A competitive firm has a production function described as follows. Q = f(K, L) = 100K}L* where K and L are levels of capital and labor in production respectively. (a) Find the optimal bundle of capital and labor to produce 400000 units of output, if the wage is w=$8 and the rental price of capital is r=$1. Also, find cost of producing 400000 units of output. (b) Suppose that in the short run this firm must use 40000 units of capital but can vary its amount of labor freely. How does optimal number of labor and cost of production changes? (consider prices and quantity given part a) (c) Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (d) If the wage is w=$10 and the price of output is p=$2, how much labor will the firm demand in the short run? (e) Write down an equation for the firms short-run demand for labor as a function of w and p. (f) Write down an equation for the firms short-run cost function as a function of O. r. w and p.
A competitive firm has a production function described as follows. Q = f(K, L) = 100K}L* where K and L are levels of capital and labor in production respectively. (a) Find the optimal bundle of capital and labor to produce 400000 units of output, if the wage is w=$8 and the rental price of capital is r=$1. Also, find cost of producing 400000 units of output. (b) Suppose that in the short run this firm must use 40000 units of capital but can vary its amount of labor freely. How does optimal number of labor and cost of production changes? (consider prices and quantity given part a) (c) Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (d) If the wage is w=$10 and the price of output is p=$2, how much labor will the firm demand in the short run? (e) Write down an equation for the firms short-run demand for labor as a function of w and p. (f) Write down an equation for the firms short-run cost function as a function of O. r. w and p.
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.3P
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Transcribed Image Text:A competitive firm has a production function described as follows. Q = f(K, L) = 100K}L where K
and L are levels of capital and labor in production respectively.
(a) Find the optimal bundle of capital and labor to produce 400000 units of output, if the wage is w=$8
and the rental price of capital is r=$1. Also, find cost of producing 400000 units of output.
(b) Suppose that in the short run this firm must use 40000 units of capital but can vary its amount of
labor freely. How does optimal number of labor and cost of production changes? (consider prices
and quantity given part a)
(c) Write down a formula that describes the marginal product of labor in the short run as a function
of the amount of labor used.
(d) If the wage is w=$10 and the price of output is p=$2, how much labor will the firm demand in the
short run?
(e) Write down an equation for the firms short-run demand for labor as a function of w and p.
(f) Write down an equation for the firms short-run cost function as a function of Q, r, w and p.
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