Consider the production function q=5L^(0.3) K^(0.5) The marginal product of labor is MPL=1.5L^(-0.7)K^(0.5) . Assume that...

Consider the production function q=5L^(0.3) K^(0.5) The marginal product of labor is MPL=1.5L^(-0.7)K^(0.5) . Assume that capital is fixed at in the short run.

Derive the formula for the short-run total product and graph it. (Hint: Substitute in the production function

Derive the formula for the short-run average product of labor (Hint: Divide the short-run total product by)

Expert Solution

Rahul Sunny answered 2 years ago

Suppose marginal product of labor (MPL) = 0.3*K and wage = $ 2 while the marginal...

Suppose marginal product of labor (MPL) = 0.3*K and wage = $ 2 while the marginal product of capital (MPK) = 0.7*L and price of capital = $ 1. (a) What the marginal Rate of technical substitution between labor and capital at L = 50 and K = 100? (b) What is the relative wage ratio? (c) Is the input allocation L=50 and K=100 optimal?

Assume that the marginal product of labor (MPL) = 10. And the marginal product of capital...

Assume that the marginal product of labor (MPL) = 10. And the marginal product of capital (MPK = 6. Assume also that the price of labor (PL) = 4 and the price of capital (PK) = 2. Do you agree or disagree that the firm should substitute capital for labor? Explain why with a narrative explanation and a graph.

A firm has the production function Q = 4LK. The marginal products are given by MPL...

A firm has the production function Q = 4LK. The marginal products are given by MPL = 4K and MPK = 4L. Suppose that w = r = 25. Write out the expression for the long run total cost curve. Does this firm experience economies or diseconomies of scale? Does this firm experience increasing, decreasing or constant returns to scale? TC = 25Q0.5 ; Economies of Scale; IRS

A firm has a production function of Q = KL + L, where MPL = K...

A firm has a production function of Q = KL + L, where MPL = K + 1 and MPK = L. The wage rate (W) is $100 per worker and the rental (R) is $100 per unit of capital. a. In the short run, capital (K) is fixed at 4 and the firm produces 100 units of output. What is the firm's total cost? b. In the long run, what is the total cost of producing 100 units of...

A firm’s production function is given by Q(L,K)=5L+2k. Firm’s budget is 200,000 dollars. How much labor...

A firm’s production function is given by Q(L,K)=5L+2k. Firm’s budget is 200,000 dollars. How much labor and capital should this firm optimally hire assuming that price of labor is 2 dollars per unit and price of capital is 5 dollars per unit? Does this production function satisfy the law of diminishing returns in the short run? What about decreasing returns to scale?

3. Consider the production function Q = K2L , where L is labor and K is...

3. Consider the production function Q = K2L , where L is labor and K is capital. a.[4] What is the Marginal Product of Capital for this production function? Is it increasing, decreasing, or constant? Briefly explain or show how you arrived at your answer. b.[4] Does this production function exhibit increasing, constant or decreasing returns to scale? Briefly explain or show how you arrived at your answer. c.[5] If the firm has capital fixed at 15 units in the...

Consider the production function Q = K2L , where L is labor and K is capital....

Consider the production function Q = K2L , where L is labor and K is capital. a.[4] What is the Marginal Product of Capital for this production function? Is it increasing, decreasing, or constant? Briefly explain or show how you arrived at your answer. b.[4] Does this production function exhibit increasing, constant or decreasing returns to scale? Briefly explain or show how you arrived at your answer. c.[5] If the firm has capital fixed at 15 units in the short...

Let the production function be Q=K^(1/3)L^(1/5). Is the Marginal Product of Labor increasing decreasing or constant?...

Let the production function be Q=K^(1/3)L^(1/5). Is the Marginal Product of Labor increasing decreasing or constant? Show your work.

5. The marginal product of labor (MPL) intersect with the average product of labor (APL) at...

5. The marginal product of labor (MPL) intersect with the average product of labor (APL) at the point where APL reaches its maximum. Show mathematically that MPL = APL at the point of intersection.

A Korean electronic chip manufacturer has a production function given by Q=L^(0.5)K^(0.5). Assume the Wage rate...

A Korean electronic chip manufacturer has a production function given by Q=L^(0.5)K^(0.5). Assume the Wage rate is $45 and the cost of capital is $60. Use the Excel to determine the amount of capital, K, needed to produce 20 units of output for each value of labor, L. starting from L=2 and going to 40 in increments of 1. Plot this isoquant and upload your excel sheets. A Korean electronic chip manufacturer has a production function given by Q=L^(0.5)K^(0.5). Assume...

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