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Suppose that q 30, L 2, and K-10 is a point on the production function q=f(L,...
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
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
1. Suppose the production of digital cameras is characterized by the production function q F(K, L)- KL (MPL = K, MPK = L), where q represents the number of digital cameras produced. Suppose that...
1. Suppose the production of digital cameras is characterized by the production function q F(K, L)- KL (MPL = K, MPK = L), where q represents the number of digital cameras produced. Suppose that the price of labor is $10 per unit and the price of capital is S1 per unit. (a) Graph the isoquant for q-121 000. (b) On the graph you drew for part a), draw several isocost lines including one that is tangent to the isoquant you...
Suppose that a firm’s production function is given by Q = KL + K, with MPK...
Suppose that a firm’s production function is given by Q = KL + K, with MPK = L + 1 and MPL = K. At point A, the firm uses K = 3 units of capital and L = 5 units of labor. At point B, along the same isoquant, the firm would only use 1 unit of capital. a) Calculate how much labor is required at point B. b) calculate the elasticity of substitution between A and B. Does...
2) Assume that a firm faces the following production function: q(L, K) = {1/4K 3/4 a)...
2) Assume that a firm faces the following production function: q(L, K) = {1/4K 3/4 a) Does this function represent increasing, decreasing or constant return to scale? b) Do we have diminishing productivity for factors of production? c) Find short-run cost function if K=256, w=3 and r=4
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
Given the following production functions: F(L,K) = L + K F(L,K) = (L + K)^2 F(L,K)...
Given the following production functions: F(L,K) = L + K F(L,K) = (L + K)^2 F(L,K) = (L + K)^1/2 1. Determine the returns to scale for each function. 2. For the rest of this exercise assume that the price of labor, w, and the price of capital, r, equal 1: w = r = 1. Find the conditional input demand functions of labor and capital (the cost-minimizing combinations of labor and capital). 3. Now find the cost functions for...
Assume a firm' production function is Q = 3K +L • In this case, inputs (K...
Assume a firm' production function is Q = 3K +L • In this case, inputs (K and L) are perfect substitutes. Can you give a real example where this production function works? Assume price of capital is r = 5, and price of labor is w = 1 How many units of capital and labor is need to produce Q=60 in cheapest way? O Show your logic using cost minimization condition, and Analyze it graphically
Specific Output Functions, Q = f(L,K): Below are some specific output functions. For each production function...
Specific Output Functions, Q = f(L,K): Below are some specific output functions. For each production function (1) Explain how the firm uses the inputs capital (K), and labor (L): (2) Provide an illustration of the corresponding isoquants the preference yield - include three isoquants with unique levels of output; (3) Provide a general form of the production function and create two specific production functions; and (4) Calculate the MRTS Lx for each of your proposed production functions (if possible). (1)...
A packaging firm relies on the production function Q(L,K) = KL + L. Assuming the firm’s...
A packaging firm relies on the production function Q(L,K) = KL + L. Assuming the firm’s optimal input combination is interior (i.e. it uses positive amounts of both inputs), what is its long-run marginal cost function? a. ???? = 2√??? b. ???? = √ ?? /? c. ???? = 2√??? – r d. ???? = (2?/ √??) − r
1. Suppose the production of digital cameras is characterized by the production function q F(K, L)- KL (MPL = K, MPK = L), where q represents the number of digital cameras produced. Suppose that the price of labor is $10 per unit and the price of capital is S1 per unit. (a) Graph the isoquant for q-121 000. (b) On the graph you drew for part a), draw several isocost lines including one that is tangent to the isoquant you...
2) Assume that a firm faces the following production function: q(L, K) = {1/4K 3/4 a) Does this function represent increasing, decreasing or constant return to scale? b) Do we have diminishing productivity for factors of production? c) Find short-run cost function if K=256, w=3 and r=4
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
Assume a firm' production function is Q = 3K +L • In this case, inputs (K and L) are perfect substitutes. Can you give a real example where this production function works? Assume price of capital is r = 5, and price of labor is w = 1 How many units of capital and labor is need to produce Q=60 in cheapest way? O Show your logic using cost minimization condition, and Analyze it graphically
Specific Output Functions, Q = f(L,K): Below are some specific output functions. For each production function (1) Explain how the firm uses the inputs capital (K), and labor (L): (2) Provide an illustration of the corresponding isoquants the preference yield - include three isoquants with unique levels of output; (3) Provide a general form of the production function and create two specific production functions; and (4) Calculate the MRTS Lx for each of your proposed production functions (if possible). (1)...
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