Suppose the marginal product of labor in the economy is given by MPN = 0.002(16,000 - N), while the supply of labor is 1000 + 1000w

Question

(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 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)?

Answer 1

(a) The market-clearing real wage rate equates the demand and supply of labor. Setting w = MPN = 0.002(16,000 - N), we get w = 32 - 0.002(1000 + 1000w) = 32 - 2 - 2w. Using algebra gives 3w = 30, so w = 10. Plugging into the labor supply equation gives N = 1000 + (1000 × 10 ) = 11,000.
(b) Setting w = MPN = 0.002(16,000 - N), we get w = 32 - 0.002(500 + 1000w) = 32 - 1 - 2w. Using algebra gives 3w = 31, so w = 10.333. Plugging into the labor supply equation gives N = 500 + (1000 × 10.333 ) = 10,833.
(c) Setting w = MPN = 0.0025(16,000 - N), we get w = 40 - 0.0025(500 + 1000w) = 40 - 1.25 - 2.5w. Using algebra gives 3.5w = 38.75, so w = 11.071. Plugging into the labor supply equation gives N = 500 + (1000 × 11.071 ) = 11,571.