1. EC6012 Lecture 6
Stephen Kinsella
Notation
Balance Sheet
EC6012 Lecture 6 Transactions
Matrix
Government Money with Portfolio Choice
Equation System
Endogenous Money
Problem 1
Stephen Kinsella Steady State
Solutions
Pictures
Next Time
Dept. Economics,
University of Limerick.
stephen.kinsella@ul.ie
January 20, 2008
2. EC6012 Lecture 6
Notation Stephen Kinsella
Notation
Balance Sheet
Balance Sheet
Transactions
Matrix
Equation System
Transactions Matrix Endogenous Money
Problem 1
Steady State
Equation System Solutions
Pictures
Endogenous Money Next Time
Problem 1
Steady State Solutions
Pictures
Next Time
3. 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 )
V Wealth of Households, in nominal terms
Bh,cb Bills held by households, central banks.
4. Balance Sheet for PC.
Households Production Government Central Bank
Money +H −H 0
Bills +Bh −B +Bcb 0
Balance (net worth) -V +V 0
0 0 0 0
5. Transactions matrix for PC.
Central Bank
Households Production Government Current Capital
Consumption -C +C 0
Govt. Expenditures +G -G 0
Income = GDP +Y -Y 0
Interest Payments -r−1 · Bh−1 +r−1 · B−1 +r−1 · Bcb−1 0
Central Bank Profits +r−1 · Bcb−1 −r−1 · Bcb−1 0
Taxes -T +T 0
Change in Money −∆H +∆H 0
Change in Bills −∆BH +∆B −∆Bcb 0
0 0 0 0 0 0
Table: Transactions matrix for PC.
6. Equation System EC6012 Lecture 6
Stephen Kinsella
Notation
Balance Sheet
Y = G +C (1) Transactions
Matrix
YD = Y − T + r−1 · Bh−1 (2)
Equation System
T = θ · (Y + r−1 · Bh−1 ) (3) Endogenous Money
Problem 1
V = V−1 + (YD − C ) (4) Steady State
Solutions
C = α1 · YD + α2 · V−1 , 0 < α1 < α2 < 1 (5) Pictures
Next Time
Hh YD
= (1 − λ0 ) − λ1 · r + λ2 · (6)
V V
Bh YD
= λ 0 + λ 1 · r − λ2 · (7)
V V
Hh = V − Bh (8)
7. Endogenous Money EC6012 Lecture 6
Stephen Kinsella
Notation
Balance Sheet
∆Bs = Bs − Bs−1 = (G + r−1 · Bs−1 ) − (T + r−1 · Bcb−1 )
(9) Transactions
Matrix
∆Hs = Hs − Hs−1 = ∆Bcb (10)
Equation System
Bcb = Bs − Bh (11) Endogenous Money
Problem 1
r = r (12) Steady State
Solutions
Pictures
Next Time
8. Problem 1 EC6012 Lecture 6
Stephen Kinsella
Notation
Balance Sheet
Transactions
Matrix
Equation System
Endogenous Money
Problem 1
Steady State
Solutions
Pictures
Next Time
9. EC6012 Lecture 6
Stephen Kinsella
α3 = α2 · (1 − α1 )/α2 (13) Notation
∆V = α2 · (α3 − V−1 ) (14) Balance Sheet
V∗ Transactions
= α3 (15) Matrix
YD ∗ Equation System
∗
Bh · r Endogenous Money
∗
r = (16)
V∗ Problem 1
Steady State
Solutions
Pictures
Next Time
10. Money Demand With Random Shocks EC6012 Lecture 6
Stephen Kinsella
110
Notation
Balance Sheet
Held money balances
35.0 Transactions
(continuous line) Matrix
Equation System
30.0
Endogenous Money
Problem 1
25.0 Steady State
Solutions
Pictures
20.0 Next Time
Money demand
(dotted line)
15.0
10.0
1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999
Figure 4.1 Money demand and held money balances, when the economy is subjected
to random shock
Figure: Money Demand
22.5
11. EC6012 Lecture 6
Evolution of Money/Shares Balances
Stephen Kinsella
112 Monetary Economics
Notation
Share of Share of
money balances bills Balance Sheet
Transactions
0.250 0.800
Matrix
Share of bills in
household portfolios
Equation System
0.240 0.790 Endogenous Money
Problem 1
0.230 0.780 Steady State
Solutions
Pictures
0.220 0.770 Next Time
0.210 0.760
Share of money balances
in household portfolios
0.200 0.750
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Figure 4.3 Evolution of the shares of bills and money balances in the portfolio of
Figure:households, following anthe sharespointsbills rate of interest on bills
Evoluation fo increase of 100 of in the and money balances in
household portfolios.
Figure 4.3 shows how the allocation of wealth between cash and bills
changes when the interest rate goes up. As such, there is nothing surprising
here. The model is built in such a way that higher interest rates induce house-
holds to hold more interest paying bills, following the well-known principle
that households tend to hold more of an asset when its rate of return is higher
12. Next Time EC6012 Lecture 6
Stephen Kinsella
Summarise Chapter 4
Notation
Homework Balance Sheet
Presentations Transactions
Matrix
Equation System
Endogenous Money
Problem 1
Steady State
Solutions
Pictures
Next Time
