Econ 349 > Answer Key for Problem Set 2
1. Indifference curves for a given individual can not cross each other because it would violate transitivity and rationality. Try to prove this by drawing two indifference curves that do intersect and then explain why this would be a contradiction.
2. Yes, please explain this one!
3. Volkswagens are less expensive than Mercedes-Benzes!
4. Indifference curves: in each of these examples, it's assumed that
hamburgers are measured on the horizontal axis.
a) upward sloping curves (bowed away from the vertical axis) with the direction of higher utility to the northwest.
b) negatively sloped linear indifference curves with the direction of higher utility to the northeast.
c) downward sloping curves (bowed away from the origin) with the direction of higher utility to the southwest.
d) upward sloping curves (bowed away from the horizontal axis) with the direction of higher utility to the southeast.
6. We did this in class.
7. Ms Phashun: If forced to buy at least C-min clothing, then her utility (U2) is lower than if she could freely allocate her income at U1.
9. Assuming that alcoholic drinks are measured on the x-axis, then Tyler will have relatively steeper indifference curves compared to Zhuli. That is, Tyler's MRS will be greater than Zhuli's for a given amount of alcoholic drink. A larger MRS indicates that Tyler is willing to sacrifice more of the other good (nonalcoholic drink) compared to Zhuli in order to get one more alcoholic drink. In equilibrium, since each person faces the same relative prices in the market, each person will adjust their purchases such that their MRS will equal the ratio of the market prices. This implies that Tyler will consume more alcoholic drinks than Zhuli.
10. The budget line will have three segments: a steep section reflecting the full price, a middle segment reflecting the 25% discount, and a third segment reflecting a 50% discount for miles beyond 50,000.
12. See graph below. The black line represents Eric's original budget line. The black line also represents his indifference curve! Thus, any combination that falls along the budget line will maximize his utility. (Question: what will be his level of utility along this line?)
The green line represents the supermarket promotion.
The red line represents the higher price of potatoes. In this case, Eric will maximize utility by buying all meat and no potatoes (i.e., a corner solution).
14. We did this one in class.
15. This is similar to #3 above. There is a difference between "willingness to buy" and "ability to buy". That’s what demand curves are all about.
16. Fraser initially locates at a corner solution with U1. When his income rises to $80,000, Fraser buys one car with utility U2.
17. Bugs Bunny: Bugs initially locates at point A with utility U1. After the price of carrots increases, the budget line pivots inward and forces Bugs to relocate to point C with utility U2. The substitution effect is from A to B along the original utility curve. The income effect is from B to C (where the red line is the hypothetical budget constraint).
18. a) MRS = -3/1 (if you plot fajitas on the x-axis); b) MRS = -6/1
19. We did this one in class.
22. This question calls for a corner solution. You can illustrate corner solutions using the normal convex indifference curves rather than the concave curves.
23. This is nearly identical to #26 below.
24. Intertemporal choice. Point E (where the red lines cross) is the endowment of 1/3 k in year 1 and 2/3 k in year 2. A positive interest rate will rotate the budget line around the endowment point E so that the line is flatter (assuming year 2 consumption is measure on the horizontal axis).
25. Last year's budget line is in blue (and his utility was U1). This year's budget line is in red (and his utility is U2). This year's consumption of grapes must be lower than last year's. This is because grapes are more expensive this year, hence Mr. Mathers has an incentive (substitution effect) to sell more of his grapes on the market rather than consume them himself.
26. We did this one in class.
27. Mister Convex (aka Zhun) should be the one buying some of both types of records. Mister Concave (aka Shaoze) will locate at a "corner solution" and only buy one type of music.
28. We did this one in class (though we had the axes reversed). Hannah's initial choice is shown below with utility U1. When the two "free" candy bars are taken away, Hannah's choice depends on whether spinach is a normal or inferior "bad". Where do you think she'll end up under either scenario?
29. Shaylyn initially choose a 1-bedroom apartment (which leaves her with $1500 of AOG). After the subsidy, the price of apartments falls to $250 and, let's say, she chooses a 2-bedroom apartment. I've not shown the indifference curves so as to keep the graph clean. If, instead, Shaylyn is simply given the cash equivalent value of the subsidy (which is $500 for two rooms), her budget line becomes the red line. It is possible to draw a set of indifference curves such that Shaylyn would rather have the straight cash subsidy instead of the reduced price housing (in other words, she could get to a higher indifference curve on the upper segment of the red line).
33. The market demand is found by adding up the individual quantities demanded at each price. The easiest way to derive the market demand is to rewrite the demand equation as Q = 25 - 1/4 P. Since there are 20 identical consumers, we can simply multiply Q times 20 to get the market demand: 20*Q = 20(25-1/4 P) = 500 - 5P. Thus, the market demand is Q = 500 - 5P.
34. a) MRSSB = MUB/MUS = (.2*9.5/4.5)/(.2*4.5/9.5) = - 9/4
b) MRSSB = - 1
c) Yes, Boris's indifference curves are convex since the MRS declines as he consumes more bread.