Question

# Suppose the production function is Y=100(N-0.01N^2). And the marginal product of labor is MPN=100-2N. The aggregate...

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

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 - 0.01N2)

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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