Question

Suppose the production function is Y=100(N-0.01N^2). And the marginal product of labor is MPN=100-2N. The aggregate quantity of labor supplied is NS=50+1.5w-Tr, where w is the real wage rate and Tr = 20 is the lump-sum transfer that household received from the government. The full-employment level of output is

less than or equal to 2,000 |
||

more than 2,000, but less than or equal to 2,500 |
||

more than 2,500, but less than or equal to 3,500 |
||

more than 3,500, but less than or equal to 4,000 |
||

more than 4,000 |

Answer #1

To derive labor demand function, put MPN = w

=> MPN = w

=> 100 - 2N = w

=> N = (100 -w)/2

=>N = 50 -0.5w

Labor demand function: Nd = 50 - 0.5w

Labor supply function : Ns = 50 +1.5w -Tr

At labor market equilibrium point; Ns = Nd = N

=> 50 + 1.5w - Tr = 50 - 0.5w

put Tr = 20

=> 50 + 1.5w - 20 = 50 - 0.5w

=> 30 + 1.5w = 50 - 0.5w

=>1.5w + 0.5w = 50 - 30

=> 2w = 20

=> w = (20/2)

=> w = 10

Equilibrium real wage is 10.

and

N =Nd = Ns

=> N = 50 - 0.5w

=> N = 50 - 0.5(10)

=> N = 45

Equilibrium level of labor is 45.

------------------------

Y = 100 (N - 0.01N^{2})

Put N = 45

=> Y = 100(45 - 0.01(45)^{2})

=> Y = 100*(45 - 20.25)

=>Y = 100 * 24.75

=> Y= 2475.

The full employment level of output is more than 2000, but less than or equal to 2500.

Answer: Option (B) i.e.,more than 2000, but less than or equal to 2500.

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