1. 2. Consider a special case of the consumer optimization problem discussed in class where the
representative consumer's preference are represented by the utility function U ( C , l ) = ln ( C ) +
ln ( l ) where is a preference parameter and is positive. Suppose that the consumer knows that he
will not get any dividend income and that he will not have to pay any taxes at all. Therefore, his
budget constraint is C = w N s The consumer also faces the time constraint l + N s = h . The
notation is borrowed from the textbook. (a) Maximize the consumer's utility function subject to
constraints (2) and (3). Solve for consumption in terms of , h and w only. Solve for leisure and
labour supply in terms of and h only. Your answer must include intermediate steps. (b)
According to your solution to part (a), how does real wage income affect consumption? Briefly
explain. (c) According to your solution to part (a), how does the real wage rate affect labour
supply? Provide an explanation centered around the substitution and income effects of a change
in the wage rate.