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THE CONSUMPTION FUNCTION. Looking at Aggregate Demand (closed economy) Ep = C + Ip + G Assuming G is exogenous, this leads to enquiring into determinants of Consumption and Investment Consumption is of particular interest (multipliers, etc) Previously we have:

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the consumption function
THE CONSUMPTION FUNCTION
  • Looking at Aggregate Demand (closed economy)
  • Ep = C + Ip + G
  • Assuming G is exogenous, this leads to enquiring into determinants of Consumption and Investment
  • Consumption is of particular interest (multipliers, etc)
  • Previously we have:
    • C = (1 - s)Y (0  s < 1)
    • or, C = C(Y - T)
  • We need to model the behaviour of C
early formulation keynes 1936
EARLY FORMULATION: KEYNES (1936)
  • Keynes (1936) made three main assertions:
  • C = C(Y), (not r)
  • 0  MPC  1, (where MPC is dC/dY)
  • APC falls as Y increases (APC is C/Y)
  • Taken together these imply a Consumption Function of the form: C = A + bY
    • where A and b are positive constants
    • APC = A/Y + b
    • MPC = b
    • and A/Y must fall as Y increases
graph of the basic consumption function
GRAPH OF THE BASIC CONSUMPTION FUNCTION
  • As Y increases, C/Y falls: also dC/dY  C/Y

C

45O

C = A + bY

dC/dY = b

A

0

Y

early empirical evidence
EARLY EMPIRICAL EVIDENCE
  • Keynes hadn’t have much statistical evidence on consumption
  • Early estimates in the 1940s for the USA and elsewhere were conflicting.
  • Short-medium term annual data (1929-45)
    • C = A + bY; A 0; b  0.7
  • Long-term data (1869-1945)
    • C = bY: A  0, b  0.9
  • Which is “right”?
  • We need a proper model to answer this.
long and meduim run evidence on consumption
LONG AND MEDUIM RUN EVIDENCE ON CONSUMPTION
  • 1929-45: C = A + bY
  • 1869-45; C = b*Y

C

45O

b* 0.9

C = b* Y

C = A + bY

b 0.7

0

Y

models of aggregate consumption
MODELS OF AGGREGATE CONSUMPTION
  • Basic Intertemporal Choice model (Fisher)
  • The Life-Cycle theory of Consumption (Modigliani, etc)
  • The Permanent Income theory of Consumption (Friedman)
intertemporal choice
INTERTEMPORAL CHOICE
  • Generally we require: PV(C)  or  PV(Y)
  • i.e. C1 + C2  (1+r)  or  Y1 + Y2 (1+r)
  • or  Ci  (1+r)i  or   Yi  (1+r)i
  • Households maximize Utility over expected lifetime
  • i.e. Max: U = U (C1, ..., Ci , ... , Cn)
  • s.t.  Ci  (1+r)i  or   Yi  (1+r)i(i : 1  n)
intertemporal choice1
INTERTEMPORAL CHOICE

Indifference Curves represent U = U(C1 , C2 )

C2

C1

0

intertemporal choice2
INTERTEMPORAL CHOICE

Endowment at E: OB = PV(Y) = y1 + y2  (1 + r)

Slope of AB is  (1 + r)

Y2

A

.

E

y2

y1

Y1

0

B

intertemporal choice3
INTERTEMPORAL CHOICE

Why is slope AB = - (1 + r) ?

Suppose (present) savings increase by €100

i.e. C1 = - 100

This allows an increase in C2 of 100(1 + r)

i.e. C2 = +100 (1 + r)

Slope AB = C2  C1 = 100 (1 + r)/ - 100

= - (1 + r)

a change in r
A CHANGE IN r

An increase in r: AB pivots at E  CD

Y2

C

A

.

E

y2

y1

Y1

0

D

B

optimal c
OPTIMAL C

Saving is (oy1- oc*1) : future dis-saving is (oc*2 - oy2)

Y2

A

c*2

c*

.

y2

E

0

c*1

y1

B

Y1

changes in y and c
CHANGES IN Y AND C

Y2 increases: E’  E”, AB  CD, c’1  c”1

Y2

C

A

.

E”

.

E’

0

c’1

c”1

B

D

Y1

a increase in r saver
A INCREASE IN r : SAVER

Income effect 1 3; Substitution effect 3  2

Y2

C

F

A

2

3

1

.

y2

E

0

y1

Y1

c31

c21

D

B

G

c11

a increase in r borrower
A INCREASE IN r : BORROWER

Inc. effect 1  2; Sub. effect 2  3

Y2

C

A

.

F

E

3

1

2

0

Y1

y1

c31

c11

c21

D

G

B

imperfect capital markets
IMPERFECT CAPITAL MARKETS

Borrowing rate (EB) > lending rate (AE)

C2

A

.

Y2

E

0

Y1

B

C1

credit borrowing constraint
CREDIT (BORROWING) CONSTRAINT

.

C2

I”

Constraint: ADB

I’

A

Consumer cannot

borrow more than Y1B

E

Y2

D

0

Y1

B

C1

the life cycle hypothesis
THE LIFE-CYCLE HYPOTHESIS
  • Income shows a marked life-cycle variation
  • It is low in the early years, reaches a peak in late middle age and declines, especially on retirement
  • Smoothing consumption over a lifetime is a rational strategy (diminishing MUy)
  • This implies C/Y will vary during the lifetime of an individual
the life cycle hypothesis1
THE LIFE-CYCLE HYPOTHESIS

.

C2

E’: low Y1/Y2  high C1/Y1

E”: high Y1/Y2  low C1/Y1

A

E’

.

C2*

.

E”

C1

B

0

Y1’

C1*

Y1”

the life cycle hypothesis2
THE LIFE-CYCLE HYPOTHESIS

Y, C and W over the life-cycle

Y, C

Ct

Yt

Age

18

65

+W

Wt

Age

W

the life cycle model
THE LIFE-CYCLE MODEL
  • Let retirement age = 65; life expectancy = 75
  • Years to retirement = R (= 65 – present age)
  • Expected life = T (= 75 – present age)
  • Assuming no pension, no discounting:
  • CT = W + RY is the lifetime constraint
  • i.e. C = (W + RY)/T
  • and C = (1/T)W + (R/T)Y
  • or C = W + Y ( = 1/T;  = R/T)
the life cycle model1
THE LIFE-CYCLE MODEL
  • C = W + Y
  • MPC =  C Y = 
  • APC = C Y =  (W  Y) + 
  • clearly MPC < APC
  • for a “typical” individual, age 35
  • R=30, T = 40
  •  = 1/T  0.03;  (MPC) = RT  0.75
  • APC = [0.03 (W  Y) + 0.75] > MPC
the life cycle model2
THE LIFE-CYCLE MODEL
  • Saving and Consumption behaviour may depend on population age-structure
  • Does Social Security displace personal savings?
  • What is the effect of Medicare (USA) or Medical Cards for over 70s (IRL) on Savings?
  • Savings and Uncertainty:
    • “rational” behaviour: run down wealth to zero
    • individual circumstances unpredictable (care needs)
    • individual life expectancy unpredictable
    • on average even selfish people will die with W > 0
the permanent income hypothesis
THE PERMANENT INCOME HYPOTHESIS
  • Cp = kYp (0  k  1 )
  • Y = Yp+ Ytr
  • C = Cp + Ctr
  • Permanent income is the return to all wealth, human and non-human:
  • Yp = rW
  • which implies: Cp = rkW
  • NB: C is not related to Ytr i.e. dC dYtr = 0
measuring permanent income and consumption 1
MEASURING PERMANENT INCOME AND CONSUMPTION (1)
  • Are Cpand Yp observable?
  • E(Ytr ) = 0
  • E(Ctr ) = 0
  • which imply that E(Y) = E(Yp ), etc.
  • However this is ex ante: ex post, actual measures may reveal more
  • (a) in a recession: Y < Yp :  Ytr < 0
  • (b) in a boom: Y > Yp :  Ytr > 0
measuring permanent income and consumption 2
MEASURING PERMANENT INCOME AND CONSUMPTION (2)
  • Cross-section measurements of C and Y

C

45o

Ci, Yi.

.

.

.

.

Ci = A + bYi

.

.

Cm

.

0

Y

Ym

measuring permanent income and consumption 3
MEASURING PERMANENT INCOME AND CONSUMPTION (3)
  • Where Yj > Ym, Ytr > 0 and Yj > Ypj

C

45o

Cp =kYp

Cj

Ci = A + bYi

Cm

Ytrj

0

Y

Yj

Ym

Ypj

measuring permanent income and consumption 4
MEASURING PERMANENT INCOME AND CONSUMPTION (4)
  • Aggregate: Ytr > 0 in boom, < 0 in recession
  • Measured C/Y should  be < in boom than in recession (Recent experience?)
  • Aggregate Ctr = 0: individual Ctr is > or < 0
  • Average Ctr = 0 for all income groups
  • Measuring Yp:
    • Adaptive expectations: Yp = f(Yt, Y t - 1, ...Y t-n)
    • Rational expectations: only new information (shocks) change Yp
    • Consumption V Consumption Expenditure, which highlights the role of durables (Investment and saving rather than consumption
measuring permanent income and consumption 5
MEASURING PERMANENT INCOME AND CONSUMPTION (5)
  • Also we may express the PYH as an error-correction model:
  • Ypt = Ypt-1 + j(Yt – Ypt-1) 0 < j < 1
  • which with: Ct = Cpt = kYpt
  • gives: Ct = kYpt = kYpt-1 + kj(Yt – Ypt-1)
  • Re-arranging: Ct = (k – kj)Ypt-1 + kjYt
  • j  0 implies slow adaptation, j  1 implies rapid adaptation
  • assume k = 0.9, j = 0.3, so kj = 0.27
  • then: Ct = (0.9 – 0.27)Ypt-1 + 0.27Yt or 0.63Ypt-1 + 0.27Yt
  • However this is not an explicitly forward-looking model.
  • Now suppose C = Cp = kYp, then Yp = 1/k(Cp)
  • Thus Ct = (0.63/k)Ct – 1 + 0.27Yt = 0.7Ct – 1 + 0.27Yt
permanent income and recession
PERMANENT INCOME AND RECESSION
  • Y < Yp in short-run (mild) recession
  • Suppose there is a shock to the system (financial crisis)
  • Pwople expect a severe long-drawn-out recession: i.e. Yp falls, ie. E(Y) falls
  • It is possible that initiallyY > Yp
  • C (and Cp) will fall
  • If people anticipate a fall in Yp, then C/Y may fall
  • Current (mid-2009) situation: big fall in W, both the Permanent and Life-cycle theories predict that this will hit C (independently of current measured Y)
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