ECON20402 - MACROECONOMICS IIB
Dr. Sakir Devrim Yilmaz

Lecture 1:
Introduction to Intertemporal
Macroeconomics

IS/LM Framework
Goods market
Y = C +I +G
C = C + c (Y − T ); c ∈ (0,1)
I = I − br , b > 0
G =G
T =T =G

Money market

M
= L(r ,Y )
P
L = hY − kr ; h, k > 0
M M
=
P P

2

Intertemporal Macroeconomics
• Behind these abstract variables (C,I,G,T) there are rational agents with preferences and facing budget constraints.
• These agents live for more than one period.
• Their decisions today impact on their available choices tomorrow. • Agents seek to maximise their lifetime utilities subject to their lifetime budget constraints.
• Intertemporal macroeconomics helps to explain this dynamic process.
3

Keynesian Consumption Function
C = C + cY , C > 0, 0 < c < 1
• Marginal Propensity to Consume (MPC) between 0 and 1.
• Average Propensity to Consume (APC) decreasing in Y:

C C
C
APC = = + c; As Y ↑ ,
↓
Y Y
Y
• Income determines consumption and interest rate does not have a crucial role.
4

Burda & Wyplosz - MACROECONOMICS 4ed.

Variability of GDP Components, 1970-2001
14%
12%

USA euro area

10%
8%
6%
4%
2%
0%
C/Y

I/Y

G/Y

Consumption

Investment

Government
Consumption

5

© Oxford University Press, 2005. All rights reserved.

Keynesian Consumption Function (2)
• Keynesian consumption function relates current consumption with current income.
This problem can be solved by working with dynamic
(as opposed to static) models.

• Keynesian consumption function does not tell us anything about the agent’s behaviour.
This problem can be solved by introducing microeconomic foundations into our macroeconomic models. 6

ECON20402 MACROECONOMICS IIB

Consumption and Household’s
Intertemporal Choices

Assumptions
• Representative agent
• Rational expectations (agents do not make systematic errors)
• No uncertainty about the future
• People live for 2 periods (young and old)
• Constant population
• Constant labour supply (perfectly inelastic)
• The interest rate is given
• All variables are real (adjusted by inflation)
8

Endowment, wealth, and consumption

9

Burda & Wyplosz - MACROECONOMICS 4ed.

Consumption tomorrow

Endowment, wealth...
D

Endowments M, A and P for interest rate r imply the identical wealth 0B.
M (student, low Y1 today, high Y2 tomorrow)

Y2

A
(Professional athlete, high Y1
P
today, low Y2 tomorrow)

slope = - (1+r )
0

Y1

B

Consumption today

10

© Oxford University Press, 2005. All rights reserved.

Burda & Wyplosz - MACROECONOMICS 4ed.

Consumption tomorrow

Endowment, wealth...
D

Y2

and consumption possibilities

A

slope = - (1+r )
0

Y1

B

Consumption today

11

© Oxford University Press, 2005. All rights reserved.

Algebra of the Lifetime Budget Constraint
Y1 = Income when young C1 = Consumptio n when young
Y2 = Income when old

C2 = Consumptio n when old

Young : Y1 = C1 + S1 ⇒ S1 = Y1 − C1 ≥ 0 or < 0 (disaving ) (1a)

Old : Y2 + S1 (1 + r ) = C2

(1b)

Replacing (1a) into (1b) :
Lifetime Budget Constraint : C1 +

C2
Y
= Y1 + 2
1+ r
1+ r

( 2)

Y2
= Total wealth (today)
Let W = Y1 +
1+ r
C
C1 + 2 = W (3)
1+ r
PDV of consumptio n = PDV of wealth (here just Y )
(PDV = Present Discounted Value)
12

Burda & Wyplosz - MACROECONOMICS 4ed.

Endowment, wealth... and consumption possibilities
C2 D = (1 + r )Y1 + Y2 = (1 + r )W
Budget line : C2 = [(1 + r )Y1 + Y2 ] − (1 + r )C1 slope :

Y2

dC2
= −(1 + r ) dC1 A

slope = - (1+r )
0

Y1

B

= Y1 +

Y2
=W
(1 + r )

C1

13

© Oxford University Press, 2005. All rights reserved.

Optimal consumption

14

Burda & Wyplosz - MACROECONOMICS 4ed.

Indifference curves
Consumption tomorrow

U = U (C1,C2 ) ( 4)
∂U
Slope : -

∂U

∂C1
∂C2

or -

'
UC1
'
UC 2

(Marginal Rate of Substitution)