Demand, price effects, income effects
income effects
Demand more !
1
Demand
• Back to preferences
p
• Price effects
– Normal goods
– Perfect complements
– Perfect substitutes
• Income effects
Income effects
– Normal goods
– Giffen goods (?)
• intervention
• Observable implications
2
Price effects (for standard goods)
Price effects (for standard goods)
• ∂X(p,M)/ ∂p<0.
(p, )/ p
– Changes in demand with respect to own price is negative.
• Elasticity ‐
(in this case its positive but it can be either greater or smaller than 1
ih
ll h 1
• Who cares about this?
– Consumer?
– Producers?
• Revenue – Government?
• Think of taxes to discourage behavior • Think of taxes to raise revenue
3
Back to Cobb‐Douglas
Back to Cobb
Douglas
u  x, y   x y
 1
M
(1   ) M
X ( pX ) 
, Y
pX
pY
20
800
P
elasticitiy
dX/dp
15
10
600
400
5
200
0
0
0
50
100
150
200
250
Cobb-Douglass
Cobb
Douglass very practical
because it’s a one parameter
per good, constant elasticity
demand curve. It a very good
place to start.
300
‐5
‐200
‐10
‐400
4
y
Decomposition into Substitution and Income Effects
ff
Substitution
Effect
Total or
Observed
Effect
Income
Eff t
Effect
x
5
Demand and Compensated demand
• Cobb‐Douglas U
u x, y   x  y 1
• Demand for good x is X(p,M).
– Cobb‐Douglas
bb
l
X ( pX , M ) 
M
pX
• e(p,u) is the expenditure function e(p u) is the expenditure function
– minimum income to reach a given level of utility.
– Min
– Notice we get back the homothetic property (to double utility you must double expenditures)
you must double expenditures)
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Demand and Compensated demand
Demand and Compensated demand
M
• Demand for good x
Demand for good x
X ( pX , M ) 
pX
• e(p,u) Expenditure function
• Compensated demand • So we can now find Slutzky
So we can now find Slutzky’ss equation
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Slutzky’ss equation
Slutzky
• Lets evaluate this
Lets evaluate this
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Pratical value of Slutzky’s equation
• You can’t measure
• So figuring out how to compensate people say for a sudden shock to heating oil…may be difficult. Except for Slutzky’s equation.
• You can observe x* you can measure the total y
effect and the income effect So you can figure out by the formula
g
y
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Substitutes
• Blu‐ray vs DVD
• Blu‐ray is better but DVD is cheaper. They are used for Blu ray is better but DVD is cheaper They are used for
the exact same thing. • Fix the price of DVD player $32 (amazon
p
p y
(
sells a Sony y
DVD • Assume rentals of disc cost the same (Netflix $2 more per month rather than 8.99, so we are not too far off)
th th th 8 99
tt f
ff)
• Now lets worry about how to price a Blu‐ray player
• Clearly if we sell it at $31, No one buys a DVD player .
Clearly if we sell it at $31 No one buys a DVD player
• Clearly if we sell it at $3000 on those who really care q
y
g g
y
about the increased quality are going to buy it.
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Substitutes
• So U(X, DVD, BR) where X depends on everything else BR is whether one has Blu‐ray and DVD is y
whether one has DVD. y
,
• Because they are substitutes no one wants both, for now assume they are a small part of the budget. So we can simply consider that choice
• U(BR,DVD)= DVD+αBR
– What do indifference curves look like?
• Max U(BR,DVD)= DVD+αBR sbjt to PD DVD+PBBR<M
So buy Blu‐ray if PB<αPD
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Consumer choice
BR
Budget set when BR
is expensive
Budget set when BR
is Cheap
Indifference curves
Slope -1/α
DVD
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Individual Demand
PBR
QBR
Buy
Blu-ray
Blu
ray
α*31
*31
1
Buy
DVD
31
α*31
PBR
1
QBR
13
Aggregte Demand
PBR
Customers with α>10
310
Customers with α=1
31
BR
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Complements
• Normal goods ∂X/∂p
g
/ px<0, ∂X/∂p
, / py≥0
• Substitutes goods changes are non linear
• Complements goods ∂X/∂px<0, ∂X/∂py<0
• Example DVD players and DVD rentals
– U=(DVD, DISC)= DVD*DISC
– But does that quite capture the idea?
• Strict complement X=βY
Strict complement X=βY
– So by definition ∂X/∂px = β∂Y/∂px <0
– and ∂X/∂py = β∂Y/∂py<0
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Summary of Price effects
Summary of Price effects
• Expect own price effect to be negative
Expect own price effect to be negative
• Expect responses to other prices to vary quite a bit
– Some
Some cases you buy more (because this good has become cases you buy more (because this good has become
relatively cheaper)
– Some cases you buy less (because you need to reallocate to afford the complement).
ff d h
l
)
• Figuring these characteristics of demand is critical for businesses and government
businesses and government
• The other argument from the budget set is income.
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Income effect
Income effect
• Normal goods ∂X/∂M>0,
Normal goods ∂X/∂M>0
• Inferior goods ∂X/∂M<0,
• Standard empirical case
S d d
ii l
– Up to some income M ∂X/∂M>0, then past M
∂ /∂
∂X/∂M<0, as you switch to higher quality goods.
h h h
l
d
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Demand for calories as
calories as function of income
Trevon Logan JEH Logan JEH
2007 These are annual
per person
13=442 000 calories 13=442.000
calories
a year (1212 year)
Range 12=572/day
14 3300/d
14=3300/day
18
From Logan JEH 2009,
Note that this elasticity is declining over time So there is both cross sectional
Note that this elasticity is declining over time. So there is both cross sectional and time variation
19
Energy consumption and Birth rates over time
70
60
50
40
30
20
10
0
0
1000
2000
1956
1986
Poly. (1976)
3000
4000
5000
1966
1996
Poly. (1996)
6000
7000
8000
9000
10000
11000
1976
Poly. (1956)
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Income Effect
Income Effect
• Engel
Engel curve traces consumption as income curve traces consumption as income
rises
y
x
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Inferior Good
Inferior Good
y
x
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Intertemporal Choice
Intertemporal Choice
• First two slides from last time
First two slides from last time
• u(x1, x2) = v(x1) + v(x2)
• Budget (1+r)x
d
( ) 1 + x2 = (1+r)M
( ) 1 + M2
• FOC 0  v ( x1 )  (1  r )v x 2 
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Intertemporal Optimization
Intertemporal Optimization
x2
In this case you are poor
when young rich when old
(M1,M
M2)
Repayment
Period 1
B
Borrowing
i
x1
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Interest Rate Increase
Borrower’s Income Falls
x2
(M1,M2)
x1
25
Interest Rate Increase
Creditor’s Income Rises
x2
(M1,M2)
x1
26
Neither Borrower Nor Lender Be
Differences in Borrowing/Lending Rates
x2
(M1,M2)
x1
27
100% propensity to consume
100% propensity to consume
x2
((M1,,M2)
x1
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Conclusion From Week 2
Conclusion From Week 2
• Demand framework useful for a variety of purposes
y p p
• We did the basics
– No asymmetric information (you always know everything about the market and the goods)
b
h
k
d h
d)
– No risk (you are sure what you want and what you get)
– Continuity
Continuity – NO TRANSACTION COSTS
• More of this in most Econ classes
– But EC121ab, EC 106 come back heavily to those topics
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