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.