Suppose household preferences are described by the utility function U (c, l) = ?c + ? ln(l)

where c is the consumption of market goods, l is the leisure hours for the household, and ?, ? > 0 are constant parameter values.

(a) Let the market (and real) wage in the economy be w and the total number of hours available to the household be h. Use the information to find the optimal choice of leisure and consumption as functions of ?, ?, h and w. For ease, assume that the household does not have any nonmarket income and no tax on the household.

(b) Based on your answer from part (a) what is the optimal labour supply Ns for the household? Does the labour supply function make sense, i.e. how does it depend on w? How does the labour supply function depend on the parameter value ? (for example what happens lim Ns or lim Ns)?

??0 ???

(40 marks) Suppose household preferences are described by the utility function U(c, E) = 00 + ,61n() where c is the consumption of market goods, 1? is the leisure hours for the household, and 0, > 0 are constant parameter values. (a) Let the market (and real) wage in the economy be to and the total number of hours available to the household be h. Use the information to nd the optimal choice of leisure and consumption as functions of 6, 6, h and w. For ease, assume that the household does not have any nonmarket income and no tax on the household. (b) Based on your answer from part (a) what is the optimal labour supply N 3 for the household? Does the labour supply function make sense, i.e. how does it depend on w? How does the labour supply function depend on the parameter value ,8 (for example what happens lim N 3 or lim N 8)? ,6>0 ,6>oo