## Implications of Utility Maximization

The marginal-utility-ratio-equals-price-ratio result has another implication for the economy as a whole that can initially be surprising. Even if two consumers have very different preferences between two goods, they will have the same ratio of marginal utilities for the two goods, because utility maximization implies that MRS equals the ratio of the prices.11

11 Technically, this is true only of consumers who are consuming a positive amount of both goods, or who are at “interior” solutions in economists’ lingo. We’ll discuss this issue in the next section.

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This might seem odd. First of all, we have said that you can’t compare utility levels across people. Second, even if you could—if, say, Jack consumes 9 packs of gum and 1 iTunes download, while Meg consumes 9 downloads and only 1 pack of gum—it would seem that Jack likes gum a lot and would therefore be willing to pay more for another pack of gum (and a lot less for iTunes) than Meg.

This assertion would be true if both Jack and Meg had to consume the same bundle, but they don’t have to. They can choose how much of each good they want to consume. Because Jack likes gum a lot, he will consume so much of it that he drives down his marginal utility until, by the time he and Meg both reach their utility-maximizing consumption bundles, they will both end up placing the same relative marginal utilities on the two goods. This outcome occurs because the relative value they place on any two goods (on the margin) comes from the relative prices. Because Meg and Jack face the same prices, the goods they consume will end up with the same relative marginal utilities.

Figure 4.19 shows this outcome. To keep the picture simple, we assume Jack and Meg have the same incomes. Because they also face the same relative prices, their budget constraints are the same. Jack really likes gum relative to iTunes downloads, so his indifference curves tend to be flat: He has to be given a lot of iTunes to make up for any loss of gum. Meg has the opposite tastes. She has to be given a lot of gum to make up for giving up an iTunes download, so her indifference curves are steep. Nevertheless, both Jack and Meg’s utility-maximizing bundles are on the same budget line, and they will pick consumption points where their marginal rates of substitution at those bundles are the same (and match the relative prices). We’ve drawn the indifference curves for Jack (UJ) and Meg (UM) so that they are tangent to the budget line and therefore contain the utility-maximizing bundle.

Figure 4.19: Figure 4.19 Two Consumers’ Optimal Choices
Figure 4.19: Although they have the same budget constraint, Jack and Meg have different relative preferences and, therefore, different optimal consumption bundles. Because Jack likes gum relative to iTunes downloads, his indifference curve (UJ) is flat and he consumes much more gum than iTunes at his optimal consumption bundle at point J. Meg’s indifference curve (UM) is much steeper and reflects her relative preference for iTunes downloads over gum; her utility-maximizing bundle is shown at point M. Although their consumption bundles are different, the MRS is the same at these points.

Even though Jack and Meg have the same MRSXY, the amounts of each good they consume are different. Jack, the gum lover, maximizes his utility by choosing a bundle (J) with a lot of gum and not many iTunes downloads. Meg’s optimal consumption bundle (M), on the other hand, has a lot of iTunes downloads and little gum. Again, both consumers end up with the same MRS in their utility-maximizing bundles because each consumes a large amount of the good for which he or she has the stronger preference. By behaving in this way, Jack and Meg drive down the relative marginal utility of the good they prefer until their marginal utility ratio equals the price ratio.

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Note that these two indifference curves cross. Although earlier we learned that indifference curves can never cross, the “no crossing” rule applies only to the indifference curves of one individual. Figure 4.19 shows indifference curves for two different people with different preferences, so the transitivity rule we talked about before doesn’t hold. If you like gum more than iTunes, and your friend likes iTunes more than, say, coffee, that doesn’t imply you have to like gum more than coffee. So the same consumption bundle (say, 3 packs of gum and 5 iTunes downloads) can offer different utility levels to different people.