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For José, the highest total utility for all possible combinations of goods occurs at point S, with a total utility of 103 from consuming one T-shirt and six movies.
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.
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 [link] . 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. [link] tracks the step-by-step series of decisions José needs to make ( Key : T-shirts are $14, movies are $7, and income is $56). The following Work It Out feature explains how marginal utility can effect decision making.
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 |
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 [link] , 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 [link] ) 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.
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