Chapter 5 5 1 The Consumers Optimization Problem

Chapter 5 5 -1

The Consumer’s Optimization Problem • Individual consumption decisions are made with the goal of maximizing total satisfaction from consuming various goods and services • Subject to the constraint that spending on goods exactly equals the individual’s money income 5 -2

Consumer Theory • Assumes buyers are completely informed about: • • Range of products available Prices of all products Capacity of products to satisfy Their income • Requires that consumers can rank all consumption bundles based on the level of satisfaction they would receive from consuming the various bundles 5 -3

Typical Consumption Bundles for Two Goods, X & Y (Figure 5. 1) 5 -4

Properties of Consumer Preferences • Completeness • For every pair of consumption bundles, A and B, the consumer can say one of the following: w A is preferred to B w B is preferred to A w The consumer is indifferent between A and B • Transitivity • If A is preferred to B, and B is preferred to C, then A must be preferred to C • Nonsatiation • More of a good is always preferred to less 5 -5

Utility • Benefits consumers obtain from goods & services they consume is utility • A utility function shows an individual’s perception of the utility level attained from consuming each conceivable bundle of goods 5 -6

Indifference Curves • Locus of points representing different bundles of goods, each of which yields the same level of total utility • Negatively sloped & convex 5 -7

Typical Indifference Curve (Figure 5. 2) 5 -8

Marginal Rate of Substitution • MRS shows the rate at which one good can be substituted for another while keeping utility constant • Negative of the slope of the indifference curve • Diminishes along the indifference curve as X increases & Y decreases • Ratio of the marginal utilities of the goods 5 -9

Slope of an Indifference Curve & the MRS (Figure 5. 3) Quantity of good Y 600 A T C (360, 320) 320 I T’ B 0 360 800 Quantity of good X 5 -10

(Figure 5. 4) Quantity of Y Indifference Map IV III II I Quantity of X 5 -11

Marginal Utility • Addition to total utility attributable to the addition of one unit of a good to the current rate of consumption, holding constant the amounts of all other goods consumed 5 -12

Consumer’s Budget Line • Shows all possible commodity bundles that can be purchased at given prices with a fixed money income or 5 -13

Consumer’s Budget Constraint (Figure 5. 5) 5 -14

Typical Budget Line (Figure 5. 6) Quantity of Y • A B • Quantity of X 5 -15

Shifting Budget Lines 100 80 R A Quantity of Y 120 (Figure 5. 7) F 100 A B N C B D 160 200 240 125 200 250 Z Quantity of X Panel A – Changes in money income Quantity of X Panel B – Changes in price of X 5 -16

Utility Maximization • Utility maximization subject to a limited money income occurs at the combination of goods for which the indifference curve is just tangent to the budget line 5 -17

Utility Maximization • Consumer allocates income so that the marginal utility per dollar spent on each good is the same for all commodities purchased 5 -18

Constrained Utility Maximization (Figure 5. 8) 50 Quantity of pizzas 45 • A 40 • B • D E IV • R 30 III 20 C • 15 10 0 10 20 30 40 50 60 70 II T I 80 90 100 Quantity of burgers 5 -19

Individual Consumer Demand • An individual’s demand curve for a specific commodity relates utilitymaximizing quantities purchased to market prices • Money income & prices held constant • Slope of demand curve illustrates law of demand—quantity demanded varies inversely with price 5 -20

Deriving a Demand Curve (Figure 5. 9) Quantity of Y 100 Px=$10 Px=$8 Px=$5 Price of X ($) 0 50 65 90 100 125 200 Quantity of X 10 8 5 Demand for X 0 50 65 90 Quantity of X 5 -21

Market Demand & Marginal Benefit • List of prices & quantities consumers are willing & able to purchase at each price, all else constant • Derived by horizontally summing demand curves for all individuals in market • Because prices along market demand measure the economic value of each unit of the good, it can be interpreted as the marginal benefit curve for a good 5 -22

Derivation of Market Demand (Table 5. 1) Quantity demanded Price Consumer 1 Consumer 2 Consumer 3 Market demand $6 3 0 0 3 5 5 1 0 6 4 8 3 1 12 3 10 5 4 19 2 12 7 6 25 1 13 10 8 31 5 -23

Derivation of Market Demand Figure (5. 10) 5 -24

Substitution & Income Effects • When price changes, total change in quantity demanded is composed of two parts • Substitution effect • Income effect 5 -25

Substitution & Income Effects • Substitution effect • Change in consumption of a good after a change in its price, when the consumer is forced by a change in money income to consume at some point on the original indifference curve • Income effect • Change in consumption of a good resulting strictly from a change in purchasing power 5 -26

Income & Substitution Effects: A Decrease in Px (Figure 5. 12) Total effect of price decrease 9 = = Substitution + Income effect + 4 5 Total effect of = Substitution + Income price decrease effect 3 = 5 + (-2) 5 -27

Substitution & Income Effects • Consider the substitution effect alone: • Amount of good consumed must vary inversely with price • Income effect reinforces the substitution effect for a normal good & offsets it for an inferior good 5 -28

Summary of Substitution & Income Effects (Table 5. 2) Substitution Effect Income Effect Normal Good X rises Inferior Good X rises X falls Normal Good X falls Inferior Good X falls X rises Price of X decreases: Price of X increases: 5 -29