Question

Q=180√LK^0.8

L=5

K=10

1).Construct marginal product of labour and marginal product of capital

2If L=5, K=10 Measure average product of labour and average product of capital

3.return to scale production function

4.if K=5, L=10 calculate marginal rate of products.

5.law of diminishing marginal returns of labour and law of diminishing marginal returns of capital

6.how about the cross partial effect of this production function

Answer 1

Q=100K^0.5L^0.5.

K = 100, L = 25.

a.) The marginal product of capital and marginal product of labor are:

MPK = Q'(K) = 50L^0.5/K^0.5 = 25.

MPL = Q'(L) = 50K^0.5/L^0.5 = 100.

b.) If the price of capital was r = Rs.20 per unit, then the wage rate w is:

MPK/r = MPL/w,

25/20 = 100/w,

w = Rs.80.

C.) If r = Rs.25, then the input rate of capital K will be:

MPK/r = MPL/w,

MPK/25 = 100/80,

MPK = 31.25,

MPK = 50L^0.5/K^0.5 = 31.25,

50*5/K^0.5 = 31.25,

K = (250/31.25)^2 = 64 units.