Consider the Romer model of labor supply. Specifically, an individual who seeks to maximize
U(consumption) + V(leisure)
subject to the budget constraint:
where P is the price of consumption, W is the nominal wage rate, and L is time devoted to work.
(a) Argue that if W and P both increase proportionately the optimal choice of how much to work does not change.
(b) What would happen to optimal labor supply if W were to increase. Analyze what happens to labor supply if P increases. Specifically, does our theory predict what will happen? Explain your answer. If income and substitution effects are roughly offsetting on average, what would you predict would happen to average desired labor supply in the event of an increase in P ?