comparative statics analysis

Copyright (c) 2000 by Harcourt, Inc. All rights reserved.

Comparative Statics Analysis

• This chapter studies how people change their choices when conditions such as income or changes in the prices of goods change.


Demand Function

• The elements that determine the quantity demanded are the prices of X and Y, the person’s income (I), and the person’s preferences for X and Y.

• Assume preferences do not change during the analysis.

);,,(demanded X ofQuantity spreferenceIPPd YXx


Homogeneous Demand Function

• Individual demand functions are homogeneous since quantity demanded does not change when prices and income increase in the same proportion.

• The budget constraint PXX + PYY = I is identical to the budget constraint 2PXX + 2PYY = 2I.

• Graphically the lines are the same.


Changes in Income

• When a person’s income increase the budget line shifts out from I1 to I2 to I3.

• The slope of the budget lines are the same since the prices have not changed .


Quantity of Yper week

Y3

U1

I1

Quantity of Xper week

X10

FIGURE 3.1: Effect of Increasing Income on Quantities of X and Y Chosen

X2 X3

Y2

Y1U2

U3

I2 I3


Normal Goods

• A normal good is one that is bought in greater quantities as income increases.

• If the quantity increases more rapidly than income the good is called a luxury good as with good Y in Figure 3.1.

• If the quantity increases less rapidly than income the good is called a necessity good as with good X in Figure 3.1.


APPLICATION 3.1: Engel’s Law

• In general, the fraction of income spent on food declines as income increases.

• This finding was discovered by Prussian economists Ernst Engel (1821-1896).


TABLE 1: Percentage of Total Expenditures of Various Items in Belgian Families in 1853

Annual IncomeExpenditure Item $225-$300 $450-$600 $750-$1000Food 62.0% 55.0% 50.0%Clothing 16.0 18.0 18.0Lodging, light, and fuel 17.0 17.0 17.0Services (education, legal, health) 4.0 7.5 11.5Comfort and recreation 1.0 2.5 3.5Total 100.0 100.0 100.0


TABLE 2: Percentage of Total Expenditures by U.S. Consumers on Various Items, 1997

Annual IncomeExpenditure Item Lowest Fifth Middle Fifth Highest FifthFood 16.8% 14.3% 11.8%Clothing 7.6 5.0 5.0Housing 48.7 31.5 30.1Other Items 26.9 49.2 53.1Total 100.0 100.0 100.0


Inferior Goods

• An inferior good is one that is bought in smaller quantities as income increases.



Y3

Quantity of Zper week

Z30

FIGURE 3.2: Indifference Curve Map Showing Inferiority

Z2 Z1

Y1

Y2

U1

U2

U3

I1 I2 I3


Changes in a Good’s Price

• A change in a good’s price alters both the slope and intercept of the budget line.

• A change in quantity demanded that is caused by substitution of one good for another is called the substitution effect.

• A change in quantity demanded caused by a change in real income is the income effect.



Y*

Old budget constraint

B

Substitutioneffect

New budget constraint


X* XB0

FIGURE 3.3: Income and Substitution Effects of a Fall in Price

U1



Y**

Y*


B

Substitutioneffect

Incomeeffect

Total increase in X



X* XB X**0

FIGURE 3.3: Income and Substitution Effects of a Fall in Price

U1

U2


The Effects Combined

• Using the hamburger-soft drink example from Chapter 2, suppose the price of soft drinks falls from $.50 to $.25.

• Previously the consumer could purchase up to 20 soft drinks, but now he or she can purchase up to 40.

• This price decrease shifts the budget line outward and increases utility.


The Effects Combined

• If the consumer bought his or her previous choice it would now cost $7.50 so that $2.50 would be unspent.

• If the individual stayed on the old indifference curve he or she would equate MRS to the new price ratio (consuming 1 hamburger and 4 soft drinks).

• This move is the substitution effect.


Substitution and Income Effects from an Increase in Price

• An increase in PX will shift the budget line in as shown in Figure 3.4.

• The substitution effect, holding “real” income constant, is the move on U2 from X*, Y* to point B.

• Because the higher price causes purchasing power to decrease, the movement from B to X**, Y** is the income effect.



Y*New budget constraint



X*0

FIGURE 3.4: Income and Substitution Effects of an Increase in Price

U2




Substitutioneffect


B


XB X*0


U1

U2



Y**


Incomeeffect

Substitutioneffect

Total reductionin X


B


X** XB X*0


U1

U2


Substitution and Income Effects from an Increase in Price

• In Figure 3.4, both the substitution and income effects cause the individual to purchase less soft drinks do to the higher price of soft drinks.


Substitution and Income Effects for a Normal Good: Summary

• As shown in Figures 3.3 and 3.4, the substitution and income effects work in the same direction with a normal good.

• When the price falls, both the substitution and income effects result in more purchased.

• When the price increases, both the substitution and income effects result in less purchased.



• This provides the rational for drawing downward sloping demand curves.

• This also helps to determine the steepness of the demand curve.

• If either the substitution or income effects are large, the change in quantity demanded will be large with a given price change.



• If the substitution and income effects are small, the effect of a given price change in the quantity demanded will also be small.

• This kind of analysis also offers a number of insights about some commonly used economic statistics.


APPLICATION 3.2: The Consumer Price Index and Its Biases

• The Bureau of Labor Statistics calculates the (CPI) as a principal measure of inflation.

• To construct the CPI, a typical basket of goods purchased by consumers in the base year (currently 1982) is calculated. The ratio of the current cost of the basket to the 1982 price is the value of the CPI.

• The rate of change in the CPI between two periods is the reported rate of inflation


An Algebraic Example

• The CPI is defined as the ratio of the costs of these two market baskets

• If the basket cost $100 in 1982 prices and $175 in 2002, the value of the CPI would be 1.75 and with a measured 75 percent increase in prices over the 20 year period.

.2000)CPI(for 82

00

B

B


Substitution Bias in the CPI

• The CPI does not take into account the real possibility that consumers would substitute among commodities because of changes in relative prices.

• In Figure 1, the typical individual is initially consuming X82, Y82 maximizing utility on U1 with 1982 constraint I.


Quantity ofY per year

Y82

Quantity ofX per year

U1I I’I”0 X82

FIGURE 1: Substitution Bias of the Consumer Price Index


New Product Bias in the CPI

• New products typically experience sharp declines in prices and rapidly grow in rates of acceptance.

• If the CPI does not include these new products, this source of welfare increase is omitted.

• The CPI basket is revised but not rapidly enough to eliminate this bias.


Outlet Bias in the CPI

• The typical basket is bought at the same retail outlets every month.

• This method can omit the benefits of sales or other bargains.

• The CPI does not currently take such price-reducing strategies and thus tends to overstate inflation.


Consequences of the CPI Biases

• There is a general agreement that the CPI overstates inflation by as much as 0.75 to 1.0 percent per year.

• Politicians have proposed caps on government Cost of Living Adjustments (COLAs) tied to the CPI but none have been enacted. However, in the private sector few COLAs provide full offsets to inflation measured by the CPI.


Substitution and Income Effects for Inferior Goods

• With an inferior good, the substitution effect and the income effects work in opposite directions.

• The substitution effect results in decreased consumption for a price increase and increased consumption for a price decrease.



Y**



U2

B


X** X*0

FIGURE 3.5: Income and Substitution Effects for an Inferior Good

U1


Giffen’s Paradox

• If the income effect of a price change is strong enough with an inferior good, it is possible for the quantity demanded to change in the same direction as the price change.

• Legend has it that this phenomenon was observed by English economist Robert Giffen.


The Lump Sum Principle

• The intuitive explanation of the lump-sum principle is that a single-commodity tax affects people in two ways:– it reduces their purchasing power,– it directs consumption away from the good

being taxed.

• The lump-sum tax only has the first of these two effects.


Generalizations of the Lump-Sum Principle

• The utility loss associated with taxing will be minimized by taxing goods for which the substitution effect is small.

• Even though the tax will reduce purchasing power, it will minimize the impact of directing consumption away from the good being taxed.



Y**

Y*

U2

U1




X* X**

B

0

FIGURE 3.7: Effect on the Demand for Y from a Decrease in the Price of X: Substitutes


Complements

• Two goods are complements if an increase in the price of one causes a decrease in the demanded of the other or vice versa.


Substitutes

• Two goods such that if the price of one increases, the demand for the other rises are substitutes.



U1

X

X


Budget constraint for P9

X’

(a) Individual’s indifference curve map

0

Price

P9


X’

(b) Demand curve

0

FIGURE 3.8: Construction of an Individual’s Demand Curve



U1

U2

X

X

X

X



-


X’ X” X’”


0

Price

P9

XP0


X’ X”

(b) Demand curve

0




U1

U2

U3

X

X

X

X



Budget constraint for P-


X’ X” X’”


0

Price

P9

XP0

XP-


X’ X” X’”

(b) Demand curve

0




U1

U2

U3

X

X

X

X



Budget constraint for P-


X’ X” X’”


0

Price

P9

XP0

XP-dX


X’ X” X’”

(b) Demand curve

0



Consumer Surplus

• The extra value individuals receive from consuming a good over what they pay for it is called consumer surplus.


APPLICATION 3.6: Valuing Clean Air

• By looking at the ceteris paribus relationship between air pollution levels in various locations and the prices of houses in these locations, it is possible to infer the amount that people will pay to avoid dirty air.

• This information allows the computation of a compensated demand curve for clean air.



• In Figure 1, the vertical axis shows the price home buyers are willing to pay to avoid air pollution and the horizontal axis shows the quantity of clean air purchased.

• The national average is reflected at point E as home buyers pay $50 and consume an average of 55 micrograms of suspended particulates per cubic meter.


Price($)

8085

50

60

40

20D

Air quality(mg/m3)

75 50

55

25 0

E

100

FIGURE 1: Compensated Demand Curve for Clean Air



• Consumers are paying $2,250 ($50 times 45 micrograms) extra to avoid dirty air.

• At E0 consumers also receive a consumer surplus equal to the shaded area in Figure 1.

• This consumer surplus of 788 per household can be multiplied by the total number of households to estimate total consumer surplus from clean air.

comparative statics analysis

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