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)

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