Suppose a worker chooses consumption c and leisure l to

Question

Assignment 1, Econ 751-

Q1. Housing in San Francisco is much more expensive than in Madison. Suppose wages and the prices of all consumer goods (other than housing) are the same in the two places, and compare two workers with identical preferences and equal non-labor incomes, one living in each place. Analyze the following assertion:

"After paying for housing the San Francisco worker has less money to spend on leisure and other goods than the Madison worker, but both face the same relative prices for all other goods. So, aside from housing, the comparison boils down to the effect of a parallel shift in the budget constraint. This means that the San Francisco worker will supply more labor than the Madison worker."

Is the above statement generally true? If so, prove it. If not, can you find a restriction on the consumers' preferences which would make the statement true?

Q2. Can the data in Ashenfelter and Plant (JOLE January 1990) be used to get a rough estimate of the elasticity of labor supply? If not, explain why. If so, compute an estimate, and explain whether it is a Marshallian, or a Hicksian, or a Frisch elasticity.

Q3. Suppose a worker chooses consumption, C, and leisure, l, to maximize the utility function

U(C, l) = α((C- γ)^ρ -1/ρ) + ((l- γ₀)^ρ_0-1/ρ₀)

subject to the budget constraint C = w(T-l) + μ, where T is the time endowment, w is the real wage and μ is real non-labor income.

a. Suppose ρ = 0. Derive the Marshallian labor supply curve (the supply price of labor as a function of hours worked).

b. Suppose (instead) that ρ = -2, with ρ₀ = ½, α = 6, γ₀ = 96, T = 168, μ = 0 and γ = 50. Plot the labor supply curve, and comment on whether it has any chance of fitting long-run trends in real wages and hours worked.