Income and Substitution Effect
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![Page 1: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/1.jpg)
INCOME AND SUBSTITUTION EFFECTS:
APPLICATIONS
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INCOME AND SUBSTITUTION EFFECTS:APPLICATIONS
Subsidy on one product only v. Increase in income (at equal cost to government)
Consumption v. Saving (Inter-temporal choice)
Labour v. Leisure
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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: television licence, electricity, transport, … )
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AN INCREASE in INCOME v. A SUBSIDY on ONE PRODUCT ONLY
Mxpxp AA 2211
Mxpxtp BB 2211
Budget constraint is given by
The government can
(1) give a subsidy on food (x1)
(2) give a increase in income
BCC txMxpxp 12211
Note: Equal cost to the government
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AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT ONLY
But which makes the consumer better off ?
X2
X1
A
U0
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AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT ONLY
But which makes the consumer better off ?
X2
X1
A
The subsidy on food leaves the consumer at B (better off than at A)
B
U0
U1
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AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT ONLY
But which makes the consumer better off ?
X2
X1
A
The subsidy on food leaves the consumer at B (better off than at A)
B
U0
U1
Mxpxtp BB 2211
Mxpxp AA 2211
![Page 8: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/8.jpg)
AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT ONLY
To illustrate the equal cost nature of the the subsidy v. the income increase, you draw a line parallel to the original budget constraint which passes through the point B (as B must be affordable after the income increase).
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AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT ONLY
But which makes the consumer better off ?
X2
X1
A
The increase in income leaves the consumer
at C (better off than at B)
B
C
U0
U1
U2
![Page 10: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/10.jpg)
AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT ONLY
But which makes the consumer better off ?
X2
X1
A
The increase in income leaves the consumer
at C (better off than at B)
B
C
U0
U1
U2
BCC txMxpxp 12211
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CONSUMPTION v. SAVING
Persons often receive income in “lumps”, e.g. monthly salary, yearly bonus, tax rebate ...
How is a lump of income spread over the following month, year, (saving now for consumption later)?
How is consumption financed by borrowing now against income to be received at the end of the month?
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CONSUMPTION v. SAVING
Divide time into two periods (today and tomorrow)
Assume that a person has income in the first period only (today)
Assume that a person consumes in both periods (today and tomorrow)
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CONSUMPTION v. SAVING
ttt YCi
C
11
1This is equivalent to
the budget constraint we met before, so we
can apply the same techniques to analyse
changes in consumption and
saving.Mxpxp 2211
Where Ct is consumption today, Ct+1 is consumption tomorrow, i is the interest rate and Y is income
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CONSUMPTION v. SAVING
Divide time into two periods (today and tomorrow)
Assume that a person has income in both periods (today and tomorrow)
Assume that a person consumes in both periods (today and tomorrow)
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CONSUMPTION v. SAVING
11 1
1
1
1
tttt Yi
YCi
C
With income in both periods the budget constraint looks like this
Income in period t and t+1
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CONSUMPTION v. SAVING
ttt YCi
C
11
1
11 1
1
1
1
tttt Yi
YCi
C
represents the current “price” of future consumption
1/ 1+i
1/1+irepresents the current “price” or “value” of
future income
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CONSUMPTION v. SAVING
Consumption tomorrow is called saving
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CONSUMPTION v. SAVING
ttt YCi
C
11
1(Income in period t only)
What happens if the interest rate increases? Ct+1
Ct Yt
(1+i)Yt
![Page 19: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/19.jpg)
CONSUMPTION v. SAVING
ttt YCi
C
11
1(Income in period t only)
What happens if the interest rate increases? Ct+1
Ct Yt
(1+i)Yt
i The budget line pivots out from Yt
![Page 20: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/20.jpg)
CONSUMPTION v. SAVING
ttt YCi
C
11
1(Income in period t only)
What happens if the interest rate increases? Ct+1
Ct Yt
(I+i)Yt
i
There is an increase in the value of consumption tomorrow, i.e. the price of future consumption decreases
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CONSUMPTION v. SAVING
ttt YCi
C
11
1(Income in period t only)
Ct+1
Ct Yt
(I+i)Yt
i
Slope of the budget line = -(1+i*)
Slope of the budget line = -(1+i)
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CONSUMPTION v. SAVING
ttt YCi
C
11
1(Income in period t only)
Ct+1
Ct Yt
(I+i)Yt
i
ab
Isolating the income and substitution effects
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CONSUMPTION v. SAVING
ttt YCi
C
11
1(Income in period t only)
Ct+1
Ct Yt
(I+i)Yt
i The substitution effect is a to b. Ct and Ct+1 ( St)
ab
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CONSUMPTION v. SAVING
ttt YCi
C
11
1(Income in period t only)
Ct+1
Ct Yt
(I+i)Yt
i
cb
The income effect is b to c, usually Ct and Ct+1 ( St)
![Page 25: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/25.jpg)
CONSUMPTION v. SAVING
ttt YCi
C
11
1(Income in period t only)
Ct+1
Ct Yt
(I+i)Yt
i
a
Overall effect is unclear Why? IE: Ct
SE: Ct
Overall: ?Ct ?StC??
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(1+i)Yt+Yt+1
CONSUMPTION v. SAVING(Income in both periods)
Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
(Yt,Yt+1)
Yt+1/ (1+i) Yt+1
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(1+i)Yt+Yt+1
CONSUMPTION v. SAVING(Income in both periods)
Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
Yt+1/ (1+i) Yt+1
A lender type person
A lender consumers less in period t than their income in period t (Ct<Yt)
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(1+i)Yt+Yt+1
CONSUMPTION v SAVING(Income in both periods)
Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
Yt+1/ (1+i) Yt+1
A borrower type person
A borrower consumers more in period t than their income in period t (Ct>Yt)
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CONSUMPTION v SAVING(Income in both periods)
What happens if the interest rate increases? Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
The budget constraint pivots around (Yt,Yt+1) and the
outcome can be different for borrowers and lenders.
(Yt,Yt+1)
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CONSUMPTION v SAVING(Income in both periods)
What happens if the interest rate increases? Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
(Yt,Yt+1)
LENDER
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CONSUMPTION v SAVING
(Income in both periods)
What happens if the interest rate increases? Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
(Yt,Yt+1)
LENDER
Utility is higher but we cannot be certain if Ct+1 or Ct rise or fall
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CONSUMPTION v SAVING(Income in both periods)
What happens if the interest rate increases? Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
(Yt,Yt+1)
LENDER
Could end up here
![Page 33: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/33.jpg)
CONSUMPTION v SAVING(Income in both periods)
What happens if the interest rate increases? Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
(Yt,Yt+1)
LENDER
Or here
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CONSUMPTION v SAVING
(Income in both periods)
What happens if the interest rate increases? Ct+1
Ct Yt
Yt+1
11 1
1
1
1
tttt Yi
YCi
C
BORROWER
(Yt,Yt+1)Utility is lower but…….??
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CONSUMPTION v SAVING
Do the case of a decrease in interest rates.
You can also show the income and substitution effects in the two period model.
![Page 36: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/36.jpg)
LABOUR and LEISUREFramework 24 hours a day There is only two things you can do with
your time–Work (paid labour market)– Leisure– Ignores housework (extension possible)
You divide all you time between these two activities.
When you work in the paid labour market, you are paid a market wage.
![Page 37: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/37.jpg)
LABOUR and LEISURE
24.w = w.Leisure + p.Consumption
Rearranging:
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 amount of endowment spent on consumption
C= 24w/p – (w/p)Leisure
![Page 38: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/38.jpg)
LABOUR and LEISURE
What happens if the wage rate increases?
C
Leisure 24h
24w/p
Slope = -w/p
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LABOUR and LEISURE
C
Leisure24h
24w1/p
w The budget line pivots out from here
24w2/p
What happens if the wage rate increases?
W2 > W1
![Page 40: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/40.jpg)
LABOUR and LEISUREMore labour or more leisure…….?
Use income and substitution effects
C
Leisure24h
24w1/p
w
NB: Is leisure a normal or an inferior good?
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LABOUR and LEISUREMore labour or more leisure…….?
C
Leisure24h
24w1/p
A
![Page 42: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/42.jpg)
LABOUR and LEISUREMore labour or more leisure…….?
C
Leisure24h
24w1/p
w
Total Effect ?
A
Depends (to some extent) on whether Leisure is assumed to be normal or inferior
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LABOUR and LEISUREMore labour or more leisure…….?
C
Leisure24h
24w1/p
w
SE: A to B
A
IE: Depends on whether Leisure is assumed to be normal or inferior
![Page 44: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/44.jpg)
LABOUR and LEISUREMore labour or more leisure…….?
C
Leisure24h
24w1/p
w
SE: A to B
AB
IE: Depends on whether Leisure is assumed to be normal or inferior
![Page 45: Income and Substitution Effect](https://reader031.fdocuments.net/reader031/viewer/2022020715/54550f3fb1af9f907f8b4573/html5/thumbnails/45.jpg)
LABOUR and LEISUREMore labour or more leisure…….?
C
Leisure24h
24w1/p
w
AB
Overall we could end up here if leisure is “very normal”
C
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LABOUR and LEISUREMore labour or more leisure…….?
C
Leisure24h
24w1/p
w
SE: A to B
AB
IE: B to C
Depends on whether Leisure is assumed to be normal or inferior
C
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LABOUR and LEISURE
Increase in wage rate
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 GOOD
Overall effect: Leisure?? Labour Supply??