Homework:
You may work together, but turn in your own individual answers.
1. Figure 1 above shows a consumer's budget constraint for buying apples and oranges, as well as the indifference curve passing through the utility-maximizing bundle A.
a. Explain why the consumer does not choose bundle B.
b. Explain why the consumer does not choose bundle C.
c. Explain why the consumer does not choose bundle D. Hint: draw a bundle on the same indifference curve as A, but with both more apples and more oranges than D.
2. Figure 2 above shows 2 different budget constraints faced by a consumer choosing bundles of apples and oranges. Suppose that when both X and Y are affordable (on the steeper budget constraint), the consumer chooses Y. When both Y and Z are affordable (on the flatter budget constraint), the consumer chooses Z.
a. Based on revealed preference, explain why the consumer must prefer Z over X.
b. Draw two indifference curves, one passing through Y and another passing through Z, that are consistent with these choices.
c. Now suppose instead that the consumer always chooses Y, regardless of which of the two budget constraint is in effect. Is it possible to conclude, based on revealed preference, whether the consumer prefers Z over X or vice versa? Explain.
d. Redraw the graph in Figure 2, and draw an indifference curve passing through Y that is consistent with the choices the consumer made in part (c). Hint: Such an indifference curve must have a "kink" at bundle Y, similar to the indifference curves for perfect complements discussed in lecture.
e. Explain why the indifference curve in part (d) must be "kinked" and not "smooth" at bundle Y.
3. In the top panel of Figure 3, we see two budget constraints faced by a consumer choosing between apples and oranges. When the price of apples is $1 per unit, the consumer chooses bundle A. When the price of apples rises to $2 per unit, the consumer chooses bundle B. In the bottom panel of Figure 3, draw the consumer's individual demand curve for apples.
4. Suppose a consumer's marginal utility for beer is 2, and marginal utility for juice is 1. Beeris $3 per unit, while juiceis $1 per unit.
a. Find the consumer's marginal rate of substitution between beer and juice and the ratio of the price of beer to the price of juice. Also calculate the consumer's marginal utility per dollar spent on each good. Is the consumer maximizing utility?
b. Should the consumer increase consumption of beer or juice? Explain how increasing consumption of one of the goods by 1 unit (while decreasing consumption of the other good by an amount of equal cost) could increase the consumer's utility. As usual, assume the goods are perfectly divisible.