# Utility Maximization: Equalizing Marginal Utility per Dollar.

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Utility Maximization: Equalizing Marginal Utility per Dollar

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. 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 Now, use marginal analysis Sammy’s problem of finding his optimal consumption choice into a “how much” problem Sammy’s problem of finding his optimal consumption choice into a “how much” problem

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. 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 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

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 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? Is Sammy better off by spending an additional \$1 on either good, and if so, by how much is he better off?

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

Sammy’s Marginal Utility per Dollar

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. 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 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 In the consumption bundle, the marginal utilities per dollar spent for each and every good or service in that bundle are equal

Marginal Utility per Dollar If Sammy has, in fact, chosen his optimal consumption bundle, his marginal utility per dollar spent on clams and potatoes must be equal. 6 5 4 3 2 1 B C B P MU C /P C P /P P C 543210 0246810 Total utility (utils) Quantity of clams (pounds) Quantity of potatoes (pounds) At the optimal consumption bundle, the marginal utility per dollar spent on clams is equal to the marginal utility per dollar spent on potatoes.

Marginal Utility and the Law of Demand Price of fried claims rises. 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 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 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 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

Marginal Utility and the Law of Demand Why? Why? A utility-maximizing consumer chooses a consumption bundle for which the marginal utility per dollar spent on all goods is the same 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 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

Marginal Utility and the Law of Demand The opposite happens also, if the price of clams fell 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 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 Consumers can increase his or her utility by purchasing more clams and less of other goods when the price of clam falls

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 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 When a price of a good decreases, an individual will normally consume more of that good and less of other goods

Utility Maximization: Equalizing Marginal Utility per Dollar Notes

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

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 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

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

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

Sammy’s Marginal Utility per Dollar

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. 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 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 In the consumption bundle, the marginal utilities per dollar spent for each and every good or service in that bundle are equal

Marginal Utility per Dollar 6 5 4 3 2 1 B C B P MU C /P C P /P P C 543210 0246810 Total utility (utils) Quantity of clams (pounds) Quantity of potatoes (pounds)

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

Marginal Utility and the Law of Demand Why? 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 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

Marginal Utility and the Law of Demand The opposite happens also, if the price of clams fell 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 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 Consumers can increase his or her utility by purchasing more clams and less of other goods when the price of clam falls

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