Question

Suppose that the production function is Y=K^0.2L^0.8 in an economy when K is capital and L is labour.

a. What fractions of income do capital and labour receive? Explain your answer.

b. How much is economic profit? Explain your answer.

Answer 1

Y = k^ 0.2 L^0.8

MPK = dY/dK = 0.2*(L/K)^0.8

MPL= = 0.8*(K/L)^0.2

a.

Share of labor in total income is the part of Income/production which is spent on the labor resource. Similarly, share of capital in total income is the part of income/production which is spent on the capital resource

Total amount spent on capital = r*MPK

where MPK = marginal product of capital

r = rental rate of capital

w = wage rate

So, fraction of income that capital receives = (r*MPK) / Y

= (0.2r*(L/K)^0.8) / (K^0.2L^0.8)

= (0.2r/K)

Similarly,

fraction of income that labor receives = (w*MPL) / Y

= (0.8w*(K/L)^0.2)/Y

= (0.8w*(K/L)^0.2) / (K^0.2L^0.8)

= (0.8w/L)

b.

Economic Profit is the difference between total revenue and total cost = TR - TC

= p*Y - L*MPL - K*MPK

where p = price of output