Use calculus to find the MPK and MPL Find the Slope of the Isoquant Production Function:...
Use calculus to find the MPK and MPL
Find the Slope of the Isoquant
Production Function: Q=50+6L-.5L^2+22K-.25K^2
Homework Answers
Q = 50 + 6L -0.5L2 + 22K - 0.25K2
Marginal product of capital , MPK = dQ/dK = 22K1-1 - (2)(0.25)K2-1
= 22 - 0.5K
Marginal product of labor , MPL = dQ/dL = 6L1-1- (2)(0.5)L2-1
= 6 - L
Slope of the isoquant = MRTS = -MPL/MPK = -[(6-L)/(22-0.5K)]
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Use calculus to find the MPK and MPL
Find the Slope of the Isoquant
Production Function:...
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) Suppose the production function is q = 12 K.5L.5 . Calculate the MRTS (MPK/MPL) when: a) K = 200, L = 300 b) K = 50, L = 400 c) K= 900, L = 2000
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9. Use the Cobb-Douglass production function (Y AK L1-a) to find the general form of MPK...
9. Use the Cobb-Douglass production function (Y AK L1-a) to find the general form of MPK and MPL. Also show that the production function exhibits diminishing returns to both labor and capital.
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The negative of the slope of an isoquant on a tangent line a particular (L,K) bundle of factor inputs is equal to the __ Assume questions are ordered top to bottom as a, b, c, d. Fig. 2: Bank Contour Plot Production Function:Q(L,K)=104 Machines 100 100 100 300 500 700 900 hr/hr (K) Human Bank Tellers hr/hr (L) 0 2 0 40 60 80 100 Oratio of the wage rate to the capital rental rate (w/r) Omarginal rate of technical...
4 Consider three points on a firm's isoquant curve corresponding to Q-100; points A, B, and...
4 Consider three points on a firm's isoquant curve corresponding to Q-100; points A, B, and C (a) At point A, L-10, K-20, MPL-3, and MPK-1. Find the slope of the isoquant at point A coluet point B have L-11. Based on your amswer to part(e), what aus ta lepne L-12 Blased on your anser ht vaue ork coepond to point B? Assume that at point B, MPL = 2.5 and MPK = 1.25. What is the slope of the...
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and bo...
1. Suppose the production function is given by Q = LK, where MPL = K and MPK - L. The level of output Q = 100 and both wage and interest rates are equal to one, so that war- a) Given that the wage increases to 4. determine the elasticity of demand for labour at the new wage. Indicate whether the wage bill will increase or decrease as wage increases to 6. b) Find the linear demand function for labour...
(a) Consider the production function, q = 100K2L1.5 Calculate the marginal product of labor, MPL, and...
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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...
9. Use the Cobb-Douglass production function (Y AK L1-a) to find the general form of MPK and MPL. Also show that the production function exhibits diminishing returns to both labor and capital.
The negative of the slope of an isoquant on a tangent line a particular (L,K) bundle of factor inputs is equal to the __ Assume questions are ordered top to bottom as a, b, c, d. Fig. 2: Bank Contour Plot Production Function:Q(L,K)=104 Machines 100 100 100 300 500 700 900 hr/hr (K) Human Bank Tellers hr/hr (L) 0 2 0 40 60 80 100 Oratio of the wage rate to the capital rental rate (w/r) Omarginal rate of technical...
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