1 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 5 ) _ 3 0 K a s ı m 2 0 1 2 CEVAPLAR 1. Tekelci bir firmanın sabit bir ortalama ve marjinal maliyet ( = =$5) ile ürettiğini ve =53 şeklinde bir piyasa talep eğrisi ile karşı karşıya kaldığını varsayalım. a) Tekelci firmanın kârını maksimize eden fiyat ve miktarı hesaplayınız. Firma ne kadar kâr elde etmektedir? b) İkinci bir firmanın piyasaya girdiğini varsayalım., 1. firmanın üretim miktarını ise 2. firmanın üretim miktarını gösteriyor olsun. Piyasa talebi ise + =53 şeklinde verilmiş olsun. 2. firmanın da ilk firma ile aynı maliyet eğrilerine sahip olduğu varsayımı altında her bir firmanın kârını ve cinsinden fonksiyonlarla gösteriniz. c) Cournot modelinde olduğu gibi, her bir firmanın, kârını maksimize edecek üretim miktarını belirlerken rakibinin üretim miktarını sabit kabul ettiğini varsayalım. Bu durumda, her bir firmanın reaksiyon eğrilerini (fonksiyonlarını) bulunuz. d) Cournot dengesinde ve değerlerini hesaplayınız. Piyasa fiyatını ve her bir firmanın kârını hesaplayınız. a) To maximize profit =53 5, we find / = 2 +48=0. =24, so =29. Profit is equal to 576. b) =53, = =53 5 and = =53 5. c) The problem facing Firm 1 is to maximize profit, given that the output of Firm 2 will not change in reaction to the output decision of Firm 1. Therefore, Firm 1chooses to maximize, as above. The change in with respect to a change in is 53 2 5=0, implying =24 /2. Since the problem is symmetric, the reaction function for Firm 2 is =24 /2. d) Solve for the values of and that satisfy both reaction functions: =24 1/2 24 /2. So =16 and =16. The price is =53 =21. Profit is = = =256. Total profit in the industry is + =512.
2 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 5 ) _ 3 0 K a s ı m 2 0 1 2 2. Tekelci bir firmanın 800 birim üretim yaptığını ve birim başına 40 TL fiyat uyguladığını varsayalım. a) Tekelci firmanın sattığı ürünün talep esnekliğinin -2 olduğu durumda, üretilen son birimin marjinal maliyetini hesaplayınız. b) Son birim üretimin ortalama maliyetinin 15 TL olduğu durumda firmanın kârını hesaplayınız. a) The monopolist's pricing rule is: / = 1/ using -2 for the elasticity and 40 for price, solve to find =20. b) Total revenue is price times quantity, or $40 800 =$32000. Total cost is equal to average cost times quantity, or $15 800 =$12000, so profit is $20000.
3 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 5 ) _ 3 0 K a s ı m 2 0 1 2 3. A firm operating in a monopolistically competitive market faces demand and marginal revenue curves as given below: P = 10-0.1Q The firm's total and marginal cost curves are: TC = - 10Q + 0.0333Q 3 + 130 where P is in dollars per unit, output rate Q is in units per time period, and total cost C is in dollars. a. Determine the price and output rate that will allow the firm to maximize profit or minimize losses. b. Compute a Lerner index. a. Calculate MR and equate it to MC. MC = MR - 10 + 0.10Q 2 = 10-0.2Q 0.1Q 2 + 0.2Q - 20 = 0 The quadratic formula yields: Q 1 = 13.17 Q 2 = -15.15. Use Q 1 since negative quantities are not meaningful. At Q 1 = 13.17 P = 10-0.1(13.17) = 8.68 b. Computation of monopoly power. The Lerner index is computed below: L P = MC P At Q = 13.17, P = 8.68, and MC = 7.34 L = (8.68 7.34)/8.68 = 0.154 4. Suppose that the market demand for mountain spring water is given as follows: P = 1200 - Q Mountain spring water can be produced at no cost. a. What is the profit maximizing level of output and price of a monopolist? b. What level of output would be produced by each firm in a Cournot duopoly in the long run? What will the price be? c. What will be the level of output and price in the long run if this industry were perfectly competitive? a. The monopoly level of output is found where marginal revenue equals marginal cost. The marginal revenue curve has the same price intercept as the demand curve and twice the slope. Thus:
4 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 5 ) _ 3 0 K a s ı m 2 0 1 2 b. MR = 1,200-2Q Setting MR equal to MC (which is zero in this problem) yields: 1,200-2Q = 0 Q = 600 P = 1,200-600 = 600 The Cournot equilibrium is found by using the reaction curves of the two firms to solve for levels of output. The reaction curve for firm 1 is found as follows: R1 = PQ 1 = (1,200 - Q)Q 1 = 1,200Q 1 - (Q 1 + Q 2 )Q 1 = 1,200Q 1 - Q 1 2 - Q 2 Q 1 The firm's marginal revenue MR1 is just the incremental revenue R1 resulting from an incremental change in output Q 1 : MR1 = R1/ Q 1 = 1,200-2Q 1 - Q 2 Setting MR1 equal to zero (the firm's marginal cost) and solving for Q 1 yields the reaction curve for Q 1 : Firm 1's Reaction Curve: Q 1 = 600 - (1/2)Q 2 Going through the same calculations for firm 2 yields: c. Firm 2's Reaction Curve: Q 2 = 600 - (1/2)Q 1 Solving the reaction curves simultaneously for Q 1 and Q 2 yields: Q 1 = Q 2 = 400. Thus the total output is 800 and the price will be $400. In the industry were perfectly competitive, price will be equated to marginal cost. P = 1,200 - Q = 0 or Q= 1,200 and P = 0 5. Two large diversified consumer products firms are about to enter the market for a new pain reliever. The two firms are very similar in terms of their costs, strategic approach, and market outlook. Moreover, the firms have very similar individual demand curves so that each firm expects to sell one-half of the total market output at any given price. The market demand curve for the pain reliever is given as: Q = 2600-400P. Both firms have constant long-run average costs of $2.00 per bottle. Patent protection insures that the two firms will operate as a duopoly for the foreseeable future. Price and quantities are per bottle. If the firms act as Cournot duopolists, solve for the firm and market outputs and equilibrium prices. Begin by solving for P. Q = 2600-400P Q - 2600 = -400P P = 6.5-0.0025Q
5 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 5 ) _ 3 0 K a s ı m 2 0 1 2 Denote the two firms A and B and solve for reaction functions. Set MR A = MC One can verify that: TR A = P A Q A TR A = (6.5-0.0025Q)Q A TR A = 6.5Q A - 0.0025[(Q A + Q B )Q A ] TR A = 6.5Q A - 0.0025Q A 2-0.0025Q A Q B MR A = 6.5-0.005Q A - 0.0025Q B 6.5-0.005Q A - 0.0025Q B = 2-0.005Q A = 4.5 + 0.0025Q B Q A = 900-0.5Q B Q B = 900-0.5Q A Substitute expression for Q B into Q A Q A = 900-0.5(900-0.5Q A ) Q A = 900-450 + 0.25Q A Q A - 0.25Q A = 450 Q A (1-0.25) = 450 450 Q A = = 0. 75 600 Substitute expression for Q A into Q B Q B = 900-0.5(900-0.5Q B ) Q B = 900-450 + 0.25Q B Q B - 0.25Q B = 450 Q B (1-0.25) = 450 450 QB = = 600 0.75 Q T = Q A + Q B Q T = 600 + 600 = 1200 P = 6.5-0.0025(1200) P = $3.5 per bottle