1. Consider a representative consumer who has preferences over an aggregate consumption good c and leisure l. Her preferences are described by the utility function: - U(c, 1) = ln(c) + In(1) The consumer has a time endowment of h hours which can be used to work at the market or enjoyed as leisure. The real wage rate is w per hour. The worker pays a proportional wage tax of rate t, so the worker's after-tax wage is (1 - t)w. The consumer also has dividend income of 7. (Note that there is no lump-sum tax here.) (a) Set up the consumer's utility maximization problem. (b) Analyze what would happen to consumption and leisure if the tax rate t increased: (a) show the effect of an increase in t on a graph. (b) Explain the economic intuitions for your results 2. Suppose that a consumer can earn a higher wage rate for working "overtime." That is, for the first q hours the consumer works, he or she receives a real wage rate of w, and for hours worked more than q he or she receives w2, where w> w. Suppose that the consumer pays no taxes and receives no nonwage income, and he or she is free to choose hours of work. (a) Draw the consumer's budget constraint, and show his or her optimal choice of consump- tion and leisure. (b) Show that the consumer would never work q hours, or anything very close to q hours. Explain the intuition behind this. (c) Determine what happens if the overtime wage rate, w2, increases. Explain your results in terms of income and substitution effects. You will need to consider the cases of a worker who initially works overtime and a worker who initially does not work overtime.