Question

Let f(L_A)=C(L_A)^1/3. let total available labor be 1000, 20% of which is employed in industry. Suppose the price of the agricultural good is $1. The wage rate in rural sector is $2. Find the value of C such that the agricultural surplus is twice as large as the average agicultural surplus.

Answer 1

Solution:-

Given Production Function is f(LA)=C (LA)^1/3.

* Marginal product of labour(MPL) can be found out by partially differentiating this function w.r.t. LA.

* Therefore, MPL= 1/3 C (LA)^-1/3..........[equation1]

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

* From equation 1, we have 1/3 C (LA)^-1/3 = 2 (Given WA= $2)..........[equation 2]

* Also given is the total available labour in the economy = 1000

* Labour employed in the agricultural industry (LA) = 20% of 1000 = 200

1/3 C(LA)^-1/3 = 2

C(LA)^-1/3 = 6

C= 6(LA)1/3

C= 6(200)1/3

C= 6*5.74

C= 34.44

* Substituting this value of (LA) in equation 1, we get C = 34.44.