Section 1: Answer all three of the following three questions
1. On a new FOX game show, both Bill and Ted have each accumulated $25,000 in winnings. Suppose the show's host offers each of these men the option of taking a $25,000 check or of getting a $25,000 Fiji vacation. Use indifference curve analysis to explain why Bill prefers the cash to the vacation, even though Ted is indifferent between the two.

Bill and Ted clearly have very different preferences. To see why the two differ on whether to take cash or a vacation, we look at how an addition of $25,000 in income (the cash winnings) affects their budget constraint. For simplicity, assume that both have the same budget constraint when comparing the quantity purchased of Vacation Pleasure and of All Other Goods (AOG). Although we need the same axis labels for both, it isn't necessary to assume that their constraints are the same, it just makes things easier to compare.

The cash prize would shift each budget constraint out to the right, from the dark red line to the dark blue line on each graph below. Bill's indifference curve intersects the budget constraint at a higher point (pt B) on the new budget constraint than does Ted's indifference curve (pt T).

The vacation prize shifts the budget constraint in the same manner as the cash prize, but with one important exception. Because the vacation prize is "payment in kind" (e.g. a gas voucher), the budget constraint is now "kinked". The new budget constraint is the dark blue line that is horizontal from the vertical intercept of the old constraint, moving the distance of the value of the vacation ($25,000), and then the negatively sloped line below this point. Note that below the "kink" point, the budget constraint associated with each prize is identical.

If Bill and Ted were to be indifferent between the two prizes, it would be because their indifference curves were tangent to this second constraint at a point below the "kink" point. This is true for Ted, whose indifference curve is tangent to the constraint at pt T. This is not true for Bill, whose indifference curve intersects the constraint at pt B (at the kink point). Notice that if this were the cash prize, Bill could locate on a higher indifference curve (IC₂). The dotted dark blue line, where this intersection occurs, corresponds with what the budget constraint would be if this were the cash prize.

Ted gets the same utility out of each prize, so he is indifferent between the two. Bill gets greater utility out of the cash prize, so he prefers the cash to the vacation.

2. Frik consumes differing quantities of nachos (N) and good X (X), while Frak consumes differing quantities of nachos and good Y (Y). Both individuals are trying to determine whether or not they're at an equilibrium.

Use indifference curve analysis to discuss each person, in turn, stating whether that person is at an equilibrium and (if necessary) what that person should do to arrive at the equilibrium.

a. Frik is currently consuming where the marginal utility associated with consuming nachos is twice as large (in absolute value) as the marginal utility associated with consuming good X, even though the price of nachos is only half the price of good X.

Remember that the marginal utility of consuming nachos, divided by the marginal utility of consuming good X is equal to the marginal rate of substitution between these two goods (MRS_N,X). In turn, MRS_N,X is the slope of the indifference curve. The slope of the indifference curve here (in absolute value) equals 2, whereas the slope of the budget constraint is 1/2 (also in absolute value). Of course, in reality, MRS_N,X = -2, while the slope of the budget constraint is -1/2 (i.e. P_N/P_X = -1/2).

Frik is not at an equilibrium because equilibrium requires that MRS_N,X = P_N/P_X. If Frik consumes more nachos, and less good X, then his MRS_N,X will gradually decrease until he is at equilibrium (note that prices will stay the same). Given the prices of these two goods, Frik doesn't consume enough nachos at the start.

b. Frak's marginal rate of substitution for nachos and good Y (MRS_N,Y) is always equal to a value of 4 (in absolute value), even though the nachos are only 1/4 of the price of good Y.

Here, we don't necessarily know whether Frak is currently at an equilibrium, because we don't know how much he's consuming of these two goods. If MRS_N,Y is always equal to 4 in absolute value, then his indifference curve is linear (i.e. a straight line) - unlike the example above where we only know the value of the MRS at one point. A constant MRS implies that nachos and good Y are very close substitutes. Because the budget constraint is also linear (with a slope of 1/4), Frak must consume at one of the end points on the budget constraint. Which one? Because these are close substitutes, Frak should choose the good with the lower price. Therefore, equilibrium occurs where Frak consumes only nachos.

3. For off-campus students, the University of Louisville sells two types of parking permit, green and blue. Blue permits are more expensive but they allow you to park somewhat closer to campus than the green permits. The university will only sell you one parking permit per year, but assume that the price of each permit is constant over time.

a. Use this information along with indifference curve analysis to describe your decision to purchase a parking permit.

In answering this question, it is important to note a few things. First, that these goods are clearly substitutes. Consequently, an indifference curve associated with these goods is linear. Second, blue permits are of higher quality than green permits because the blue permits allow you to park closer. This tells us that the slope of these indifference curves is less than one. Third, the price of green permits is less than the price of blue permits. This informs us that the budget constraint also has a slope that's less than one. Let's assume that the slope of the indifference curves is less than the slope of the budget constraint. Fourth, limiting permit purchases to one is the same as having a quota.

Putting these observations into the graph below, we see one possible way that a person decides on which permit to buy.

This person consumes a green permit, because this is where his/her indifference curve intersects the budget constraint (note that this is only one possibility, we could have also shown that this person will purchase a blue permit by drawing a budget constraint that is further out).

b. Use this information along with indifference curve analysis to describe how your decision is affected by the fact that your income steadily increases during your academic career.

If this person's income steadily increases, then the budget constraint shifts (parallel) out to the right. The constraint continues to shift until it is far enough to the right that this person switches over to a blue permit.

This process is seen in the graph above. The budget constraint shifts out (from BC₁ to BC₂ and then to BC₃). All the while, this person is able to reach higher and higher indifference curves (moving from IC₁ to IC₂ and then to IC₃). Notice that the quota is revealed when the budget constraint shifts to the right because, in spite of higher income, this person can only buy one (green) permit.

When the budget constraint reaches BC₃, however, this person is able to continue beyond the third indifference curve, IC₃, and reach a still higher indifference curve, IC₄, that intersects the last budget constraint where it is better to now buy a blue permit. This person moves to their final budget constraint, and as a result switches from buying a green permit to buying a blue permit.