Theory of Demand
ECON 212 Lecture 7
Tianyi Wang
Queen’s Univerisity
Winter 2013
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
1 / 46
Intro
Note: Quiz 1 can be picked up at Distribution Center.
Second Quiz covers: Preferences, Budget and Optimal Choices.
Core of theory of demand: how does demand change in di¤erent
enviroments.
Can have many directions. We will look at:
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e¤ect of changes in price, and
e¤ect of changes in income.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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E¤ect of Changes in Price
What happens to optimal choices when price changes.
Derive demand function from consumer’s optimal choices.
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Winter 2013
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Lecture 7
Winter 2013
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Demand Function
Note, demand curve derived from de…nition: letting Px changes while
holding others constant.
See class notes for examples.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Demand Function (Cont’d)
Demand curve is also a "willingness to pay curve"
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MRS says willness to substitute.
Px , or willing to sacri…ce Px unites of y.
MRS = Py
Py
Px Py = Px.
To translate into value, Py
Willing to pay Px for additional unit of x.
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Lecture 7
Winter 2013
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E¤ect of Changes in Income
Income Consumption Curve (ICC): traces out optimal bundles on X-Y
space as income changes.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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E¤ect of Changes in Income
Income Consumption Curve (ICC): traces out optimal bundles on X-Y
space as income changes.
Engel curve (EC): depicts optimal choices on I-X space.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
13 / 46
E¤ect of Changes in Income
Income Consumption Curve (ICC): traces out optimal bundles on X-Y
space as income changes.
Engel curve (EC): depicts optimal choices on I-X space.
Normal good V .S. Inferior good.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
13 / 46
E¤ect of Changes in Income
Income Consumption Curve (ICC): traces out optimal bundles on X-Y
space as income changes.
Engel curve (EC): depicts optimal choices on I-X space.
Normal good V .S. Inferior good.
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Normal: positive slope for both ICC and EC
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
13 / 46
E¤ect of Changes in Income
Income Consumption Curve (ICC): traces out optimal bundles on X-Y
space as income changes.
Engel curve (EC): depicts optimal choices on I-X space.
Normal good V .S. Inferior good.
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I
Normal: positive slope for both ICC and EC
Inferior: negative slope for both ICC and EC
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
13 / 46
E¤ect of Changes in Income
Income Consumption Curve (ICC): traces out optimal bundles on X-Y
space as income changes.
Engel curve (EC): depicts optimal choices on I-X space.
Normal good V .S. Inferior good.
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Normal: positive slope for both ICC and EC
Inferior: negative slope for both ICC and EC
With Quasilinear utility function, both are vertical line. (Math and
intuition?)
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Market Demand
Horizontal summation of individual demand.
See class notes for examples.
Usually assume identical individuals.
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Lecture 7
Winter 2013
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Income and Substitution E¤ect
Does price increase always decreases demand (Gi¤en good)?
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Income and Substitution E¤ect
Does price increase always decreases demand (Gi¤en good)?
Decrease (increase) in price can have ambiguous e¤ect.
– relatively cheaper, buy more.
– richer, buy less (inferior good).
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
15 / 46
Income and Substitution E¤ect
Does price increase always decreases demand (Gi¤en good)?
Decrease (increase) in price can have ambiguous e¤ect.
– relatively cheaper, buy more.
– richer, buy less (inferior good).
These ambiguities include:
– the e¤ect of wage rates on labor supply.
– the e¤ect of interest rates on savings.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
15 / 46
Income and Substitution E¤ect
Does price increase always decreases demand (Gi¤en good)?
Decrease (increase) in price can have ambiguous e¤ect.
– relatively cheaper, buy more.
– richer, buy less (inferior good).
These ambiguities include:
– the e¤ect of wage rates on labor supply.
– the e¤ect of interest rates on savings.
Price changes involve two seperate e¤ects:
– Substitution e¤ect: good 1 becomes cheaper, more attractive than
good 2 (opp. cost changes)
– Income e¤ect: b/c good 1 is cheaper, can buy more of it with a
given amount of income. Purchasing power increased.
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Lecture 7
Winter 2013
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Substitution E¤ect
How to seperate?
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Substitution E¤ect
How to seperate?
1
keep relative price changes, take away (grant) money to keep sth. …xed.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Substitution E¤ect
How to seperate?
1
2
keep relative price changes, take away (grant) money to keep sth. …xed.
reimburse and hold the relative prices.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
16 / 46
Substitution E¤ect
How to seperate?
1
2
keep relative price changes, take away (grant) money to keep sth. …xed.
reimburse and hold the relative prices.
Hicks Decomposition: …x (initial) utility level.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
16 / 46
Substitution E¤ect
How to seperate?
1
2
keep relative price changes, take away (grant) money to keep sth. …xed.
reimburse and hold the relative prices.
Hicks Decomposition: …x (initial) utility level.
Slutsky Decomposition: …x purchasing power (not income).
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
16 / 46
Substitution E¤ect
How to seperate?
1
2
keep relative price changes, take away (grant) money to keep sth. …xed.
reimburse and hold the relative prices.
Hicks Decomposition: …x (initial) utility level.
Slutsky Decomposition: …x purchasing power (not income).
We will use Hicks below (clean intuition).
– how much consumer would require in payment to accept a change.
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Lecture 7
Winter 2013
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Winter 2013
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Point A is original optimizing bundle.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Point A is original optimizing bundle.
Decrease in price of X rotate budget line outward, and new optimal
bundle is C.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Point A is original optimizing bundle.
Decrease in price of X rotate budget line outward, and new optimal
bundle is C.
Point B is the optimal bundle, that if we reduce the income just
enough so that the consumer could just obtain the original utility
level, at di¤erent relative prices.
– this is the sub. e¤ect.
– Note the hypothetic budget at B is smaller than that at A (why?).
– We seperate sub. e¤ect out by taking away implicit income changes.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
22 / 46
Point A is original optimizing bundle.
Decrease in price of X rotate budget line outward, and new optimal
bundle is C.
Point B is the optimal bundle, that if we reduce the income just
enough so that the consumer could just obtain the original utility
level, at di¤erent relative prices.
– this is the sub. e¤ect.
– Note the hypothetic budget at B is smaller than that at A (why?).
– We seperate sub. e¤ect out by taking away implicit income changes.
Point C is the optimal bundle, that if we hold the new relative prices
and add back the income that we took away.
– this is the inc. e¤ect.
– shift the hypothetic BC back to get implied changes in consumption.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
22 / 46
Point A is original optimizing bundle.
Decrease in price of X rotate budget line outward, and new optimal
bundle is C.
Point B is the optimal bundle, that if we reduce the income just
enough so that the consumer could just obtain the original utility
level, at di¤erent relative prices.
– this is the sub. e¤ect.
– Note the hypothetic budget at B is smaller than that at A (why?).
– We seperate sub. e¤ect out by taking away implicit income changes.
Point C is the optimal bundle, that if we hold the new relative prices
and add back the income that we took away.
– this is the inc. e¤ect.
– shift the hypothetic BC back to get implied changes in consumption.
See class note for examples.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Hicks substitution e¤ect also know as Compensated Demand Curve.
– consumers are compensated just enough to obtain the original utiliy.
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Lecture 7
Winter 2013
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Hicks substitution e¤ect also know as Compensated Demand Curve.
– consumers are compensated just enough to obtain the original utiliy.
Note sign of substitution e¤ect must be negative
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Hicks substitution e¤ect also know as Compensated Demand Curve.
– consumers are compensated just enough to obtain the original utiliy.
Note sign of substitution e¤ect must be negative
Sign of income e¤ect can be positive or negative (normal v.s. inferior)
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Hicks substitution e¤ect also know as Compensated Demand Curve.
– consumers are compensated just enough to obtain the original utiliy.
Note sign of substitution e¤ect must be negative
Sign of income e¤ect can be positive or negative (normal v.s. inferior)
Therefore Gi¤en good must be inferior good.
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Lecture 7
Winter 2013
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Tianyi Wang (Queen’s Univerisity)
Lecture 7
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Slustsky de…nes substitution e¤ect by keeping purchasing power
constant.
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both original BC and hypothetical BC go through A.
Note incomes are di¤erent.
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Lecture 7
Winter 2013
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Application: Consumption and Leisure Choice
In practice, instead of taking income as given, consumer earn it by
supplying labour.
Assume:
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Application: Consumption and Leisure Choice
In practice, instead of taking income as given, consumer earn it by
supplying labour.
Assume:
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Consumer’s endowment of time T = 24 hours,
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Application: Consumption and Leisure Choice
In practice, instead of taking income as given, consumer earn it by
supplying labour.
Assume:
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Consumer’s endowment of time T = 24 hours,
Time can be used in labour (L) and leisure (R).
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
26 / 46
Application: Consumption and Leisure Choice
In practice, instead of taking income as given, consumer earn it by
supplying labour.
Assume:
I
I
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Consumer’s endowment of time T = 24 hours,
Time can be used in labour (L) and leisure (R).
earn wage (w ) on each working hour.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
26 / 46
Application: Consumption and Leisure Choice
In practice, instead of taking income as given, consumer earn it by
supplying labour.
Assume:
I
I
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I
Consumer’s endowment of time T = 24 hours,
Time can be used in labour (L) and leisure (R).
earn wage (w ) on each working hour.
Consumer values consumption (C ) and leisure (R), max U (C , R ).
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
26 / 46
Application: Consumption and Leisure Choice
In practice, instead of taking income as given, consumer earn it by
supplying labour.
Assume:
I
I
I
I
I
Consumer’s endowment of time T = 24 hours,
Time can be used in labour (L) and leisure (R).
earn wage (w ) on each working hour.
Consumer values consumption (C ) and leisure (R), max U (C , R ).
Need to use wages to buy consumption good, Price = 1.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
26 / 46
Application: Consumption and Leisure Choice
In practice, instead of taking income as given, consumer earn it by
supplying labour.
Assume:
I
I
I
I
I
Consumer’s endowment of time T = 24 hours,
Time can be used in labour (L) and leisure (R).
earn wage (w ) on each working hour.
Consumer values consumption (C ) and leisure (R), max U (C , R ).
Need to use wages to buy consumption good, Price = 1.
Formulate consumer’s problem, see class notes for example.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Backward bending labour supply
We can …nd demand for leisure from optimal choices, by varying wage
rate (see graph below).
Since: supply of labour + demand for leisure = 24 hours.
L=T
R. (See graph below).
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Substitution e¤ect makes an hour of leisure more expensive.
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Substitution e¤ect makes an hour of leisure more expensive.
Income e¤ect increases your overall endowment.
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Substitution e¤ect makes an hour of leisure more expensive.
Income e¤ect increases your overall endowment.
Sub. e¤ect if negative.
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Substitution e¤ect makes an hour of leisure more expensive.
Income e¤ect increases your overall endowment.
Sub. e¤ect if negative.
If leisure is normal good, consume more when income raises.
— Income e¤ect is positive.
— Inc. e¤ect counteracts sub. e¤ect.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Substitution e¤ect makes an hour of leisure more expensive.
Income e¤ect increases your overall endowment.
Sub. e¤ect if negative.
If leisure is normal good, consume more when income raises.
— Income e¤ect is positive.
— Inc. e¤ect counteracts sub. e¤ect.
Labour supply curve bends baceward.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
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Compensating Variation and Equivalent Variation
Two ways to measure consumer welfare.
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Price changes result in welfare change.
Rather than describe welfare in utility terms, we would like to describe
it in terms of dollars.
Suppose price of X increases, (utility level drops):
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
38 / 46
Compensating Variation and Equivalent Variation
Two ways to measure consumer welfare.
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Price changes result in welfare change.
Rather than describe welfare in utility terms, we would like to describe
it in terms of dollars.
Suppose price of X increases, (utility level drops):
1
Ask how much money to compensate a consumer, at the new price,
such that she obtains her initial utility level.
— This is Compensating Variation.
Tianyi Wang (Queen’s Univerisity)
Lecture 7
Winter 2013
38 / 46
Compensating Variation and Equivalent Variation
Two ways to measure consumer welfare.
I
I
Price changes result in welfare change.
Rather than describe welfare in utility terms, we would like to describe
it in terms of dollars.
Suppose price of X increases, (utility level drops):
1
Ask how much money to compensate a consumer, at the new price,
such that she obtains her initial utility level.
— This is Compensating Variation.
2
Ask how much money to take away from a consumer, at the initial
price, such that the e¤ect is equivalent to the price change.
— This is Equivalent Variation.
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Note: these are pure income e¤ects.
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Lecture 7
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Note: these are pure income e¤ects.
Note: Change in consumer surplus includes both inc. e¤ect and sub.
e¤ect.
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Lecture 7
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Note: these are pure income e¤ects.
Note: Change in consumer surplus includes both inc. e¤ect and sub.
e¤ect.
Which measure is higher depends on income elasticity.
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Lecture 7
Winter 2013
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Note: these are pure income e¤ects.
Note: Change in consumer surplus includes both inc. e¤ect and sub.
e¤ect.
Which measure is higher depends on income elasticity.
However as the budget share of most goods are small, they are
virtually identical.
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Lecture 7
Winter 2013
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