An individual's preferences over a consumption good, c, and leisure, l, are dened by the utility function u(l, c) = ln l + ln c.

An individual’s preferences over a consumption good, c, and

leisure, l, are defined by the utility function

u(l, c) = ln l + ln c.

She initially has an endowment of one unit of leisure time, ωl = 1, and none of the consumption

good, ωc = 0. The consumption good is the numeraire and the wage rate is w. Let L = 1 − l

denote her labor supply.

(i) (8 points) Show that the individual’s labor supply is unresponsive to the wage rate.

(ii) (4 points) Explain your result in (i) in terms of income and substitution effects.

(iii) (10 points) Now suppose that the individual has an endowment of one unit of the consumption good, as well as her endowment of leisure time, that is, (ωl , ωc ) = (1, 1). Derive an

expression for her labor supply, and show that it is increasing in the wage rate.