Content check — Economics, Chapter 6: Consumer Choices

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Chapter 6: Consumer Choices

4 problems · 0 figures

Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either call her on the land-line phone for five cents per minute or he can drive to see her, at a round-trip cost of $2 in gasoline money. He has a total of $10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilimometer that measures his total utility from personal visits and from phone minutes. Using the values in Table 6.6, figure out the points on Jeremy’s consumption choice budget constraint (it may be helpful to do a sketch) and identify his utility-maximizing point.

Table 6.6 in the book ↗

Round Trips	Total Utility	Phone Minutes	Total Utility
0	0	0	0
1	80	20	200
2	150	40	380
3	210	60	540
4	260	80	680
5	300	100	800
6	330	120	900
7	200	140	980
8	180	160	1040
9	160	180	1080
10	140	200	1100

Answer

The rows of the table in the problem do not represent the actual choices available on the budget set; that is, the combinations of round trips and phone minutes that Jeremy can afford with his budget. One of the choices listed in the problem, the six round trips, is not even available on the budget set. If Jeremy has only $10 to spend and a round trip costs $2 and phone calls cost $0.05 per minute, he could spend his entire budget on five round trips but no phone calls or 200 minutes of phone calls, but no round trips or any combination of the two in between. It is easy to see all of his budget options with a little algebra. The equation for a budget line is:

\begin{matrix} Budget & = & P_{RT} \end{matrix} \times Q_{RT} + P_{PC} \times Q_{PC}

where P and Q are price and quantity of round trips (_RT) and phone calls (_PC) (per minute). In Jeremy’s case the equation for the budget line is:

\begin{matrix} $10 & = & $2 \times Q_{RT} + $.05 \times Q_{PC} \\ \frac{$10}{$.05} & = & \frac{{$2Q}_{RT} + {$.05Q}_{PC}}{$.05} \\ 200 & = & {40Q}_{RT} + Q_{PC} \\ Q_{PC} & = & 200 - {40Q}_{RT} \end{matrix}

If we choose zero through five round trips (column 1), the table below shows how many phone minutes can be afforded with the budget (column 3). The total utility figures are given in the table below.

Round Trips	Total Utility for Trips	Phone Minutes	Total Utility for Minutes	Total Utility
0	0	200	1100	1100
1	80	160	1040	1120
2	150	120	900	1050
3	210	80	680	890
4	260	40	380	640
5	300	0	0	300

Adding up total utility for round trips and phone minutes at different points on the budget line gives total utility at each point on the budget line. The highest possible utility is at the combination of one trip and 160 minutes of phone time, with a total utility of 1120.

6-2 §6.SCQ source ↗

Take Jeremy’s total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremy’s utility.

Answer

The first step is to use the total utility figures, shown in the table below, to calculate marginal utility, remembering that marginal utility is equal to the change in total utility divided by the change in trips or minutes.

Round Trips	Total Utility	Marginal Utility (per trip)	Phone Minutes	Total Utility	Marginal Utility (per minute)
0	0	-	200	1100	-
1	80	80	160	1040	60/40 = 1.5
2	150	70	120	900	140/40 = 3.5
3	210	60	80	680	220/40 = 5.5
4	260	50	40	380	300/40 = 7.5
5	300	40	0	0	380/40 = 9.5

Note that we cannot directly compare marginal utilities, since the units are trips versus phone minutes. We need a common denominator for comparison, which is price. Dividing MU by the price, yields columns 4 and 8 in the table below.

Round Trips	Total Utility	Marginal Utility (per trip)	MU/P	Phone Minutes	Total Utility	Marginal utility (per minute)	MU/P
0	0	-	-	200	1100	60/40 = 1.5	1.5/$0.05 = 30
1	80	80	80/$2 = 40	160	1040	140/40 = 3.5	3.5/$0.05 = 70
2	150	70	70/$2 = 35	120	900	220/40 = 5.5	5.5/$0.05 = 110
3	210	60	60/$2 = 30	80	680	300/40 =7.5	7.5/$0.05 = 150
4	260	50	50/$2 = 25	40	380	380/40 = 9.5	9.5/$0.05 = 190
5	300	40	40/$2 = 20	0	0	-	-

Start at the bottom of the table where the combination of round trips and phone minutes is (5, 0). This starting point is arbitrary, but the numbers in this example work best starting from the bottom. Suppose we consider moving to the next point up. At (4, 40), the marginal utility per dollar spent on a round trip is 25. The marginal utility per dollar spent on phone minutes is 190.

Since 25 < 190, we are getting much more utility per dollar spent on phone minutes, so let’s choose more of those. At (3, 80), MU/P_RT is 30 < 150 (the MU/_PM), but notice that the difference is narrowing. We keep trading round trips for phone minutes until we get to (1, 160), which is the best we can do. The MU/P comparison is as close as it is going to get (40 vs. 70). Often in the real world, it is not possible to get MU/P exactly equal for both products, so you get as close as you can.

6-3 §6.SCQ source ↗

Explain all the reasons why a decrease in a product's price would lead to an increase in purchases.

Answer

This is the opposite of the example explained in the text. A decrease in price has a substitution effect and an income effect. The substitution effect says that because the product is cheaper relative to other things the consumer purchases, the consumer will tend to buy more of the product (and less of the other things). The income effect says that after the price decline, the consumer could purchase the same goods as before, and still have money left over to purchase more. For both reasons, a decrease in price causes an increase in quantity demanded.

6-4 §6.SCQ source ↗

As a college student you work at a part-time job, but your parents also send you a monthly “allowance.” Suppose one month your parents forgot to send the check. Show graphically how your budget constraint is affected. Assuming you only buy normal goods, what would happen to your purchases of goods?

Answer

This is a negative income effect. Because your parents’ check failed to arrive, your monthly income is less than normal and your budget constraint shifts in toward the origin. If you only buy normal goods, the decrease in your income means you will buy less of every product.

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Problems and answers are adapted from Principles of Economics 3e by Steven A. Greenlaw, David Shapiro and Daniel MacDonald, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/principles-economics-3e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.