Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Utility The pleasure people get from their economic activity. To identify all of the factors that affect utility would be virtually impossible Don’t forget the ceteris paribus assumption.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Utility from Consuming Two Goods A person receives utility from the consumption of two goods “X” and “Y” which we show in functional notation by The other things that appear after the semicolon are assumed to be held constant.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Measuring Utility –Because the real-world is constantly in flux, ceteris paribus is difficult to impose. –There is no unit of utility measurement. –However, it is possible to do a fairly complete job of studying choices without having to measure utility.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Assumptions about Utility Basic Properties of Preferences –Preferences are complete : The assumption that an individual is able to state which of any two options is preferred. –Preferences are transitive: The property that if A is preferred to B, and B is preferred to C, then A must be preferred to C.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Quantity of Y per week Y* Quantity of X per week ? ? X*0 FIGURE 2.1: More of a Good Is Preferred to Less

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Indifference Curves A curve that shows all the combinations of goods or services that provide the same level of utility.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Hamburgers per week 6 A B C E F D U1U Soft drinks per wek FIGURE 2.2: Indifference Curve

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Movements Along an Indifference Curve –Why the negative slope? –Why the changing slope? –Willingness to trade.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Indifference Curves and the Marginal Rate of Substitution Marginal Rate of Substitution (MRS): The rate at which an individual is willing to reduce consumption of one good when he or she gets one more unit of another good. –Also, the negative of the slope of an indifference curve. –The MRS between points A and B on U 1 in Figure 2.2 is (approximately) 2.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Diminishing Marginal Rate of Substitution In Figure 2.3 the person is willing to give up one hamburger to gain one more soft drink between points B and C. Between points C and D, the consumer is only willing to give up ½ a hamburger to gain one more soft drink.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Hamburgers per week 6 A B C G D U1U Soft drinks per week FIGURE 2.3: Balance in Consumption Is Desirable

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Diminishing Marginal Rate of Substitution The MRS diminishes along an indifference curve moving from left to right. This reflects the idea that consumers prefer a balance in consumption.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Hamburgers per week 6 A B C G D U1U Soft drinks per week FIGURE 2.4: Indifference Curve Map for Hamburgers and Soft Drinks 5 5 U2U2 U3U3 H

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Application 2.2:Product Positioning in Marketing One practical application of utility theory in marketing is the positioning of products in comparison with competitors. Assume consumers have preferences for taste and crunchiness in breakfast cereal as represented by U 1 in Figure 1.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Application 2.2:Product Positioning in Marketing One practical application of utility theory in marketing is the positioning of products in comparison with competitors If X and Y represent competitors positioning, a cereal at point Z would increase utility to consumers. If competitors have similar costs, this should offer good market prospects for the new cereal.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Taste Z U1U1 Y X Crunchiness FIGURE 1: Product Positioning

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. (a) A useless good Smoke grinders per week U 1 U 2 U 3 Food per week010 (b) An economic bad Houseflies per week U 1 U 2 U 3 Food per week010 (c) Perfect substitute Gallons of Exxon per week U 1 U 2 U 3 Gallons of Mobil per week 0 (d) Perfect complements Right shoes per week U 4 U 3 U 1 U 2 Left shoes per week FIGURE 2.5: Illustrations of Specific Preferences

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Particular Preferences In Figure 2.5(c) the two goods are perfect substitutes in that the consumer views them as essentially the same. –In this example the MRS = 1. In Figure 2.5(d) the two goods are perfect complements in that they must be used together (like left and right shoes) to gain utility.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Choices are Constrained People are constrained in their choices by the size of their incomes. Of the choices the individual can afford, the person will choose the one that yields the most utility. This implies that people will…

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. First: Spend Their Entire Income Since both goods (and only these goods) provide more utility the consumer will spend his or her entire income on the goods. The only other alternative is to throw the income away which does not increase utility.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Second: Equate MRS with the Ratio of Prices Suppose the individual is currently consuming where MRS = 1. Assume the price of hamburgers is $1 and the price of soft drinks is $.50. This yields a price ratio (P H /P S ) of ($.50/$1) = ½.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Equality of MRS with the Ratio or Prices The person could give up one hamburger (freeing $1) and purchase one soft drink using $.50. –Since his or her MRS =1, the person would be just as happy as before but would now have an additional $.50 to spend which would enable him or her to increase utility. The only way utility can not be increased further is when MRS = price ratio.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Graphic Analysis of Utility Maximization An individual’s budget constraint is the limit on goods and services a person can buy.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Budget Constraint from Figure 2.6 If all income is spent on X, X max can be purchased. If all income is spent on Y, Y max can be purchased. The line joining X max and Y max represents the various mixed bundles of good X and Y that can be purchased using all income.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Quantity of Y per week Y max Not affordable Income Affordable Quantity of X per week 0 X max FIGURE 2.6: Individual’s Budget Constraint for Two Goods

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Budget Constraint Why does it slope down? What is the slope and what does it mean? What do the intercepts mean?

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Algebraic Budget Constraint Since all income must be spent on either X or Y we have –Amount spent on X + Amount spent on Y = I or

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Algebraic Budget Constraint Solving equation 2.3 for Y Recall slope and intercepts

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Hamburgers per week Y* B A C D Income U2U2 Soft drinks per week 0 X* FIGURE 2.7: Graphic of the Utility Maximization U3U3 U1U1

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Utility Maximization At point C all income is spent. At point C indifference curve U 2 is tangent to the budget line so that the or

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Numerical Example of Utility Maximization Assume the individual can choose between hamburgers (Y) and soft drinks (X) whose prices are P Y = $1.00 and P X =$.50. The individual has $10.00 to spend (I). The individual gets measurable utility from X and Y as follows

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. TABLE 2.1: Alternative Combinations of Hamburgers (Y) and Soft Drinks (X) That Can Be Bought with $10.00 (When P X =$1.00, P Y =$.50)

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Using the Model of Choice The utility maximization model can be used to explain many common observations. –People with the same income prices still consume different bundles of goods.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. (a) Hungry Joe Hamburgers per week 8 04 (b) Thirsty Teresa Income 2 16 (c) Extra-thirsty Ed U0U0 U1U1 U2U2 Soft drinks per week 20 FIGURE 2.9: Differences in Preferences Result in Differing Choices Soft drinks per week Soft drinks per week Hamburgers per week Hamburgers per week U0U0 U0U0 U1U1 U1U1 U2U2 U2U2 Income

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. Using the Model of Choice –Panel (a) shows people will not buy useless goods –Panel (b) shows they will not buy bads. –Panel (c) shows that people will buy the least expensive of two perfect substitutes –Panel (d) shows that perfect complements will be purchased together.

Copyright (c) 2000 by Harcourt, Inc. All rights reserved. (a) A useless good Smoke grinders per week U 1 E E E E U 2 U 3 Food per week Income 010 (b) An economic bad Houseflies per week U 1 U 2 U 3 Food per week 010 (c) Perfect substitute Gallons of Exxon per week U 1 U 2 U 3 Gallons of Mobil per week 0 (d) Perfect complements Right shoes per week U 3 U 1 U 2 Left shoes per week FIGURE 2.10: Utility-Maximizing Choices for Special Types of Goods