Question

1. A firm's production function is f(x) -[min,3x2l. If the price of factor 1 is 4 per unit and the price of factor 2 is 6 per unit, then its supply function is given by the equation S(p)-

Answer 1

q = f(x1, x2) = [min{x1, 3x2}]^1/2

This represents a quasi-Leontief production function representing two complementary inputs. The isoquants will be L-shaped and production is optimized when

x1 = 3x2 [i.e. x1 = x2/3]

Total cost (C) = P1.x1 + P2.x2

C = 4x1 + 6x2

Substituting x1 = 3x2 in production function,

q = [min{x1, x1}]^1/2 = [x1]^1/2

Squaring,

x1 = q²

Similarly,

q = [min{3x2, 3x2}]^1/2 = [3x2]^1/2

Squaring,

3x2 = q²

x2 = q²/3

Therefore,

C = 4 x (q²) + 6 x (q²/3)

C = (4q²) + (2q²)

C = 6q²

Supply function is the Marginal cost function (MC), where

MC = dC/dq = 12q

Therefore,

12q = p [Where p is output price]

q = S(p) = p/12 [Supply function]