1. INTERMEDIATE MICROECONOMICS AND ITS APPLICATION
Chapter 3
Individuals’ Demand
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2. Comparative Statics Analysis
This chapter studies how people change their choices when conditions such as income or changes in the prices of goods affect the amount that people choose to consume.
This type of investigation is sometimes called comparative statics analysis because it compares two utility-maximizing choices.
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3. Demand Functions
If we knew a person’s preferences and all the economic forces that affect his or her choices, we could predict how much of each good would be chosen.
This summarizes this information in a demand function: a representation of how quantity demanded depends on prices, income, and preferences.
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4. Demand Function
The three 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.
Preferences appear to the right of the semicolon because we assume that preferences do not change during the analysis.
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5. 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.
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6. Changes in Income
When a person’s income increase, while prices remain the same, the quantity purchased of each good might increase.
This situation is shown in Figure 3.1 where the increase in income is shown as 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 .
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7. FIGURE 3.1: Effect of Increasing Income on Quantities of X and Y Chosen
Quantity of Y
per week Y1 U1 I1
Quantity of X
per week X1
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8. 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
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9. 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
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10. Changes in Income
In response to the increase in income the 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.
Increases in income make it possible for a person to consume more reflected in the outward shift in the budget constraint that allows an increase in overall utility.
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11. 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.
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12. APPLICATION 3.1: Engel’s Law
One important generalization about consumer behavior is that the fraction of income spent on food tends to decline as income increases.
This finding was discovered by Prussian economists Ernst Engel ( ).
Table 1 show Engel’s data with Table 2 showing recent data for U.S. consumers.
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13. TABLE 1: Percentage of Total Expenditures of Various Items in Belgian Families in 1853
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14. TABLE 2: Percentage of Total Expenditures by U. S
TABLE 2: Percentage of Total Expenditures by U.S. Consumers on Various Items, 1997
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15. Inferior Goods
An inferior good is one that is bought in smaller quantities as income increases.
In Figure 3.2 as income increases from I1 to I2 to I3, the consumption of inferior good Z decreases.
Goods such as “rotgut” whiskey, potatoes, and secondhand clothing are examples of inferior goods.
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16. FIGURE 3.2: Indifference Curve Map Showing Inferiority
Quantity of Y
per week Y1 U1 I1 Z1
Quantity of Z
per week
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17. FIGURE 3.2: Indifference Curve Map Showing Inferiority
Quantity of Y
per week Y2 U2 Y1 U1 I1 I2 Z2 Z1
Quantity of Z
per week
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18. FIGURE 3.2: Indifference Curve Map Showing Inferiority
Quantity of Y
per week Y3 U3 Y2 U2 Y1 U1 I1 I2 I3 Z2 Z1 Z3
Quantity of Z
per week
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19. Changes in a Good’s Price
A change in the price of one good causes both the slope and an intercept of the budget line to change.
The change also involves moving to a new utility-maximizing choice on another indifference curve with a different MRS.
The quantity demanded of the good whose price has changed changes.
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20. Substitution Effect
The part of the change in quantity demanded that is caused by substitution of one good for another is called the substitution effect.
This results in a movement along an indifference curve.
Consumption has to be changed to equate MRS to the new price ratio of the two goods.
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21. Income Effect
The part of the change in quantity demanded that is caused by a change in real income is called the income effect.
The price change also changes “real” purchasing power and consumers will move to a new indifference curve that is consistent with this new purchasing power.
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22. Substitution and Income Effects from a Fall in Price
As shown in Figure 3.3, when the price of good X falls, the budget line rotates out from the unchanged Y axis so that the X intercept lies father out because the consumer can now buy more X with the lower price.
The flatter slope means that the relative price of X to Y (PX/PY) has fallen.
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23. Substitution Effect from a Fall in Price
The consumer was originally maximizing utility at X*, Y* in Figure 3.3.
After the fall in the price of good X, the new utility maximizing choice is X**, Y**.
The substitution effect is the movement on the original indifference curve to point B.
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24. FIGURE 3.3: Income and Substitution Effects of a Fall in Price
Quantity of Y
per week Y* U1 X*
Quantity of X
per week
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25. 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 X* XB
Quantity of X
per week
Substitution
effect
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26. 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 X* XB
X**
Quantity of X
per week
Substitution
effect
Income
effect
Total increase in X
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27. Substitution Effect from a Fall in Price
If the individual had to stay on the U1 with the new price ratio, the consumer would choose B since that is the point where the MRS is equal to the slope of the new budget line (shown by the dashed line).
Staying on the same indifference curve is the same as holding “real” income constant.
The consumer buys more good X.
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28. Income Effect
The movement from point B to X**, Y** results from the increase in purchasing power.
Because PX falls but nominal income (I) remains the same, the individual’s “real” income increases so that he or she can be on utility level U3.
The consumer buys more good X.
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29. 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.
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30. 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.
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31. The Effects Combined
Even with constant real income the consumer will buy more soft drinks since the opportunity cost of eating a burger in terms of the soft drinks forgone is now higher.
Since real income has increased the person will choose to buy more soft drinks so long as soft drinks are a normal good.
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32. 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.
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33. FIGURE 3.4: Income and Substitution Effects of an Increase in Price
Quantity of Y
per week U2
New budget constraint Y*
Old budget constraint X*
Quantity of X
per week
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34. FIGURE 3.4: Income and Substitution Effects of an Increase in Price
Quantity of Y
per week U2 U1 B
New budget constraint Y*
Old budget constraint XB X*
Quantity of X
per week
Substitution
effect
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35. FIGURE 3.4: 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
X** XB X*
Quantity of X
per week
Income
effect
Substitution
effect
Total reduction
in X
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36. 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.
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37. 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.
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38. Substitution and Income Effects for a Normal Good: Summary
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.
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39. Substitution and Income Effects for a Normal Good: Summary
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.
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40. APPLICATION 3.2: The Consumer Price Index and Its Biases
The Bureau of Labor Statistics monthly calculates the Consumer Price Index (CPI) which is a principal measure of inflation in the U.S..
To construct the CPI, a typical market basket of commodities purchased by consumers in the base year (currently 1982) is calculated.
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41. APPLICATION 3.2: The Consumer Price Index and Its Biases
The ratio of the current cost of the basket to the base year price is the measure of the value of the CPI.
The rate of change in the CPI between two periods is the reported rate of inflation.
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42. An Algebraic Example
Suppose the 1982 typical market basket contained X82 of good X and Y82 of good Y.
The prices of these goods are and
The cost of this bundle in the 1982 base year would be written as
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43. An Algebraic Example
To compute the cost of the same bundle of goods in, say 2000, requires that we compute the cost of the bundle using current prices
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44. 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 2000, the value of the CPI would be 1.75 and with a measured 75 percent increase in prices over the 18 year period.
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45. 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.
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46. FIGURE 1: Substitution Bias of the Consumer Price Index
Quantity of
Y per year
Y82 U1 I’ I I”
X82
Quantity of
X per year
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47. Substitution Bias in the CPI
Suppose the 2000 relative prices change so that PX/PY falls.
The cost of the 1982 bundle in terms of 2000 prices is reflected in the constraint I’ which is flatter and goes though the 1982 bundle.
The consumer would substitute X for Y and stay on U1 on budget line I’’.
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48. Substitution Bias in the CPI
Since I’’ is inside I’ (which is used to compute the CPI), the CPI tends to overstate the inflation rate.
Unfortunately, adjusting the CPI to take such substitution into account is difficult because it would require that we know the utility function of the typical consumer.
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49. 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.
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50. 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.
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51. Consequences of the CPI Biases
Measuring and correcting for these biases is not an easy task.
The CPI is such a widely used measure of inflation that any change becomes a hot political issue.
However, there is a general agreement that the CPI overstates inflation by as much as 0.75 to 1.0 percent per year.
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52. Consequences of the CPI Biases
Politicians have proposed caps on Cost of Living Adjustments (COLAs) tied to the CPI on government programs, but none have yet been enacted.
However, the private sector has adjusted so that few private COLAs provide full offsets to inflation measured by the CPI.
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53. 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.
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54. Substitution and Income Effects for Inferior Goods
The income effect results in increased consumption for a price increase and decreased consumption for a price decrease.
Figure 3.5 shows the two effects for an increase in PX.
The substitution effect, holding real income constant, is shown by the move from X*, Y* to point B both on U2.
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55. FIGURE 3.5: Income and Substitution Effects for an Inferior Good
Quantity of Y
per week Y* U2
Old budget constraint
Quantity of X
per week X*
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56. FIGURE 3.5: Income and Substitution Effects for an Inferior Good
Quantity of Y
per week B
New budget constraint Y* U2
Y**
Old budget constraint U1
Quantity of X
per week X*
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57. FIGURE 3.5: Income and Substitution Effects for an 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*
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58. Substitution and Income Effects for Inferior Goods
The income effect reflects the reduced purchasing power due to the price increase.
Since X is an inferior good, the decrease in income results in an increase in the consumption of X shown by the move from point B on U1 to the new utility maximizing point X**, Y** on U1.
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59. Substitution and Income Effects for Inferior Goods
Since X** is less than X* the price increase in X results in a decrease in the consumption of X.
This occurs because the substitution effect, in this example, is bigger than the income effect.
Thus, if the substitution effect dominates, the demand curve is negatively sloped.
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60. 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.
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61. Giffen’s Paradox
When the price of potatoes rose in Ireland the consumption of potatoes also increased.
Potatoes were not only an inferior good but constituted the source of a large portion of Irish people’s income.
The situation I which an increase in a good’s price leads people to consume more of the good is called Giffen’s paradox.
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62. The Lump Sum Principle
The “lump-sum principle” hold that taxes that are imposed on general purchasing power will have a smaller welfare costs than will taxes imposed on a narrow selection of commodities.
Consider Figure 3.6 where the individual initially has I dollars to spend and chooses to consume X* and Y* yielding U3 utility.
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63. FIGURE 3.6: The Lump-Sum Principle
Quantity of Y I Y* U3
Quantity of X
per week X*
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64. The Lump Sum Principle
A tax on only good X raises its price resulting in budget constraint I’ and consumption reduced to X1, Y1 and utility level U1.
A general income tax that generates the same total tax revenue is represented by budget constraint I’’ that goes though X1, Y1.
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65. FIGURE 3.6: The Lump-Sum Principle
Quantity of Y I Y1 Y* I’ Y2 U3 U1
Quantity of X
per week X1 X*
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66. FIGURE 3.6: The Lump-Sum Principle
Quantity of Y I Y1 Y* I’ I” Y2 U3 U2 U1
Quantity of X
per week X1 X2 X*
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67. The Lump Sum Principle
The utility maximizing choice on I’’ is X2, Y2 yielding utility level U2.
The lump-sum general income tax generates the same amount of tax revenue but leaves the consumer on a higher utility level (U2) than the utility level associated with the tax only on good X (U1).
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68. 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.
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69. Generalizations of the Lump-Sum Principle
The utility lass associated with the need to collect a certain amount of tax revenue 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.
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70. APPLICATION 3.3: The Lump-Sum Principle in Practice
The most commonly proposed real-world approximation to a lump-sum tax is a general tax on income.
However, such tax still effects the choice of how much to work and other income influencing decisions.
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71. APPLICATION 3.3: The Lump-Sum Principle in Practice
Estimates suggest as much as a 22 percent loss in utility from an income tax rather than a pure lump-sum tax.
A income subsidy (negative tax) is also subject to the lump-sum principle.
Studies suggest that subsidies on food, housing and medical generate $.88, $.56, and $.68 for $1 subsidy respectively.
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72. Changes in the Price of Another Good
When the price of one good changes, it usually has an affect on the demand for the other good.
In Figure 3.3, the increase in the price of X (a normal good) caused both an income and substitution effect that caused a reduction in the quantity demanded of X.
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73. Changes in the Price of Another Good
In addition, the substitution effect caused a decrease in the demand for good Y as the consumer substituted good X for good Y.
However, the increase in purchasing power brought about by the price decrease causes an increase in the demand for good Y (also a normal good).
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74. Changes in the Price of Another Good
Since, in this case, the income effect had a dominant effect on good Y, the consumption of Y increased due to a decrease in the price of good X.
With flatter indifference curves as shown in Figure 3.7, the situation is reversed.
A decrease in the price of good X causes a decrease in good Y, as before.
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75. FIGURE 3.7: 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*
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76. FIGURE 3.7: 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* B
New budget constraint U2 U1
Quantity of X
per week X*
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77. FIGURE 3.7: 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*
Y** B
New budget constraint U2 U1
Quantity of X
per week X*
X**
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78. Changes in the Price of Another Good
However, in this case, the income effect is much smaller than the substitution effect so that the consumer ends up consuming less of good Y at Y** after the decrease in the price of X.
Thus, the effect of a change in the price of one good has an ambiguous effect on the demand for the other good.
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79. Complements
Complements are goods that go together in the sense that people will increase their use of both goods simultaneously.
Two goods are complements if an increase in the price of one causes a decrease in the demanded of the other or a decrease in the price of one good causes an increase in the demand for the other.
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80. Substitutes
Substitutes are goods that are goods that are used for essentially the same purpose.
Two goods such that if the price of one increases, the demand for the other rises are substitutes.
If the price of one good decreases and the demand for the other good decreases, they are also substitutes.
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81. APPLICATION 3.4: Gas Prices and Automobiles
Gasoline and automobiles are complements as fuel costs constitute between 10 and 20 percent of the total cost of operating a car.
Fluctuating gas prices can have important impacts on the types of cars people drive in the long run.
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82. APPLICATION 3.4: Gas Prices and Automobiles
Between 1973 and 1980 gasoline prices increase nearly four-fold in the U.S. resulting in smaller more fuel-efficient cars being purchased.
With the decline of gasoline prices in the 1980s, consumers again bought larger cars.
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83. APPLICATION 3.4: Gas Prices and Automobiles
In 1991 a “gas guzzler” tax on automobiles was instituted which can rise to $7,700 for automobiles getting less than 12.5 miles per gallon.
However, sport utility vehicles (SUVs) are exempt from the tax which may help to explain the increased popularity of such vehicles.
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84. Construction of Individual Demand Curves
An individual demand curve is a graphic representation between the price of a good and the quantity of it demanded by a person holding all other factors (preferences, the prices of other goods, and income) constant.
Demand curves limit the study to the relationship between the quantity demanded and changes in the own price of the good.
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85. Construction of Individual Demand Curves
In Panel a of Figure 3.8 an individual’s indifference curve map is drawn using three different budget constraints in which the price of X decreases.
The decreasing prices are P’X, P”X, and P’’’X respectively.
The individual’s utility maximizing choices of X are X’, X’, and X’’’ respectively.
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86. FIGURE 3.8: Construction of an 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 9 X X’
Quantity of X
per week
(b) Demand curve
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87. FIGURE 3.8: Construction of an Individual’s Demand Curve
Quantity of Y
per week
Budget constraint for P 9 X
Budget constraint for P X - X U 2 U 1 X’ X”
X’”
Quantity of X
per week
(a) Individual ’
s indifference curve map
Price P 9 X P X X’ X”
Quantity of X
per week
(b) Demand curve
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88. FIGURE 3.8: Construction of an Individual’s Demand Curve
Quantity of Y
per week
Budget constraint for P X 9
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
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89. FIGURE 3.8: Construction of an Individual’s Demand Curve
Quantity of Y
per week
Budget constraint for P X 9
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
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90. Construction of Individual Demand Curves
These three choices show that the quantity demanded of X increases as the price of X falls.
Panel b shows how the three price and quantity choices can be used to construct the demand curve.
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91. Construction of Individual Demand Curves
The price of X is shown on the vertical axis and the quantity of X is shown on the horizontal axis.
The demand curve (dX) is downward sloping showing that when the price of X falls, the quantity demanded of X increases.
As previously shown, this result follows from the substitution and income effects.
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92. Shape of the Demand Curve
If a good, say X, has close substitutes, a increase in its price will cause a large decrease in the quantity demanded as the substitution effect will be large.
The demand curve for a type of breakfast cereal will likely be relatively flat due to the strong substitution effect.
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93. Shape of the Demand Curve
If the good has few substitutes, the substitution effect of a price increase or decrease will be small and the demand curve will be relatively steep.
Water is an example of a good with few substitutes.
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94. Shape of the Demand Curve
Food has no substitutes so it might be thought that no change in consumption would occur with a price increase.
But food constitutes a large part of an individual’s budget so that price changes will cause relatively larger effects on the quantity demanded that might be thought due to the income effect.
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95. Shifts in an Individual’s Demand Curve
When one of the variables that are held constant (price of another good, income or preferences) on a demand curve changes, the entire curve shifts.
Figure 3.9 shows the kinds of shifts that might take place.
If X is a normal good and income increases, demand increases as shown in Panel a.
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96. FIGURE 3.9: Shifts in Individual’s Demand CurvePX PX PX P1 P1 P1 X X X X1 X2 X1 X2 X2 X1
(b)
(c)
(a)
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97. FIGURE 3.9: Shifts in Individual’s Demand CurvePX PX PX P1 P1 P1 X X X X1 X2 X1 X2 X2 X1
(b)
(c)
(a)
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98. Shifts in an Individual’s Demand Curve
If X and Y are substitutes and the price of Y increases, the demand for X increases as shown in Panel b.
Alternatively, if X and Y are complements, the increase in the price of Y will cause a decrease in the demand for X as shown in Panel c.
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99. Shifts in an Individual’s Demand Curve
Changes in preferences can also shift demand curves.
Panel b could represent an increased preference for cold drinks when a sudden hot spell occurs.
Increased environmental consciousness during the 1980’s and 1990s increased the demand for recycling and organic food.
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100. APPLICATION 3.5: Fads, Seasons, and Health Scares
Fads (sometimes termed bandwagon effects) are when preferences cause extremely large increases in demand followed later by large decreases in demand.
While fads are hard to predict, seasonal items are easy to predict.
Increased demand for turkeys in November and Christmas trees are examples.
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101. APPLICATION 3.5: Fads, Seasons, and Health Scares
Health scares can cause large decreases in the demand for products.
Examples include the long term decline in smoking and the decreased demand for Chinese food because of the concern for its fat content.
Recent “scientific” studies have also affected demand such as the increase in the demand for tomatoes in 1998.
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102. Demand Curve Terminology
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.
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103. Compensated Demand Curves
Since nominal income is held constant along a demand curve, a decline in the price of the good increases purchasing power and increases the utility of the consumer.
An alternative would be to hold utility constant and examine reactions to changes in the price of a good.
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104. Compensated Demand Curves
In Panel a of Figure 3.10 the price of good X is decreased from P’X to P”X to P’’’X causing the decline in the relative price of X (PX/PY).
This generates tangency points between the slope of indifference curve U2 (MRS) and the slope of the relative prices (shown by the tangent lines).
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105. FIGURE 3.10: Construction of a Compensated Demand Curve
Quantity of Y X’
Quantity of X ’ PX
(a) Individual’s indifference curve map
PX’ X’
Quantity of X
(b) Compensated demand curve
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106. FIGURE 3.10: Construction of a Compensated Demand Curve
Quantity of Y X’ X”
Quantity of X ’ PX
(a) Individual’s indifference curve map
PX’
PX’’ X’ X”
Quantity of X
(b) Compensated demand curve
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107. FIGURE 3.10: Construction of a Compensated Demand Curve
Quantity of Y X’ X”
X’”
Quantity of X ’ PX
(a) Individual’s indifference curve map
PX’
PX’’
PX’” X’ X”
X’”
Quantity of X
(b) Compensated demand curve
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108. FIGURE 3.10: Construction of a Compensated Demand Curve
Quantity of Y X’ X”
X’”
Quantity of X ’ PX hx
(a) Individual’s indifference curve map
PX’
PX’’
PX’” hx X’ X”
X’”
Quantity of X
(b) Compensated demand curve
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109. Compensated Demand Curves
In Panel b the vertical axis is the price of good X and the horizontal axis is the quantity of good X demanded.
The tangency points in Panel a generate the curve hx shown in panel b.
In this curve utility (instead of nominal income) is held constant.
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110. Compensated Demand Curves
The curve hX is called a “compensated” demand curve since the effects of the price changes on purchasing power are compensated so as to prevent the individual’s welfare to increase from the price declines.
Price increases would have to be compensated by increased income.
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111. Compensated Demand Curves
A demand curve drawn on the assumption that other prices and utility are held constant is a compensated demand curve.
Income effects of price changes are compensated for along the curve, and it reflects only substitution effects.
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112. Consumer Surplus
The extra value individuals receive from consuming a good over what they pay for it is called consumer surplus.
Consumer surplus is also what people would be willing to pay for the right to consume a good at its current price.
This concept is used to study the welfare effects of price changes.
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113. Consumer Surplus The compensated demand curve is shown in Figure 3.11.
At the price P0 the individual chooses to consume X0 as shown at point E0.
If the price were to increase to P1 the consumer would choose zero consumption but would be compensated with income to keep utility constant.
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114. Consumer Surplus
Suppose, starting at X0, the price of X were increased very slightly (P) so that the consumer still consumed approximately X0.
To compensate for this price increase, his or her purchasing power would have to be increased by P·X0 if utility is to remain constant.
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115. FIGURE 3.11: Consumer Surplus
Price P1 E0 P0 hx
Quantity of X
per period X0
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116. Consumer Surplus
This compensation would allow the individual to continue to consume the original set of goods consumed before the price rise.
Repeating this experiment many times would result in a movement up along hX.
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117. Consumer Surplus
Summing all of these compensations as price increases from P0 to P1 would yield the shaded area P1E0P0.
This is the total increase in purchasing power that must be provided to this person to make him or her equally well off at P1 (where no X is consumed) as at P0 (where X0 is consumed).
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118. Consumer Surplus
Thus the shaded triangle in Figure 3.11 shows what this individual would voluntarily pay for the right to be allowed to choose to consume X0 at its current price P0.
Hence, at E0this person is receiving consumer surplus in the amount of P1E0P0.
Lower prices increase consumer surplus while higher prices lower it.
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119. 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.
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120. APPLICATION 3.6: Valuing 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 $50 and consume an average of 55 micrograms of suspended particulates per cubic meter.
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121. FIGURE 1: Compensated Demand Curve for Clean Air
Price
($) 85 80 60 E 50 40 20 D
Air quality
(mg/m3)
100 75 50 25 55
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122. APPLICATION 3.6: Valuing 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.
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