Transcript スライド 1 - GRIPS
Chapter 5: Applying Consumer Theory
• From chap 2&3, we learned that supply & demand curves yield a market equilibrium.
• From chap 4, we learned that a consumer maximizes his/her utility subject to constraints.
• This chapter does: – Derive demand curves from one’s u-max problem – How Δin income shifts demand (income elasticity) – Two effects of a price change on demand – Deriving labor supply curve using consumer theory – Inflation adjustment
5.1 Deriving Demand Curves
• A consumer chooses an optimal bundle of goods subject to budget constraints.
• From the consumer’s optimum choice, we can derive the demand function:
x 1 = x 1 (p 1 , p 2 , Y)
• By varying own price (
p 1
), holding both
p 2
we know how much
x 1
and
Y
constant, is demanded at any price. →Use this info to draw the demand curve.
Figure 5.1
Deriving an Individual’s Demand Curve Suppose that the price of beer changes while the price of wine remains constant. Y =
p
beer Q beer +
p
wine Q wine Original prices:
p
beer =12,
p
wine =35 Income: Y = 419 The consumer can consume 12 (=419/35) units of wine or 35 (=419/12) units of beer if she consumes only one of the two.
Draw the budget line.
The price of beer changes:
p
beer =6,
p
beer =4 She can now consume 70 (=419/6) or 105(=419/4) units of beer.
Figure 5.1
Continued.
Change
P beer
and
Y
holding constant.
P wine
→ New budget constraint → New optimal bundle of goods.
Tracing these optimal x beer *, we can draw the demand curve for beer on Price Quantity space.
5.2 How changes in Income shift demand curves
• How does demand curve change when income shifts, holding prices constant?
Figure 5.2 Effect of Budget Increase on an Individual’s Demand Curve • Suppose that the income of the consumer increases. • Income increases to $628 and $837 for same prices. • She can now consume 18 (=628/35) units of wine or 52 (=628/12) units of beer if she consumes either one.
• Or she can now consume 24 (=837/35) units of wine or 70 (=837/12) units of beer if she consumes either one.
• The budget line expands outward, and she consumes more wine and beer because she can!
Figure 5.2
Continued.
Change
Y
holding
P beer
and
P wine
constant.
→ Budget line shifts outward → New optimal bundle of goods Demand curves shifts outward as
Y
increases
if the good is normal
.
Engel curve summarizes the relationship between income and quantity demanded, holding prices constant.
Income Elasticity of Demand
= How much quantity demanded changes when income increases.
% %
in Q
d
in Y
Q
d
/
Q
d
Y Q
d
Normal good Luxury Necessity Inferior good
η≥ 0 η> 1 η< 1 η< 0
As
Y
rises,
Q d
also rises
Q d
increases by a greater proportion than
Y Q d
increases by a lesser proportion than
Y
As
Y
rises,
Q d
decreases
Figure 5.3
Income-Consumption Curves and Income Elasticities
Figure 5.4
A Good that is both Inferior and Normal
5.3 Effects of a Price Change
• A decrease in
p 1
holding
p 2
on individual’s demand: &
Y
constant has two effects
Substitution effect
: Change in
Q d
due to consumer’s behavior of substituting good 1 for good 2 (because
x 1
now relatively cheap), holding utility constant.
Income effect
: Change in
Q d
increased income (lower
p 1
due to effectively = higher buying power), holding prices constant.
Total effect = Substitution effect + Income effect
x 2
Total Effect
Suppose the consumer is maximizing utility at point
A
.
If the price of good
x 1
falls, the consumer will maximize utility at point
B
.
This can be decomposed into two effects.
B A
U 2 U 1 x 1 Total increase in x 1
x 2
Substitution Effect
A
To isolate the substitution effect, we hold the utility level constant but allow the relative price of good
x 1
to change The substitution effect is the movement from point
A
to point
C
C
U 1
The individual substitutes good
x 1
for good
x 2
because good
x 1
is now relatively cheaper
x 1 Substitution effect
x 2
A
Income Effect
C
The income effect occurs because the individual’s “real” income changes when the price of good
x 1
changes The income effect is the movement from point
C
to point
B
B
U 1 U 2
If
x
is a normal good, the individual will buy more because “real” income increased
Substitution Income effect effect Total effect x 1
What if
x 1
is an inferior good?
Ordinary Goods and Giffen Goods
Ordinary Goods: As Giffen Goods: As
P P
decreases,
Q d
decreases,
Q d
increases. ∂x 1 /∂p 1 decreases. ∂x 1 /∂p 1 < 0 > 0
5.5 Deriving Labor Supply Curve
• We normally use consumer theory to derive
demand
behavior. But here, we derive labor
supply
curve using consumer theory.
• Individuals must decide how to allocate the fixed amount of time they have.
• The point here is “time is money.” When we do not work, we sacrifice or forgo wage income. That is, the opportunity cost of time is equal to the wage rate.
Model
Utility function: u=
U
(
Y
,
N
) where
N
= Leisure time and
Y
is the consumption of other goods, which is equal to the labor income (wages). Time constraint:
H
(labor time) +
N
= 24 hours Max u =
U
(
Y
,
N
) Subject to
Y
=
w 1 H
=
w 1
(24 – N)
Y = 24w
The Budget Line
The time constraint: H + N =24
Y = wH N (Leisure) Leisure H (Labor time)
The labor time determines how much the consumer can consumes the other goods.
Figure 5.8
Demand for leisure Given 24hrs and wage
w 1
Original optimum at
e 1
To derive demand for leisure, increase wage to
w 2
New optimum at
e 2
A higher wage means a higher price of leisure Demand curve for leisure on Price-Quantity space
Figure 5.9
Supply Curve of Labor
Substitution and Income Effects
• Both effects occur when
w
changes – Substitution effect: When
w
rises, the price for leisure increases due to higher opportunity cost, and the individual will choose less leisure – Income effect: Because leisure is a normal good, with increased income, she will choose more leisure • The income and substitution effects move in opposite directions if leisure is a normal good.
Figure 5.10
Income and Substitution Effects of a Wage Change
Case 1: Substitution effect > Income effect Consumption
（
Y)
C B
The substitution effect is the movement from point
A
to point
C
The income effect is the movement from point
C
to point
B
A
U 1 U 2
The individual chooses less leisure at B as a result of the increase in
w
Substitution effect Income effect Total effect Leisure
（
N)
Case 2: Substitution effect < Income effect Consumption
（
Y)
The substitution effect is the movement from point
A
to point
C C A B
The income effect is the movement from point
C
to point
B
U 2
The individual chooses more leisure at B as a result of the increase in
w
U 1 Substitution effect Income effect Total effect Leisure
（
N)
Figure 5.11
Labor Supply Curve that Slopes Upward and then Bends Backward Application: Will you stop working if you win a lottery?
Tax revenue and Tax rates Application: What is the optimal (i.e., maximizes the tax revenue) marginal tax rate? Sweden 58% (vs. actual 65%) Japan: 54 % (vs. 24 %)
Child-Care Subsidies: The same resource for subsidy and the lump-sum payment. This means that the budgets lines go through e 2 .
5.4 Cost of Living Adjustments
• Nominal price: Actual price of a good • Real price: Price adjusted for inflation • Consumer Price Index (Laspeyres index): Weighted average of the price increase for each good where weights are each good’s budget share in base year
Year 2000 P 1 \120 P 2 \500
Example
Price index 100 Year 2000 P 1 \120 2007 \240 \1,000 200 2007 \108 P 2 \500 Price index 100 \550 ??
In the first case, both relative and real prices remain unchanged.
Real price = Nominal price / Price index, e.g., \240/2.00.
In the second case, it is not clear how we should compute the price index (P). One reasonable way may be
P
s
1
p
1
p
1
s
2
p
2
p
1
p
2
p
2 where s: budget share
Price Index
Laspeyres index (L p ) weight:
base year
quantity = (Cost of buying the base year’s bundles in the current year) / (Actual cost in the base year)
L
p
t
p x
1 1 0 0
p x
1 1 0
t
p x
2 2 0 0
p x
2 2 0 1 0 1 0
p x p
1
t
Y
0
p
1 0 0 2 0
p x p
2 2
t
Y
0
p
2 0 Paasche index (P p ) weight:
current year
quantity
P
p
t
p x
1 1
t
0
p x
1 1
t
t
p x
2 2
t
0
p x
2 2
t t
p x p
1 1
t
1
t
Y
t
p
1 0
t
p x p
2
t
2 2
t
Y
t
p
2 0