A firm produces output Q by using capital K and labor L in fixed proportions, i.e....
- Julia operates a cost-minimizing firm that produces a single output using labor (L) and capital (K). The firm's production function is Q f(L, K) = min{L, K}}. The per-unit price of labor is w = 1 and the per-unit price of capital is r = 1. Recently, the government imposed a tax on Julia's firm: For each unit of labor that Julia employs, she must pay a tax of £t to the government. (a) Graph the Q unit of...
A firm produces toasters using capital (K) and labor (L). The price of capital is r > 0 and the price of labor is w > 0. The quantity Q of toasters produced is given by the function: Q = f(L, K) = L^(1/2) K^(1/3) (a) What type of returns to scale does the firm have? (b) Assume that the firm minimizes costs and that all factors are variable . i. Explain the conditions that hold when the plant produces...
a firm produces output according to the following function q= f(L,K) = L^1/2K^3/2. The cost of labor is $2 per hour and the rental cost of capital is $12 per hour. a) Determine the returns to scale for this function. b) Suppose the firm wishes to produce at cost $56. How Much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b. d. Suppose that there are...
a firm produces output according to the following function q= f(L,K) = L^1/2K^3/2. The cost of labor is $2 per hour and the rental cost of capital is $12 per hour. a) Determine the returns to scale for this function. b) Suppose the firm wishes to produce at cost $56. How Much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b. d. Suppose that there are...
A factory produces output (Q) using capital (K) and labor (L) according to the production function Y(K,L)=K1/5*L4/5 Let r denote the price per unit capital, and w denote the price per unit labor, so that the total expenditure on these factors is rK + wL. a) As the factory manager, you have been told to produce 625 units of output. Give the equation for the relevant isoquant, written with L as a function of K. b) If r = 80...
A firm produces output (Q) using inputs of labor (L) and capital (K), whose prices are w and r, respectively. Production is subject to increasing marginal cost. Both inputs are normal. Now suppose w rises. Discuss each of the statements below, explaining whether it is correct or incorrect and why: a) "The increase in w will increase the firm's demand for K as well as its demand for L." b) "If the elasticity of capital-labor substitution (σ) is zero for...
Consider a firm using two inputs; capital (K) and labor (L) in production. The firm's production technology is characterized by the following production function: Q = F(K, L) = 40K L In the short run (SR), the quantity of the capital (K) that the firm uses is fixed at K = 10 whereas the quantity of the labor input can be varied. Price of labor is $4,000 per worker and the price of capital is $2,000 per capital. (PL=$4,000 and...
Suppose that a firm uses capital (K) and labor (L) to produce widgets, and that the production function for widgets is given by Q = K 1/3L1/2 Assume that r = $4 and w = $4, where r is the price of capital and w is the wage rate. Finally, suppose that the price of widgets, p, is $8. a) Suppose that K = 64 in the short run. Given that w = 4, how many workers should this firm...
Suppose a firm has the production function: Q=2KL, where K is capital, L is labor and Q is quantity. If capital is fixed at 4 in the short run. Suppose the cost of a unit of capital is $2 (r=2), and the cost of a unit of labor is $4 (w=4). What is the short run total cost function in terms of Q? A. TC=4+Q B. TC=4+0.5Q C. TC=8+Q D. TC=8+0.5Q
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. Let w= 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q when the prices labor and capital are w = 1 and...