Answer to Question #90863 in Macroeconomics for Gurwinder Kaur

Question

2. The firm’s marginal product of labour is given by MPL = 12 – 0.02L, where L is the number of workers employed by the firm.

a. If the firm’s product sells at price P = $10 per unit, how many workers would the firm employ at the market wage rate w = $12?

b. If the firm’s product sells at price P = $10 per unit, how many workers would the firm employ at the market wage rate w = $13?

c. Use your answers to the previous 2 questions to calculate the (arc) wage rate elasticity of demand for labour (if the firm’s product sells at price P = $10 per unit).

Answer 1

a) P*MPL=w

10*(12 – 0.02L)=12

L=(120-12)/0.2 = 540 (workers)

b) P*MPL=w

10*(12 – 0.02L)=13

L=(120-13)/0.2 = 535 (workers)

c) 12=100%

13 =x

x = 13*100/12=108.33

108.33-100 = 8.33 (percentage change in wage rate)

540 = 100%

535 = x

x=535*100 / 540 = 99.07

99.07-100=-0.93 (percentage change in the number of workers)

The elasticity of demand is equal to = percentage change in wage rate / percentage change in the number of workers

The elasticity of demand = 8.33/ (-0.93) = -8.95

it is an inelastic demand for labor — when the wage changes by 1%, the demand for labor changes by less than 1%