Econ 100A Spring 2001HW 3: Production, Costs, Competition1. Should a competitive firm ever produce when it is losing money?Recall a competitive firm’s two-pronged decision: It first decides what outputmaximizes its profits (p=MC(q*)), then determines whether that amount, q*, justifiesproduction at all. That is, how do shut down profits compare to profits at q*?The firm stays in business if π(q*) > π(0), where π(x) = R(x) – C(x) = p×x – [VC(x) + F] = px –VC(x) – FSo π(q*) = pq* – VC(q*) – F and π(0) = p×0 – VC(0) – F = –FTherefore, the firm will produce q* if π(q*) > π(0) Ø pq* – VC(q*) – F > – F Ø pq* > VC(q*)or, equivalently, the familiar shut down rule: produce if p > VC(q*)/q* = AVC(q*).Hence, a competitive firm will choose to produce as long as its revenues exceed itsvariable costs at its profit maximizing level of output, q*. Its profits may be negative,but the revenues in excess of the variable costs chip away at the firm’s fixed costs,thus making it more costly to shut down than to produce. Elsewhere, as illustrated inthe diagram below, a firm making losses in the short run may realize positive profitsin the long run.Long Run ProfitShort Run LossLRACSRAVCSRACSRMCLRMCp = MRQSRQLR2. Explain how it is possible for a market to have a horizontal supply curve (constantmarginal and average cost) and yet each firm has an increasing marginal cost curve.A competitive firm’s supply curve is its marginal cost curve above the minimum ofits average variable cost curve. In turn, the market supply curve is the horizontal sumof the individual firms’ supply curves. If there are n identical firms in a competitivemarket, each with (inverse) supply curve P=5q-2 above P=$1, say, then the marketsupply curve is given by Q = n(P + 2)/5, or, alternatively, the inverse supply curve isgiven by P=5Q/n – 2 for P>$1, and 0 otherwise. As illustrated in the diagram below,100 such identical firms can yield an almost horizontal market supply curve in spiteof the individual firms’ (rather steeply increasing) marginal cost curves.Market Supply Curves When the Number of Firms Varies01020304050607080901000 20406080100120QP ($)S1 firmS2 firmsS3 firmsS4 firmsS5 firmsS100 firmsThe left-most and steepest line above represents an individual firm’s MC curve abovethe minimum of its AVC and, hence, its supply curve. As we throw more such,identical firms, the market supply flattens out.3. Many marginal cost curves are U-shaped. As a result, it is possible that the MC curvehits the demand or price line at two output levels. Which is the profit maximizingoutput? Why?Consider a firm in a competitive market facing the dilemma described in thefollowing diagram:MCp* = MRQLOWQHIGHABThis firm’s MC curve is U-shaped and the price line, or MR line, intersects it atpoints A and B. The manager of the firm knows that her profit maximizing level ofoutput will be described by P*=MC. So how much should she produce?Well, thankfully, she took Econ 100A, so the question of which level of output tochoose is a breeze to her: she knows that if MC is downward sloping at QLOW, thenthe additional cost of producing the (QLOW+1) st unit is actually lower than that ofQLOW. Elsewhere, since she’s in a competitive market, her marginal revenue is simplythe market price, P*. Hence, the marginal profit from producing the (QLOW+1) stunit,P* - MC(QLOW+1), is positive since MC(QLOW+1) is below the price line (seediagram above). Thus, producing the (QLOW+1)st unit yields positive profits andtherefore QLOW can’t be profit maximizing. (In fact, it turns out to be something like aprofit minimizing level of output: a U-shaped MC curve implies an S-shaped totalcost curve. Try reproducing the two diagrams from Figure 8.3 in the textbook, onlyreplacing the green, bowl shaped total cost curve in the upper panel by something likea flattened “S”. QLOW occurs when the slope of the first hump of the S equals theslope of the blue revenue line.)4. If California computer manufacturers compete with manufacturers elsewhere in acompetitive world-wide market, what will be the effect of a large increase inelectricity prices (a primary input in the manufacture of computers) in onlyCalifornia on A. the supply curve of a typical California firmElectricity is an input in the production of computers. An increase in electricity priceswould cause an upward shift in both the marginal and average variable cost curves ofa typical Californian firm. Since, in a competitive market, a firm’s supply curve is itsMC curve above the minimum of its AVC curve, the typical Californian computermanufacturer’s supply curve will shift up and inwards, as in the diagram below. AVCBeforeSBeforeSAfterAVCAfterMCAfterMCBeforePminAfterPminBeforeAt the higher electricity prices, the firm’s supply is zero for prices below PminAfter, andfollows its MC curve thereafter. Before the price increase, the lowest price for whicha typical firm’s supply is nonzero was PminBefore. (Note that in the diagram above, theminima of the two AVC curves appear to be aligned vertically; i.e. they appear toaccur at the same level of output, but this need not be the case.) B. the world supply curveAssume all firms in the world are identical. So before the increase in electricityprices, the world supply curve is horizontal at the minimum of their average variablecost, PminBefore. After the price increase, Californian firms become “higher cost” andno longer contribute to world supply for prices between PminBefore and PminAfter. As aresult, the world supply curve takes the form of a step function, as in the long-runworld supply of cotton example at page 253 of the textbook. In the diagram below,the upper panel represents world supply before the rate increase, while the lowerpanel shows it afterwards. The rest of the world can only supply up to quantityROWMAX. Beyond ROWMAX, Californian firms supply at the higher cost, yielding astep in the LR supply curve.World SBeforePminAfterPminBeforeQPminBeforeWorld SAfterROWMAX$ per computer$ per computerDLowDHighQLowQhigh - AfterRest of WorldCaliforniaDHighDLowQhigh - Before C. the market equilibrium quantity and priceAs seen in both panels of the above diagram, if world demand is low, say at DLow,then the market equilibrium occurs at quantity QLow and price PminBefore, and the ratehike in California has no effect on market equilibrium, though it drives Californianproducers out of business.If, on the
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