Columbia College.
Economics 3213
Professor Xavier Presents...
(1) Doc, Grumpy, Sneezy, Bashful, Happy, Sleepy, and Dopey
What is a Utility Function?
Show how to represent levels of utility by a Family of INDIFFERENCE CURVES.
Can these curves shift in a way that the budget constraint can?
(2) 
Queen
Suppose that to remain at the same level of utility an individual would have to receive one additional unit of consumption as compensation for one less unit of leisure. Would it be utility maximizing for the individual to work more if at that point the additional output obtained is more than one? If it is less than one? Restate your answer using the concepts of indifference curves and the production function.
(3) Prince
Imagine that a worker receives a wage rate w and works L hours. The government taxes his income at the constant rate T. He spends all his income in cookies so his budget constraint is C=wL(1-T). The worker has normal preferences over leisure and cookies (represented by the usual indifference curves).
(a) Draw the budget constraint of this individual.
(b) Display graphically what the optimal consumption-labor choice is for this worker.
(c) Imagine that the government increases this guy tax rate from T to T'. What is the new budget constraint? In the new optimum, is he going to consume more or less? Is he going to work more or less? (Explain your answers in terms of wealth and substitution effects)
(4) Snow White
Consider the worker described in the previous question. Suppose now that, on top of being taxed by the government, the worker also received a TRANSFER, which we call S, from the government. The transfer is NOT related to how much he works (transfers that are not related to how much you work are often called LUMP SUM transfers). Hence, the guy's total revenue is his income (after tax, like in problem 3) plus the transfer.
(a) write down an expression for the budget constraint.
(b) Draw the budget constraint of this individual.
(c) Display graphically what the optimal consumption-labor choice is for this worker.
(d) Imagine that the government increases this guy tax rate from T to T' and, AT THE SAME TIME, it increases the TRANSFER, S, so as to allow him to achieve the SAME QUANTITY OF CONSUMPTION AND LEISURE that he had previous to the increase. What is the new budget constraint? In the new optimum, is he going to consume more or less? Is he going to work more or less? Is your answer different from (3c)? If so, why? (Explain your answers in terms of wealth and substitution effects)