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 equilibrium real wage is

less than or equal to 10 |
||

more than 10, but less than or equal to 15 |
||

more than 15, but less than or equal to 20 |
||

more than 20, but less than or equal to 25 |
||

more than 25 |

Answer #1

In order to maximize profit a firm hires that amount of input such that Marginal product of that input = Real wage

Here Input is Labor(N). So profit maximizing condition is MPN(Marginal product of labor) = w(real wage)

So, MPN = w => 100 - 2N = w => N = (1/2)(100 - w) ---------Labor demand

Here Labor Supply is given by :

NS = 50 + 1.5w - Tr and here Tr = 20 => NS = 30 + 1.5w.

At equilibrium we have : Labor demand = Labor Supplied => N = NS => (1/2)(100 - w) = 30 + 1.5w

=> 100 - w = 60 + 3w =. w = 10

Thus, Equilibrium wage = 10

Hence, the correct answer is **(a) less than or equal to
10.**

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