Question

1. Consider an economy with the following production function: Y = K1/2N1/2. The economy has 1,000 units of capital and 1,000 workers.

   1. a) Derive the labor demand curve for this economy, (Recall that the real wage, w = MPN. This can be used to solve for N as a function of the other variables).

   2. b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage rate?

   3. c) Suppose that Congress, concerned about the welfare of the working class, passes a law requiring firms to pay workers a real wage of 1 unit of output. How many workers will be hired at this wage?

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d) In terms of total labor income, are workers better off at the market wage or the government-mandated wage?

Answer 1

a)

Given

Y=K^1/2N^1/2

Marginal Product of labor=MPN=dY/dN=0.5K^1/2N^-1/2

Set MPN =w for profit maximization

0.5K^1/2N^-1/2=w

Squaring both sides, we get

0.25K/N=w²

N=0.25K/w²

b)

N=0.25K/w²

Set K=1000, N=1000

1000=0.25*1000/w²

1000=250/w²

or

w=0.5 (real wage rate)

c)

N=0.25K/w²

Set w=1, K=1000

N=0.25*1000/1²=250 (Number of people hired)

d)

Total labor income in case of market wage=0.5*1000=500 units

Total labor income in case of government mandated wage=1*250=250 units

Total labor income is hire in case of market wage. So, we can say that workers are better off in case of market wage.