Question

Suppose the marginal product of labor in the economy is given by MPN 0.002 (16, 000- N) 3. (20 points) while the supply of labor is SN 1000+ 1000w. a. Find the market-clearing real wage rate and level of employment b. What happens to the wage rate and employment if wealth rises, reducing the supply of labor to SN =500+ 1000w? c. What happens to the wage rate and employment if after wealth has risen as in part (b), there is a productivity shock that increases the marginal product of labor to MPN = 0.0025(16, 000 - N)? 1

Answer 1

Answer;

Given that MPN = w = 0.002(16000 - N) and labor supply is N = 1000 + 1000w or w = 0.001(N - 1000)

a) At equilibrium demand for labor is equal to its supply. This implies

0.002(16000 - N) = 0.001(N - 1000)

32000 - 2N = N - 1000

N = 33000/3 = 11000 (level of employment)

w = 0.001*10000 = $10 (equilibrium wage)

b) New labor supply is w = 0.001(N - 500)

New equilibrium has

0.002(16000 - N) = 0.001(N - 500)

32000 - 2N = N - 500

N = 32500/3 = 10833 (level of employment)

w = 0.001*10333 = $10.33 (equilibrium wage)

c) New equilibrium has

0.0025(16000 - N) = 0.001(N - 500)

40000 - 2.5N = N - 500

N = 40500/3.5 = 11571.43 (level of employment)

w = 0.001*11071.43 = $11.071 (equilibrium wage)