Question

Suppose that the production function is ? = ? ? in an economy,

when K is capital and L is labour.

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

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

Answer 1

a. The share of income received by labor will be given as:

(MPl × Units of labor) ÷ Y

Now, Y = KL.

The marginal product of labor can be calculated by taking the first order derivative of Y with respect to L.

We get, MPl = K

Thus, the share of income becomes: (K × L) ÷ Y.

Putting the value of Y, we get (K×L) ÷ KL = 1

Similarly, the share of capital can be given as:

(MPk × K ) ÷ Y

Now, MPk = L

Thus, share of capital = (L × K ) ÷ LK = 1

Thus, the total income is either paid to capital only or labor only. (Share of income tells us the proportion of income paid to that factor of production out of total income).

b. Economic profit = Y - Labor income - Capital income

Now, note here that we'll not use the shares of capital and labor. We need to use the total income paid to capital and labor.

Total income paid to capital is K × MPk

Total income paid to labor is L × MPl

Thus, economic profit = Y - K × L - L × K

Putting the value of Y, we get:

= KL - KL - KL = -KL

This implies that there will be economic loss since the value of economic profit has a negative sign.