Subject: Advanced Macroeconomics

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, !) = In(C) + 0 In(1) (1) where o 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 = WN' (2) The consumer also faces the time constraint 1+ N' = h. (3) 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 0, h and w only. Solve for leisure and labour supply in terms of 0 and h only. Your answer must include intermediate steps. (b) According to your solution to part (a), how does real wage income affect con- sumption? 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