INCOME AND SUBSTITUTION EFFECTS: APPLICATIONS

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INCOME AND SUBSTITUTION EFFECTSAPPLICATIONS
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INCOME AND SUBSTITUTION EFFECTSAPPLICATIONS

• 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
Budget constraint is given by
The government can (1) give a subsidy on food
(x1)
Note Equal cost to the government
(2) give a increase in income
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AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT
ONLY
But which makes the consumer better off ?
X2
A
U0
X1
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AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT
ONLY
But which makes the consumer better off ?
X2
The subsidy on food leaves the consumer at B
(better off than at A)
B
A
U1
U0
X1
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AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT
ONLY
But which makes the consumer better off ?
X2
The subsidy on food leaves the consumer at B
(better off than at A)
B
A
U1
U0
X1
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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
The increase in income leaves the consumer at C
(better off than at B)
U2
C
B
A
U1
U0
X1
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AN INCREASE in INCOME v A SUBSIDY on ONE PRODUCT
ONLY
But which makes the consumer better off ?
X2
The increase in income leaves the consumer at C
(better off than at B)
U2
C
B
A
U1
U0
X1
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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
This is equivalent to the budget constraint we
met before, so we can apply the same techniques
to analyse changes in consumption and saving.
Where Ct is consumption today, Ct1 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
With income in both periods the budget constraint
looks like this
Income in period t and t1
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CONSUMPTION v. SAVING

represents the current price of future
consumption
1/ 1i

represents the current price or value of
future income
1/1i
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CONSUMPTION v. SAVING
Consumption tomorrow is called saving
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CONSUMPTION v. SAVING
(Income in period t only)
What happens if the interest rate increases?
Ct1
(1i)Yt
Ct
Yt
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CONSUMPTION v. SAVING
(Income in period t only)
What happens if the interest rate increases?
Ct1
?i
The budget line pivots out from Yt
(1i)Yt
Ct
Yt
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CONSUMPTION v. SAVING
(Income in period t only)
What happens if the interest rate increases?
Ct1
There is an increase in the value of consumption
tomorrow, i.e. the price of future consumption
decreases
?i
(Ii)Yt
Ct
Yt
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CONSUMPTION v. SAVING
(Income in period t only)
Slope of the budget line -(1i)
Ct1
?i
Slope of the budget line -(1i)
(Ii)Yt
Ct
Yt
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CONSUMPTION v. SAVING
(Income in period t only)
Ct1
Isolating the income and substitution effects
?i
(Ii)Yt
Ct
Yt
a
b
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CONSUMPTION v. SAVING
(Income in period t only)
Ct1
?i
The substitution effect is a to b. ?Ct and ?Ct1
(? St)
(Ii)Yt
Ct
Yt
a
b
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CONSUMPTION v. SAVING
(Income in period t only)
Ct1
The income effect is b to c, usually ?Ct and
?Ct1 (? St)
?i
(Ii)Yt
Ct
Yt
c
b
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CONSUMPTION v. SAVING
(Income in period t only)
Overall effect is unclear
Why? IE ?Ct SE ?Ct Overall ?Ct
?St
Ct1
?i
C??
(Ii)Yt
a
Ct
Yt
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CONSUMPTION v. SAVING
(Income in both periods)
Ct1
(1i)YtYt1
(Yt,Yt1)
Yt1
Ct
Yt
Yt1/ (1i) Yt1
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CONSUMPTION v. SAVING
(Income in both periods)
A lender consumers less in period t than their
income in period t (CtltYt)
Ct1
A lender type person
(1i)YtYt1
Yt1
Ct
Yt
Yt1/ (1i) Yt1
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CONSUMPTION v SAVING
(Income in both periods)
A borrower consumers more in period t than their
income in period t (CtgtYt)
Ct1
(1i)YtYt1
A borrower type person
Yt1
Ct
Yt
Yt1/ (1i) Yt1
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CONSUMPTION v SAVING
(Income in both periods)
What happens if the interest rate increases?
Ct1
The budget constraint pivots around (Yt,Yt1) and
the outcome can be different for borrowers and
lenders.
(Yt,Yt1)
Yt1
Ct
Yt
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CONSUMPTION v SAVING
(Income in both periods)
What happens if the interest rate increases?
Ct1
LENDER
Yt1
(Yt,Yt1)
Ct
Yt
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CONSUMPTION v SAVING
(Income in both periods)
What happens if the interest rate increases?
Ct1
LENDER
Utility is higher but we cannot be certain if
Ct1 or Ct rise or fall
(Yt,Yt1)
Yt1
Ct
Yt
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CONSUMPTION v SAVING
(Income in both periods)
What happens if the interest rate increases?
Ct1
LENDER
Could end up here
(Yt,Yt1)
Yt1
Ct
Yt
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CONSUMPTION v SAVING
(Income in both periods)
What happens if the interest rate increases?
Ct1
LENDER
Or here
(Yt,Yt1)
Yt1
Ct
Yt
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CONSUMPTION v SAVING
(Income in both periods)
What happens if the interest rate increases?
Ct1
BORROWER
Utility is lower but.??
(Yt,Yt1)
Yt1
Ct
Yt
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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.

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LABOUR and LEISURE

• Framework
• 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.

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LABOUR and LEISURE
24.w w.Leisure p.Consumption
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
Rearranging
C 24w/p (w/p)Leisure
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LABOUR and LEISURE
What happens if the wage rate increases?
C
Slope -w/p
24w/p
Leisure
24h
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LABOUR and LEISURE
What happens if the wage rate increases?
C
W2 gt W1
24w2/p
?w
The budget line pivots out from here
24w1/p
Leisure
24h
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LABOUR and LEISURE
More labour or more leisure.?
Use income and substitution effects
C
NB Is leisure a normal or an inferior good?
?w
24w1/p
Leisure
24h
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LABOUR and LEISURE
More labour or more leisure.?
C
24w1/p
Leisure
24h
A
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LABOUR and LEISURE
More labour or more leisure.?
Total Effect ?
C
Depends (to some extent) on whether Leisure is
assumed to be normal or inferior
?w
24w1/p
Leisure
24h
A
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LABOUR and LEISURE
More labour or more leisure.?
SE A to B
C
IE Depends on whether Leisure is assumed to be
normal or inferior
?w
24w1/p
Leisure
24h
A
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LABOUR and LEISURE
More labour or more leisure.?
SE A to B
C
IE Depends on whether Leisure is assumed to be
normal or inferior
?w
24w1/p
Leisure
24h
A
B
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LABOUR and LEISURE
More labour or more leisure.?
Overall we could end up here if leisure is very
normal
C
?w
24w1/p
Leisure
24h
A
B
C
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LABOUR and LEISURE
More labour or more leisure.?
SE A to B
C
IE B to C Depends on whether Leisure is
assumed to be normal or inferior
?w
24w1/p
Leisure
24h
A
B
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??