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

SOLUTION:-

* Given Production Function is f(LA)=C (LA)1/2.

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

* Therefore, MPL= 1/2 C (LA)-1/2..................................................................[equation1]

* For there to be zero 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 1/2 C (LA)-1/2 = 2 (Given WA= $2)................................................................[equation 2]

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

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

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

(The calculation is shown below)

$\frac{1}{2}C(L_A)^{-1/2}=2$

  $C(L_A)^{-1/2}=4$

$C=4(L_A)^{1/2}$

$C=4(400)^{1/2}$

$C=80$

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