Answer to Question #227834 in Economics of Enterprise for kaurr

Question #227834

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


1
Expert's answer
2021-08-23T10:39:42-0400

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.


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