In a certain economy, the production function is [ Y=Aleft(150 N-N^{2} ight), ] where (Y) is the

In a certain economy, the production function is

\[ Y=A\left(150 N-N^{2}\right), \]

where \(Y\) is the output, \(A\) is productivity, and \(N\) is the total hours worked. The marginal product of labor associated with this production function is

\[ M P N=A(150-2 N) \]

Initially, \(A=1.0\), but a beneficial productivity shock raises \(A\) to 1.2 .

a. The supply of labor is

\[ N S=40+0.2 w \]

where \(w\) is the real wage. Find the equilibrium levels of output, hours worked, and the real wage before and after the productivity shock. Recall that the MPN curve is the same as the labor demand curve, with the real wage replacing the MPN.

b. Repeat part (a) if the labor supply is

\[ N S=20+0.6 w . \]

c. How does the positive productivity shock shift the ND curve? What does the slope of the NS curve mean? Given the same productivity shock, how do the different slopes of the labor supply curve in parts (a) and (b) affect the wages? Show your results graphically. Based on your graph, explain how the slopes of the NS curve affect the procyclical behavior of wages.