income and substitution effects: applications · income and substitution effects: applications...

INCOME AND SUBSTITUTION EFFECTS:

APPLICATIONSAPPLICATIONS

INCOME AND SUBSTITUTION EFFECTS:APPLICATIONS

Subsidy on one product only v. Increase in income (at equal cost toIncrease in income (at equal cost to government)C i S i (I Consumption v. Saving (Inter-temporal choice))

Labour v. Leisure

AN INCREASE in INCOME v. A SUBSIDY on ONE PRODUCT ONLY

Involves equal cost to the government Example: food stamps used in the US

for welfare recipients (Ireland: p (television licence, electricity, transport,

)… )

AN INCREASE in INCOME v. A SUBSIDY on ONE PRODUCT ONLY

B d t t i t i i b

Mxpxp AA

Budget constraint is given by

Mxpxp 2211The government can

BB

(1) give a subsidy on food (x1)

Mxpxtp BB 2211

(2) give a increase in incomeNote: Equal cost to the(2) give a increase in income

BCC txMxpxp

cost to the government

txMxpxp 12211

AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT ONLY

But which makes the consumer better off ?But which makes the consumer better off ?

X2

A

U0

X1



X2 The subsidy on foodThe subsidy on food leaves the consumer at B (better off than at A)B (better off than at A)

BA

BU1

U0

1

X1



X2 The subsidy on foodThe subsidy on food leaves the consumer at B (better off than at A)MAA B (better off than at A)

B

Mxpxp AA 2211

AB

U1

U0

1

Mxpxtp BB 2211

X1


To illustrate the equal cost nature of the the subsidy v the income increase youthe subsidy v. the income increase, you draw a line parallel to the original budget constraint which passes through theconstraint which passes through the point B (as B must be affordable after the income increase)income increase).



X2 The increase inU2 The increase in income leaves the consumerC

U2

the consumer at C (better off

than at B)BA

than at B)BU1

U0

1

X1



X2 The increase inU2 The increase in income leaves the consumerC

U2

the consumer at C (better off

than at B)B

C

Athan at B)B

U1

U0

1

BCC txMxpxp 12211

X1

CONSUMPTION v SAVINGCONSUMPTION v. SAVING

Persons often receive income in “lumps”, e.g. monthly salary, yearly bonus, tax g y y, y y ,rebate ...

How is a lump of income spread over the How is a lump of income spread over the following month, year, (saving now for consumption later)?consumption later)?

How is consumption financed by borrowing now against income to beborrowing now against income to be received at the end of the month?


Divide time into two periods (today and tomorrow)and tomorrow)Assume that a person has income in h fi i d l ( d )the first period only (today)

Assume that a person consumes inAssume that a person consumes in both periods (today and tomorrow)

CONSUMPTION v SAVINGCONSUMPTION v. SAVINGThis is equivalent to

ttt YCi

C

111

qthe budget constraintwe met before, so we i1 ,

can apply the same techniques to analyse q y

changes in consumption and Mxpxp p

saving.Mxpxp 2211

Where Ct is consumption today, Ct+1 is consumption tomorrow, i is the interest rate co su pt o to o o , s t e te est ateand Y is income


Divide time into two periods (today Divide time into two periods (today and tomorrow)

Assume that a person has income in both periods (today and tomorrow)both periods (today and tomorrow)

Assume that a person consumes in b th i d (t d d t )both periods (today and tomorrow)

CONSUMPTION v SAVINGCONSUMPTION v. SAVINGWith income in both periods theWith income in both periods the budget constraint looks like this

1111

tttt YYCC 11 11

tttt Y

iYC

iC

Income in period t and t+1

CONSUMPTION v SAVINGCONSUMPTION v. SAVING1

ttt YCi

C

111

represents the current “price” f f t ti

1/ 1+i

11 YYCC

of future consumption

11 11

tttt Y

iYC

iC

1/1+irepresents the current “price” or “value” of

future income


CConsumption tomorrow is called saving

CONSUMPTION v. SAVINGttt YC

iC

11

1(Income in period t only)i1

What happens if the interest rate increases?Ct+1Ct+1

(1+i)Yt

CtYt


iC

11



i

(1+i)Y

i The budget line pivots out(1+i)Yt line pivots out from Yt

CtYt


iC

11



i

There is an increase in the value of

i consumption tomorrow, i.e. the price of future

(I+i)Yt

pconsumption decreases

CtYt


iC

11


Ct+1 Slope ofCt+1

i

Slope of the budget line = -(1+i*)i line (1 i )

Slope of(I+i)Yt

Slope of the budget line = -(1+i)line (1+i)

CtYt


iC

11


Ct+1 Isolating the incomeCt+1

i

Isolating the income and substitution effects

i

(I+i)Yt

CtYtab


iC

11


Ct+1Ct+1

ii The substitution

(I+i)Yt effect is a to b. Ctand Ct+1 ( St)

CtYtab


iC

11


Ct+1 The income effect isCt+1

i

The income effect is b to c, usually Ctand Ct+1 ( St)i and Ct+1 ( St)

(I+i)Yt

CtYtcb


iC

11


Ct+1

Overall effect is unclear Why? IE: CtCt+1

i

is unclear y

SE:Ct

i Overall: ?Ct ?StC??(I+i)Yt

CtYta

CONSUMPTION v. SAVING(Income in both periods)

11

Ct+1

11 11

11

tttt Y

iYC

iC

Ct+1

(1+i)Yt+Yt+1

Yt+1(Yt,Yt+1)

CtYt Yt+1/ (1+i) Yt+1

CONSUMPTION v. SAVING(Income in both periods)

11 11

11

tttt Y

iYC

iC

Ct+1

11 iiA lender consumers less in period t than their income inCt+1 period t than their income in period t (Ct<Yt)

(1+i)Yt+Yt+1 A lender type person

Yt+1


CONSUMPTION v SAVING(Income in both periods) 11 1

11

1

tttt Yi

YCi

C

Ct+1A borrower consumers more Ct+1 in period t than their income in period t (Ct>Yt)

(1+i)Yt+Yt+1

p ( )

Yt+1A borrower type person



11

1

tttt Yi

YCi

C


The budget constraint pivots around (Yt,Yt+1) and the ( t, t 1)

outcome can be different for borrowers and lenders.

Yt+1(Yt,Yt+1)

CtYt


11

1

tttt Yi

YCi

C

What happens if the interest rate increases?Ct+1Ct+1 LENDER

Yt+1 (Yt,Yt+1)

CtYt


11

1

tttt Yi

YCi

C


Utility is higher butUtility is higher but we cannot be certain if Ct+1 or Ct

Y(Yt,Yt+1)

certain if Ct+1 or Ctrise or fall

Yt+1

CtYt


11

1

tttt Yi

YCi

C


Could end upCould end up here

Yt 1(Yt,Yt+1)Yt+1

CtYt


11

1

tttt Yi

YCi

C


Or hereOr here

Yt+1(Yt,Yt+1)Yt+1

CtYt


11

1

tttt Yi

YCi

C

What happens if the interest rate increases?Ct+1Ct+1 BORROWER

Y (Yt,Yt+1)Utility is lower but…….??Yt+1

( t, t+1) but…….??

CtYt

CONSUMPTION v SAVINGCONSUMPTION v SAVING

Do the case of a decrease in interest ratesrates.

You can also show the income and b i i ff i h i dsubstitution effects in the two period

model.

LABOUR and LEISURELABOUR and LEISUREFrameworkFramework 24 hours a day There is only two things you can do with There is only two things you can do with

your time– Work (paid labour market)– Work (paid labour market)– Leisure

Ignores housework (extension possible)– Ignores housework (extension possible) You divide all you time between these two

activitiesactivities. When you work in the paid labour market,

you are paid a market wageyou are paid a market wage.

LABOUR and LEISURELABOUR and LEISURE24.w = w.Leisure + p.Consumption p p

Where 24.w is the value of initial endowment, w.Leisure is the amount of the endowment spent on leisure and p.Consumption is the

Rearranging:

amount of endowment spent on consumption

Rearranging:

C= 24w/p – (w/p)Leisure

LABOUR and LEISUREWhat happens if the wage rate increases?

CC

Slope = -w/p

24w/p

Leisure24h

LABOUR and LEISUREWhat happens if the wage rate increases?

C / W > WC

24w2/p W2 > W1

w The budget line pivots out

24w1/pline pivots out from here

Leisure24h

LABOUR and LEISUREMore labour or more leisure…….?U i d b tit ti ff tUse income and substitution effects

C NB: Is leisure a normalC

NB: Is leisure a normal or an inferior good?

w

24w1/p

Leisure24h

LABOUR and LEISUREMore labour or more leisure…….?

CC

24w1/p

Leisure24hA


CTotal Effect ?

C

Depends (to some extent) on whetherw extent) on whether Leisure is assumed to be normal or inferior24w1/pbe normal or inferior

Leisure24hA


CSE: A to B

C

IE: Depends on whether Leisure isw whether Leisure is assumed to be normal or inferior24w1/por inferior

Leisure24hA


CSE: A to B

C

IE: Depends on whether Leisure isw whether Leisure is assumed to be normal or inferior24w1/por inferior

Leisure24hAB


C

Overall we could end up here if leisure is

C

“very normal”

w

24w1/p

Leisure24hAB C


CSE: A to B

C

IE: B to C

w Depends on whether Leisure is assumed to

24w1/p be normal or inferior

Leisure24hAB C

LABOUR and LEISURELABOUR and LEISUREIncrease in wage rateg

Substitution effect: w price of leisure Substitution effect: w price of leisure leisure and labour supply

Income effect: w income (value of the initial endowment) ) leisure and labour supply

IF LEISURE IS A NORMAL GOODIF LEISURE IS A NORMAL GOOD

Overall effect: Leisure?? Labour Supply??Overall effect: Leisure?? Labour Supply??

income and substitution effects: applications · income and substitution effects: applications...

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