Utility Maximization

Utility and Consumption Utility is a measure of personal satisfaction. A util is a unit of utility. A utility function shows the relationship between a consumer’s utility and the combination of goods and services—the consumption bundle—he or she consumes.

Utility and Consumption Panel (b) shows the marginal utility curve, which slopes downward due to diminishing marginal utility. It increases until it reaches its maximum utility level of 64 utils at 8 clams consumed and decreases after that. Panel (a) shows how Cassie’s total utility depends on her consumption of fried clams. That is, each additional clam gives Cassie less utility than the previous clam.

Principle of Diminishing Marginal Utility The marginal utility of a good or service is the change in total utility generated by consuming one additional unit of that good or service. According to the principle of diminishing marginal utility, successive units of a good or service add less total utility than do previous units.

Occasional Ups & Downs of Marginal Utility In rare cases, diminishing marginal utility doesn’t hold. For example, the first few times you go skiing, your utility may increase as you become more skilled and able to enjoy rather than fear the experience.

Occasional Ups & Downs of Marginal Utility For other goods, it is better to have none than to have not enough. For example, too little flooring would provide less utility than no flooring at all—because you would have to store a useless amount of the good. the principle of diminishing marginal utility applies in the majority of cases, so it will form the foundation of our analysis of consumer behavior.

Budget Constraints and Budget Lines A budget constraint limits the cost of a consumer’s consumption bundle to no more than the consumer’s income. A consumer’s consumption possibilities are the set of all affordable consumption bundles given the consumer’s income and prevailing prices. A consumer’s budget line (BL) shows the consumption bundles available to a consumer who spends all of his or her income.

Budget Constraints and Budget Lines The BL is also the boundary between the set of affordable consumption bundles (the consumption possibilities) and the unaffordable ones. The budget line (BL) shows all possible combinations of quantities of tomatoes and clams Sammy can buy if all income is spent.

The Optimal Consumption Bundle A consumer’s optimal consumption bundle is the consumption bundle that maximizes total utility given their budget constraint. Table 5.1 shows that Sammy derives utility from both clams and tomatoes. Due to the budget constraint, however, Sammy must choose some combination of both goods.

The Optimal Consumption Bundle Table 51.2 shows how Sammy’s total utility varies for the different consumption bundles along his budget line. Each of six possible consumption bundles (A through F from the previous figure) is given in the first column. Since total utility is highest at 72.0, C is Sammy’s optimal consumption bundle.

The Optimal Consumption Bundle Panel (a): the budget line and six possible consumption bundles. This is Sammy’s optimal consumption bundle. Sammy’s total utility is maximized at bundle C, where he consumes 2 pounds of clams and 6 pounds of tomatoes. Panel (b): how total utility is affected by each consumption bundle, which must lie on his budget line. As more clams are consumed, due to his fixed budget, Sammy must consume fewer tomatoes.

Spending the Marginal Dollar The marginal utility per dollar spent on a good or service is the additional utility from spending one more dollar on that good or service.

Marginal Utility per Dollar In panel (a), the first column shows different possible amounts of clam consumption. Panel (b) provides the same information for tomatoes. The next step is to derive marginal utility per dollar for each good.

Marginal Utility per Dollar To determine whether a consumer should buy more of one good or another, compare the marginal utility per dollar received from each good, not just the marginal utility received from each good.

Optimal Consumption Sammy’s optimal consumption bundle is C, where his marginal utility per dollar spent on clams, (MUC)/(PC) equals his marginal utility per dollar spent on tomatoes, (MUT)/(PT).

The Optimal Consumption Rule The optimal consumption rule says that in order to maximize utility, a consumer must equate the marginal utility per dollar spent on each good and service in the consumption bundle.

Summary and Review 1) What measures consumer satisfaction? Utility. 2) With what units is utility measured? U.tils 3) What is the change in total utility caused by consuming one more unit of a good? Marginal utility.

Summary and Review 4) What curve represents the relationship between marginal utility and the quantity of a good or service consumed? Marginal utility curve. 5) What is the principle of diminishing marginal utility? The principle states that in most cases, each successive unit of a good or service consumed generates less utility than the previous unit.

Summary and Review 6) What limits the cost of a consumer’s consumption bundle to no more than the consumer’s income? The budget constraint. 7) What is consumption bundle that maximizes total utility called? The optimal consumption bundle.

Summary and Review 8) What is marginal utility per dollar? The marginal utility of a good divided by its price. 9) What is the optimal consumption rule? The rule states that the optimal consumption bundle occurs at the quantities of each good where their marginal utility per dollar is the same.

Walkthrough: Free-Response Question 1 1. Refer to the table provided. Assume you have $20 to spend. a. Draw a correctly labeled budget line. b. Determine the marginal utility and the marginal utility per dollar spent on the fourth drink. c. What is the optimal consumption rule? d. How many drinks and snacks should you purchase to maximize your total utility? (6 points) 1 point: Graph with “Quantity of snacks” and “Quantity of drinks” as axis labels 1 point MU / P = 3.5 utils per dollar 1 point: Total utility is maximized when the marginal utility per dollar is equal for all goods. 1 point: Straight budget line with intercepts at 5 snacks and 0 drinks and 0 snacks and 10 drinks 1 point: 6 drinks, 2 snacks 1 point: MU = 7 utils