As we have suggested in the chapter, it is often important to know whether workers will work more or less as their wage increases.
A. In each of the following cases, can you tell whether a worker will work more or less as his wage increases?
(a) The worker’s tastes over consumption and leisure are quasilinear in leisure.
(b) The worker’s tastes over consumption and leisure are homothetic.
(c) Leisure is a luxury good.
(d) Leisure is a necessity.
(e) The worker’s tastes over consumption and leisure are quasilinear in consumption.
B. Suppose that tastes take the form u(c,ℓ) = (0.5c−ρ +0.5ℓ−ρ )−1/ρ.
(a) Set up the worker’s optimization problem assuming his leisure endowment is L and his wage is w.
(b) Set up the Lagrange function corresponding to your maximization problem.
(c) Solve for the optimal amount of leisure.
(d) Does leisure consumption increase or decrease as w increases? What does your answer depend on?
(e) Relate this to what you know about substitution and wealth effects in this type of problem.