would be \$40 and its total cost, (ATC)q would be (\$60) (2) = \$120, so its loss from operating, \$80, is greater than its loss fi-om shutdng down altogether. In Figure XV we see that the furm should shut

dowi because P=\$20<AVC=\$33.33.

Now suppose instead that P=\$40. Here we see that MR=MC at 4 units. But should die firm operate? Checking, we see that this price lies between average variable and average total cost (AVC 8c ), so the firm will operate at a loss. Its profits will be negadve and are given by [P-(ATC)]q = -\$30. Sdll, this loss is smsdler than its \$50 loss from shutting down endrely, so the firm will stay open, hire labor, and produce.

As a final example, if P=\$80, the firm \vould equate marginal revenue and marginal cost by producing 8 uniu. Here Tt = (P-(ATC)]q = [\$80- \$56.25]8 = \$190. The firm will be eager to stay open to reap this profit. Graphically we see that P=\$80>ATC=\$56.25.

EFnCIENCY AND THE SOCIAL OPTIMUM

In general, an economy is efficient when all

Fig. XV

Pi=MH=AH=\$80

Pi=M(bAR40

P=MR=AR=\$20

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