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
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Find the optimal values of capital (K) and labor (N) given the
production function: Q =...
5. Find the optimal values of capital (K) and labor (N) given the production function: Q...
5. Find the optimal values of capital (K) and labor (N) given the production function: Q = 100[0.2K0.5 + 0.8Nº.512 subject to the constraint: 10K + 4N = 4100 (10 points)
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 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?...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the...
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the number of units of outputs, labor and capital. Labor cost is $2 per unit, capital cost is $1 per unit and output sells at $8 per unit. Show that the profit function is 1=16L"2 + 24K12 - 2L-K and hence find the maximum profit and the values of Land K at which it is achieved. HINT: do not forget to check the second sufficient...
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...
A factory produces output (Q) using capital (K) and labor (L) according to the production function...
A factory produces output (Q) using capital (K) and labor (L) according to the production function Y(K,L)=K1/5*L4/5 Let r denote the price per unit capital, and w denote the price per unit labor, so that the total expenditure on these factors is rK + wL. a) As the factory manager, you have been told to produce 625 units of output. Give the equation for the relevant isoquant, written with L as a function of K. b) If r = 80...
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)
5. Find the optimal values of capital (K) and labor (N) given the production function: Q = 100[0.2K0.5 + 0.8Nº.512 subject to the constraint: 10K + 4N = 4100 (10 points)
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 monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the number of units of outputs, labor and capital. Labor cost is $2 per unit, capital cost is $1 per unit and output sells at $8 per unit. Show that the profit function is 1=16L"2 + 24K12 - 2L-K and hence find the maximum profit and the values of Land K at which it is achieved. HINT: do not forget to check the second sufficient...
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...
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