Daniel l. Rubinfeld

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336 Part:3 Market Structure and Competitive Strategy Chapter 10 Market Power.: Monopoly and Monopsony 337 S/Q MC S/Q p] Pc p] = P 2 D2 D, D] D] P j A :].P y Po A MC+t Y MC Quantity Quantity Quantity Shifting the demand curve shows that a monopolistic market has no supply cl~'Ve-i.e., there is no one-to-one tionship between price and quantity produced. In (a), the demand curve D] shifts to new de~and curve D 2 • But new mar£inal revenue CUl'Ve MR, intersects marcinal cost at the san1e point that the old margmal revenue curve o - 0 b 1 did. The profit-maximizing output therefore remains the same, although price falls from PI to P 2 . In.( ), t 1C new ginal revenue curve MR2 intersects marginal cost at a higher output level Q2' But because demand IS now more tic, price remains the same. In §S.2, we explain that a firm maximizes its profit by choosing the output at which marginal revenue is equal to marginal cost. Analyzina the effect of a tax on a monopolist is straightforward. Suppose a specific tax ~f t dollars per lmit is levied, so that the monopolist must remit t dollars to the aovernment for everv unit it sells. Therefore, the firm's marginal (and averaae) o c~st is increased by _ tl{e amount of the tax t. If MC was the firm's origi: nal marginal cost, its optimal production decision is nov\' given by MR = MC + t Graphically, we shift the rnarginal cost curve upward by an amount t, and find the new intersection with marginal revenue. Figure 10.5 shows this. Here and Po are the quantity and price before the tax is imposed, and Ql and PI are the quantity and price after the tax. . Shiftina o the marainal cost curve upward results in a smaller quantIty and 0 • higher price. Sometimes price increases by less than Yle tax, bu t ~10t alw.ays-:-~ Fiaure 105 price increases bv more than the tax. ThIS would be ll11posslble m 0' J 1 . competitive market, but it can happen with a monopolist because the re atIonship between price and marginal cost depends on the elasticity of demand. Suppose, for example, that a monopolist faces a constant e!asticity. demand curve, with elasticity - 2, and has constant marginal cost Me EquatI~n (10.2) then tells us that price will equal twice marginal cost With a tax t, mar~m~l :ost increases to MC + t, so price increases to 2(MC + t) = 2MC + 2t; that IS, 1tnse: by twice the amount of the tax. (However, t I 1e manop a 1· IS t' s plO . t" 1 t no . netheles!> falls with the tax.) a tax t per Ulut, the firm's effective marginal cost is increased by the amOlmt t to
338 Part 3 Market Structure and Competitive Strategy The firm should increase output fron .. each plant until the incremental from the last tmit produced is zero. Start by setting incremental profit from put at Plant 1 to zero: ~7T ~(PQT) _ ~Cl = 0 ~Ql ~Ql ~Ql Here ~(PQT)/~Ql is the revenue from producing and selling one more unit, marginal revenue, MR, for all of the firm's output. The next term, ~Cl/LlQlt marginal cost at Plant 1, Mel' We thus have MR - Mel = 0, or 10 Market Power: Monopoly and Monopsony 6 NO'N vve can find the profit-maximizing output levels Ql' Q2' and QT' First, the intersection of MeT with MR; that point determines total output QT' draw a horizontal line from that point on the marginal revenue curve to vertical axis; point MR* determines the firm's marginal revenue. The interctions of the marginal revenue line with Mel and Mel give the outputs Ql and se for the two plants, as in equation (10.3). Note that total output QT determines the firm's marginal revenue (and hence 1 its price P*). Ql and Q2' however, determine marginal costs at each of the two plants. Because MeT was found by horizontally summing Mel and Me 2 , we know that Ql + Q2 = QT' Thus these output levels satisfy the condition that MR :::: MC l = Me2· Similarly, we can set incremental profit from output at Plant 2 to zero, MR = Mel Putting these relations together, we see that the firm should produce so that (10.3) Figure 10.6 illustrates this principle for a firm with two plants. Me1 and are the marginal cost curves for the two plants. (Note that Plant 1 has higher. marginal costs than Plant 2.) Also shown is a curve labeled MeT' This is the firm's total marginal cost and is obtained by horizontally summing Mel S/Q pure monopoly is rare. Markets in which several firms compete 'with one another are much more common. We say more about the forms this competition can take in Chapters 12 and 13. But we should explain here why each firm in a market with several firms is likely to face a downward-sloping demand curve, and, as a result, produce so that price exceeds marginal cost. Suppose, for example, that four firms produce toothbrushes, which have the market demand curve s11O"wn in Figure 10.7(a). Let's assume that these Market Demand 2.00 S/Q / Demand Faced by Firm A p: 1.60 1.50 P* ------------ lAO MR*F-------~------~~----~ O=AR LOO "--___ LI ___ --'-___ --L __ ::-_____ _ 30,000 Quantity 3,000 5,000 7,000 (a) shows ~he market demand for toothbrushes. Part (b) shows the demand for toothbrushes as seen by Firm A. market pnce of $1.50, elasticity of market demand is -1.5. Firm A, however, sees a much more elastic demand D A because of competition from other firms. At a price of $1.50, Firm A's demand elasticity is - 6. Still, Firm A some monopoly power: Its profit-maximizing price is $1.50, which exceeds marginal cost. A firm with two plants maximizes profits by choosing output levels C1 and that marginal revenue MR (whidl depends on total output) equals margmal similari7 to the way. we obtained a competitive industry'S supply cun'e in Chapter 8 by . surnrnmg the margmal cost curves of the individual firms.
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Daniel l. Rubinfeld

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