Question

Homer consumes only donuts and beer. When he consumes less than 10 beers, Homer would gladly drink one more. After drinking 10 beers, Homer is so drunk that he does not notice any additional bottle he drinks (that is, the benefit of an additional bottle of beer is zero). Drinking more than 17 beers is beyond the processing capability of Homer’s liver and any additional bottle makes him sick (beer is no longer a “good” for Homer). Homer’s preferences for donuts are somewhat similar. As long as he eats less than 15 donuts, an additional donut increases his utility. If he eats more than 15 donuts, then additional donuts make him worse off.

1. Sketch Homer’s indifference curve passing through point (8 donuts, 8 beers).

2. Sketch Homer’s indifference curve passing through point (15 donuts, 16 beers)

Hint 1: Homer does not have “standard” indifference curves. That is, his indifference curves could be downward or upward sloping, convex, or concave, or only locally convex or concave.

Hint 2: For each of the above questions, it is possible to (and you should!) sketch Homer’s entire indifference curves.

Homer consumes beer and donuts. Beer is an inferior good. One day the price of donuts falls.

3. Use a graph (measuring quantity of donuts on the horizontal axis) to show what happens to the budget line.

4. Show the substitution and income effect of the change of the price of donuts on Homer’s beer consumption. Explain how does your diagram show that beer is an inferior good.

5. Does Homer end up drinking more or less beer than before? Justify your answer carefully.

Answer 1

Plot donuts consumed on x-axis and beers consumed on y-axis. The entire graph can be divided into 6 sub segments.

By definition, goods are commodities which increases utility the more they are consumed. Neutrals are commodities which do not change the utility the more they are consumed. Bads are commodities which decreases utility the more they are consumed.

In segment A, donuts is less than 15 (hence they are good) beer is less 10 (it is good).

In segment B, donuts is greater than 15 (hence they are bad) beer is less 10 (it is good).

In segment C, donuts is less than 15 (hence they are good) beer is more than 10 but less than 17 (it is neutral).

In segment D, donuts is more than 15 (hence they are bad) beer more than 10 but less than 17 (it is neutral).

In segment E, donuts is less than 15 (hence they are good) beer is more than 17 (it is bad).

In segment F, donuts is more than 15 (hence they are bad) beer is more than 17 (it is bad).

Indifference curves for the corresponding segments is plotted in figure 1.

Figure 1

a) At point (8,8) both beer and donuts are good. Homer’s indifference curve passing through point (8 donuts, 8 beers) is depicted in figure 2.

Figure 2

B) Homer’s indifference curve passing through point (15 donuts, 16 beers) is depicted in figure 3.

Figure 3

C) Let M be the income of Homer. If the price of donuts falls, this means Homer can buy more of donuts as he was able to do before. New budget line is shown in light blue color figure 4 (where p2 < p1).

Figure 4

D) The substitution (B1 to B0) and income effect (B0 to B2) of the change of the price of donuts on Homer’s beer consumption is shown in Figure 5. Beer is an inferior good because the quantity of beer consumed has fallen.

Figure 5

E) The final consumption of beer and donuts is depicted in figure 6.As the price of donuts fall, income effect would dictate Homer to increase the consumption of both the goods (if beer were also normal good). But since beer is an inferior good, income effect dictates the quantity of beers consumed by Homer to be reduced. On the other hand, substitution effect dictates that the cheaper product should be consumed more. Since price of donuts has fallen, it means according to substitution effect, consumption of donuts has to be increased and consumption of beers has to be decreased (from B1 to B2). Since both income and substitution results in reduction in the quantity of beer consumed. Therefore, Homer ends up drinking less beer than before.

Figure 6