# In this chapter, look for the answers to these questions:

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Unit IV Utility (Chapter 10)

In this chapter, look for the answers to these questions:
How does the budget constraint represent the choices a consumer can afford? What determines how a consumer divides her resources between two goods? Why the principle of diminishing marginal utility applies to the consumption of most goods and services How to use marginal analysis to find the optimal consumption bundle What income and substitution effects are

Introduction Key concept: People face tradeoffs
Buying more of one good leaves less income to buy other goods. Working more hours means more income and more consumption, but less leisure time. Reducing saving allows more consumption today but reduces future consumption. This chapter explores how consumers make choices like these.

Utility UTILITY -- Benefit or satisfaction person receives from consumption of g/s 19th Century, Economists created universal psychological unit called a Util (representative unit by which utility measured)

Temperature vs. Utility
Temperature -- abstract concept, units of temperature (placed arbitrarily) concept of utility helps us make predictions about consumption choices in much the same way that the concept of temperature helps us make predictions about physical phenomena

Total and Marginal Utility
Total Utility Total utility is the total benefit that a person gets from the consumption of a good or service. Total utility generally increases as the quantity consumed of a good increases. Marginal Utility Marginal utility is the change in total utility that results from a one-unit increase in the quantity of a good consumed.

Diminishing Marginal Utility
We call the general tendency for marginal utility to decrease as the quantity of a good consumed increases the principle of diminishing marginal utility. Think about your own marginal utility from the things that you consume.

Law of Diminishing Marginal Utility
Total Utility 10 20 30 8 6 4 2 -2 1 3 5 7 Total Utility (Utils) Marginal Utility (Utils) (1) Tacos Consumed Per Meal (2) Total Utility, Utils (3) Marginal Utility, Utils TU 1 2 3 4 5 6 7 10 18 24 28 30 ] 10 8 6 4 2 -2 Units Consumed Per Meal Marginal Utility MU Units Consumed Per Meal

Is Marginal Utility Really Diminishing?
Are all goods really subject to diminishing marginal utility? Of course not; there are a number of goods for which, at least over some range, marginal utility is surely increasing. Examples are: Downhill skiing, which involves more fear than enjoyment at the start, but then becomes pleasurable after its mastered. People who are not accustomed to drinking coffee find it bitter. If you need two rolls of wallpaper to finish a room, the marginal utility of the second roll is larger than that of the first roll. So why does it make sense to assume diminishing marginal utility? Most goods don’t suffer from the above qualifications. In the relevant range of consumption, marginal utility is still diminishing.

The Budget Constraint: What the Consumer Can Afford
Two goods: pizza and Pepsi A “consumption bundle” is a particular combination of the goods, e.g., 40 pizzas & 300 pints of Pepsi. Budget constraint: the limit on the consumption bundles that a consumer can afford Graphically represented as the budget line

A C T I V E L E A R N I N G 1: Budget constraint
The consumer’s income: \$ Prices: \$10 per pizza, \$2 per pint of Pepsi A. If the consumer spends all his income on pizza, how many pizzas does he buy? B. If the consumer spends all his income on Pepsi, how many pints of Pepsi does he buy? C. If the consumer spends \$400 on pizza, how many pizzas and Pepsis does he buy? D. Plot each of the bundles from parts A-C on a diagram that measures the quantity of pizza on the horizontal axis and quantity of Pepsi on the vertical axis, then connect the dots.

A C T I V E L E A R N I N G 1: Answers
D. The consumer’s budget constraint shows the bundles that the consumer can afford. (budget line) Pepsis A. \$1000/\$10 = 100 pizzas B. \$1000/\$2 = 500 Pepsis C. \$400/\$10 = 40 pizzas \$600/\$2 = 300 Pepsis B C A Pizzas

The Slope of the Budget Line
Pepsis From C to D, “rise” = –100 Pepsis “run” = +20 pizzas Slope = –5 Consumer must give up 5 Pepsis to get another pizza. C D Pizzas

The Slope of the Budget Constraint
The slope of the budget constraint (budget line) equals the rate at which the consumer can trade Pepsi for pizza the opportunity cost of pizza in terms of Pepsi the relative price of pizza:

A C T I V E L E A R N I N G 2: Exercise
Pepsis Show what happens to the budget constraint (budget line) if: A. Income falls to \$800 B. The price of Pepsi rises to \$4/pint. Pizzas

A C T I V E L E A R N I N G 2A: Answers
Pepsis A fall in income shifts the budget constraint inward. Consumer can buy \$800/\$10 = 80 pizzas or \$800/\$2 = 400 Pepsis or any combination in between. Pizzas

A C T I V E L E A R N I N G 2B: Answers
An increase in the price of one good pivots the budget constraint inward. Pepsis Consumer can still buy 100 pizzas. But now, can only buy \$1000/\$4 = 250 Pepsis. Notice: slope is smaller, relative price of pizza now only 4 Pepsis. Pizzas

The Income and Substitution Effects
A fall in the price of Pepsi has two effects on the optimal consumption of both goods. Income effect A fall in the price of Pepsi boosts the purchasing power of the consumer’s income, allowing him to reach a higher budget line. Substitution effect A fall in the price of Pepsi makes pizza more expensive relative to Pepsi, causes consumer to buy less pizza & more Pepsi.

The Budget Line Quantity of potatoes (pounds) A B C D E F Consumption bundle 1 2 3 4 5 Quantity of clams (pounds) 10 8 6 Quantity of potatoes Unaffordable consumption bundles 10 A 8 B 6 C Affordable consumption bundles that cost all of Sammy's income 4 Affordable consumption bundles D 2 E F Sammy’s Budget Line, BL 1 2 3 4 5 Quantity of clams (pounds) The budget line represents all the possible combinations of quantities of potatoes and clams that Sammy can purchase if he spends all of his income. It is also the boundary between the set of affordable consumption bundles (the consumption possibilities) and unaffordable ones.

Sammy’s Utility from Clam and Potato Consumption
20

Optimal Consumption Choice
The optimal consumption bundle is the consumption bundle that maximizes a consumer’s total utility given his or her budget constraint. 21

Sammy’s Budget and Total Utility
Sammy’s total utility is the sum of the utility he gets from clams and the utility he gets from potatoes. 22

Optimal Consumption Bundle
Sammy’s Budget Line Quantity of potatoes (pounds) The optimal consumption bundle… A 10 B 8 C 6 D 4 E 2 F BL 1 2 3 4 5 Quantity of clams (pounds) (b) Sammy’s Utility Function Sammy’s total utility is maximized at bundle C, where he consumes 2 pounds of clams and 6 pounds of potatoes. This is Sammy’s optimal consumption bundle. Total utility (utils) 80 B C 70 D A 60 E 50 Utility function 40 … maximizes total utility given the budget constraint 30 F 20 10 1 2 3 4 5 Quantity of clams (pounds) 10 8 6 4 2 Quantity of potatoes (pounds)

Food for Thought on Budget Constraints
Budget constraints aren’t just about money. In fact, there are many other budget constraints affecting our lives. Examples are: Limited amount of closet space for clothes. A fixed number of hours in a day. A dieter on the Weight Watchers plan is only allowed a maximum number of points regarding the food they can eat each day whereby each food is assigned a certain number of points. The dieter is just like a consumer choosing a consumption bundle: points are the equivalent of prices, and the overall point limit is the equivalent of total income.

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. 25

Sammy’s Marginal Utility per Dollar
Sammy’s income is \$20. 26

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

Optimal Consumption Rule
The 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. 28

Theory of Consumer Behavior
REMEMBER: The optimal consumption bundle is the consumption bundle that maximizes a consumer’s total utility given his or her budget constraint. Explains how consumers allocate their money incomes among the many goods and services available for purchase

Theory of Consumer Behavior
Numerical Example: Utility-Maximizing Combination of Products A and B Obtainable with an Income of \$10 (2) Product A: Price = \$1 (3) Product B: Price = \$2 (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (1) Unit of Product First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 24 20 18 16 12 10 8 7 6 5 4 3 12 9 2 Compare Marginal Utilities Then Compare Per Dollar - MU/Price Choose the Highest Check Budget - Proceed to Next Item

Theory of Consumer Behavior
Numerical Example: Utility-Maximizing Combination of Products A and B Obtainable with an Income of \$10 (2) Product A: Price = \$1 (3) Product B: Price = \$2 (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (1) Unit of Product First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 24 20 18 16 12 10 8 7 6 5 4 3 12 9 2 Again, Compare Per Dollar - MU/Price Choose the Highest Buy One of Each – Budget Has \$5 Left Proceed to Next Item

Theory of Consumer Behavior
Numerical Example: Utility-Maximizing Combination of Products A and B Obtainable with an Income of \$10 (2) Product A: Price = \$1 (3) Product B: Price = \$2 (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (1) Unit of Product First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 24 20 18 16 12 10 8 7 6 5 4 3 12 9 2 Again, Compare Per Dollar - MU/Price Buy One More B – Budget Has \$3 Left Proceed to Next Item

Theory of Consumer Behavior
Numerical Example: Utility-Maximizing Combination of Products A and B Obtainable with an Income of \$10 (2) Product A: Price = \$1 (3) Product B: Price = \$2 (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (1) Unit of Product First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 24 20 18 16 12 10 8 7 6 5 4 3 12 9 2 Again, Compare Per Dollar - MU/Price Buy One of Each – Budget Exhausted

Theory of Consumer Behavior
Numerical Example: Utility-Maximizing Combination of Products A and B Obtainable with an Income of \$10 (2) Product A: Price = \$1 (3) Product B: Price = \$2 (b) Marginal Utility Per Dollar (MU/Price) (a) Marginal Utility, Utils (1) Unit of Product First Second Third Fourth Fifth Sixth Seventh 10 8 7 6 5 4 3 24 20 18 16 12 10 8 7 6 5 4 3 12 9 2 Final Result – At These Prices, Purchase 2 of Item A and 4 of B

Theory of Consumer Behavior
Algebraic Restatement: MU of Product A Price of A MU of Product B Price of B = 8 Utils \$1 16 Utils \$2 = Optimum Achieved - Money Income is Allocated so that the Last Dollar Spent on Each Product Yields the Same Extra or Marginal Utility

CHAPTER SUMMARY Consumers maximize a measure of satisfaction called utility. Each consumer has a utility function that determines the level of total utility generated by his or her consumption bundle, the goods and services that are consumed. A good’s or service’s marginal utility is the additional utility generated by consuming one more unit of the good or service. We usually assume that the principle of diminishing marginal utility holds: consumption of another unit of a good or service yields less additional utility than the previous unit. A budget constraint limits a consumer’s spending to no more than his or her income. It defines the consumer’s consumption possibilities, the set of all affordable consumption bundles. A consumer who spends all of his or her income will choose a consumption bundle on the budget line. An individual chooses the consumption bundle that maximizes total utility, the optimal consumption bundle. The optimal consumption rule says that at the optimal consumption bundle the marginal utility per dollar spent on each good and service—the marginal utility of a good divided by its price—is the same.