In a certain economy the production function is
Y = A(100N - 0.5N2),
Where Y is output, A is productivity, and N is total hours worked. The marginal product of labour associated with this production function is
MPN = A(100 - N).
Initially, A = 1.0, but a beneficial productivity shock raises A to 1.1.
a. The supply of labour is
NS = 45 + 0.lw,
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 (from Chapter 3) that the MPN curve is the same as the labour demand curve, with the real wage replacing the MPN.
b. Repeat part (a) if the labour supply is
NS = 10 + 0.8w.
c. Some studies show that the real wage is only slightly procyclical. Assume for the sake of argument that this finding is correct. Would a calibrated RBC model fit the facts better if the labour supply is relatively insensitive to the real wage, or if it is relatively sensitive? Justify your answer diagrammatically and relate it to your answers to parts (a) and (b).