127 Reading: Choosing with Marginal Utility

Choosing with Marginal Utility

Most people approach their utility-maximizing combination of choices in a step-by-step way. This step-by-step approach is based on looking at the tradeoffs, measured in terms of marginal utility, of consuming less of one good and more of another. You can think of this step-by-step approach as the “biggest bang for the buck” principle.

For example, say that José starts off thinking about spending all his money on T-shirts and choosing point P, which corresponds to four T-shirts and no movies, as illustrated in Figure 6.2.

The points on the graph show how a budget is affected by spending choices. Spending more money at the movies (y-axis) means that Jose' has less money to spend on T-shirts (x-axis).
Figure 6.2 .A Choice between Consumption Goods. José has income of $56. Movies cost $7 and T-shirts cost $14. The points on the budget constraint line show the combinations of movies and T-shirts that are affordable.

 

José chooses this starting point randomly; he has to start somewhere. Then he considers giving up the last T-shirt, the one that provides him the least marginal utility, and using the money he saves to buy two movies instead. Table 6.4 tracks the step-by-step series of decisions José needs to make (Key: T-shirts are $14, movies are $7, and income is $56).

Table 6.4. A Step-by-Step Approach to Maximizing Utility
Try Which Has Total Utility Marginal Gain and Loss of Utility, Compared with Previous Choice Conclusion
Choice 1: P 4 T-shirts and 0 movies 81 from 4 T-shirts + 0 from 0 movies = 81      –      –
Choice 2: Q 3 T-shirts and 2 movies 63 from 3 T-shirts + 31 from 0 movies = 94 Loss of 18 from 1 less T-shirt, but gain of 31 from 2 more movies, for a net utility gain of 13 Q is preferred over P
Choice 3: R 2 T-shirts and 4 movies 43 from 2 T-shirts + 58 from 4 movies = 101 Loss of 20 from 1 less T-shirt, but gain of 27 from two more movies for a net utility gain of 7 R is preferred over Q
Choice 4: S 1 T-shirt and 6 movies 22 from 1 T-shirt + 81 from 6 movies = 103 Loss of 21 from 1 less T-shirt, but gain of 23 from two more movies, for a net utility gain of 2 S is preferred over R
Choice 5: T 0 T-shirts and 8 movies 0 from 0 T-shirts + 100 from 8 movies = 100 Loss of 22 from 1 less T-shirt, but gain of 19 from two more movies, for a net utility loss of 3 S is preferred over T

DECISION MAKING BY COMPARING MARGINAL UTILITY

José could use the following thought process (if he thought in utils) to make his decision regarding how many T-shirts and movies to purchase:

Step 1. From Table 6.4, José can see that the marginal utility of the fourth T-shirt is 18. If José gives up the fourth T-shirt, then he loses 18 utils.

Step 2. Giving up the fourth T-shirt, however, frees up $14 (the price of a T-shirt), allowing José to buy the first two movies (at $7 each).

Step 3. José knows that the marginal utility of the first movie is 16 and the marginal utility of the second movie is 15. Thus, if José moves from point P to point Q, he gives up 18 utils (from the T-shirt), but gains 31 utils (from the movies).

Step 4. Gaining 31 utils and losing 18 utils is a net gain of 13. This is just another way of saying that the total utility at Q (94 according to the last column in Table 6.3) is 13 more than the total utility at P (81).

Step 5. So, for José, it makes sense to give up the fourth T-shirt in order to buy two movies.

José clearly prefers point Q to point P. Now repeat this step-by-step process of decision making with marginal utilities. José thinks about giving up the third T-shirt and surrendering a marginal utility of 20, in exchange for purchasing two more movies that promise a combined marginal utility of 27. José prefers point R to point Q. What if José thinks about going beyond R to point S? Giving up the second T-shirt means a marginal utility loss of 21, and the marginal utility gain from the fifth and sixth movies would combine to make a marginal utility gain of 23, so José prefers point S to R.

However, if José seeks to go beyond point S to point T, he finds that the loss of marginal utility from giving up the first T-shirt is 22, while the marginal utility gain from the last two movies is only a total of 19. If José were to choose point T, his utility would fall to 100. Through these stages of thinking about marginal tradeoffs, José again concludes that S, with one T-shirt and six movies, is the choice that will provide him with the highest level of total utility. This step-by-step approach will reach the same conclusion regardless of José’s starting point.

Another way to look at this is by focusing on satisfaction per dollar. Marginal utility per dollar is the amount of additional utility José receives given the price of the product.

marginal utility per dollar marginal utility/price

For José’s T-shirts and movies, the marginal utility per dollar is shown in Table 6.5.

Table 6.5 Marginal Utility per Dollar
Quantity of T-Shirts Total Utility Marginal Utility Marginal Utility per Dollar Quantity of Movies Total Utility Marginal Utility Marginal Utility per Dollar
1 22 22   22/$14=1.6 1 16 16 16/$7=2.3
2 43 21   21/$14=1.5 2 31 15 15/$7=2.14
3 63 20   20/$14=1.4 3 45 14 14/$7=2
4 81 18   18/$14=1.3 4 58 13 13/$7=1.9
5 97 16   16/$14=1.1 5 70 12 12/$7=1.7
6 111 14   14/$14=1 6 81 11 11/$7=1.6
7 123 12   12/$14=1.2 7 91 10 10/$7=1.4

José’s first purchase will be a movie. Why? Because it gives him the highest marginal utility per dollar and it is affordable. José will continue to purchase the good which gives him the highest marginal utility per dollar until he exhausts the budget. José will keep purchasing movies because they give him a greater “bang for the buck” until the sixth movie is equivalent to a T-shirt purchase. José can afford to purchase that T-shirt. So José will choose to purchase six movies and one T-shirt.

Self Check: Defining Utility

Answer the question(s) below to see how well you understand the topics covered in the previous section. This short quiz does not count toward your grade in the class, and you can retake it an unlimited number of times.

You’ll have more success on the Self Check if you’ve completed the three Readings in this section.

Use this quiz to check your understanding and decide whether to (1) study the previous section further or (2) move on to the next section.

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