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 |
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more than 2,000, but less than or equal to 2,500 |
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more than 2,500, but less than or equal to 3,500 |
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more than 3,500, but less than or equal to 4,000 |
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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.
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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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