Part 2 Demand © 2006 Thomson Learning/South-Western

Chapter 2 Utility and Choice © 2006 Thomson Learning/South-Western

Utility from Consuming Two Goods Assume that person receives utility from consumption of two goods “X” and “Y,” which we show in functional notation by Other factors that appear after semicolon assumed to be held constant.

Measuring Utility Two problems affect ability to to measure utility directly: Because real-world constantly in flux, ceteris paribus assumption difficult to impose No units to measure utility directly However, possible to study choices fairly completely without direct utility measurement

Assumptions about Utility Basic Properties of Utility Preferences Preferences complete : assume that individual can state which of any two options is preferable. Preferences transitive: if A is preferred to B, and B is preferred to C, then A must be preferred to C.

More Is Better: Defining an Economic “Good” Economic good: yields positive benefits to consumer. Thus, more quantity of a good is always better than less. Figure 2-1: shows all points in the darkly shaded area preferable to amount X* of good X and Y* of good Y. Movement into shaded area unambiguously better since person gets more of one good without losing any of the other.

FIGURE 2-1: More Preferred to Less Quantity of Y per week ? Y* ? Quantity of X per week X*

Voluntary Trades, Indifference Curves Fig. 2.1: areas marked with question marks difficult to compare to X*, Y* since they involve more of one good but less of the other. Trading one good (such as money) for another good (such as a candy bar): essence of demand.

Indifference Curves Curve that shows all combinations of goods or services that provide same level of utility. Figure 2-2: horizontal axis measures quantity of soft drinks consumed by individual per week; vertical axis measures the quantity of hamburgers consumed per week.

Indifference Curves Curve U1 in Figure 2-2 includes all hamburgers/soft drink combinations that yield same utility level. Point A--6 hamburgers and 2 soft drinks-- produces same utility as point B--4 burgers and 3 drinks. Since all points on the curve yield same utility, consumer has no reason to prefer one point over another.

FIGURE 2-2: Indifference Curve Hamburgers per week A 6 B 4 3 C D 2 U1 Soft drinks per week 2 3 4 5 6

Points Above Indifference Curve Figure 2-2, points such as E are above (to northeast) of U1. Since E has more of both goods than point C, E is preferred to C (more is better). Because of transitivity, E is preferred to any point on U1. Points above indifference curve preferred to points on curve.

FIGURE 2-2: Indifference Curve Hamburgers per week A 6 B 4 E 3 C D 2 U1 Soft drinks per week 2 3 4 5 6

Points Below Indifference Curve Figure 2-2: points such as F are below (to the southeast) of given indifference curve. Point C is preferred to point F since C provides more of both goods. Because of transitivity, all points on U1 preferred to point F. Points on indifference curve are preferred to points below it.

FIGURE 2-2: Indifference Curve Hamburgers per week A 6 B 4 E 3 C D F 2 U1 Soft drinks per week 2 3 4 5 6

Slope of Indifference Curve Figure 2-2: from point A to point B, person willingly gives up two hamburgers to gain one soft drink, since consumer is equally happy at either point. Slope of U1: approximately -2 between points A and B: hamburgers decline by two units to gain one unit of soft drinks.

Indifference Curves: Marginal Rate of Substitution Marginal Rate of Substitution (MRS): Rate at which individual will reduce consumption of one good to get one more unit of other good. Measured as negative of indifference curve slope Figure 2-2: MRS between points A and B on U1 (approximately)-2.

Diminishing Marginal Rate of Substitution Fig. 2.3: On indifference curve U1 , consumer will only give up one hamburger to gain one more soft drink between points B and C. Between points C and D, consumer will give up only ½ hamburger to gain one more soft drink.

FIGURE 2-3: Consumer Prefers Balanced Consumption Hamburgers per week A 6 B G 4 3 C D 2 U1 Soft drinks per week 2 3 4 6

Diminishing Marginal Rate of Substitution MRS diminishes along indifference curve moving from left to right. Reflects idea that consumers prefer balanced consumption Figure 2.3: Point G reflects bundle that is “between” points A and D. Since it is above U1,point G preferable to any bundle on indifference curve.

Indifference Curve Maps Since every hamburger/ soft drink combination must yield some level of utility, every point must have one (and only one) indifference curve passing through it. Indifference curve map shows utility an individual obtains from all possible consumption options. Figure 2-4 shows three of infinite number of indifference curves in map.

Labeling Indifference Curves Since utility can not be measured, labeling indifference curves has no meaning except to indicate that utility increases from U1 to U2 and then to U3 in Figure 2-4. In any indifference curve map, all we can assume is that utility increases as we move to higher indifference curves.

FIGURE 2-4: Indifference Curve Map for Hamburgers and Soft Drinks per week A 6 H 5 B G 4 U3 3 C U2 D 2 U1 Soft drinks per week 2 3 4 5 6

Illustrating Particular Preferences Figure 2-5(a): good on vertical axis (smoke grinders) is useless, so consumer only gains utility from more of good on horizontal axis (food). Figure 2-5(b); good on vertical axis is economic “bad” (houseflies); consumer only gains utility from consuming less of bad.

FIGURE 2-5: Illustrations of Specific Preferences Smoke Houseflies grinders per week per week U 1 U 2 U 3 U 1 U 2 U 3 10 Food per week 10 Food per week (a) A useless good (b) An economic bad Gallons Right shoes of Exxon per week per week 4 U 4 3 U 3 2 U 2 1 U 1 U 1 U 2 U 3 Gallons of Mobil 1 2 3 4 Left shoes per week per week (c) Perfect substitute (d) Perfect complements

Particular Preferences Figure 2-5(c): two goods are perfect substitutes--consumer views them as essentially the same; MRS = 1 Figure 2-5(d): two goods are perfect complements--they must be used together (like left and right shoes) to gain utility.

Income and Utility: A Simple Case When choosing to allocate income between two goods (e.g. hamburgers and soft drinks) consumer will: Spend entire income on two goods, and Choose combination of goods for which the MRS (marginal rate of substitution) between the two goods equals the ratio of their prices.

Income and Utility: A Simple Case Since both goods (and only these goods) provide more utility with additional consumption, consumer will spend entire income on these goods. Only other alternative: throw income away--does not increase utility.

Equality of MRS with the Ratio or Prices Suppose individual currently consumes where MRS = 1. Assume price of hamburgers is $1 and price of soft drinks is $.50. Yields a price ratio (PH/PS) of ($.50/$1) = ½.

Equality of MRS with Price Ratios Person could give up one hamburger (freeing $1) and purchase one soft drink using $.50. Since MRS =1, person would be just as happy as before giving up burger, but would now have additional $.50 to spend– could thus increase utility. Only way utility cannot be increased further: when MRS = price ratio.

Showing Utility Maximization Graphically Individual’s budget constraint is limit that person’s income places on combinations of goods and services consumer can buy. Figure 2-6: individual has a fixed amount of income to spend on two goods, X and Y.

Budget Constraint from Figure 2-6 If all income is spent on X, Xmax can be purchased. If all income is spent on Y, Ymax can be purchased. The line joining Xmax and Ymax represents various mixed bundles of goods X and Y that consumer can purchase using all income.

FIGURE 2-6: Individual’s Budget Constraint for Two Goods Quantity of Y per week Ymax Quantity of X per week Xmax

FIGURE 2-6: Individual’s Budget Constraint for Two Goods Quantity of Y per week Ymax Income Not affordable Affordable Quantity of X per week Xmax

Budget Constraint Budget line’s downward slope reflects fact that more X can be purchased only if less Y is purchased. If Y is expensive relative to X, budget line will be relatively flat (Y on vertical axis). If Y is relatively inexpensive compared to X, budget line will be relatively steep.

Budget Constraint Algebra Assume individual has I dollars of income to spend on goods X and Y. Suppose price of X is Px and price of Y is PY. Total amount spent on X and Y are Px·X and PY·Y ,respectively.

Budget Constraint Algebra Since all income must be spent on either X or Y, we have Amount spent on X + Amount spent on Y = I or

Budget Constraint Algebra Solving equation 2.3 for Y, to express it in the standard form for linear equation, we have

Budget Constraint Algebra Equation 2.4 shows that if all income spent on Y, I/PY will be purchased, and if all income is spent on X, I/PX will be purchased. The slope of budget line (-PX/PY) represents opportunity cost of X in terms of foregone Y.

Utility Maximization Individual can afford all bundles of X and Y that fall within budget constraint represented by shaded area in Figure 2-6. Point A is affordable, but not all of the consumer’s income would be spent. Point B is affordable, but is not on the highest indifference curve that the consumer can reach, so some utility is “wasted”.

FIGURE 2-7: Graphic Demonstration of Utility Maximization Hamburgers per week B Income A U1 Soft drinks per week

FIGURE 2-7: Graphic Demonstration of Utility Maximization Hamburgers per week B D Income U3 A U1 Soft drinks per week

Utility Maximization Fig. 2.7: Point D is on higher indifference curve than C, but is not affordable given the budget constraint. Point C, where the consumer chooses X*, Y* is the affordable point that lies on (tangent to) highest indifference curve, so represents utility maximization.

FIGURE 2-7: Graphic Demonstration of Utility Maximization Hamburgers per week B D Income U3 Y* C U2 A U1 Soft drinks per week X*

Utility Maximization At point C, all income is spent. At point C, indifference curve U2 lies tangent to budget line, so or

Using The Model of Choice Utility maximization model explains number of common observations. Figure 2-8 provides illustration of why people with same income choose to spend in different ways.

FIGURE 2-8: Differences in Preferences Result in Differing Choices Hamburgers per week Hamburgers per week Hamburgers per week U2 U1 U2 U0 U1 U0 U2 U1 Income 8 Income Income U0 2 Soft drinks per week Soft drinks per week Soft drinks per week 4 20 16 (a) Hungry Joe (b) Thirsty Teresa (c) Extra-thirsty Ed

Using the Model of Choice Figure 2-9 shows four indifference curve maps with budget constraint and utility- maximizing choice labeled E. Panel (a) shows that people will not buy useless goods; (b) shows they will not buy bads. Panel (c) shows that people will buy least expensive of two perfect substitutes; (d) shows that perfect complements will be purchased together.

FIGURE 2-9: Utility-Maximizing Choices for Special Types of Goods Smoke Houseflies grinders per week per week U 1 U 2 U 3 U 1 Income U 2 Income U 3 E E 10 Food per week 10 Food per week (a) A useless good (b) An economic bad Gallons Right shoes of Exxon per week per week E Income U 3 E 2 U 2 U 1 U 1 U Income 2 U 3 Gallons of Mobil 2 Left shoes per week per week (c) Perfect substitute (d) Perfect complements