In the static consumption-leisure model, suppose the representative consumer has the following utility function over consumption and leisure
u(c; l) = ln c + al (1.1)
where c denotes consumption and l leisure. a is a constant that determines how much
utility the individual obtains from a given amount of leisure. Assume that the budget con-
straint is c = (1 - t)wn, where w = W
P is the real hourly wage rate, and n is the number of
hours the individual works a week.
a. Does the utility function display diminishing marginal utility in consumption? Briefly explain.
b. Does the utility function display diminishing marginal utility in leisure? Briefly explain.
c. Assume (as usual) the representative consumer maximizes utility. Find the consumer's optimal consumption and leisure decision. Plot this representative consumer's labor supply function. Would a decrease in the tax rate t affect the optimal amount of labor supply.