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A.Friedman

 

 

 

 

 

 

 

 

ICEF-2012

 

x2

 

 

 

 

 

 

 

 

 

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Price-consumption curve

 

 

 

 

 

 

 

 

 

 

 

 

p 0

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

p1

 

 

 

 

 

 

3

 

2

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p1

 

p1

 

p2

 

 

 

 

p

2

p2

 

 

 

0

 

 

 

 

 

x1

 

 

 

 

 

 

 

 

 

p1

 

 

 

 

 

 

 

 

 

 

p3

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

p 2

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

p1

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Demand curve for

 

 

0

 

 

 

 

 

good 1

 

 

 

p1

 

 

 

 

 

 

 

 

 

x1

Ordinary good - a good for which an increase in its price decreases consumption ceteris paribus (individual demand curve is downward sloping)

Giffen good - a good for which an increase in its price results in an increase in consumption ceteris paribus (individual demand curve is upward sloping)

x2

Giffen good

0

x1

11

A.Friedman ICEF-2012

Price elasticity of demand - the percentage change in quantity demanded of good X with

respect to a percentage change in its price: X

 

 

 

X / X

.

 

 

 

 

 

 

 

 

p

X

 

pX / pX

 

For ordinary good

X

0 and for Giffen good

X

0 .

 

 

p

X

 

 

p

X

 

 

 

 

 

 

 

Cross price changes (impact of a change in the price of one good on the quantity demanded of another good)

Substitutes (goods that satisfy similar wants): an increase in the price of one good leads to an increase in the quantity demanded of the other good.

Complements (goods that tend to be used together): an increase in the price of one good leads to a decrease in the quantity demanded of the other good.

Unrelated goods: an increase in the price of one good has no impact on the quantity demanded of other good.

Cross price elasticity of demand - the percentage change in quantity demanded of good X

with respect to a percentage change in price of good Y : Xp

 

X / X

.

 

 

 

Y

 

pY / pY

Substitutes Xp 0 , complements Xp 0 , unrelated goods Xp 0 .

 

Y

Y

 

Y

1.6 Alternative approach to consumer’s theory: revealed preferences

Idea: if two

~

are affordable but only

x

is chosen, then x is revealed

~bundles x and x

preferred to

x .

 

 

 

 

 

x2

 

 

 

 

~x

x

0

x1

The weak axiom of revealed preference

If bundle x happen that

~

is revealed preferred to x

~

x is revealed preferred to

and the two bundles are not the same, then it cannot x .

12

A.Friedman

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ICEF-2012

 

 

x2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Violation of WARP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x p, I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

 

 

 

 

 

~ ~

 

 

 

 

 

 

 

 

 

 

 

~

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

~

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

x p, I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0

 

 

 

 

 

I

~

 

x 1

 

 

 

 

 

 

 

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p1

~

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

~

~

I

~

x , then

~

~

 

~

~ ~

.

Check WARP: if p1 x1

p2 x2

and x

p1 x1

p2 x2

I

for any p,I and p, I

Application of revealed preferences

Replacement of per unit subsidy on good 1 by the lump sum subsidy of equivalent money cost

x2

Isx1 p2

I

x p,I sx1

p2

 

sx

x

 

 

 

1

 

 

 

 

 

 

p2

 

 

 

 

 

0

 

 

I

I

x 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p1

p1 s

 

1.7 Price changes: Slutsky decomposition

Price change

Substitution effect the effect of a price change on quantity demanded due exclusively to the fact that its relative price has changed

Income effect

the effect of a price change on quantity demanded due exclusively to the fact that the consumer’s real income has changed

13

I comp

A.Friedman

 

 

 

 

 

ICEF-2012

Slutsky decomposition: x

i

x SE x IE

xcomp x0

x xcomp

 

i

i

i

i

i i

Slutsky substitution effect is derived under the assumption that real income stays constant:p x0 or in our example I comp I p1 x10 .

Observed response= xi xi xi0

Compensated response - the change in quantity demanded resulting from changing the price while simultaneously compensating the individual with income= xiSE xicomp xi0

 

 

x

i

 

 

x SE

 

x IE

 

 

 

 

 

 

 

Relative changes:

 

 

 

i

 

i .

 

 

 

 

 

 

 

 

p

p

 

 

 

 

 

 

 

 

 

 

 

 

p

 

 

 

 

 

 

 

 

1

 

 

 

1

 

 

1

 

 

 

 

 

 

 

 

 

 

x2

 

 

 

 

 

 

 

 

 

 

 

 

 

I comp

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

xcomp

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

 

 

 

p

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

0

 

p

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

 

x1

 

 

 

 

 

 

 

 

 

x IE

x SE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

1

 

 

 

 

 

 

 

Sign of SE

x SE

Own substitution effect is always non-positive 1 0 (from revealed preferences).p1

14

A.Friedman

 

 

 

 

 

 

 

ICEF-2012

 

 

x2

 

 

 

 

 

 

 

 

 

I comp

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

 

 

I

xcomp

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p

 

 

 

 

 

 

x

 

 

 

 

1

 

 

 

 

 

 

 

x

0

p

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p 0

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

p2

0

 

 

 

 

 

 

 

x1

Substitution effect is zero in case of kinked IC (for example in case of Leontieff preferences) Question: illustrate Slutsky decomposition for the case of Leontieff preferences

Sign of IE

x IE

 

 

x xcomp

 

 

 

 

 

 

 

 

 

 

 

 

 

i

 

i

 

 

i

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p1

 

 

 

 

p1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note: I I I comp p x0

or p

 

 

I

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

1

 

1

 

x0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

Plug back:

x IE

x0

x IE

 

 

 

 

 

 

 

 

 

 

i

 

i .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p1

1

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

As x0

0 , then

x IE

 

0

if

x IE

0 , i.e. if good i is inferior

 

i

 

 

i

1

 

 

 

 

 

 

p1

 

 

 

 

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x IE

 

 

 

 

 

x IE

 

 

 

 

 

 

 

 

 

 

 

 

 

i

0

if

i

 

0

, i.e. if good i

is normal

 

 

p1

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x IE

 

 

 

 

 

x IE

 

 

 

 

 

 

 

 

 

 

 

 

 

i

0

if

i

 

0

, i.e. if good i

is neutral with respect to income

p1

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

 

x SE

0

x IE

Own price Slutsky equation

1

 

 

1 x

1 .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p1

 

 

1

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p1

 

Conclusions:

1)If good 1 is normal, then its demand curve slopes down

2)If good 1 is Giffen, then it has to be inferior

15

 

A.Friedman

 

 

 

ICEF-2012

 

Summary: impact of an increase in the price of a good

 

 

 

Type of good

 

SE

IE

TE

 

 

Normal

 

-

-

-

 

 

Inferior but

not

-

+

-

 

 

Giffen

 

 

 

 

 

 

Giffen

 

-

+

+

 

Question: illustrate Slutsky decomposition for the case of Giffen good

1.8 Price changes: Another substitution effect

Hickes substitution effect keeps utility rather than purchasing power constant.

Here we pivot the budget line around the indifference curve rather than around the original choice.

x2

I h

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

I 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

 

 

 

 

 

x h

 

 

 

 

 

 

 

 

x

 

 

 

p

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

0

 

p

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

u 0

 

 

p10

 

 

 

 

 

 

 

p2

0

 

 

 

 

 

 

 

x1

 

x IE

x SE

 

 

 

 

 

 

 

1

1

 

 

 

 

 

 

 

Slutsky decomposition: x

xSE

x IE

xh x0

x xh

 

 

 

 

i

 

i

i

i

i

i i

 

x

i

 

x SE

x IE

 

 

 

Relative changes:

 

 

i

 

i .

 

 

 

p

p

 

 

 

 

 

 

p

 

 

 

 

 

1

 

1

 

1

 

 

 

x SE

Sign of Hicksian SE: 1 0 .p1

If p 0 , then Hicks SE=Slutsky SE.

16

A.Friedman

ICEF-2012

1.9 In-kind income

Let us suppose that instead of money income consumer is endowed with commodities bundle:

x1 , x2 , i.e. he owns x1 of the first good and bundle at market prices, he gets money income depends on prices.

x2 units of the second one. If he sells this I p1 , p2 p1 x1 p2 x2 . Note: now income

x2

 

 

 

p1

 

1

 

 

 

 

x

Agent sells good 1

x2

p2

Initial endowment

 

 

 

x2

Agent buys good 1

 

 

 

 

p1

 

 

 

 

 

 

 

 

 

 

p2

 

 

 

 

x1

0

 

 

 

 

 

 

 

 

 

 

 

x1

 

 

 

 

 

p2 x2

 

 

x1

 

 

 

 

 

p1

 

 

 

 

 

 

 

 

 

The effect of price change on budget set in case of in-kind income

x2

First good price increase

Become affordable

x2 p1 x1 p2

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Become unaffordable

 

 

B p,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p1

 

p1

 

 

 

 

 

 

 

 

 

 

 

 

p2

 

p

2

 

 

 

 

 

 

 

x1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0

 

 

 

 

1

 

 

 

 

 

 

 

 

p2

 

 

 

 

 

x

 

 

 

 

 

 

 

x

2

 

 

 

 

x1

 

 

 

 

 

 

 

 

 

 

 

p1

Utility maximization problem with in-kind income

max u x1 , x2 , , xN

x 0

N

pi xi

i 1

pi xi .

i 1N

If x - solution of UMP under price vector p , then

 

 

 

 

 

 

 

 

we say that consumer is a net buyer of good i

if x

 

 

,

x

i

 

 

 

i

 

 

 

 

consumer is said to be a net seller of good i if

x

 

 

 

.

 

 

x

i

 

 

 

 

 

i

 

 

 

 

17

A.Friedman

 

 

 

 

 

ICEF-2012

Slutsky equation with in-kind income

 

 

 

 

 

 

 

dx1 p, px

 

x1comp

x

x

 

x1

.

 

 

 

 

 

dp1

p1

1

1

 

I

 

 

 

 

Now income (or wealth) effect depends on the type of commodity (normal/inferior) and type of the agent (net buyer/net seller).

Good type

Nornal good

 

Inferior good

 

Agent type

Net buyer

Net seller

Net buyer

Net seller

Income (wealth) effect

 

+

+

 

Total effect

 

+/

+/

 

Application: Consumption-leisure model (Individual labour supply)

2 commodities:

leisure l and aggregate consumption c

 

 

 

c

 

 

 

 

 

 

Increase in utility

Utility function u c,l increases in both c

 

 

 

 

 

and l ,

 

 

 

 

 

wL

 

MRS –diminishing

C

 

 

 

p

 

 

 

 

 

 

 

 

 

 

 

w / p

Initial endowment L ,C .

 

 

 

c

 

 

 

 

Time is divided between leisure l and labour L : l L L .

Prices: w - wage rate (price of leisure),

 

p -price of consumption good

 

 

 

 

 

 

 

 

 

Budget constraint:

pc wl pC

wL

and

 

 

 

 

 

 

0 l

L

, c 0 .

 

 

 

 

 

C

L

0

l

 

L

l

Analysis of the wage rate increase

dl w, c wL

 

 

l comp

 

 

l

l

 

l comp

L

 

l

.

L

 

 

 

w

I

w

 

dw

 

 

 

 

 

 

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SE

 

IE

18

A.Friedman

ICEF-2012

c

w

c0

 

 

w0

c

 

 

 

 

l IE

 

 

0

l SE

L

l

 

 

SE: leisure becomes more expensive, thus SE reduces leisure and increases consumption of aggregate commodity

IE: Agent is a net seller of labour (he can never be a net buyer). Selling labour time at higher price rises his real income.

If leisure is normal, then it goes up due to increase in income and IE>0. If leisure is inferior, then it goes down and IE<0.

Leisure

Normal good

Inferior good

Substitution effect

 

 

Income (wealth) effect

+

 

Total effect

(if SE dominates)

 

 

+ (if IE dominates)

 

Derivation of individual labour supply p 1

c

Labour supply

 

 

 

w2

w2

 

 

 

 

 

 

 

 

 

 

 

 

 

w1

w1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

w0

 

 

 

 

 

 

 

 

 

 

w0

 

 

 

c

L0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0

 

 

 

 

 

 

 

L

1

L l

L0

L1

L2

 

 

 

L

 

 

 

 

 

 

 

 

 

L2

 

 

 

 

 

 

 

 

 

(а)

 

 

 

 

 

(b)

 

Possibility of backward bending labour supply (if leisure is normal)

19

A.Friedman

ICEF-2012

c

w

 

w2

Labour supply

IE dominates

 

 

w1

 

 

 

w2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

w1

 

 

 

 

 

 

 

w0

 

 

 

SE dominates

 

 

 

 

 

 

 

 

 

 

 

 

 

 

w0

 

 

 

c

 

L0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0

 

 

 

 

 

 

 

L

1

L l

L0

L2

L1

 

 

 

L

 

 

 

 

 

 

 

 

 

 

L2

 

 

 

 

 

 

(а)

 

 

 

 

 

(b)

 

Question. Explain why an increase in the basic wage rate per hour offered to a worker may decrease the number of hours she wishes to work while an overtime premium offered to the same worker may increase the number of hours she wishes to work?

1.10 Measuring changes in consumer’s welfare

 

 

 

 

 

 

 

Demand curve as a marginal valuation schedule

 

 

 

 

 

 

 

 

 

Consider quasi-linear utility function u x1 , x2 v x1 x2 ,

where

v 0

and v 0 ,

v 0 0 . Let p

 

1. In case of interior solution MRS

 

x

v

 

p

or v x p .

 

 

1

 

1

 

2

12

 

 

 

 

 

 

 

1

 

 

1

 

1

1

 

 

 

 

 

 

 

 

 

 

p1 , v p

Inverse demand function

p10

 

v x1

x 0

x1

1

 

Ordinary (Marshallian) consumer surplus (CS) – the difference between what the consumer is willing to pay and what he has to pay

20

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