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In-class exercise: finding total and marginal product. .Suppose the production function is .f(L, K) LK +...
Acme produces anvils using labor (L) and capital (K) according to the production function Q= f(L,K)=LK...
Acme produces anvils using labor (L) and capital (K) according to the production function Q= f(L,K)=LK with associated marginal products MPL=K, MPK =L. The price of labor is w=2 and the price of capital is r=1. Does Acme's production function for anvils exhibit increasing, constant or decreasing returns to scale? Justify your answer
question 4 a and b please 4. Consider the production function y = LK/10, where L...
question 4 a and b please
4. Consider the production function y = LK/10, where L is labor and K is capital. (This is from Chapter 9, Exercise 4.) The factor prices are wi = 10 and wx = 100. Suppose the amount of capital, K, is fixed at 1 unit (a) Derive the short-run cost function (y). (b) Derive and graph the average total cost function ATC(y), the average variable cost function AVC(y), and the short-run marginal cost function...
1. A production function is given by f(K, L) = L/2+ v K. Given this form,...
1. A production function is given by f(K, L) = L/2+ v K. Given this form, MPL = 1/2 and MPK-2 K (a) Are there constant returns to scale, decreasing returns to scale, or increasing returns to scale? (b) In the short run, capital is fixed at -4 while labor is variable. On the same graph, draw the 2. A production function is f(LK)-(L" + Ka)", where a > 0 and b > 0, For what values of a and...
Suppose a firm’s production function is Y=f(K,L) and has the following: Output = 5,000 Wage rate...
Suppose a firm’s production function is Y=f(K,L) and has the following: Output = 5,000 Wage rate = 40 Marginal product of labor = 5 Labor = 100 Rental rate = 250 Capital = 75 Marginal Product of capital = 20 Price = 10 A. What is the firm’s total revenue? B. What is the firm’s total cost? C. What is the profit for the firm? D. What is the real wage rate for this firm? E. What is the real...
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor. a. Find marginal product of labor and marginal product of capital.b. Define what is marginal rate of technical substitution, MRTS. Calculate the MRTS for the above case.c. When K = 10, L = 16, what is the total output? Sketch this isoquant function on a diagram where K is the vertical axis and L is the horizontal axis.
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK...
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK . In the short-run, the firm's amount of capital equipment is fixed at K = 100. The rental rate of capital is r=$1, and the wage rate of labor is w=$4. a. Derive the firm's short-run total cost curve. What is the short-run average total cost? What is the short-run average variable cost? b. Find the short-run marginal cost function. What are the total...
4. Your production function is Q = LK. The wage for L is w and the...
4. Your production function is Q = LK. The wage for L is w and the rental rate for K is r. You need to produce Q units of output. (a) What is your total cost equation? (b) What is your output constraint? (c) Find the Marginal Rate of Technical Substitution (MRTS) for your production function. (d) In general (for any values of w and r), what relationship must hold between L and K at the cost minimizing bundle? (e)...
7. Production can be described by Q(L,K) = LK + L. The marginal product of labor...
7. Production can be described by Q(L,K) = LK + L. The marginal product of labor as the firm uses more L, holding K constant. The marginal rate of technical substitution of L for K __ as the firm moves from left to right along an isoquant. a. decreases; decreases b. decreases; increases c. decreases; remains constant d. increases; decreases e. increases; increases f. increases; remains constant g. remains constant; decreases h. remains constant; increases i. remains constant; remains constant
Suppose the production of paved roadways is represented as Q(L,K) = LK + L. Based on...
Suppose the production of paved roadways is represented as Q(L,K) = LK + L. Based on this production function, which of the following statements is (are) TRUE? A. In the short-run when capital is held constant, labor exhibits the law of diminishing returns. B. The isoquants for paved roadways are downward sloping and convex to the origin. C. The production function exhibits constant returns to scale. D. Both a and b are true. E. Both b and c are true....
Suppose we have a production function Q = 16.7K - K^2. If marginal revenue is $10,...
Suppose we have a production function Q = 16.7K - K^2. If marginal revenue is $10, what is the marginal revenue product of capital when K=4. Hint: Round your answer to two decimal places.
question 4 a and b please
4. Consider the production function y = LK/10, where L is labor and K is capital. (This is from Chapter 9, Exercise 4.) The factor prices are wi = 10 and wx = 100. Suppose the amount of capital, K, is fixed at 1 unit (a) Derive the short-run cost function (y). (b) Derive and graph the average total cost function ATC(y), the average variable cost function AVC(y), and the short-run marginal cost function...
1. A production function is given by f(K, L) = L/2+ v K. Given this form, MPL = 1/2 and MPK-2 K (a) Are there constant returns to scale, decreasing returns to scale, or increasing returns to scale? (b) In the short run, capital is fixed at -4 while labor is variable. On the same graph, draw the 2. A production function is f(LK)-(L" + Ka)", where a > 0 and b > 0, For what values of a and...
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK . In the short-run, the firm's amount of capital equipment is fixed at K = 100. The rental rate of capital is r=$1, and the wage rate of labor is w=$4. a. Derive the firm's short-run total cost curve. What is the short-run average total cost? What is the short-run average variable cost? b. Find the short-run marginal cost function. What are the total...
7. Production can be described by Q(L,K) = LK + L. The marginal product of labor as the firm uses more L, holding K constant. The marginal rate of technical substitution of L for K __ as the firm moves from left to right along an isoquant. a. decreases; decreases b. decreases; increases c. decreases; remains constant d. increases; decreases e. increases; increases f. increases; remains constant g. remains constant; decreases h. remains constant; increases i. remains constant; remains constant
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