Please answer all of the questions below. If you print out and hand-write this problem set, you may want to add some space for writing to each question before printing.
1. Here are a few common things that people say to one another. Tell me which assumption about the utility curve they're really discussing, and whether their statement violates that assumption:
a) "Where do you want to go out tonight?" she asked. "Wherever," he said, "I don't really care."
b) "Would you like another bite?" he inquired. "No thank you. I'm stuffed," she answered.
2. There are two places I like to go for tacos in Camarillo: Taqueria Potrillos and Establos Meat Market. I think that Taqueria Potrillos' are twice as good as Establos Meat Market's tacos, but the tacos are otherwise equivalent.
a) Write my lunchtime utility function in terms of the two types of tacos (TP and TE).
b) Normally, Potrillos' tacos cost $1.25 each, while Establos' tacos cost $1.00 each. Where do I end up going for lunch according to the utility function in (a), and why?
3. Budget constraints don't just apply to dollars; they apply to any scarce resource, including time. Suppose you can spend your time in two ways: hanging out with friends or studying for classes, which increases your GPA.
a) What are the two "goods" you can buy with the hours in your day?
b) Write a budget constraint for a day (assume you have 10 hours after eliminating sleep, class, eating, and work from your life).
c) Draw your budget constraint below, and add in your personal indifference curve over the two goods. What happens to your equilibrium consumption of the two goods if your classes get easier (hint: what happens to the "price" of grades?)?
4. A favorite joke of mine is: What's the difference between ignorance and apathy? "I don't know and I don't care." Does either "ignorance" or "apathy" violate one of our preference assumptions? If not, explain how both are consistent. If so, which assumption is violated and why?
5. Using three activities you might choose to do in a weekend, give me an example of preferences over these activities that would violate transitivity.
6. When I go to In-N-Out, I order one small soft drink for every four double-doubles I consume.
a) (1/5th of the question) Write my lunchtime utility function in terms of soft drinks (S) and double-doubles (D).
b) (4/5ths of the question) Using a diagram, show me what would happen to my consumption choice if the price of double-doubles increased. Is there a substitution effect? Why or why not?
7. Find the formula for the U=5 indifference curve as well as the marginal rate of substitution (MRS) of that indifference curve (in terms of quantities of goods X and Y) for these functions:
a) U=3X+2Y
b) U=X^(.5) Y^(.5)
8. Risk-loving Ralph has two hobbies: skydiving (S) and white-water rafting (R). His monthly utility over the two is U=10*S^(.5) R^(.5). He has $500 to spend each month on the two activities; skydiving costs $250 for each trip (i.e. per "S"), and rafting costs $100 (i.e., per "R"). How much skydiving and rafting does he consume each month? Show your work (hint: you can start with the tangency conditions!).