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Vo) 7:03 O X LTET .ll 65%i < Varian_Workb.. a function of output is R(y) = p(y)y = (100 – 2y)y. To find revenue as a function of the input, we substitute y = 2x: R(x) = (100 – 4x)2x = (200 - 8x)x. The marginal revenue product function will have the form MRP, = 200 – 16x. Setting marginal revenue product equal to factor price gives us the equation 200-16х — 4. Solving this equation gives us x* = 12.25. 318 FACTOR MARKETS (Ch. 26) If the industry were competitive, then the industry would employ the factor up to the point where the value of the marginal product was equal to 4. This gives us the equation p2 = 4, so p* = 2. How much output would be demanded at this price? We plug this into the demand function to get the equation 2 = 100 – 2y, which implies y* = 49. Since the production function is y = 2, we can solve for x* = y* /2 = 24.5. 26.1 (0) Gargantuan Enterprises has a monopoly in the production of antimacassars. Its factory is located in the town of Pantagruel. There is no other industry in Pantagruel, and the labor supply equation there is W = 10+.1L, where W is the daily wage and L is the number of person- days of work performed. Antimacassars are produced with a production function, Q = 10L, where L is daily labor supply and Q is daily output. The demand curve for antimacassars is P = 41 – price and Q is the number of sales per day. 1,000 TO00, where P is the (a) Find the profit-maximizing output for Gargantuan. (Hint: Use the production function to find the labor input requirements for any level of output. Make substitutions so you can write the firm's total costs as a function of its output and then its profit as a function of output. Solve for the profit-maximizing output.) 10,000. (b) How much labor does it use? 1,000. What is the wage rate that it pays? $110. (c) What is the price of antimacassars? $31. How much profit is made? $200,000. 26.2 (0) The residents of Seltzer Springs, Michigan, consume bottles of mineral water according to the demand function D(p) = 1,000 - p. Here D(p) is the demand per year for bottles of mineral water if the price per bottle is p. The sole distributor of mineral water in Seltzer Springs, Bubble Up, purchases mineral water at c per bottle from their supplier Perry Air. Perry Air is the only supplier of mineral water in the area and behaves as a profit-maximizing monopolist. For simplicity we suppose that it has zero costs of production. (a) What is the equilibrium price charged by the distributor Bubble Up? 1,000+c p* 2 319 (b) What is the equilibrium old by Bubble Up? D(p*) = 1,000-c 2 < > K
