Consumer Behavior and Utility Maximization HOW CONSUMERS MAKE

Consumer Behavior and Utility Maximization HOW CONSUMERS MAKE CHOICES UNDER INCOME CONSTRAINTS UTILITY MAXIMIZATION

Introduction The CONSUMER is essential to the arket. Understanding how the consumer makes his/her purchasing decisions is key.

Utility The value a consumer places on a unit of a good or service depends on the pleasure or satisfaction he or she expects to derive form having or consuming it at the point of making a consumption (consumer) choice. In economics the satisfaction or pleasure consumers derive from the consumption of consumer goods is called “utility”. Within the limits of Consumer’s incomes, consumers make their consumption choices by evaluating and comparing consumer goods with regard to their “utilities. ”

1. Understanding Utility = Satisfaction/Happiness/Pleasure one gets from consuming a good. Utility and usefulness are NOT synonymous in economics. Utility is difficult to quantify, as it differs between people and situations ie. A blanket to a person living in Arizona vs. a person living in Minnesota. Measured in “utils” (a personal measure)

1. Understanding Utility Total Utility (TU) Total amount of satisfaction or pleasure a person derives from consuming a given quantity of that product Marginal Utility (MU) The extra satisfaction a consumer derives from one additional unit of that product. In other words, the change in Total Utility that results from the consumption of one more unit Total utility = Sum of marginal utilities

Total and Marginal Utility for Ice Cream

Diminishing of Marginal Utility Explains that the more of a good a person gets, the less utility he gets from each additional unit. Consumer wants in general are insatiable, but wants for particular items can be satisfied for a time. Example: Durable goods such as an automobile

Law of Diminishing Marginal Utility law of diminishing marginal utility - marginal utility declines as more of a particular good is consumed in a given time period, ceteris paribus even though marginal utility declines, total utility still increases as long as marginal utility is positive. Total utility will decline only if marginal utility is negative

Law of Diminishing Marginal Utility (1) (2) (3) Tacos Total Marginal Consumed Utility, Per Meal Utils 1 2 3 4 5 6 7 0 ] 18 ] 24 ] 28 ] 30 ] 28 10 8 4 2 0 -2 30 TU 20 10 0 6 Marginal Utility (Utils) 0 Total Utility (Utils) Total Utility 1 2 3 4 5 6 Units Consumed Per Meal 7 Marginal Utility 10 8 6 4 2 0 -2 MU 1 2 3 4 5 6 Units Consumed Per Meal 7

Marginal utility # of slices of pizza total utility marginal utility 0 0 - 1 70 70 2 110 40 3 130 20 4 140 10 5 145 5 6 140 5 -

Utility Maximizing Rules

How much ice cream does Jill buy in a month? Buying ice cream leaves Jill less money to buy other things: each dollar spent on ice cream could be spent on hamburger for ex. In fact, consumers compare the (expected) utility derived from one additional dollar spent on one good to the utility derived from one additional dollar spent on another good. Jill, like any other rational consumer, wishes to maximize her utility. The opportunity cost of one dollar spent on ice cream is the forgone utility of one dollar that could be on hamburger.

Utility Maximizing Rules A rational consumer would buy an additional unit of a good as long as the perceived dollar value of the utility of one additional unit of that good (say, its marginal dollar utility) is greater than its market price. The Two-Good Rule MUI MUH ----- = -----$PI $PH

Optimal Purchase Mix: Ice Cream and Hamburger

Utility Maximization under An Income constraint Consumers’ spending on consumer goods is constrained by their incomes: Income = Px Qx + Py Qy + Pw Ow + …. +Pz Qz While the consumer tries to equalize MUx/Px , MUy/ Py, MUw/Pw, ………. and MUz/Pz , to maximize her utility her total spending cannot exceed her income. For example, with an and income of $86 Jill is trying to decide how much ice cream and how much hamburger she should buy. Jill’s income = 5 x 10 + 6 x 6 = 86

The Budget Line Income = QI. PI + QH. PH = (5 x 10)+(6 x 6) = 86 Ice Cream 86/10 Slope = PH/PI = 6/10 = 8. 6/14. 33 = 0. 6 8. 6 5 86/6 Hamburger o 6 14. 33

Consumer equilibrium 1. 2. All income is spent. The first condition listed above is sometimes referred to as the "equimarginal principle. "

Theory of Consumer Behavior Numerical Example: Find the Utility-Maximizing Combination of A and B, if you have an Income of $10 (1) Unit of Product (2) Product A: Price = $1 (b) Marginal (a) Utility Marginal Per Dollar Utility, (MU/Price) Utils (3) Product B: Price = $2 (b) Marginal (a) Utility Marginal Per Dollar Utility, (MU/Price) Utils First Second Third Fourth 10 8 7 6 24 20 18 16 12 10 9 8 Fifth Sixth Seventh 5 4 3 12 6 4 6 3 2

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

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

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

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

Theory of Consumer Behavior Numerical Example: Utility-Maximizing Combination of Products A and B Obtainable with an Income of $10 (1) Unit of Product First Second Third Fourth (2) Product A: Price = $1 (b) Marginal (a) Utility Marginal Per Dollar Utility, (MU/Price) Utils 10 8 7 6 (3) Product B: Price = $2 (b) Marginal (a) Utility Marginal Per Dollar Utility, (MU/Price) Utils 24 20 18 16 12 10 9 8 Fifth 5 12 Final Result – At 5 These Prices, 6 Sixth 4 4 6 3 Purchase 3 of Item A and 44 of B 2 2 Seventh 3

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

From ‘Utils’ to ‘Benefit’ Because Utils cannot be compared between people, and cannot be compared to dollars… economists must measure satisfaction in Benefit is the same concept as utility, but it is measured in dollars (according to the consumer’s WILLINGNESS TO PAY. Total Benefit ($), Marginal Benefit ($)

Golden Rule of Consumption A rational consumer will continue to purchase until… MB = MC To consume one more would mean your marginal cost is greater than your marginal benefit

ASSIGMENT Two-Good Practice Problem Given MU, and an income/budget constraint of $20… find the Utility-Maximizing Combination of A and B (3) Product B: Price = $5 (2) Product A: Price = $2 Unit MU Mu/p 1 20 10 1 30 6 2 10 5 2 20 4 3 6 3 3 15 3 4 3 1. 5 4 5 1 0. 5 5 -5 1 -

Two-Good Practice Problem Given TU, and an income/budget constraint of $9… find the Utility- Maximizing Combination of A and B (3) Product B: Price = $1 (2) Product A: Price = $2 Unit TU MU 1 22 - 2 32 10 3 40 4 5 MU/P Unit TU MU MU/P 1 10 - 5 2 16 6 3 8 4 3 20 4 2 46 6 3 4 22 2 1 48 8 4 5 20 -2 -1

The Problem with Utils Answer the following problem: If Henry derives 5 utils from the 1 st candy bar, 3 utils from the 2 nd candy bar, 0 utils from the 3 rd candy bar, and -5 utils from the 4 th candy bar… How many candy bars should Henry consume if each candy bar … Is absolutely free (MC = 0) Costs $2 Costs $4

Review Questions – Utility What is the marginal utility of the third cup of peanuts Brian consumes? A. 3 units of utility B. 9 units of utility C. 12 units of utility D. 2 units of utility E. 14 units of utility

Review Questions – Utility If the price of peanuts is $1 per cup and the price of jelly beans is $2 per cup, and Brian wants to maximize his utility, what should he purchase first? A. 1 cup of peanuts because peanuts produce a lower total utility B. 1 cup of peanuts because the price of peanuts is lower C. 1 cup of peanuts, because the marginal utility per dollar for peanuts is lower than the marginal utility per dollar of jelly beans D. 1 cup of jelly beans, because the marginal utility per dollar for jelly beans is higher than the marginal utility per dollar of peanuts E. 1 cup of jelly beans, because jelly beans produce a higher total utility

Review Questions – Utility If TU = total utility, MU = marginal utility, and P = price, in order to maximize utility, a consumer should purchase the mix of hamburgers and hot dogs where A. the MU of hamburgers equals the MU of hot dogs B. the MU equals the TU of hamburgers, and the MU equals the TU of hot dogs C. the TU of hamburgers equals the TU of hot dogs D. the MU / P of hamburgers equals the MU / P of hot dogs E. the TU / P of hamburgers equals the TU / P of hot dogs

Review Questions – Utility Every day Molly spends her lunch money consuming apples, at $1 each, and oranges, at $2 each. At her current level of consumption, molly’s marginal utility of apples is 12 and her marginal utility of oranges is 18. If she has already spent all of her lunch money, how should Molly change her consumption decision to maximize utility? A. She should make no changes; she is consuming the utility maximizing combination of apples and oranges. B. She should increase her apple consumption and decrease her orange consumption until the marginal utility per dollar is equal for both. C. She should decrease her apple consumption and increase her orange consumption until the marginal utility per dollar is equal for both. D. She should increase her apple consumption and decrease her orange consumption until the marginal utility is equal for both. E. She should decrease her apple consumption and increase her orange consumption until the marginal utility is equal for both.

Review Questions – Utility If generic peanut butter is an inferior good, a decline in consumer income causes A. the price of generic peanut butter to go down. B. the demand for name-brand peanut butter to go up. C. the supply of generic peanut butter to go up. D. the demand for generic peanut butter to go up. E. the price of bread to go down.