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Homework 2 - Producer Theory, Perfect Comp.pdf

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Kathleen Wong

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ECO204: Homework Assignment 2 th Solutions will be released on Thursday, November 14 , 2013 at 5pm. Questions 6 and 7 were from last year’s test. 1. True, False or Uncertain. For each of the sections below, carefully read the statement and determine whether the statement is true, false or uncertain. In order to receive full credit for the problem, you must expl ain the reason for your answ er. Answers that are given without an explanation will not receive any credit. If the answer you give is based on any assumptions, be sure to state them clearly. a. When firms increase their level of output, they will always choose combinations of labor and capital such that the marginal products of each factor input are at its maximum. b. Each firm in a perfectly competitive market faces a downward sloping demand curve. c. Perfectly competitive firms will shut down if their marginal cost of production is above the market price. d. Long-run average cost curves for a firm are U-shaped because input factors suffer from diminishing returns. e. Firms that experience decreasing returns to scale will have isoquants drawn further and further apart from one another. f. In the short-run, increasing output will cause the firm’s average cost to increase. 2. Suppose Firm A has the production function q = L KA, while Firm B has the production function q = L K . Suppose that each firm is limited to 64 units of capital B in the short run. a. Calculate each firms’ MPL and MPK. b. Describe the returns to scale for each of the firms. c. In the short run and for a fixed level of output, which of the two firms will have a larger marginal product of labor? 3. Len sells lemonade on a busy street corner with a production function of F(L,S) = 0.5LS 2, where output is measured in gallons, L represents the pounds of lemons and S represents the pounds of sugar. Using the method of the Lagrange multiplier, solve for Len’s demand for lemons and sugar as a function of P L and P Sn order to produce q gallons of lemonade. 4. Suppose that each firm in a 2erfectly competitive industry has the production function C(q) = 50 + 0.5q + 0.08q . a. If the market price is $8.50 in the short run, what is the equilibrium level of output produced by each firm? What is each firm’s profit in the short run? b. Will firms enter or exit the industry? c. What is the total number of units produced in the long run? What is the market price of the product in the long run? 5. Can you determine whether this firm is experiencing increasing returns to scale,
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