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:
x1= x1(p1, p2, Y)
• By varying own price (p1), holding both p2 and Y constant,
we know how much x1 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 = pbeerQbeer + pwineQwine
Original prices: pbeer=12, pwine=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: pbeer=6, pbeer=4
She can now consume 70 (=419/6) or 105(=419/4) units of
beer.
Figure 5.1
Continued.
Change Pbeer holding Pwine
and Y constant.
→ New budget constraint
→ New optimal bundle of
goods.
Tracing these optimal xbeer*,
we can draw the demand
curve for beer on PriceQuantity 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 Pbeer and Pwine
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 Qd Qd / Qd Qd Y



% in Y
Y / Y
Y Qd
η≥ 0
As Y rises, Qd also rises
Luxury
η> 1
Qd increases by a greater
proportion than Y
Necessity
η< 1
Qd increases by a lesser
proportion than Y
η< 0
As Y rises, Qd decreases
Normal good
Inferior good
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 p1 holding p2 & Y constant has two effects
on individual’s demand:
Substitution effect: Change in Qd due to consumer’s
behavior of substituting good 1 for good 2 (because x1
now relatively cheap), holding utility constant.
Income effect: Change in Qd due to effectivelyincreased income (lower p1 = higher buying power),
holding prices constant.
Total effect = Substitution effect + Income effect
Total Effect
Suppose the consumer is maximizing
utility at point A.
x2
If the price of good x1 falls, the consumer
will maximize utility at point B.
This can be decomposed into two effects.
B
A
U2
U1
x1
Total increase in x1
Substitution Effect
To isolate the substitution effect, we hold
the utility level constant but allow the
relative price of good x1 to change
x2
The substitution effect is the movement
from point A to point C
A
C
U1
Substitution effect
The individual substitutes
good x1 for good x2
because good x1 is now
relatively cheaper
x1
Income Effect
The income effect occurs because the
individual’s “real” income changes when
the price of good x1 changes
x2
The income effect is the movement
from point C to point B
B
A
C
U2
U1
Substitution Income
effect
effect
Total effect
If x is a normal good,
the individual will buy
more because “real”
income increased
x1
What if x1 is an inferior good?
Ordinary Goods and Giffen Goods
Ordinary Goods: As P decreases, Qd increases. ∂x1/∂p1 < 0
Giffen Goods: As P decreases, Qd decreases. ∂x1/∂p1 > 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 = w1 H = w1 (24 – N)
The Budget Line
Y = 24w
The time constraint:
H + N =24
Y = wH
Leisure
N (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 w1
Original optimum at e1
To derive demand for
leisure, increase wage to w2
New optimum at e2
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)
The substitution effect is the movement
from point A to point C
The income effect is the movement
from point C to point B
B
C
A
U2
U1
Substitution effect
Income effect
Total effect
The individual chooses
less leisure at B as a
result of the increase in w
Leisure （N)
Case 2: Substitution effect < Income effect
The substitution effect is the movement
from point A to point C
Consumption（Y)
The income effect is the movement
from point C to point B
B
C
A
U1
Substitution effect
Income effect
Total effect
U2
The individual
chooses more leisure
at B as a result of the
increase in w
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 e2.
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
Example
Year
P1
P2
Price
index
Year
P1
P2
Price
index
2000
\120
\500
100
2000
\120
\500
100
2007
\240
\1,000
200
2007
\108
\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
p1  p1
p2  p2
P  s1
 s2
p1
p2
where s: budget share
Price Index
Laspeyres index (Lp)
weight: base year quantity
= (Cost of buying the baseyear’s bundles in the
current year) / (Actual
cost in the base year)
Paasche index (Pp)
weight: current year quantity
p1t x10  p2t x20
Lp  0 0
p1 x1  p20 x20
p10 x10 p1t p20 x20 p2t
 0
 0
0
Y p1
Y p20
p1t x1t  p2t x2t
Pp  0 t
0 t
p1 x1  p2 x2
t t
1 1
t
t
1
0
1
t t
2 2
t
t
2
0
2
px p
px p


Y p
Y p