Question

Consider the following production functions

Y = AK1/2L1/2

Y=AK+3L

a. Fixing total factor productivity (A) at 2 and labor employment (L) at 16 units, what is the marginal product of capital when capital employment (K) is 25, 35, and 45 for each production function? Do these production functions exhibit diminishing returns to capital employment? Explain.

b. Are labor and capital complements under these production functions? Explain.

c. Is either production function a “Cobb-Douglas” function? Explain. 3. Describe the difference between a “real” wage rate and a “nominal” wage rate. How is a nominal wage rate converted into its real equivalent?

Answer 1

Y = A squareroot k squareroot L Y = A(k + 3L) A = 2 L = 16 Now , y = 2 squareroot k 16 = 8 squareroot k mp_k = partialdifferential y/ partialdifferential kv = 4/ squareroot k At k = 4/ squareroot 25 = 0.8 At k = 4.35 mP_x = 0.67 At k = 45 mp_k = 4/ squareroot 45 = 0.59 \r\n Y = A(K + 3L) Y = 2(k + 48) partialdifferential y/partialdifferential k = 2 mp_k = 2 At k = 25 mp_k = 2 At k = 35 mp_k = 2 At k = 45 mp_k = 2 since mp_k is constant so it will be constant for all k \r\n Y = A squareroot k squareroot L y = 8 squareroot k partail differential y/partialdifferential = 45/ squareroot k mp_k = 4/ squareroot k now d/dk mp_k = -2/(k)^3/2 therefore mp_k = - ve < 0 \r\n so mp_k is ling so the proq^n y = A squareroot k squareroot L means diminishing returns to capital Y = A(k + 3L) Y = 2(k + 3 times 16)