Question

Let f(L_A)=C (L_A)^1/2. Let total available labor be 2000, 20% of which is employed in industry. Suppose the price of the agricultural good is $1. The wage in the rural sector is $2. Find the value of C such that the agricultural surplus is zero.

Answer 1

Given Production Function is f(L_A)=C (L_A)^1/2.

Marginal product of labour(MP_L) can be found out by partially differentiating this function w.r.t. L_A.

Therefore, MP_L= 1/2 C (L_A)^-1/2..................................................................[equation 1]

For there to be zero agricultural surplus, the marginal product of labour should exactly be equal to the wages paid to him. Therefore, MP_L= WA.

From equation 1, we have

1/2 C (L_A)^-1/2 = 2 (Given W_A= $2)................................................................[equation 2]

Also given is the total available labour in the economy = 2000

Labour employed in the agricultural industry (L_A) = 20% of 2000 = 400

Substituting this value of (L_A) in equation 1, we get C = 80.

(The calculation is shown below)