Transcript File

Chapter
21
The Theory of
Consumer Choice
Budget Constraint: What the Consumer can Afford
• Budget constraint
– Limit on the consumption bundles that a
consumer can afford
• Trade-off between goods
• Slope of the budget constraint
• Rate at which the consumer can trade one good
for the other
• Change in the vertical distance
• Divided by the change in the horizontal distance
– Relative price of the two goods
2
Figure 1
The consumer’s budget constraint (table)
Number
of Pizzas
Pints
of Pepsi
Spending
on Pizza
Spending
on Pepsi
Total
spending
100
90
80
70
60
50
40
30
20
10
0
0
50
100
150
200
150
300
350
400
450
500
$1,000
900
800
700
600
500
400
300
200
100
0
$0
100
200
300
400
500
600
700
800
900
1,000
$1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
The budget constraint shows the various bundles of goods that the consumer can buy
for a given income. Here the consumer buys bundles of pizza and Pepsi. The table and
graph show what the consumer can afford if his income is $1,000, the price of pizza is
$10, and the price of Pepsi is $2.
3
Figure 1
The consumer’s budget constraint (graph)
Quantity
of
Pepsi
B
500
C
250
Consumer’s
budget constraint
A
0
50
100
Quantity of Pizza
The budget constraint shows the various bundles of goods that the consumer can
buy for a given income. Here the consumer buys bundles of pizza and Pepsi. The
table and graph show what the consumer can afford if his income is $1,000, the
price of pizza is $10, and the price of Pepsi is $2.
4
Preferences: What the Consumer Wants
• Indifference curve
– Shows consumption bundles that give the
consumer the same level of satisfaction
– Combinations of goods on the same curve
• Same satisfaction
• Slope of indifference curve
– Marginal rate of substitution
• Rate at which a consumer is willing to trade one
good for another
– Not the same at all points
5
Figure 2
The consumer’s preferences
Quantity
Of Pepsi
C
B
D
MRS
A
1
0
I2
Indifference
curve, I1
Quantity of Pizza
The consumer’s preferences are represented with indifference curves, which show the
combinations of pizza and Pepsi that make the consumer equally satisfied. Because the
consumer prefers more of a good, points on a higher indifference curve (I2 here) are
preferred to points on a lower indifference curve (I1). The marginal rate of substitution
(MRS) shows the rate at which the consumer is willing to trade Pepsi for pizza. It measures
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the quantity of Pepsi the consumer must be given in exchange for 1 pizza.
Preferences: What the Consumer Wants
• Four properties of indifference curves
1. Higher indifference curves are preferred to
lower ones
– Higher indifference curves – more goods
2. Indifference curves are downward sloping
3. Indifference curves do not cross
4. Indifference curves are bowed inward
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Figure 3
The impossibility of intersecting indifference curves
Quantity
Of Pepsi
A
C
B
0
Quantity of Pizza
A situation like this can never happen. According to these indifference curves, the
consumer would be equally satisfied at points A, B, and C, even though point C has more
of both goods than point A.
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Figure 4
Bowed indifference curves
Quantity
Of Pepsi
14
MRS=8
A
8
1
4
3
B
MRS=1
Indifference
curve
1
0
2
3
6
7
Quantity of Pizza
Indifference curves are usually
bowed inward. This shape
implies that the marginal rate
of substitution (MRS) depends
on the quantity of the two
goods the consumer is
consuming. At point A, the
consumer has little pizza and
much Pepsi, so he requires a
lot of extra Pepsi to induce him
to give up one of the pizzas:
The marginal rate of
substitution is 6 pints of Pepsi
per pizza. At point B, the
consumer has much pizza and
little Pepsi, so he requires only
a little extra Pepsi to induce
him to give up one of the
pizzas: The marginal rate of
substitution is 1 pint of Pepsi
per pizza.
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Preferences: What the Consumer Wants
• Two extreme examples of indifference curves
• Perfect substitutes
– Two goods with straight-line indifference
curves
– Marginal rate of substitution – constant
• E.g.: nickels and dimes bundles
• Perfect complements
– Two goods with right-angle indifference
curves
• E.g.: right shoe and left shoe bundle
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Figure 5
Perfect substitutes and perfect complements
(b) Perfect Complements
(a) Perfect Substitutes
Left
shoes
Nickels
6
4
I2
7
5
I1
2
I1
0
1
I2
2
I3
3
Dimes
0
5
7
Right
shoes
When two goods are easily substitutable, such as nickels and dimes, the indifference curves
are straight lines, as shown in panel (a). When two goods are strongly complementary, such
as left shoes and right shoes, the indifference curves are right angles, as shown in panel (b). 11
Optimization: What the Consumer Chooses
• The consumer’s optimal choices
• Optimum
– Point where indifference curve and budget
constraint touch
– Best combination of goods available to the
consumer
– Slope of indifference curve
• Equals slope of budget constraint
• Marginal rate of substitution = relative price
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Figure 6
The consumer’s optimum
Quantity
of
Pepsi
Budget constraint
Optimum
B
A
I3
I2
I1
Quantity of Pizza
0
The consumer chooses the point on his budget constraint that lies on the highest indifference
curve. At this point, called the optimum, the marginal rate of substitution equals the relative
price of the two goods. Here the highest indifference curve the consumer can reach is I2. The
consumer prefers point A, which lies on indifference curve I3, but the consumer cannot afford
this bundle of pizza and Pepsi. By contrast, point B is affordable, but because it lies on a lower
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indifference curve, the consumer does not prefer it.
Optimization: What the Consumer Chooses
• How changes in income affect the
consumer’s choices
• Higher income
– Consumer can afford more of both goods
– Shifts the budget constraint outward
– New optimum
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Figure 7
An Increase in Income
Quantity
of
Pepsi
New budget constraint
1. An increase in income shifts the
budget constraint outward . . .
3. . . . and
Pepsi
consumption
New optimum
Initial
optimum
I2
2. . . . raising
pizza
consumption . . .
I1
Initial
budget
constraint
0
Quantity of Pizza
When the consumer’s income rises, the budget constraint shifts out. If both goods are normal
goods, the consumer responds to the increase in income by buying more of both of them.
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Here the consumer buys more pizza and more Pepsi.
Optimization: What the Consumer Chooses
• How changes in income affect the
consumer’s choices
• Normal good
– Good for which an increase in income raises
the quantity demanded
• Inferior good
– Good for which an increase in income reduces
the quantity demanded
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Figure 8
An inferior good
Quantity
of
Pepsi
3. . . . but Pepsi
consumption falls,
making Pepsi an
inferior good
New budget constraint
1. When an increase in income shifts the
budget constraint outward . . .
Initial
optimum
New optimum
I1
Initial budget
constraint
0
I2
2. . . . pizza consumption rises,
making pizza a normal good. . .
Quantity of Pizza
A good is an inferior good if the consumer buys less of it when his income rises. Here Pepsi is
an inferior good: When the consumer’s income increases and the budget constraint shifts
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outward, the consumer buys more pizza but less Pepsi.
Optimization: What the Consumer Chooses
• How changes in prices affect the consumer’s
choices
• Price of one good falls
– Rotates the budget constraint outward
• Steeper slope
• Change in relative price
– Income effect
– Substitution effect
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Figure 9
A change in price
Quantity
of Pepsi
D
New budget
constraint
1,000
New optimum
B
3. . . . and
raising Pepsi
consumption
1. A fall in the price of Pepsi rotates
the budget constraint outward. . .
500
Initial
budget
constraint
I2
Initial optimum
I1
A
0
100
2. . . . reducing pizza consumption
Quantity of Pizza
When the price of Pepsi falls, the consumer’s budget constraint shifts outward and changes
slope. The consumer moves from the initial optimum to the new optimum, which changes his
purchases of both pizza and Pepsi. In this case, the quantity of Pepsi consumed rises, and the
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quantity of pizza consumed falls.
Optimization: What the Consumer Chooses
• Income effect
– Change in consumption
– When a price change moves the consumer
• To a higher or lower indifference curve
• Substitution effect
– Change in consumption
– When a price change moves the consumer
• Along a given indifference curve
• To a point with a new marginal rate of
substitution
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Table
1
Income and substitution effects when the price of
Pepsi falls
Good
Income effect
Substitution effect
Total effect
Pepsi
Consumer is richer,
so he buys more Pepsi
Pepsi is relatively
cheaper, so consumer
buys more Pepsi
Income and substitution
effects act in same
direction, so consumer
buys more Pepsi
Pizza
Consumer is richer,
so he buys more pizza
Pizza is relatively
More expensive,
so consumer buys
less pizza.
Income and substitution
effects act in opposite
directions, so the
total effect on pizza
consumption is
ambiguous.
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Figure 10
Income and substitution effects
Quantity
of Pepsi
New budget
constraint
C
New optimum
Income
effect
B
Initial
budget
constraint
Substitution
effect
I2
A
Initial optimum
I1
0
Substitution effect
Quantity
of Pizza
The effect of a change in
price can be broken down
into an income effect and a
substitution effect. The
substitution effect—the
movement along an
indifference curve to a point
with a different marginal rate
of substitution—is shown
here as the change from
point A to point B along
indifference curve I1. The
income effect—the shift to a
higher indifference curve—is
shown here as the change
from point B on indifference
curve I1 to point C on
indifference curve I2.
Income effect
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Optimization: What the Consumer Chooses
• Deriving the demand curve
– Quantity demanded of a good for any given
price
– Initial optimum point
• Initial price of the good
• Initial quantity of the good
– A change in price of the good (new price)
• New optimum
• New optimum quantity
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Figure 11
Deriving the demand curve
(a) The Consumer’s Optimum
(b) The Demand Curve for Pepsi
Price of
Pepsi
Quantity
of Pepsi
New budget constraint
B
A
$2
750
I2
B
1
A
250
Demand
I1
0
Initial budget
constraint
Quantity
of Pizza
0
250
750 Quantity
of Pepsi
Panel (a) shows that when the price of Pepsi falls from $2 to $1, the consumer’s optimum moves
from point A to point B, and the quantity of Pepsi consumed rises from 250 to 750 pints. Demand
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curve in panel (b) reflects this relationship between the price and the quantity demanded.
Three Applications
• Do all demand curves slope downward?
• Law of demand
– When the price of a good rises, people buy
less of it
• Downward slope of the demand curve
• Giffen good
– An increase in the price of the good raises the
quantity demanded
• Income effect dominates the substitution effect
• Demand curve – slopes upward
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Figure 12
A Giffen good
Quantity of
Potatoes
B
Initial budget
constraint
1. An increase in the price of potatoes
rotates the budget constraint inward . . .
Optimum with high
price of potatoes
D
New
budget
constraint
2. . . . which
increases
potato
consumption
if potatoes
are a Giffen
good.
E
Optimum with low
price of potatoes
C
I1
I2
A
0
Quantity of Meat
In this example, when the price of potatoes rises, the consumer’s optimum shifts from point C
to point E. In this case, the consumer responds to a higher price of potatoes by buying less
meat and more potatoes.
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The search for Giffen goods
• Potatoes - Giffen good during the Irish potato
famine of the 19th century
– Price of potatoes rose
• Large income effect
• People – cut back on the luxury of meat
• Buy more of the staple food of potatoes
• Chinese province of Hunan, rice
– Poor households exhibited Giffen behavior
• Lower price of rice (with subsidy voucher)
– Households - reduce their consumption of rice
• Higher price of rice (remove the subsidy)
– Households – increase consumption of rice
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Three Applications
• How do wages affect labor supply?
• Trade-off between leisure and consumption
• Bundle of goods: leisure and work
– Given wage
– Budget constraint
– Optimum
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Figure 13
The work-leisure decision
Consumption
$5,000
Optimum
I3
2,000
I2
I1
0
60
100
Hours of leisure
This figure shows Sally’s budget constraint for deciding how much to work, her indifference
curves for consumption and leisure, and her optimum.
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Three Applications
• How do wages affect labor supply?
• Increase in wage
– Budget constraint shifts outward
• Steeper
• New optimum
– If enjoy less leisure
• Work more
• Upward-sloping labor supply curve
• Substitution effect dominates
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Three Applications
• How do wages affect labor supply?
• Increase in wage
– Budget constraint shifts outward
• Steeper
• New optimum
– If enjoy more leisure
• Work less
• Backward-sloping labor supply curve
• Income effect dominates
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Figure 14
An increase in the wage (a)
. . . the labor supply curve slopes upward.
(a) For a person with these preferences . . .
Wage
Consumption
BC2
Labor supply
B
I2
1. When the wage rises . . .
BC1
A
I1
0
Hours of Leisure
2. . . . hours of leisure decrease . . .
0
3. . . . and hours of labor increase
Hours of Labor
Supplied
The two panels of this figure show how a person might respond to an increase in the wage. The graphs on the
left show the consumer’s initial budget constraint, BC1, and new budget constraint, BC2, as well as the
consumer’s optimal choices over consumption and leisure. The graphs on the right show the resulting laborsupply curve. Because hours worked equal total hours available minus hours of leisure, any change in leisure
implies an opposite change in the quantity of labor supplied. In panel (a), when the wage rises, consumption
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rises and leisure falls, resulting in a labor-supply curve that slopes upward.
Figure 14
An increase in the wage (b)
. . . the labor supply curve slopes backward
(b) For a person with these preferences . . .
Wage
Consumption
BC2
1. When the wage rises . . .
I2
Labor supply
I1
BC1
0
Hours of Leisure
2. . . . hours of leisure increase . . .
0
Hours of Labor
3. . . . and hours of labor decrease Supplied
The two panels of this figure show how a person might respond to an increase in the wage. The graphs on the
left show the consumer’s initial budget constraint, BC1, and new budget constraint, BC2, as well as the
consumer’s optimal choices over consumption and leisure. The graphs on the right show the resulting laborsupply curve. Because hours worked equal total hours available minus hours of leisure, any change in leisure
implies an opposite change in the quantity of labor supplied. In panel (b), when the wage rises, both
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consumption and leisure rise, resulting in a labor-supply curve that slopes backward.
Income effects on labor supply: historical
trends, lottery winners,& Carnegie conjecture
• Labor- supply curve, over long periods
– Slope backward
• A hundred years ago
– People worked six days a week
• Today
– Five-day workweeks
– Length of the workweek has been falling
– Wage of the typical worker (adjusted for inflation)
has been rising
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Income effects on labor supply: historical
trends, lottery winners,& Carnegie conjecture
• Explanation: Advances in technology
– Higher worker productivity
– Increase in demand for labor
•
•
•
•
•
Higher equilibrium wages
Greater reward for working
Income effect dominates substitution effect
More leisure
Less work
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Income effects on labor supply: historical
trends, lottery winners,& Carnegie conjecture
• Winners of lotteries
– Large increase in incomes
– Large outward shifts in budget constraints
• Same slope
• No substitution effect
– Income effect on labor supply
• Substantial
• People who win the lottery – tend to quit their jobs
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Income effects on labor supply: historical
trends, lottery winners,& Carnegie conjecture
• Andrew Carnegie, 19th century
– “The parent who leaves his son enormous wealth
generally deadens the talents and energies of the
son, and tempts him to lead a less useful and less
worthy life than he otherwise would”
– Income effect on labor supply – substantial
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Three Applications
• How do interest rates affect household
saving?
• Income decision
– Consume today or Save for future
• Bundle of goods
– Consumption today and Consumption in the
future
– Relative price = interest rates
– Optimum: Budget constraint & Indifference
curves
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Figure 15
The consumption-saving decision
Consumption
when Old
$110,000
Optimum
55,000
I3
I2
I1
0
$50,000
100,000 Consumption
when Young
This figure shows the budget constraint for a person deciding how much to consume in the
two periods of his life, the indifference curves representing his preferences, and the optimum.
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Three Applications
• How do interest rates affect household
saving?
• Increase in interest rates
– Budget constraint – shifts outward
• Steeper
– Consumption in the future – rises
– If consume less today
• Substitution effect dominates; Save more
– If consume more today
• Income effect dominates; Save less
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Figure 16
An increase in the interest rate
(a) Higher Interest Rate Raises Saving
Consumption
When
old BC2
1. A higher interest rate rotates
the budget constraint outward . . .
(b) Higher Interest Rate Lowers Saving
Consumption
When
old BC2
1. A higher interest rate rotates
the budget constraint outward . . .
I2
I2
I1
BC1
I1
BC1
0
Consumption
when Young
2. . . . resulting in lower consumption
when young and, thus, higher saving.
0
Consumption
when Young
2. . . . resulting in higher consumption
when young and, thus, lower saving.
In both panels, an increase in the interest rate shifts the budget constraint outward. In panel (a), consumption
when young falls, and consumption when old rises. The result is an increase in saving when young. In panel
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(b), consumption in both periods rises. The result is a decrease in saving when young.