Deficiency ProgramPerloff Econ 100A 2003 Midterm 1 Solutions A1. (22 points) Before the competitive fringe enters the market the firm functions as a monopoly, producing QM, where MC = MR at a price pM, the price that corresponds to QM on the demand curve. MC pm D MR Qm When the competitive fringe enters the market, it acts as a price ceiling. As supply for the fringe is infinite at p*, the market equilibrium price cannot be greater than p*. The dominant firm will still produce where MC = MR, but the entrance of the fringe has shifted the Demand and MR curve faced by the dominant firm. The residual demand for the dominant firm is horizontal at p* until it intersects the market demand, and is then equal to the market demand. The MR the firm can now expect to get is capped at p*, until the quantity where the fringe supply intersects the market demand. At higher levels of output the dominant firm’s MR curve will be the same as that it faced as a monopoly. The dominant firm will produce Qd, where MC = MR’. The price the dominant firm will charge is pd = Dr(Qd). The competitive fringe will then produce QT = D(pd) – Qd, remaining demand at the price set by the dominant firm. Note: The competitive fringe and the dominant firm must charge the same price in the market and new market price, pd, cannot be greater than p*. If Qd > D(p*), it must be that the market clearing price pd<p*. At this price the competitive fringe will not produce anything. If Qd < D(p*), the competitive fringe will produce Qf = D(p*) – Qd, and the market clearing price is p*.QT Qd MRr Dr MC P* B1. (16 Points) Price Support The price support is set at PS. The demand at that price is of QD and the supply is of QS. The government buys the excess supply at a price of PS. PS HGFIJECDBAPE Price SupportQDQEQS Without Price Support With Price Support Change Consumer Surplus A+B+C A -B-C Producer Surplus D+E B+C+J+D+E +B+C+J Government Exp 0 -C-E-J-I-G-H -C-E-J-I-G-H Welfare A+B+C+D+E A+B+D-I-G-H -C-E-I-G-H Deficiency Program Consumers buy at a price of PD. To ensure a supply of QD, government gives a payment of PS – PD to the producers in addition to the price of PD they get from consumersAPS BEDeficiency PaymentsPE GCFPD DQD B2. (16 points) A monopoly publisher either pays an author (i) a royalty of α percentage of the revenues from the book, or (ii) a lump-sum amount of L dollars. Show how the compensation scheme affects the price the publisher sets and the number of books that the publisher sells. The publisher’s objective is to maximize profits. Let Π(Q) denote profits when the monopolist produces Q. Then we can write the monopolist’s problem as: Without Deficiency Payment With Deficiency Payment Change Consumer Surplus A+B A+B+C+F +C+F Producer Surplus C+D B+C+ D+E +B+E Government Exp 0 -B-C-E-F-G -B-C-E-F-G Welfare A+B+C+D A+B+C+D-G -G Maximize Π(Q) = R(Q) – C(Q) = P(Q)*Q – C(Q), where C(Q) is the cost function. (8 points) Under scheme (i), the monopolist’s problem is Maximize Π(Q) = (1-α)R(Q) – C(Q) = (1-α)P(Q)*Q – C(Q) = P’(Q)*Q – C(Q), where P’(Q) = (1-α)P(Q). Aside: if demand is linear, P(Q) = a – bQ, then P’(Q) = (1-α)a - (1-α)bQ. So it is ‘as if’ the monopolist faces a new (inverse) demand curve which has a lower P-intercept and the same Q-intercept. This also implies that the marginal revenue schedule, MR(Q) = a – 2bQ will change in the same manner. That is, MR’(Q) = (1-α)a – (1-α)2bQ. Since marginal cost has not changed, quantity and price will change under this scheme.P(Q) pt p* (1-α)pt MR’(Q) Q P(q) MR(q) P’(Q) MC(Q) (p*,Q*) denotes the optimal price and quantity set by the publisher when there is no royalty. (pt ,Qt) denotes the optimal price and quantity set by the publisher when there is a royalty. Qt Q* Note that the publisher receives (1-α)pt for each unit sold and consumers pay pt > p* in the new equilibrium. The number of books sold in the new equilibrium is Qt < Q*. (8 points) Under scheme (ii), the monopolist’s problem is Maximize Π(Q) = R(Q) – C(Q) – L = P(Q)Q – C(Q) – L . The Q* under this scheme is determined by: Π’(Q*) = R’(Q*) – C’(Q*) = 0, where F’( ) denotes the partial derivative of the function F. The marginal revenue and marginal cost are NOT affected by a lump-sum tax. Hence there is no change in the (p*,Q*) with a lump-sum tax. The Q* that solves Maximize Π(Q) = R(Q) – C(Q) – L is the same as the Q* that solves Maximize Π(Q) = R(Q) – C(Q) (i.e., profit without the lump-sum payment.) Thus, p* does not change when a lump-sum payment is imposed. Note that the signs of the effects on price and quantity under each scheme are independent of the magnitudes of (α,L). Furthermore, note that the only thing that will be affected under the lump-sum scheme is the publisher’s profit.B3. (16 points) A (8 points) a) b)P MC, AC FirmMarket (long run) MC1 MC2 D AC1 A P1P1 S1 S2 B C P2 AC2 P2q1 q2 q Q1 Q2 Q Given that entry and exit are costless, firms are identical, and input prices are constant, this perfectly competitive market will have a horizontal long-run market supply, i.e. equilibrium prices will be constant, independent of demand and equal to the minimum long-run average cost (Ch.8, p.256). Assuming that the firms’ marginal cost curves are upward-sloping and that the firms have to spend some fixed costs to enter the market, the MC curve intersects the AC curve at its minimum (as shown in panel a). Now the new technology lowers each firm’s marginal cost at each quantity, so that both marginal cost and average cost curves shift down (as shown in panel a). We assume here that each firm can enjoy the new technology, and therefore each firm’s marginal and average cost curves now become MC2 and AC2 respectively. (Note that MC2 crosses AC2 at its minimum again.) Market price shifts down from P1 to P2, where P2 is again equal to the minimum long-run average cost. Market quantity increases from Q1 to Q2 due to lower price. It is interesting to notice that each firm’s optimal quantity (reached at minimum AC, the only point where firms don’t lose money in the long run) can either increase, decrease or stay the same depending on the exact shape of MC curve, fixed cost, and the exact effect of the new technology (e.g. whether it shifts MC down uniformly at
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