Econ 203
Consumer demand
Have: basics of consumer choice problem:
- preferences
- constraints
- optimal choice: tangency condition
on budget line
p1
bundle satisfying MRS=
p2
For individual consumer, with well behaved
preferences, facing fixed prices and given
income, this bundle is unique.
So what?
1. optimal bundle - quantity of each good
individual wishes to consume, depending
on prices and income
2. don't care about any single individual
3. what if change prices, and/or income how will optimal quantities respond?
- optimal bundle will change if BL changes
position: change in M, p1 , and/or p2
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Econ 203
Consumer demand
Focus: how do quantities vary as prices vary?
Def'n: quantity demanded of a good: quantity
consumer is willing to purchase at a given price
of the good.
Def'n: demand curve: quantity of a good as a
function of its price, for fixed income and prices
of all other goods.
Method of derivation?
how do quantities demanded change in
response to changes in budget set:
1. simplest case: changes in M, constant prices
- shows how quantities vary with income
- income consumption path
- why care?
changes as economies become richer
changes in tax policies - redistribution,
tax increase/decrease
2. change in price of one good ( ∆p1), with
constant M and price of good 2:
- derive demand curve for good 1
- trace out price consumption path
- income and substitution effects
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Econ 203
Consumer demand
1. Change income, with prices constant
Set-up:
o
o
o
1. initial budget set { M , p1 , p2 }
individual chooses bundle
B o = {x1o , x2 o }
p1o x1o + p2 o x2 o = M o
o
p
o
ii) MRS ( B ) = 1 o
p2
satisfying: i)
2. M increases to
M ′ > M o , prices constant
- new budget set, with intercepts
- slope of new BL?
3. Is bundle
B o still optimal?
No: interior of budget set - can buy more of
both goods, be better off (non-satiation)
4. New bundle? quantities of both may
increase, or one decrease - quantity of at
least one good must increase when M
increases - if more is better, so move to new
budget line.
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Econ 203
Consumer demand
5. Income expansion path: as income
increases, trace path of optimal bundles
6. Slope of income expansion path?
∆x
normal goods:
>0
∆M
(superior goods)
∆x
inferior goods:
<0
∆M
If only two goods, at least one must be
normal.
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Econ 203
Consumer demand
2. change in price of one good ( ∆p1), with
constant M and price of good 2
o
o
o
1. initial income and prices {M , p1 , p2 }
2. given well-behaved preferences, initial
o
o
o
optimal bundle B = {x1 , x2 } where
p1o x1o + p2 o x2 o = M o
o
p
o
ii) MRS ( B ) = 1 o
p2
i)
3. Suppose p1 ↓ , to p1′ < p1
i) new budget set: intercepts? slope?
o
ii) is B still optimal?
o
4. Properties of new optimal bundle,
i)
p1′ x1′′ + p2 o x2′′ = M o
B′′?
new bundle costs the same as original
p1′
p1o
ii) MRS ( B′′) =
< o
o
p2
p2
as p1 ↓ , MRS ↓ : relatively more of good 1
Page 5 of 8
Econ 203
Consumer demand
Explanation: income and substitution effects of
a price change.
1. Income effect:
p1 ↓ with M, p2 fixed → budget set expands
- even though no more money to spend
- why? relative income ↑ : any given bundle
at initial prices now costs less, so as if
more income to spend
- income effect isolates this effect: move
back to original IC at new relative prices:
o
bundle B′ satisfies U ( B′) = U ( B )
p1′
= MRS ( B′′) = MRS ( B′)
o
p2
and
2. Substitution effect:
p1
falls: good 1 now
p1 ↓, p2 fixed ⇒
p2
relatively cheaper in market
ex: { p1 , p2 } = (2, 4); { p1′ , p2 } = (1, 4)
Initially, 1 unit of good 1 "costs" 2/4=1/2 units of
good 2
o
o
o
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Econ 203
Consumer demand
New price: unit of good 1 costs
1
units of good 2
4
So: even at same utility level, facing new price
ratio individual will adjust bundle
Results? for
x1o , x1′′ > 0 , when p1 changes,
Substitution effect: always negative
- price and quantity move in opposite direction,
so
∆x1
<0
∆p1
- if price falls, individual would buy more of it,
less of other, at given utility level
- this is key factor for prediction that demand
curves have negative slope
Income effect: positive for normal goods
- quantity and income change in same direction
(which is opposite to direction of ∆p ):
p1 ↓⇒ budget set ↑ (as if M ↑) ⇒ x1 ↑
negative for inferior goods: change in quantity in
same direction as price change
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Econ 203
Consumer demand
Overall effect of price change?
depends on relative values of above effects
a) normal good (
reinforcing:
∆x
> 0 ): effects
∆M
p1 ↓⇒ x1 ↑ from substitution effect and
⇒ x1 ↑ from income effect
demand curve always has negative slope
∆x
b) inferior good (
< 0 ): effects work in
∆M
opposite directions:
p1 ↓⇒ x1 ↑ from substitution effect and
⇒ x1 ↓ from income effect
demand curve sometimes has negative
slope: if good not too inferior - so substitution
effect larger than income effect (in absolute
value).
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