Question

(a) Suppose the marginal product of labor is 8 and the marginal product of capital is 2. If the wage rate is $4 and the price of capital is $2, then in order to minimize costs should the firm hire more workers or rent more capital? Please explain.

(b) Suppose the production function is given by Q = min{K, L}. How much output is produced when 10 units of labor and 9 units of capital are employed? Please explain.

Answer 1

(a)

Marginal Rate of Technical Substitution (MRTS) = Slope of Isoquant = marginal product of labor / marginal product of capital

MRTS = 8 / 2 = 4

Slope of isocost line = w / r = 4 / 2 = 2

Since, MRTS > w / r

MPl / MPk > w / r

In order to minimize cost, the firm should more labor than capital as the additional unit of labor gives more productivity to the firm.

(b)

Q = Min(K,L)

When L = 10

and K = 9

Q = Min(9, 10)

Q = 9

So, 9 units of output is produced if 10 units of labor and 9 units of capital is produced. It is because both the inputs have to used in the fixed proportions and the lower input quantity shall be chosen in the production function.

Such a function is called Leontief Production Function