In the short term, a firm cannot vary its capital and operates with K = 9.  It can, however, vary the amount of labor (L) that it uses.  For each production function below, explain why the firm will or will not experience diminishing marginal returns to labor in the short run. q = 35L + 40K q = L0.5 K0.5 q = min{3L,2}

Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function             Q=F(L,K)              Q=10L^0.25 K^0.25             where L is their number of workers and K is units of capital. The wage rate is $500 per week and a unit of capital costs $500 per week. Suppose that when initially producing 10 square feet a week, they use 1 unit of capital.a. What is their short-run cost of remodeling 80 square feet per week?    Instructions: Round your answer to the nearest whole number.    $ b. What is their short-run average cost of remodeling 80 square feet per week?    Instructions: Round your answer to the nearest whole number.    $ c. What is their long-run cost of remodeling 80 square feet per week?    Instructions: Round your answer to the nearest whole number.    $ d. What is their long-run average cost of remodeling 80 square feet per week?    Instructions: Round your answer…

Ma4. A firm produces output with the production function, Q = F(K, L) = K0.5L0.5 with r=4 and w= 2. The firm is using K=16 and just enough L to produce 16 units of output in the short run. How much could the firm save if it were producing 16 units in the long run?

= 100KL. If the price of capital is $81 per day and the price of labor is $27 dollars per day, what is the minimum cost Suppose the production function for a product is given by q of producing 900 units of output?

Question 2: Suppose a production function is given by F(K,L) = KL² the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes the cost of producing any given output?

Suppose a firm is producing computer monitors utilizing the following technology: Q=F(K,L)=L1/3K2/3 Q – weekly output   L – labor hours     K – hours of capital use Would the firm with the above production function be able to produce monitors using only capital (no labor)?  Explain.

In the short run, a firm which has production function f(L, M) = 4L1/2M1/2 must use 4 machines. If the cost of labor is £4 per unit and the cost of machines is £4 per unit, what is the short-run total cost of producing 48 units of output? Use Lagrange

Problem 1: Your firm has employed an economist to estimate your firm's production function. After gathering the appropriate data, the economist estimates that your is of the form shown below. You also know that capital is fixed at 8 units in the short run. 12 Q=K³L²³ a. Calculate the average product of labor when 27 units of labor are utilized and interpret your result. b. Calculate the marginal product of labor when 27 units of labor are utilized and interpret your result. c. Suppose the firm can hire labor at a wage of $5 per hour and output can be sold at a price of $15 per unit. Determine the profit-maximizing levels of labor and output. d. What is the maximum price of capital at which the firm will still make nonnegative profits?

Suppose a firm has the following production function Q (K, L) =K0.5 L0.4. Show mathematically whether the firm has increasing, decreasing, or constant returns to scale.

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