Question

A company’s production function is given by Y = A(40N – N2 +100). Suppose the price of output is $6 per unit and A =1. (Hint: you need to get MPN from the production function to solve the questions below.)

1. What will be the demand for labor if the nominal wage is $24?

2. What will be the demand for labor when the TFP is increased such as A=2 (still assuming W=$24)?

Answer 1

Ans. Y = A*(40N - N^2 + 100)

Marginal Product of Labour, MPN = dY/dN = A*(40 - 2N)

a) At A = 1,

MPN = (40 - 2N)

At cost minimizing level of labour,

Wage = Price of Output*MPN

=> 24 = 6*(40 - 2N)

=> N = 18 units of labour

Thus, at given productivity and wage, 18 units of labour should be hired.

b) At A = 1,

MPN = 2*(40 - 2N) = (80 - 4N)

At cost minimizing level of labour,

Wage = Price of Output*MPN

=> 24 = 6*(80 - 4N)

=> N = 19 units of labour

Thus, at given productivity and wage, 19 units of labour should be hired.

Hence, with increase in productivity, the demand for labour will increase from 18 units of labour to 19 units of labour

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