Individual Demand Curves Chapter 3 Individual Demand Curves © 2006 Thomson Learning/South-Western

Demand Functions Knowing person’s preferences and all economic forces that affect choices allows prediction of how much of each good person would choose in face of scarcity Summarizes this information in demand function: representation of how quantity demanded depends on prices, income, and preferences.

Demand Function Three elements determine quantity demanded: {3.1} Three elements determine quantity demanded: Prices of X and Y Income (I) Person’s preferences for X and Y. Preferences appear to right of semicolon-- assume that preferences do not change during analysis (static)

Changes in Income When income increases and prices remain same, quantity of each good purchased might increase. Shown in Figure 3-1 where increase in income shows as shift of budget line outward from I1 to I2 to I3. Slope of budget lines remain same because prices have not changed .

FIGURE 3-1: Effect of Increasing Income on Quantities of X and Y Chosen Quantity of Y per week Y1 U1 Quantity of X per week I1 X1

FIGURE 3-1: Effect of Increasing Income on Quantities of X and Y Chosen Quantity of Y per week Y2 U2 Y1 U1 I1 I2 Quantity of X per week X1 X2

FIGURE 3-1: Effect of Increasing Income on Quantities of X and Y Chosen Quantity of Y per week Y3 Y2 U3 U2 Y1 U1 I1 I2 I3 Quantity of X per week X1 X2 X3

Changes in Income Response to increased income: quantity of X purchased increases from X1 to X2 and X3 while the quantity purchased of Y also increases from Y1 to Y2 to Y3. Income increases allow more consumption, reflected in outward shift in budget constraint. Allows increase in overall utility.

Normal Goods & Inferior Goods Normal good: bought in greater quantities as income increases Inferior good: bought in smaller quantities as income increases.

FIGURE 3-2: Indifference Curve Map Showing Inferiority Quantity of Y per week Y1 U1 Quantity of Z per week Z1 I1

FIGURE 3-2: Indifference Curve Map Showing Inferiority Quantity of Y per week Y2 U2 Y1 U1 I2 I1 Quantity of Z per week Z2 Z1

FIGURE 3-2: Indifference Curve Map Showing Inferiority Quantity of Y per week Y3 U3 Y2 U2 Y1 U1 I1 I2 I3 Quantity of Z per week Z2 Z1 Z3

Changes in Good’s Price Change in price of one good causes both slope and intercept of budget line to change. Change in one good’s price creates new utility-maximizing choice on another indifference curve with a different MRS. Change in quantity demanded of good with price change

Substitution Effect Part of change in quantity demanded for other goods caused by substitution of one good for another: called substitution effect Movement along an indifference curve Consumption has to change to equate MRS to new price ratio of two goods.

Income Effect Price change creates difference in real purchasing power; consumers move to new indifference curve consistent with new purchasing power Part of change in quantity demanded caused by change in real income: called income effect.

Substitution and Income Effects from a Fall in Price Figure 3-3: when price of good X falls, budget line rotates out from unchanged Y axis such that X intercept lies farther out-- consumer can now buy more X with lower price. Flatter slope means that relative price of X to Y (PX/PY) has fallen.

FIGURE 3-3: Income and Substitution Effects of a Fall in Price Quantity of Y per week Y* U1 Quantity of X per week X*

FIGURE 3-3: Income and Substitution Effects of a Fall in Price Quantity of Y per week Old budget constraint Y* B New budget constraint U1 Quantity of X per week X* XB Substitution effect

FIGURE 3-3: Income and Substitution Effects of a Fall in Price Quantity of Y per week Old budget constraint Y** Y* U2 B New budget constraint U1 Quantity of X per week X* XB X** Substitution effect Income effect Total increase in X

Figure 3-4: Relative Size of Substitution Effects Right Shoes Exxon . A,B U1 I I’ I’ I U1 Mobil Left Shoes (a) Small Substitution Effect ’ (b) Large Substitution Effect

Substitution and Income Effects from an Increase in Price Increase in PX will shift budget line in toward origin, as in Figure 3-5. Substitution effect, holding “real” income constant: move on U2 from X*, Y* to point B Because higher price decreases purchasing power, movement from B to X**, Y** is income effect

FIGURE 3-5: Income and Substitution Effects of an Increase in Price Quantity of Y per week U2 New budget constraint Y* Old budget constraint Quantity of X per week X*

FIGURE 3-5: Income and Substitution Effects of an Increase in Price Quantity of Y per week U2 U1 B New budget constraint Y* Old budget constraint Quantity of X per week XB X* Substitution effect

FIGURE 3-5: Income and Substitution Effects of an Increase in Price Quantity of Y per week U2 U1 B Y** New budget constraint Y* Old budget constraint Quantity of X per week X** XB X* Income effect Substitution effect Total reduction in X

Substitution and Income Effects for a Normal Good: Summary Figures 3-3 and 3-5 show that substitution and income effects work in the same direction with a normal good. When price falls, both substitution and income effects result in more purchased. When price increases, both substitution and income effects result in less purchased.

Substitution and Income Effects for a Normal Good: Summary These effects provide rationale for downward sloping demand curves. Also help to determine steepness of demand curve If either substitution or income effects are large, change in quantity demanded will be large with given price change.

Substitution and Income Effects for Inferior Goods With inferior good, substitution and income effects work in opposite directions. Substitution effect results in decreased consumption for price increase and increased consumption for price decrease.

Substitution and Income Effects for Inferior Goods For inferior goods, income effect results in increased consumption for price increase and decreased consumption for price decrease. Figure 3-6 shows income and substitution effects for increase in PX. Substitution effect, holding real income constant, appears as move from X*, Y* to point B both on U2.

FIGURE 3-6: Income and Substitution Effects for Inferior Good Quantity of Y per week Y* U2 Old budget constraint Quantity of X per week X*

FIGURE 3-6: Income and Substitution Effects for Inferior Good Quantity of Y per week B New budget constraint Y* U2 Y** Old budget constraint U1 Quantity of X per week X*

FIGURE 3-6: Income and Substitution Effects for Inferior Good Quantity of Y per week B New budget constraint Y* U2 Y** Old budget constraint U1 Quantity of X per week X** X*

Substitution and Income Effects: Inferior Goods Income effect reflects reduced purchasing power due to price increase. X is inferior good: decreased income results in increased consumption of X-- shown by move from point B on U1 to new utility maximizing point X**, Y** on U1.

Substitution and Income Effects for Inferior Goods Since X** is less than X* ,X price increase results in decreased consumption of X. Decreased consumption happens because the substitution effect, in this example, is bigger than income effect. Thus, if the substitution effect dominates, the demand curve is negatively sloped.

Giffen’s Paradox If income effect of price change for an inferior good is strong enough, quantity demanded may change in same direction as price change. Situation in which increase in good’s price leads people to consume more of the good is called Giffen’s paradox.

The Lump Sum Principle “Lump-sum principle” holds that taxes imposed on general purchasing power will have smaller welfare costs than will taxes imposed on narrow selection of commodities. Consider Figure 3-7: individual initially has I dollars to spend and chooses to consume X* and Y* , yielding U3 utility.

FIGURE 3-7: The Lump-Sum Principle Quantity of Y I Y* U3 Quantity of X per week X*

The Lump Sum Principle Tax on only good X raises its price, resulting in budget constraint I* and consumption reduced to X1, Y1 and utility level U1. General income tax that generates same total tax revenue is represented by budget constraint I** that goes though X1, Y1.

FIGURE 3-7: The Lump-Sum Principle Quantity of Y I Y1 Y* I’ Y2 U3 U1 Quantity of X per week X1 X*

FIGURE 3-7: The Lump-Sum Principle Quantity of Y I Y1 Y* I’ I” Y2 U3 U2 U1 Quantity of X per week X1 X2 X*

The Lump Sum Principle Intuitive explanation of lump-sum principle: single-commodity tax affects consumers in two ways: Reduces purchasing power, Directs consumption away from good being taxed. The lump-sum tax only has first of these two effects.

Changes in the Price of Another Good In two-good economy, when price of one good changes, affects demand for other good. Figure 3-3: increase in price of X (a normal good) caused both income and substitution effect that caused reduction in quantity demanded of X.

Changes in the Price of Another Good In addition, substitution effect caused demand decrease for good Y as consumer substituted good X for good Y. To offset, purchasing power increase brought about by price decrease causes an increase in demand for good Y (also normal good).

Changes in the Price of Another Good In this case, income effect had dominant effect on good Y--consumption of Y increased due to decrease in X’s price. With flatter indifference curves as shown in Figure 3-8, situation reverses. Decrease in X’s price causes decrease in consumption of good Y, as before.

FIGURE 3-8: Effect on the Demand for Good Y of a Decrease in the Price of Good X Quantity of Y per week Old budget constraint Y* U1 Quantity of X per week X*

FIGURE 3-8: Effect on the Demand for Good Y of a Decrease in the Price of Good X Quantity of Y per week Old budget constraint A Y* B New budget constraint U2 U1 Quantity of X per week X*

FIGURE 3-8: Effect on the Demand for Good Y of a Decrease in the Price of Good X Quantity of Y per week Old budget constraint A Y* C Y** B New budget constraint U2 U1 Quantity of X per week X* X**

Changes in the Price of Another Good – Substitutes & Complements Here, income effect much smaller than substitution effect, so consumer ends up consuming less of good Y at Y** after decrease in X’s price. Thus, effect of change in the price of one good has an ambiguous effect on demand for the other good.

Construction of Individual Demand Curves Individual demand curve: graphic representation between price of good and quantity demanded by consumer, holding all other factors (preferences, prices of other goods, and income) constant Demand curves limit the study to the relationship between the quantity demanded and changes in the good’s price—a single-good world

Construction of Individual Demand Curves Panel a of Figure 3-9: individual’s indifference curve map drawn using three different budget constraints--Px decreases Decreasing prices: P’X, P”X, and P’’’X respectively Individual’s utility maximizing choices of quantity of X: X’, X’, and X’’’ respectively

FIGURE 3-9: Construction of Individual’s Demand Curve Quantity of Y per week Budget constraint for P 9 X U 1 X’ Quantity of X per week (a) Individual ’ s indifference curve map Price P’X X’ Quantity of X per week (b) Demand curve

FIGURE 3-9: Individual’s Demand Curve Quantity of Y Budget constraint for P’X per week Budget constraint for P’’X U 2 U 1 X’ X” X’” Quantity of X per week (a) Individual ’ s indifference curve map Price P’X P’’X X’ X” Quantity of X per week (b) Demand curve

FIGURE 3-9: Individual’s Demand Curve Quantity of Y Budget constraint for P’X per week Budget constraint for P’’X Budget constraint for P’’’X U 3 U 2 U 1 X’ X” X’” Quantity of X per week (a) Individual ’ s indifference curve map Price P 9 X P X P - X X’ X” X’” Quantity of X per week (b) Demand curve

FIGURE 3-9: Construction of an Individual’s Demand Curve Quantity of Y Budget constraint for P’X per week Budget constraint for P’’X Budget constraint for P’’’X U 3 U 2 U 1 X’ X” X’” Quantity of X per week (a) Individual ’ s indifference curve map Price P 9 X P X P - X d X X’ X” X’” Quantity of X per week (b) Demand curve

Constructing Individual Demand Curves Three choices show that quantity of X demanded increases as PX falls. Panel b shows how we can use three price and quantity choices to construct demand curve.

Constructing Individual Demand Curves PX appears on vertical axis; QdX shown on horizontal axis. Demand curve (dX) downward sloping: when PX falls, QdX increases. This result follows from substitution and income effects (as shown in ch. 2).

Shape of the Demand Curve If good X has close substitutes, increase in its price will cause large decrease in quantity demanded: substitution effect will be large. Demand curve for a type of breakfast cereal will likely be relatively flat due to strong substitution effect.

Shape of the Demand Curve If good X has few substitutes, substitution effect of price increase or decrease will be small and demand curve will be relatively steep. Water--good with few substitutes.

Shape of the Demand Curve Food as a category has no substitutes; might be thought that no change in consumption would occur with a price increase. Food constitutes large part of individual’s budget: price changes may cause relatively larger effects on quantity demanded due to income effect.

Shifts in an Individual’s Demand Curve When one variable that had been held constant (price of another good, income or preferences) changes, the entire demand curve shifts. Figure 3-10 shows kinds of shifts that might take place. If X is normal good and income increases, demand increases as shown in Panel a.

FIGURE 3-10: Shifts in Individual’s Demand Curve PX PX PX P1 P1 P1 X1 X2 X X1 X2 X X2 X1 X (a) (b) (c)

FIGURE 3-10: Shifts in Individual’s Demand Curve PX PX PX P1 P1 P1 X1 X2 X X1 X2 X X2 X1 X (a) (b) (c)

Shifts in Individual’s Demand Curve If X and Y are substitutes and PY increases, dX increases: shown in Panel b. Alternatively, if X and Y are complements, PY increase will cause dX decrease: shown in Panel c.

Shifts in Individual’s Demand Curve Preference changes can also shift demand curves. Panel b could represent increased preference for cold drinks when sudden hot spell occurs. Increased environmental consciousness during the 1980’s and 1990s increased demand for recycling and for organic food.

Be Careful in Using Terminology: Essential Distinctions A movement downward along a stationary demand curve in response to a fall in price is called an increase in quantity demanded while a rise in the price of the good results in a decrease in quantity demanded. A rightward shift in a demand curve is called an increase in demand while a leftward shift is a decrease in demand.

Consumer Surplus Fig. 3-11 shows demand curve for T-shirts. At PT of $11, individual chooses to buy ten T-shirts. In other words, the individual is willing and able to pay $11 for the tenth T-shirt. With PT of $9, individual buys fifteen T-shirts; implicit value of fifteenth shirt only $9.

Consumer Surplus Because good usually sold at single market price, people choose to buy additional units of the good up to the point at which their marginal valuation equals the good’s price (from chapter 2). Figure 3-11, PT= $7: individual will buy twenty shirts because twentieth T-shirt is worth precisely $7. Person will not buy the twenty-first T-shirt, because its worth is less than $7.

Graphical Illustration of Consumer Surplus Graphically, consumer surplus given by area below demand curve and above market price. Figure 3-11: total consumer surplus is given by area AEB ($80).

FIGURE 3-11: Consumer Surplus from T-Shirt Demand Price ($/shirt) Price (PT= $/shirt) A 15 11 9 E B d Quantity (shirts) 10 15 20

Consumer Surplus and Utility Figure 3-12: individual willing to pay BC for right to consume T-shirts rather than spending I only on other goods. Would need to be compensated by AB in other goods to maintain utility at U1

FIGURE 3-12: Consumer Surplus and Utility Price ($/shirt) A B C E U1 I U0 I’ Quantity (shirts) 20