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# Utility Maximization: Equalizing Marginal Utility per Dollar

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1. Utility Maximization: Equalizing Marginal Utility per Dollar

2. Spending the Marginal Dollar • Sammy’s optimal consumption choice is found by finding his total utility he receives from each consumption bundle on his budget line and then choosing the bundle at which total utility is maximized. • Now, use marginal analysis • Sammy’s problem of finding his optimal consumption choice into a “how much” problem

3. Spending the Marginal Dollar • The way to do this is by choosing an optimal consumption bundle as a problem of how much to spend on each good. • To find the optimal consumption bundle, we have to see whether Sammy will make himself better off by spending a little bit more of his income on clams and less on potatoes, or the opposite, more on potatoes and less on clams

4. Spending the Marginal Dollar • Marginal decisions is a question of how to spend the marginal dollar—how to allocate an additional dollar between clams and potatoes in a way that maximizes utility • Is Sammy better off by spending an additional \$1 on either good, and if so, by how much is he better off?

5. Marginal Utility per Dollar • To answer the question on Sammy, need to calculate the marginal utility dollar spend on either clams or potatoes • How much additional utility Sammy gets from spending an additional dollar on either good

6. Sammy’s Marginal Utility per Dollar

7. Optimal Consumption • Optimal consumption rule says that when a consumer maximizes utility, the marginal utility per dollar spent must be the same for all goods and services in the consumption bundle. • General rule applied to all goods and services • In the consumption bundle, the marginal utilities per dollar spent for each and every good or service in that bundle are equal

8. Marginal Utility per Dollar B C B MU / P P C C Total utility (utils) If Sammy has, in fact, chosen his optimal consumption bundle, his marginal utility per dollar spent on clams and potatoes must be equal. At the optimal consumption bundle, the marginal utility per dollar spent on clams is equal to the marginal utility per dollar spent on potatoes. MU / P P P 6 5 4 3 C 2 1 0 1 2 3 4 5 Quantity of clams (pounds) 10 8 6 4 2 0 Quantity of potatoes (pounds)

9. Marginal Utility and the Law of Demand • Price of fried claims rises. • Doesn’t change the marginal utility a consumer gets from an additional pound of clams at any given level of clam consumption • But….it reduces the marginal utility per dollar spent on fried clams • The decrease in marginal utility per dollar spent on clams gives the consumer an incentive to consume fewer clams when the price of clams rises

10. Marginal Utility and the Law of Demand • Why? • A utility-maximizing consumer chooses a consumption bundle for which the marginal utility per dollar spent on all goods is the same • If the MU per dollar spent on clams falls because the price of clams rises, the consumer can increase his or her utility by purchasing fewer clams and more of other goods

11. Marginal Utility and the Law of Demand • The opposite happens also, if the price of clams fell • If that happens, marginal utility per dollar spend on clams, increases at any given level of clam consumption • Consumers can increase his or her utility by purchasing more clams and less of other goods when the price of clam falls

12. Marginal Utility and the Law of Demand • When the price of a good increases, an individual will normally consume less of that good and more of other goods • When a price of a good decreases, an individual will normally consume more of that good and less of other goods

13. Spending the Marginal Dollar • Sammy’s optimal consumption choice is found by • Now, we will use marginal analysis

14. Spending the Marginal Dollar • To find the optimal consumption bundle, we have to see whether Sammy will make himself better off by spending a little bit more of his income on clams and less on potatoes, or the opposite, more on potatoes and less on clams

15. Spending the Marginal Dollar • Marginal decisions is a question of how to spend the marginal • Is Sammy better off by spending an additional \$1 on either good, and if so, by how much is he better off?

16. Marginal Utility per Dollar • To answer the question on Sammy, need to calculate the marginal utility dollar spend on either clams or potatoes

17. Sammy’s Marginal Utility per Dollar

18. Optimal Consumption • Optimal consumption rule says that when a consumer maximizes utility, the marginal utility per dollar spent must be the same for all goods and services in the consumption bundle. • General rule applied to all goods and services • In the consumption bundle, the marginal utilities per dollar spent for each and every good or service in that bundle are equal

19. Marginal Utility per Dollar B C B MU / P P C C Total utility (utils) MU / P P P 6 5 4 3 C 2 1 0 1 2 3 4 5 Quantity of clams (pounds) 10 8 6 4 2 0 Quantity of potatoes (pounds)

20. Marginal Utility and the Law of Demand • Price of fried claims rises. • Doesn’t change the marginal utility a consumer gets from an additional pound of clams at any given level of clam consumption • But…. • The decrease in marginal utility per dollar spent on clams

21. Marginal Utility and the Law of Demand • Why? • If the MU per dollar spent on clams falls because the price of clams rises, the consumer can increase his or her utility by purchasing fewer clams and more of other goods

22. Marginal Utility and the Law of Demand • The opposite happens also, if the price of clams fell • If that happens, marginal utility per dollar spend on clams, increases at any given level of clam consumption • Consumers can increase his or her utility by purchasing more clams and less of other goods when the price of clam falls

23. Marginal Utility and the Law of Demand • When the price of a good increases, • When a price of a good decreases,