1. EC6012 Lecture 2
Stephen Kinsella
Problem
Tobin and the Old
EC6012 Lecture 2 Yale School
The Multiplier
Review of Intermediate Concepts
Godley & Lavoie
Approach
Homework & Blogs
Stephen Kinsella References
Dept. Economics,
University of Limerick.
stephen.kinsella@ul.ie
January 16, 2008

2. Outline EC6012 Lecture 2
Stephen Kinsella
Problem
Problem Tobin and the Old
Yale School
The Multiplier
Godley & Lavoie
Tobin and the Old Yale School Approach
Homework & Blogs
References
The Multiplier
Godley & Lavoie Approach
Homework & Blogs

3. Problem EC6012 Lecture 2
Stephen Kinsella
Where is the connection? Problem
Orthodox Theory vs. Structuralist Theory Tobin and the Old
Yale School
The Multiplier
Godley & Lavoie
Approach
Homework & Blogs
References

4. Tobin’s Nobel Lecture EC6012 Lecture 2
(Sections 2.9 & 4) Stephen Kinsella
Problem
Statistics of Stocks and Flows Tobin and the Old
Yale School
”The innovation of the approach thus far described The Multiplier
is the integration of saving and portfolio decisions. Godley & Lavoie
Functions for accumulation of particular assets are Approach
Homework & Blogs
specified, and they add up to total wealth
References
accumulation for the period.”
Dynamics and Steady States
. . . dynamic solutions of a non-linear system, even
one of such small dimensionality. . . cannot be
obtained analytically but require simulations.

5. Idea EC6012 Lecture 2
Stephen Kinsella
In a sentence Problem
If investment increases, there will be an increase in output as Tobin and the Old
Yale School
a result of a ‘multiplier’ relationship between equilibrium The Multiplier
output and the autonomous components of spending Godley & Lavoie
Approach
History Homework & Blogs
Harrod→Keynes→Hicks→Kahn→Dusenberry→Metzler References
Derivation: Orthodox
Handout & Blackboard

6. Notation
Symbol Meaning
G Pure government expenditures in nominal terms
Y National Income in Nominal Terms
C Consumption of goods supply by households, in nominal terms
T Taxes
θ Personal Income Tax Rate
YD Disposable Income of Households
α1 Propensity to consume out of regular (present) income
α2 Propensity to consume out of past wealth
∆Hs Change in cash money supplied by the central bank
∆Hh Cash money held by households
H, H−1 High Powered cash money today, and yesterday (−1 )

7. The Model EC6012 Lecture 2
Stephen Kinsella
Problem
Tobin and the Old
G (1) Yale School
Y = G +C (2) The Multiplier
Godley & Lavoie
T = θ×Y (3) Approach
YD = Y − T (4) Homework & Blogs
References
C = α1 × YD + α2 × H1 (5)
∆Hs = G −T (6)
δHh = YD − C (7)
H = ∆H + H−1 (8)

8. Derivation EC6012 Lecture 2
Stephen Kinsella
If we start by solving the model for Y , everything will
Problem
become clear. Thus Y = G + C and T = θY , and by Tobin and the Old
substituting in for T and factoring, we get Yale School
The Multiplier
Godley & Lavoie
Approach
YD = Y − T (9) Homework & Blogs
= Y × (1 − θ). (10) References
By similar logic, C = α1 × YD + α2 × H−1 .

9. Derivation, continued EC6012 Lecture 2
Stephen Kinsella
Since, in period 2, H−1 = 0, we can say that Problem
C = α1 × Y (1 − θ). Substitute this into Y = G + C Tobin and the Old
and we get Yale School
The Multiplier
Godley & Lavoie
Approach
Y = G + α1 Y (1 − θ), (11) Homework & Blogs
Y − α1 (Y )(1 − θ)) = G , (12) References
Y [1 − α1 × (1 − θ)] = G , (13)
G
Y = (14)
1 − α1 + α1 θ

10. Derivation, continued EC6012 Lecture 2
Stephen Kinsella
We have numbers for α1 , G [Period1], and θ—0.6, 20, Problem
and 0.2. Plugging these into equation (14), we can Tobin and the Old
calculate Y for period 2. We obtain Yale School
The Multiplier
20 Godley & Lavoie
Y = = 38.462 38.5. Approach
1 − 0.6 + 0.6 × 0.2 Homework & Blogs
References

11. EC6012 Lecture 2
As soon as you have solved for Y , you can fill in all the
Stephen Kinsella
remaining numbers in column 2 including ∆H and
therefore H. You now have all the material you need to Problem
solve for Y in period 3 (H−1 = 12.3) and the whole Tobin and the Old
Yale School
column in period 3. And so on.
The Multiplier
The system reaches a steady state when ∆H = 0 and Godley & Lavoie
Approach
hence YD = C .
Homework & Blogs
References

12. Problems EC6012 Lecture 2
Stephen Kinsella
Fill in all the values for column 2 of table 3.4 and show
Problem
your workings. Ask me if you get stuck. Tobin and the Old
Yale School
What happens to this model if θ changes from 20% to
The Multiplier
30%? Work out the first period and then give and
Godley & Lavoie
economic explanation for the figures you see. Approach
Homework & Blogs
References

13. EC6012 Lecture 2
Steady States
Stephen Kinsella
G = T∗
= θ × W × N∗ Problem
Tobin and the Old
θ × W × N∗ = θ × Y Yale School
The Multiplier
G Godley & Lavoie
Y∗ = . (15) Approach
θ Homework & Blogs
References

14. Stock-Flow Consistency EC6012 Lecture 2
Stephen Kinsella
Problem
Tobin and the Old
C = YD − ∆Hh (16) Yale School
The Multiplier
= α1 × YD + α2 × Hh−1 (17)
Godley & Lavoie
δHh = (1 − α1 ) × YD − α2 × Hh−1 (18) Approach
1 − α1 Homework & Blogs
∆Hh = α2 × ( × YD − Hh−1 ) (19) References
α2

15. Expectations EC6012 Lecture 2
Stephen Kinsella
Problem
Cd = α1 × YD e + α2 × Hh−1 . (20) Tobin and the Old
Yale School
The Multiplier
∆Hd = Hd − Hh−1 = YD e − Cd . (21) Godley & Lavoie
Approach
Homework & Blogs
e
Hh − Hd = YD − YD . (22) References

16. Dynamics EC6012 Lecture 2
Stephen Kinsella
Problem
G + α2 × H1
Y = . (23) Tobin and the Old
1 − α1 × (1 − θ) Yale School
The Multiplier
Household’s demand for money is
Godley & Lavoie
Approach
Homework & Blogs
Hh = (1 − α1 ) × (1 − θ) × Y + (1 − α2 ) × H−1 . (24) References

17. EC6012 Lecture 2
Stephen Kinsella
Problem
Tobin and the Old
Yale School
The Multiplier
Godley & Lavoie
Approach
Homework & Blogs
References
Figure: Table 3.4 of Godley/Lavoie.

18. For Next Week EC6012 Lecture 2
Stephen Kinsella
What do you think will happen to the steady state
Problem
value(s) of output when θ changes? Why does this Tobin and the Old
happen? Post the answers on your blogs by next Yale School
Monday. The Multiplier
Godley & Lavoie
Read Godley and Lavoie (2006), Chapter 2. Approach
Homework, see stephenkinsella.net Homework & Blogs
References

19. Thanks EC6012 Lecture 2
Stephen Kinsella
Problem
Tobin and the Old
Yale School
The Multiplier
Godley & Lavoie
Approach
Homework & Blogs
References

20. References EC6012 Lecture 2
Stephen Kinsella
Wynne Godley and Marc Lavoie. Monetary Economics An Problem
Integrated Approach to Credit, Money, Income, Tobin and the Old
Yale School
Production and Wealth. Palgrave-Macmillan, 2006. URL The Multiplier
http://www.palgrave.com/products/Catalogue. Godley & Lavoie
aspx?is=0230500552. Approach
Homework & Blogs
References