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. (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) ?

A = 11,000; B = 10,833 C = 11,571

Explanation:

a. The market-clearing wage rate equates the demand and supply of labour

Solve for w first

Therefore setting w = MPN = 0.002 (1600 - N)

w = 32 - 0.002 (1000 + 1000w)

w=32 - 2 - 2w

Solve using algebra

3w=30

w=10

Now put in the value for w into the supply of labour equation

1000 + 1000w

N = 1000 + (1000 * 10)

N=11000

(b)

Setting w=MPN=0.002 (16000-N)

w=32-0.002 (500+1000w)

w=32-1-2w

Solve using algebra

3w=31

w=10.333

Substitute 10.333 for w in labour supply equation 500 + 1000w

N=500 + (1000*10.333)

N=10.833

(C)

Set w=MPN = 0.0025 (16,000 - N)

w = 40 - 0.0025 (500 + 1000w)

w=40-1.25-2.5w

Solve with algebra

3.5w = 38.75

w=11.071

Substitute 11.071 for w in labour supply equation N=500 + 1000w

N=500 + (1000 * 11.071)

N = 11,571