1. Walter Nicholson Christopher Snyder
Amherst College
Christopher Snyder
Dartmouth College
PowerPoint Slide Presentation | Philip Heap, James Madison University
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2. CHAPTER 3
Demand Curves
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3. Chapter Preview
Last chapter you learned how an individual maximizes her utility.
What were the two utility maximizing conditions?
Now we will use the utility maximization model to show how to derive an individual’s demand curve.
From there, we can see how we get the market demand curve.
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4. Individual Demand Functions
A demand function: representation of how quantity demanded depends on prices, income, and preferences.
Quantity of X demanded = dX(PX, PY, I; preferences)
The amount of soda you demand depends on: price of soda, price of a related goods, your income, and your preferences.
We will assume that over the relevant time frame, preferences remain the same.
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5. Individual Demand Functions
Suppose that both the prices of the goods you buy and your income double. How do you change your behavior?
You don’t. What matters is the relative price of goods and the real value of your income.
Demand functions are homogeneous. Quantity demanded does not change when prices and income change proportionally.
PXX + PYY = I vs. 2PXX + 2PYY = 2I
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6. Changes in Income
What happens to the quantity purchased of some good as your income increases?
Depends on whether the good is normal or inferior.
A normal good is a good that is bought in greater quantities as income increases.
An inferior good is a good that is bought in smaller quantities as income increases.
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7. Changes in Income: A Normal Good
Quantity of Y
per week
Suppose you start with I1
You maximize utility by buying X1 and Y1
Now your income increases to I2
You maximize utility by buying X2 and Y2
If your income increases to Y3, you buy X3 and Y3 Y3 Y2 Y1 U3 U2 U1 I1 I2 I3 X1 X3
Quantity of X
per week X2
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8. Changes in Income: An Inferior Good
Quantity of Y
per week
Suppose like before your income increases from I1 to I3 Y3
Now as your income increases, you buy more Y but buy less Z. U3
So Y is normal and Z is inferior. Y2 U2 Y1 I1 I2 U1 I3 Z3
Quantity of Z
per week Z2 Z1
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9. Change in A Good’s Price
What happens to the quantity purchased of some good when the price of the good falls or rises?
Substitution effect
The effect on consumption due to a change in price holding real income or utility constant.
Income effect
The effect on consumption due to a change in real income caused by a change in price.
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10. Change in a Good’s Price
Initially a consumer maximizes utility on the budget constraint at X*, Y*
Quantity of Y
per week
A decrease in the price of X will cause the budget constraint to pivot out.
The consumer now maximizes utility at X**,Y**
New budget constraint
Y** Y* U2
Old budget constraint U1
Quantity of X
per week X*
X**
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11. Change in a Good’s Price
To show the substitution effect: move the new budget constraint back so that it is tangent to the original indifference curve.
Quantity of Y
per week
This shows how much of X and Y is purchased assuming real income has not changed but X is now cheaper.
New budget constraint
Y** Y* U2
Old budget constraint U1
Quantity of X
per week X* XB
X**
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12. Change in a Good’s Price
The change in consumption from X* to XB is the substitution effect.
Quantity of Y
per week
The change from XB to X** is the income effect.
New budget constraint
Y** Y* U2
Old budget constraint U1 X* XB
X**
Quantity of X
per week
Substitution Effect
Income Effect
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13. Change in A Good’s Price
What did we show:
As the PX falls, the budget constraint pivots out.
This allows the consumer to buy more X.
The substitution effect always says buy more X when PX falls.
In our example the income effect was also positive: as real income rises, buy more of the good.
What type of good is X?
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14. A Numerical Example
Suppose you have $30. PBurger = $3 and PSoda = $ You buy 5 burgers and 10 sodas in order to maximize utility.
Now suppose PBurger = $1.50
If you still buy 5 burgers and 10 sodas you have $7.50 left over.
At this point the MRS ≠ price ratio. Buy more burgers and less soda: substitution effect
With greater purchasing power can buy more burgers and more soda: income effect
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15. Substitution and Income Effects
Any price change has both substitution and income effects. Why is the substitution effect generally more important?
In most cases income effects are small since the good constitutes only a small portion of total spending.
Think of perfect complements and perfect substitutes. What is the size of the two effects?
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16. Substitution and Income Effects
Right Shoes
Exxon U1 I I’ I I’ U1
Mobil
Left Shoes
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17. Substitution and Income Effects for Inferior Goods
What happens as the price of X increases?
The substitution effects leads to more X.
The income effect leads to less X.
Since overall the consumption of X increases when the price of X falls the substitution effect > income effect.
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18. Substitution and Income Effects for Inferior Goods
Quantity of Y
per week
The consumer starts by buying X* and Y*
If the price of X increases, the constraint pivots in and the consumer now buy X** and Y** Y* U1
Y** U2
X** X*
Quantity of X
per week
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19. Substitution and Income Effects for Inferior Goods
To show the substitution effect: move the new budget constraint back so that it is tangent to the original indifference curve.
Quantity of Y
per week
The substitution effect is from X* to XB
The income effect is from XB to X** Y* U1
Y** U2
Quantity of X
per week XB
X** X*
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20. Substitution and Income Effects for Inferior Goods
So for an inferior good:
As the price rises (falls), the substitution effects says to buy less (more)
As the price rises (falls), the income effect says to buy more (less) if the good is inferior.
The substitution effect > income effect so as price rises (falls), quantity falls (rises)
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21. Giffen’s Paradox
What if the income effect is greater than the substitution effect?
What happens when the price of a good rises?
People buy more of the good.
Ireland and potatoes.
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22. Lump Sum Principle Lump sum principle:
Taxes imposed on income have smaller welfare costs than taxes imposed on a narrow selection of commodities.
Compare an income tax and a goods tax.
Intuition behind the lump sum principle.
Substitution and income effects of the two taxes.
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23. Lump Sum Principle Quantity of Y per week
The consumer starts by buying X1 and Y1
A tax on good X would cause the consumer to change their consumption to X2 and Y2 Y1 U1 Y2 U2 X2 X1
Quantity of X
per week
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24. Lump Sum Principle
Suppose the government imposed an income tax that raises the same revenue
Quantity of Y
per week
The consumer could still afford to buy X2 and Y2.
But with this budget constraint the consumer would buy X3 and Y3 Y1 U1 Y2 U3 U2
Quantity of X
per week X2 X1
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25. Lump Sum Principle Quantity of Y per week
Utility is higher with a lump sum tax than with a tax on good X: U3 > U2
What is the implication for tax policy? Y1 U1 Y2 U3 U2 X1
Quantity of X
per week X2
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26. Individual Demand Curves
An individual demand curve shows the relationship between price and quantity demanded holding all else – income, prices of other goods, tastes etc. – constant.
We want to use our indifference curve diagram to show how to derive an individual’s demand curve for a good.
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27. Deriving an Individual’s Demand Curve
Quantity of Y per week
At a price of P’x, the consumer maximizes utility by buying X’
So at P’x the consumer demands X’ units
Price
P’x U1
Quantity of X per week X’ X’
Quantity of X per week
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28. Deriving an Individual’s Demand Curve
Quantity of Y per week
As the price of X falls the budget line pivots out and consumption increases to X’’.
So now at the new price the quantity demanded is X’’
Price
P’x U2 U1
Quantity of X per week X’
X’’ X’
X’’
Quantity of X per week
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29. Deriving an Individual’s Demand Curve
Quantity of Y per week
Once again consumption of X rises as PX falls
And quantity demanded rises as the price falls.
Price
P’x U3 U2 U1
Quantity of X per week X’
X’’
X’’’ X’
X’’
X’’’
Quantity of X per week
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30. Deriving an Individual’s Demand Curve
So as price falls, quantity demanded rises.
Quantity of Y per week
Price
P’x U3 U2 U1 dX
Quantity of X per week X’
X’’
X’’’ X’
X’’
X’’’
Quantity of X per week
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31. Shape of the Demand Curve
The shape and slope of the demand curve depends on the size of the income and substitution effect.
If good X has many (few) close substitutes the demand curve will be relatively flat (steep).
Breakfast cereal vs. water.
Food and the income effect.
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32. Shifts in an Individual’s Demand Curve
What happens to the demand curve if something other than price changes?
What about a change in income?
What about a change in the price of another good?
What about a change in preferences?
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33. Shifts in an Individual’s Demand Curve
An increase in income Px Px
Normal
Inferior P1 P1 d2 d1 d2 d1 X X X1 X2 X2 X1
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34. Shifts in an Individual’s Demand Curve
An increase in the price of Y Px
Substitutes Px
Complements P1 P1 d2 d1 d2 d1 X X X1 X2 X2 X1
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35. A Comment on Terminology
Do not confuse the terms demand and quantity demanded.
Price causes a change in quantity demanded. It does NOT change demand.
A change in factors other than price change demand.
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36. Consumer Surplus
Suppose you go to a concert. The price of a T-shirt is $25. You are willing to pay $40. What can you say?
Consumer surplus is the extra value consumers receive from consuming a good over what they pay for it.
Consumer surplus is what people would be willing to pay for the right to consume a good at its current price.
Consumer surplus gives us a way to put a dollar value on the utility people obtain from a transaction.
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37. Consumer Surplus and the Demand Curve
The demand curve shows a person’s demand for T-Shirts.
Each point shows what you are willing to pay for one more unit.
Price
($/shirt)
$11 for the 10th T-Shirt
$9 for the 15th T-Shirt 15
$7 for the 20th T-Shirt 11 9 7 10 15 20
Quantity (shirts)
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38. Consumer Surplus and the Demand Curve
If P = $7, how many T-shirts will the consumer buy? Show their consumer surplus. How much consumer surplus do they obtain?
Price
($/shirt)
They buy 20 T-Shirts.
Consumer Surplus = ½ x (15 – 7) x 20 = $80 15 11 9 7 10 15 20
Quantity (shirts)
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39. Consumer Surplus
At a price of $7 the person bought 20 T-Shirts and received $80 in consumer surplus. What is the total value of the T-Shirts?
Total Value = Total Expenditure + Consumer Surplus
$7 x 20 + $80 = $220
What happens to consumer surplus as the price of the good rises or falls?
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40. Consumer Surplus and Utility
Other goods
(per week)
You initially max utility at point E: 20 T-Shirts and $500 worth of other items. A
How much would you have to be compensated if you were not allowed to buy T-Shirts?
$80 B E
500 U1 I
T-Shirts
(per week) 20
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41. Consumer Surplus and Utility
Other goods
(per week)
How much would you be willing to pay for the right to consume T-Shirts at $7 each? A
$80 B
$80 E C U1 U0 I I’
T-Shirts
(per week) 20
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42. Consumer Surplus and Utility
What did we show?
With no T-Shirt law you would have to be compensated $80 to maintain the same level of utility.
The $80 also represents the consumer surplus you get when you buy 20 shirts at $7.
Given there is a no T-Shirt law, you would be willing to pay $80 to be able to buy T-Shirts. Again this $80 is the consumer surplus.
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43. Market Demand Curves Market demand:
total quantity of a good or service demanded by all potential buyers.
Market demand curve:
shows the relationship between the total quantity demanded of a single good or service and its price, holding all other factors constant.
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44. Constructing the Market Demand Curve
Assume there are only two people.
For each price add up the quantity demanded by each person. PX PX PX
P*X D
X*1
X*2 X* X
(a) Individual 1
(b) Individual 2
(c) Market Demand
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45. Shifts in the Market Demand Curve
What would cause the market demand curve to shift outward (increase) or shift inward (decrease)?
Think about what causes a shift in individual demand curves.
A change in income:
If people view the good as normal, an increase in income will cause the market demand curve to shift outward.
If people view the good as inferior, an increase in income will cause the market demand curve to shift inward.
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46. Shifts in the Market Demand Curve
A change in the price of a related good.
If buyers regard X and Y as substitutes, an increase in the price of Y will cause the market demand for X to shift outward.
If buyers regard X and Y as complements, an increase in the price of Y will cause the market demand for X to shift inward.
Examples?
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47. Elasticity
We want to come up with a way to measure the change in quantity demanded due to a change in own price, the price of a related good, and income.
Elasticity:
A measure of the percentage change in one variable brought about by a 1 percent change in another variable.
With percentage changes we do not have to worry about the actual units of measurement.
Think of responsiveness when talking about elasticity.
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48. Price Elasticity of Demand
Usually, eQ,P < 0. Why?
If eQ,P = -2, what does that tell you?
A 10% decrease in price will cause quantity demanded to increase by 20%.
If eQ,P = -.4, what does that tell you?
A 10% decrease in price will cause quantity demanded to increase by 4%.
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49. Price Elasticity of Demand
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50. Price Elasticity of Demand
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51. Price Elasticity of Demand
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52. Price Elasticity of Demand
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53. Determinants of Price Elasticity of Demand
What determines the price elasticity of demand?
Number of close substitutes.
Goods with many close substitutes have relatively elastic demand curves.
Time
The more time people have to respond to a change in price, the more elastic demand will be.
In the long term demand tends to be more elastic than in the short term.
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54. Price Elasticity of Demand and Total Spending
Suppose you sell cars. If you want to increase total spending, should you increase or decrease your price?
Suppose price elasticity of demand for cars = -2.
Initially people buy 1 million automobiles at $10,000 each.
Total initial spending = 1 million x $10,000 = $10 billion.
How many cars will you sell if you increase price by 10%?
Sales would fall by 20 percent (-2 x 10%) so sales fall to 800,000.
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55. Price Elasticity of Demand and Total Spending
What happens to total spending?
Total spending after the price increase would be only $8.8 billion (800,000 x $11,000).
So if demand is elastic (-2) an increase in price leads to a decrease in total spending.
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56. Price Elasticity of Demand and Total Spending
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57. Price Elasticity of Demand and Total Spending
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58. Price Elasticity of Demand and Total Spending
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59. Price Elasticity of Demand and Total Spending
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60. Price Elasticity of Demand and Total Spending
Initially total expenditure is the blue box.
After the price increase, total expenditure is the red box.
Price PX P1 P1 P0 P0 D D
Quantity
per period
Quantity
per period Q1 Q0 Q1 Q0
(b) Elastic Demand
(a) Inelastic Demand
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61. Price Elasticity: Linear Demand Curve
Depending on the demand curve, price elasticity can be the same or change as price rises and falls.
Elasticity should be measured at current prices.
Linear demand curves:
Elastic at prices above midpoint price: e < -1
Unit elastic at midpoint price: e = -1
Inelastic at prices below midpoint price: e > -1
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62. Price Elasticity: Linear Demand Curve
Q = 100 – 2P
Price 50 40 30 25 20 10
Demand
Quantity of CD
players per week 20 40 50 60 80
100
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63. Price Elasticity: Linear Demand Curve
In general:
If Q = a – bP:
eQ,P = b x (P/Q)
b is the slope of the demand curve
P and Q are the price and quantity at which you measure elasticity.

64. Price Elasticity: Linear Demand Curve
For last example: Q = 100 – 2P, so b = -2
When P = $40, Q = 20 so eQ,P = -2 x (40/20) = -4
When P = $25, Q = 50 so eQ,P = -2 x (25/50) = -1
When P = $10, Q = 80 so eQ,P = -2 x (10/80) = -0.25
Are the values consistent with what we have said?

65. Price Elasticity: Linear Demand Curve
Q = 100 – 2P
Price 50 40 30 25 20 10
Demand
Quantity of CD
players per week 20 40 50 60 80
100
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66. Price Elasticity: Unit Elastic Curve
If demand is unit elastic, e = -1 at each point on the demand curve.
Therefore, total spending is the same at each point.
Suppose Q = 1,200/P.
Price
At each price, total spending is $1,200. $6 $2
Quantity of burgers
200
600

67. Income Elasticity of Demand
Income elasticity of demand: percentage change in quantity demanded of a good in response to 1 percent change in income.
Normal goods: eQ,I > 0
Inferior goods: eQ,I < 0
If a good has an eQ,I > 1, the good is called a luxury good.
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68. Cross-Price Elasticity of Demand
Cross-price elasticity of demand: the percentage change in the quantity demanded of a good in response to a 1 percent change in price of another good.
Substitute goods: eQ,P > 0
Complementary goods: eQ,P < 0
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69. Some Price and Income Elasticities
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70. Summary
If prices and income change by the same proportionate amount economic choices are not affected.
As the price changes there is both a substitution effect and an income effect.
The direction of the income effect depends on whether the good is normal or inferior.
A change in the price of one good will affect the demand of another good: complements and substitutes.
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71. Summary
Consumer surplus measures what people are willing to pay for the right to consume a good at its current price.
Market demand curves are the horizontal sum of individual demand curves.
The price elasticity of demand is a measure of how responsive quantity demanded is to a change in price: elastic vs. inelastic.
There is a close relationship between price elasticity of demand and total spending.
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72. Summary
Cross-price elasticity is a measure of how responsive quantity demanded is to a change in the price of a related good: complements vs. substitutes.
Income elasticity is a measure of how responsive quantity demanded is to a change in income: normal vs. inferior.
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