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5. Find the optimal values of capital (K) and labor (N) given the production function: Q...
Find the optimal values of capital (K) and labor (N) given the production function: Q =...
Find the optimal values of capital (K) and labor (N) given the production function: Q = 100[0.2K0.5 + 0.8N0.5]2 subject to the constraint: 10K + 4N = 4100
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.
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. Wha...
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. What combination of labor and capital minimizes the cost of producing any output? To produce a given level of output q, how many units of L and K are needed? Express the optimal inputs choices L(q) and K(q) as functions of the level of output q
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
A production function given by: Q = 10K^1/5L^1/2 (a) Find out the equation for an isoquant...
A production function given by: Q = 10K^1/5L^1/2 (a) Find out the equation for an isoquant to produce 20 units. Show your work. (2+4 = 6 points) (b) Write down the equation for the short-run cost function where K is fixed at 243, price of capital is 10 and price of labor is 9 per unit. Show your work. (2+4 = 6 points)
A plant’s production function is Q = 2KL + K . The price of labor services...
A plant’s production function is Q = 2KL + K . The price of labor services w is $ 4 and of capital services r is $ 5 per unit. a) In the short run, the plant’s capital is fixed at K = 9. Find the amount of labor it must employ to produce Q = 45 units of output. b) How much money is the firm sacrificing by not having the ability to choose its level of capital optimally?...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm e...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
1. There is a furniture manufacturer using labor (L) and capital (K) to produce tables. Its production function is given by q= 10L^.75 K^.40. It pays a wage of $5 per hour and rents capital at a rate...
1. There is a furniture manufacturer using labor (L) and capital
(K) to produce tables. Its production function is given by q=
10L^.75 K^.40. It pays a
wage of $5 per hour and rents capital at a rate of $15. The firm
wants to find the cost-minimizing bundle of inputs to produce
10,000 tables. Assume K is on the y-axis in what
follows.
Write out the firm’s cost function.
Calculate the firm’s isocost equation.
What is the slope of the...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
QUESTION 5 The marginal product for labor is given (MP) = 3 – 0.02*L; price of...
QUESTION 5 The marginal product for labor is given (MP) = 3 – 0.02*L; price of the product is $100 and wage = 200. Based on information above, the marginal product of labor at the optimal level of employment is $3 $2 $1.5 $1 2 points QUESTION 6 If the labor elasticity of output is 0.5 and the capital elasticity of output is 0.9, then the production function exhibits constant returns to scale. economies of scale. diseconomies of scale. diminishing...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
1. There is a furniture manufacturer using labor (L) and capital
(K) to produce tables. Its production function is given by q=
10L^.75 K^.40. It pays a
wage of $5 per hour and rents capital at a rate of $15. The firm
wants to find the cost-minimizing bundle of inputs to produce
10,000 tables. Assume K is on the y-axis in what
follows.
Write out the firm’s cost function.
Calculate the firm’s isocost equation.
What is the slope of the...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
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