1. Utility Functions, Budget Lines and Consumer Demand
Overheads

2. Conditions for the consumer optimum
a. The indifference curve and the budget line are tangent
at the optimum combination of q1 and q2
b. The slope of the budget line and the slope
of the indifference curve are equal at the optimum
c. The price ratio equals the ratio of marginal utilities
d. The marginal utility per dollar for each good is equal

3. Example problem Initial prices and income p1 = 5, p2 = 10, I0 = 50
Initial equilibrium 16 q1 14
Budget Line 0 12
u = 8
u = 10.99 10 8 6 4 2 1 2 3 4 5 6 7 8 q2

4. Change in income
Subsequent prices and income p1 = 5, p2 = 10, I1 = 75.
Increase in Income 16 q1 14
Budget Line 1
Budget Line 0
u = 10.99
u = 8 12 10 8 6 4 2 1 2 3 4 5 6 7 8 q2

5. Move to a higher indifference curve
Initial equilibrium
Subsequent equilibrium 2 4 6 8 10 12 14 16 1 3 5 7 q
u = 10.99
Budget Line 1
u =
u = 8
Budget Line 0

6. Another Example Initial equilibrium
Initial prices and income p1 = 6, p2 = 4, I0 = 58
Budget Line 0
u=9.614
Initial equilibrium 16 q 14 1 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

7. Raise income so we have p1 = 6, p2 = 4, I0 = 78 Initial equilibrium
Budget Line 0
u=9.614
Initial equilibrium
Subsequent equilibrium
u=12.018 16 q 14 1 12
Budget Line 1 10 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

8. So both goods are normal goods
In these examples,
we consume more of both goods as income rises
So both goods are normal goods
So what is a Normal Good?
A Normal Good is a good that someone
will buy more of as their income increases

9. What About an Inferior Good?
An Inferior Good is a good that someone
will buy less of as their income increases

10. Inferior Good With A Rise in Income
Good 2 is inferior
u = 7
Budget Line 2
u=12.204
u=19.216 q 6 1 5
Budget Line 1 4
Budget Line 0 3 2 1 1 2 3 4 5 6 7 8 q 2

11. Inferior Good With A Rise in Income
I1 = p1 q1 + p2 q2 q1
Good 1 is inferior
I0 = p1 q1 + p2 q2 q2

12. Changes in Price Budget line will rotate rather than shift
Budget line will rotate around a fixed point
on the axis of the good whose price does not change

13. Consider a decrease in the price of good 2 from $10 to $6
Initial equilibrium
Subsequent equilibrium 2 4 6 8 10 12 14 16 1 3 5 7 q
u = 10.99
u =
u = 8
Budget Line 0
Budget Line 1

14. The quantity of good 2 increases with a fall in its price
The quantity of good 1 does not change with a fall
in the price of good 2

15. Different utility function with different prices and income
Initial prices and income p1 = 6, p2 = 4, I0 = 58
Initial equilibrium
u=9.614 16 q 14 1 12 10
Budget Line 0 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

16. Now decrease p1 from $6 to $4
Initial prices and income p1 = 6, p2 = 4, I0 = 58
u=9.614
Budget Line 0
Initial equilibrium
Subsequent equilibrium
u=10.586 16 q 14
Budget Line 1 1 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

17. The quantity of good 1 increases with a fall in its price
The quantity of good 2 decreases with a decrease
in the price of good 1
The two goods are clearly substitutes in consumption

18. Using indifference curves to determine demand
Initial prices and income p1 = 6, p2 = 3, I0 = 58.
Initial Optimum q1 = 2.80, q2 =
u = 16 q 14 1 12 10
Budget Line 0 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

19. p2 q2
Raise the price of good 2 to 4.00

20. Using indifference curves to determine demand
Next prices and income p1 = 6, p2 = 4, I0 = 58.
Next Optimum q1 = 3.00, q2 = 10.00
u = 16
u=9.614 q 14 1 12 10
Budget Line 0
Budget Line 1 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

21. p2 q2
Raise the price of good 2 to 5.00

22. Using indifference curves to determine demand
Next prices and income p1 = 6, p2 = 5, I0 = 58.
Next Optimum q1 = 3.20, q2 = 7.76
u = 16
u=9.614 q 14 1
u=8.635 12 10
Budget Line 0
Budget Line 1
Budget Line 2 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

23. p2 q2
Raise the price of good 2 to 6.00

24. Using indifference curves to determine demand
Next prices and income p1 = 6, p2 = 6, I0 = 58.
Next Optimum q1 = 3.40, q2 = 6.267
u = 16
u=9.614 q 14
u=7.962 1
u=8.635 12 10
Budget Line 0
Budget Line 2
Budget Line 1
Budget Line 3 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

25. p2 q2

26. p2 q2
Demand for good 2 10 p 2 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

27. p2 q2
Demand for good 2 10 p 2 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

28. p2 q2
Demand for good 2 10 p 2 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

29. p2 q2
Demand for good 2 10 p 2 8 6 D2 4 2 2 4 6 8 10 12 14 16 18 20 q 2

30. Plot the price and quantity combinations as we go
Increase in the price of good 2 16
u = q 14 1
u=9.614 12 10
Budget Line 1
Budget Line 0 8 6 4 2
p2 = 3, q2 = 2 4 6 8 10 12 14 16 18 20 q 2
p2 = 4, q2 =
Demand for good 2 10 p 2 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

31. Plot some more price and quantity combinations
Increase p2 some more
u = 16
u=9.614 q 14 1 12
u=8.635 10
Budget Line 0
Budget Line 1
Budget Line 2 8 6 4 2 2 4 6 8 10 12 14 16 18 20
p2 = 5, q2 = 7.760 q 2
Demand for good 2 10 p 2 8 6 4 2 2 4 6 8 10 12 14 16 18 20 q 2

32. Plot some more price and quantity combinations
Increase p2 some more
u = 16
u=9.614 q 14
u=8.635 1 12
u=7.962 10
Budget Line 0
Budget Line 3 8
Budget Line 1 6
Budget Line 2 4 2 2 4 6 8 10 12 14 16 18 20
p2 = 6, q2 = 6.267 q 2
Demand for good 2 10 p 2 8 6 D2 4 2 2 4 6 8 10 12 14 16 18 20 q 2

33. Consumer theory and the law of demand
The law of demand states that when
the price of a good rises,
and everything else remains the same,
the quantity demanded of the good will fall.

34. Consumer theory and the law of demand
When a good’s price changes, we can identify
two separate effects on the quantity demanded
When the price of a good falls, it becomes
relatively less expensive, as compared to
goods whose prices have not fallen
The consumer will demand more of this good
This is called the substitution effect

35. What is the Substitution Effect?
When the price of a good falls, consumers will
substitute it for other goods,
which are now relatively more expensive
When the price of a good rises, consumers will
substitute from it to other goods,
which are now relatively less expensive

36. Why ? The substitution effect of a price change
arises from a change in the relative price of a good,
And it always moves the quantity demanded
in the opposite direction of the price change.
With only the substitution effect,
demand curves would always have negative slope
Why ?

37. Because indifference curves slope down
If we hold real income (utility) constant
the effect of a price change on quantity
will always be negative
Consider then a change in price but hold
real income constant

38. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1
Old P New U 12
Budget Line 0 10
Budget Line 1 8 6 4 2 1 2 3 4 5 6 7 q2

39. The substitution effect
Lower the price of q2, find the new utility level
Give the consumer enough income to get to the new
utility level without the price change
At the new utility level, lower the price of q2

40. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1
Old P New U 12
Budget Line 0 10
Budget Line 1 8 6 4 2 1 2 3 4 5 6 7 q2

41. What is the substitution effect?
After changing price,
hold utility fixed at the new utility level,
and then evaluate the effect of the price change
Because indifference curves slope down,
the substitution effect is always negative

42. Price and demand another way
After changing price,
hold utility fixed at the old utility level,
and then evaluate the effect of the price change
Because indifference curves slope down,
the substitution effect is always negative

43. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1 12
Budget Line 0 10
Budget Line 1 8
New P, Old U 6 4 2 1 2 3 4 5 6 7 q 2

44. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1
Old P New U 12
Budget Line 0 10
Budget Line 1 8
New P, Old U 6 4 2 1 2 3 4 5 6 7 q 2

45. The income effect When the price of a good falls, there is a change
When a good’s price changes, we can identify
two separate effects on the quantity demanded
When the price of a good falls, there is a change
in the overall purchasing power of the consumer
The consumer will demand more or less of this good
This is called the income effect

46. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1
Old P New U 12
Budget Line 0 10
Budget Line 1 8
Substitution 6 4
Income 2 1 2 3 4 5 6 7 q 2

47. What is the Income Effect of a change in price?
The income effect is the change in quantity demanded
that arises because of the change in purchasing power
caused by a price change

48. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Budget Line 1
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1
Old P New U
Income 12
Budget Line 0 10 8
Substitution 6 4 2 1 2 3 4 5 6 7 q 2

49. Some of the benefit of a price decline is
that there is more money to spend on other goods
u = 10.99 16
u = q 14 1
Old P New U
Income 12
Budget Line 0 10
Budget Line 1 8 6 4 2 1 2 3 4 5 6 7 q 2

50. this will increase the quantity demanded
Some of the benefit of a price decline is
that there is more money to spend on other goods
For normal goods,
this will increase the quantity demanded

51. The substitution and income effects work
in the same direction (more q2)
u = 10.99 16
u = q 14 1
Old P New U
Income 12
Budget Line 0 10
Budget Line 1 8
Substitution 6 4 2 1 2 3 4 5 6 7 q 2

52. What about an Inferior Good ?
Consider a family of indifference curves 10 20 30 40 50 60 q2 q1 u1 u2 u3 u4 u5

53. q1 = 40 q2 = 15 60 50 40 30 20 10 Consider a set of prices and income
Income = 66 p1 = p2 = 1
q1 = 40 q2 = 15
Budget Line 0 10 20 30 40 50 60 q2 q1
52.8 u1 u2 u4

54. q1 = 34 q2 = 31 60 50 40 30 20 10 Consider a drop in p1
Income = 66 p1 = p2 = 1 q1 = 40 q2 = 15
Income = 66 p1 = p2 = 1
q1 = 34 q2 = 31 66 10 20 30 40 50 60 q2 q1
Budget Line 1
Budget Line 0 u2 u4

55. What has happened? Income = 66 p1 = 1.25 p2 = 1 q1 = 40 q2 = 15
Drop p1
Income = 66 p1 = p2 = 1 q1 = 34 q2 = 31
Price falls and demand falls
Is the law of demand false?

56. Let’s look closer 5 10 15 20 25 30 35 40 45 50 55 60 60 p1 falls q1 50
Budget Line 0 60
Budget Line 1
p1 falls q1
Old P New U 50
u =
u = 40
Income
Substitution 30 20 10 5 10 15 20 25 30 35 40 45 50 55 60 q2

57. Again
Budget Line 0 60
Budget Line 1
p1 falls q1
Old P New U 50
u =
u = 40
Income
Substitution 30 20 10 5 10 15 20 25 30 35 40 45 50 55 60 q2

58. What is the Income Effect of a change in price?
Some of the benefit of a price decline is
that there is more money to spend on other goods
For normal goods,
this will increase the quantity demanded
The substitution and income effects work
in the same direction

59. What is the Income Effect of a change in price?
For inferior goods, a decrease in income
will decrease the quantity demanded
The substitution and income effects work
in opposite directions

60. If the income effect is large enough,
a law of demand may not be satisfied
for inferior goods

61. Example where the income effect is not so large
I0 = p1 q1 + p2 q2 q2 q1
Drop p1
Substitution
Income

62. Another Example
Budget Line 0 u0 18 q1
Budget Line 1
Old P New U u1 16 14 12
Raise p1 10
Income
Substitution 8 6 4 2 35 40 45 50 55 60 65 q2

63. Inferior goods could disobey the law of demand
For normal goods, both substitution and income
effects work together, causing the quantity
demanded to move in the opposite direction of price.
Normal goods always obey the law of demand
For inferior goods, the substitution and income
effects of a price change work against each other.
The substitution effect moves quantity demanded
in the opposite direction as price, while the income
effect moves it in the same direction as price.
Inferior goods could disobey the law of demand

64. Most goods are such a small proportion
But,
the substitution effect almost always dominates
Most goods are such a small proportion
of income that the income effect of a
price change is usually small
So most, if not all, inferior goods
obey the law of demand

65. Consumers and markets The market demand curve is found by horizontally
summing the individual demand curves
of every consumer in the market

66. P D 20 0 16 2 12 4 8 10 4 20 Demand for Consumer 1 2 4 6 8 D15 10 15 20 2 4 6 8 D1
P D
20 0
16 2
12 4 8 10
Demand for Consumer 2 2 4 6 8 10 12 16 20 D2 4 20

67. P D 20 0 16 2 12 4 8 10 4 20 0 30 D12 Aggregate Demand for 2 Consumers
20 0
16 2
12 4
8 10
4 20
0 30 20
D12 15 10 5 5 10 15 20 25 30

68. P D1 D2 D

69. Three Consumers
P D1 D2 D3 D

70. Demand for Consumer 1 5 10 15 20 2 4 6 8 D1
Demand for Consumer 2 2 4 6 8 10 12 16 20 D2
P D1 D2 D3 D 8
Demand for Consumer 3 2 4 6 8 10 D3 6 4 2 12

71. D Aggregate Demand P D1 D2 D3 D 20 0 0 0 0 16 2 0 0 2 10 5 0 0 5 5 10 15 20 4 8 12 16 24 28 32 36 40 D

72. End of Presentation

73. Extra Stuff

74. Decrease in the price of good 2
u = 8 2 4 6 8 10 12 14 16 1 3 5 7 q
u = 10.99
u =
Budget Line 1
u =
Budget Line 2
Budget Line 0

75. Decrease in the price of good 2
u = 8 2 4 6 8 10 12 14 16 1 3 5 7 q
u = 10.99
u =
Budget Line 1
u =
Budget Line 2
Budget Line 0

76. Different utility function with different prices and income
Initial prices and income p1 = 6, p2 = 4, I0 = 58
Initial equilibrium
u = 8 16
u=9.614 q 14
u=10.586 1 12
u=12.018 10
Budget Line 0 8
Budget Line 1 6
Budget Line 2 4 2 2 4 6 8 10 12 14 16 18 20 q 2

77. q q u = 11.171 16 u=9.614 14 u=7.962 u=8.635 12 10 Budget Line 02 4 6 8 10 12 14 16 18 20 q 2

78. q q u = 11.171 16 u=9.614 14 u=7.962 u=8.635 12 10 Budget Line 02 4 6 8 10 12 14 16 18 20 q 2

79. Demand for good 2 D2 Increase in the price of good 2 q q 16 14 12 10 8
u = 16
u=9.614 q 14
u=8.635 1 12
u=7.962 10
Budget Line 0 8
Budget Line 1 6
Budget Line 2 4
Budget Line 3 2 2 4 6 8 10 12 14 16 18 20 q 2
Demand for good 2 2 4 6 8 10 12 14 16 18 20 q p D2

80. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1
Old P New U 12
Budget Line 0 10
Budget Line 1 8
New P, Old U 6 4 2 1 2 3 4 5 6 7 q 2

81. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1
Old P New U 12
Budget Line 0 10
Budget Line 1 8
New P, Old U 6 4 2 1 2 3 4 5 6 7 q 2

82. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5 14
u = 10.99 q 12 1
u = 10
Budget Line 1
Budget Line 0 8
Budget Line 3 6 4 2 1 2 3 4 5 6 7 8 q 2

83. 1 2 3 4 5 6 7 8 Decrease in p holding u fixed at 10.99 14 u = 10.99 q12 1
u = 10
Budget Line 0
Budget Line 1 8
Budget Line 3 6 4 2 1 2 3 4 5 6 7 8 q 2

84. Adjust income to keep utility at 10.99 with the new prices

85. Initial prices and income - p1 = 5, p2 = 10, I0 = 50
Initial equilibrium - q1 = 4, q2 = 3
Lower p2 from 10 to 5
New equilibrium - q1 = 4, q2 = 5
u = 10.99 16
u = q 14 1
Old P New U 12
Budget Line 0 10
Budget Line 1 8
New P, Old U 6 4 2 1 2 3 4 5 6 7 q 2

86. Demand for Consumer 3 2 4 6 8 10 D3

87. Budget Line 0 60
Budget Line 1 q1
Budget Line 2 50
u =
u =2620.5
u =
u =
u = 40 30 20 10 5 10 15 20 25 30 35 40 45 50 55 60 q2

88. Budget Line 0 60
Budget Line 1 q1
Budget Line 2 50
u =
u =2620.5
u =
u =
u = 40 30 20 10 5 10 15 20 25 30 35 40 45 50 55 60 q2

89. 60 50 40 30 20 10 q1 q2 Budget Line 0 Budget Line 1 Budget Line 2 u110 20 30 40 50 60 q2 q1 u1 u2 u3 u4 u5

90. What about an Inferior Good ?
I0 = p1 q1 + p2 q2 q2 q1
Drop p1

92. u1 u0 18 q1
Budget Line 0 16 u2
Budget Line 1 14
Budget Line 2 12 10 8 6 4 2 35 40 45 50 55 60 65 q2