12. Suppose that a firm’s production function is given by Q = K0.75L0.25, the wage rate...

12. Suppose that a firm’s production function is given by Q = K0.75L0.25, the wage rate is w = $20 per unit of labor and the rental rate is r = $100 per unit of capital.

What is the marginal rate of technical substitution between labor and capital, ????'( (where labor is graphed on the x-axis and capital is on the y-axis)?
If the firm produces 1000 units of output by using 1000 units of labor and 1000 units of capital, how much is the firm spending in total? Is it minimizing its cost of producing 1000 units? If not, explain in general terms how the firm should adjust.
What is the cost-minimizing input combination for the firm to produce 1000 units? What is the cost of this input bundle? (Round your answer to two decimal places.)
Suppose the firm wants to produce 1000 units of output, and its capital level is fixed at K = 500 in the short run. How many units of L should the firm use? What is the firm’s total cost of producing the 1000 units of output?

Expert Solution

Rahul Sunny answered 1 month ago

Suppose a competitive firm’s production function is q = L 0.5K0.5 and the wage rate is...

Suppose a competitive firm’s production function is q = L 0.5K0.5 and the wage rate is w = $5 and the rental rate is r = $0.8 (a) If K is fixed at 25 units in the short-run, what is the short-run production function? (b) What is the equation that determines how much labor the firm should hire to produce some quantity, q? (c) Use your answer to (b) to derive the short-run total cost curve. (d) What is the...

Suppose that a firm had a production function given by: q=L0.25K0.75. The wage rate (w) is...

Suppose that a firm had a production function given by: q=L0.25K0.75. The wage rate (w) is $10 and the rental rate (r) is $10. Calculate the amount of labor the firm would hire when it produces 300 units of output in a cost-minimizing way. (Round to the nearest 2 decimal places if necessary.) When you simplify, show steps please. I'm very confused

Suppose a firm’s production function is given by Q=F(K,L) . Describe the differences between the firm’s...

Suppose a firm’s production function is given by Q=F(K,L) . Describe the differences between the firm’s demand for labour in the short-run and long-run.

5. Leontief...again Suppose that a firm’s fixed proportion production function is given by q(k, l) =...

5. Leontief...again Suppose that a firm’s fixed proportion production function is given by q(k, l) = min(5k, l) (a) Calculate the firm’s long-run total, average, and marginal cost functions. (b) Suppose that k is fixed at 10 in the short run. Calculate the firm’s short-run total, average, and marginal cost functions. (c) Suppose v = 1 (cost of capital) and w = 3 (cost of labor). Calculate this firm’s long-run and short-run average and marginal cost curves.

Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor...

Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL= K1/2 / 2L1/2 & MPK = L1/2 / 2K 1/2 a) If the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output Q...

Q- A firm’s short-run cost function for the production of gizmos is given by the following...

Q- A firm’s short-run cost function for the production of gizmos is given by the following expression: C(y) = 10y2 + 200y + 100 000. Draw the cost function C(y) and calculate; A- Calculate the range of output over which it would be profitable for this firm to produce gizmos if it can sell each gizmo for $2400. Calculate the value of the output that maximizes this profit. Calculate the value of maximum profit B- Repeat these calculations and explain...

A firm’s production function is given by q = 40 ln(EW + EB + 1) where...

A firm’s production function is given by q = 40 ln(EW + EB + 1) where EW and EB are the number of whites and blacks employed by the firm, respectively. From this it can be shown that the marginal product of labor is MPE = 40 / (EW + EB + 1). Suppose the market wage for blacks is $50, the market wage for whites is $100, and the price of each unit of output is $20. (a) How...

Suppose the production function of PowerGuns Co. is given by Q = 25LK where Q is...

Suppose the production function of PowerGuns Co. is given by Q = 25LK where Q is the quantity of guns produced in the month, L is the number of workers employed, and K is the number of machines used in the production. The monthly wage rate is $3,000 per worker and the monthly rental rate for a machine is $6,000. Currently PowerGuns Co. employs 25 workers and 40 machines. Assume perfect divisibility of labor and machines. What is the total...

7. Suppose your firm’s short-run production function is given as &nbs

7. Suppose your firm’s short-run production function is given as Labor Total Output 0 0 1 5 2 12 3 20 4 28 5 34 6 39 7 43 8 46 Assume that labor can be hired for $50 per worker and that your fixed cost is $1,000. a. What is the total variable cost of producing 5 units of output? b. What is the average variable cost of producing 12 units of output? c. What is the total cost of producing 20 units of output? d. What is the average total cost of producing...

1. Suppose that a competitive firm’s marginal cost function is given by MC(q) = 4 +...

1. Suppose that a competitive firm’s marginal cost function is given by MC(q) = 4 + aq, where a > 0 and the market price is 16. a) What is the firm’s profit-maximizing level of output when a = 4? b) Suppose the firm’s fixed costs increase and the value of a decreases. How will this affect the firm’s profit-maximizing level of output? c) Suppose the firm’s producer surplus at its profit-maximizing level of output is 36. What is the...

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