A firm has the following production function where q represents the output level per week, L represents the number of hours of labor the company uses in a week, and K represents the number of machine-hours the company uses in a week: q=41,0.25 K0.25 The hourly price of capital is denoted by r, and the hourly price of labor is denoted by w. 1) Solve the firm's cost minimization problem and find optimal L* and K* levels as a function of q, w, and r. For questions (2)-(4), assume w=4 and r=1. 2) Assume the firm wants to produce 16 units this week (q-16). How many hours of labor and capital should the firm's company hire? How much will it cost to produce those 16 units? 3) Assume that the firm is in the long run (that is, the firm can adjust L and K). What is the firm's supply curve?
A firm has the following production function where q represents the output level per week, L represents the number of hours of labor the company uses in a week, and K represents the number of machine-hours the company uses in a week: q=41,0.25 K0.25 The hourly price of capital is denoted by r, and the hourly price of labor is denoted by w. 1) Solve the firm's cost minimization problem and find optimal L* and K* levels as a function of q, w, and r. For questions (2)-(4), assume w=4 and r=1. 2) Assume the firm wants to produce 16 units this week (q-16). How many hours of labor and capital should the firm's company hire? How much will it cost to produce those 16 units? 3) Assume that the firm is in the long run (that is, the firm can adjust L and K). What is the firm's supply curve?
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.3P
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