Transcript Economic Modelling - University of Hull

Economic Modelling
Review: Lectures 1-22
March 29, 2004
1
Micro-Foundation to Macro Variables
General Equilibrium with a representative household and firm
Market price (p)
and wage rate (w)
such that:
Y=C
LD = LS
LS +l = L
Households
(consumers)
Max U(C,L)
Wage payment, wL
Labour supply, L
Economy
(p, w, y, c, l, L)
Firms
(producers)
Max π(LS)
Payments for goods, p.y
Max U  c l 1
l  LS  1
pc  wLS  
c  0; l  0; LS  0
Supply of Goods
Question: List 10 different things missing
from this model.
Max   py  wLD
y  LD

y  0; LD  0
2
Population, total
East Asia & Pacific
2000
1,855,200,000
Europe & Central Asia
474,310,000
European Monetary Union
303,980,000
Middle East & North Africa
295,180,000
South Asia
658,940,000
Latin America & Caribbean
515,710,000
United States
281,550,000
Others
317,330,000
Heavily indebted poor countries (HIPC)
632,160,000
Low income
2,459,800,000
High income
902,850,000
High income nonOECD
31
11
50,794,000
852,060,000
Least developed countries (UN classification)
660,030,000
Lower middle income
2,047,600,000
Middle income
2,694,600,000
World
9
5,154,400,000
High income OECD
Upper middle income
5
5
1,355,100,000
Sub-Saharan Africa
Low & middle income
Location of Population across the Globe, 2000 (out of six bill
647,010,000
East Asia &
Europe & C
European M
Middle East
South Asia
Sub-Sahara
Latin Ameri
United State
Others
8
22
5
5
6,057,300,000
3
GDP (current US$)
2,000.00
East Asia & Pacific
2,059,100,000,000.00
Europe & Central Asia
942,080,000,000.00
European Monetary Union
6,048,400,000,000.00
Latin America & Caribbean
2,000,500,000,000.00
Middle East & North Africa
659,690,000,000.00
Sub-Saharan Africa
9,837,400,000,000.00
United Kingdom
1,414,600,000,000.00
World
Heavily indebted poor countries (HIPC)
High income
High income nonOECD
High income OECD
Least developed countries (UN classification)
0.04
322,730,000,000.00
United States
South Asia
East
Distribution of the Global Income, 2000 (31 Trillion $)
0.02
0.07
0.03
596,790,000,000.00
31,493,000,000,000.00
0.19
200,880,000,000.00
24,927,000,000,000.00
0.31
857,350,000,000.00
Asia & Pacific
Europe & Central
Asia
European
Monetary Union
Latin America &
Caribbean
Middle East &
North Africa
Sub-Saharan
Africa
United States
24,073,000,000,000.00
United Kingdom
190,520,000,000.00
Low & middle income
6,560,600,000,000.00
Low income
1,048,300,000,000.00
Lower middle income
2,347,200,000,000.00
Middle income
5,513,200,000,000.00
Upper middle income
3,170,500,000,000.00
0.06
0.010.02
South Asia
4
Solow Growth Model
Production function with capital and labour as its inputs.
Closed Economy without Government.
Firm’s Production Function
Market clearing:
Household’s Saving Decision:
Investment requirement:


Yt  At Kt Lt
Yt  Ct  It
St  sYt
It  n   Kt
St  It
Dynamics: Capital accumulation: K  1  K

I
t
t 1 t
Closure rule in the model:
5
Per Capita Output and Per Capita Capital Stock in the Steady State
y  k
Y
y
L
i  n  k
SST
S  sy  sk
0.5ks
ks
k
K
L
6
Growth Accounting

1


Y  AK L
Take log of both sides:
ln Y  ln A ln K  1 ln L
Differentiate with respect to time :
Y  A  K  1  L
Y
K
L
A
Y  g  g g  1 g
A
Y
K
L
Y
7
Capital Stock and output in the Steady State in
the Solow Model with technical progress
Fundamental equation
of economic growth:
~
dk
In steady state ~  0 
k
~
dk
~ 1
~  sk    n  ga 
k
~ 1
sk
   n  ga
1
1

~ ss 

Per Capita Effective Capital Stock in the Steady State: k
s



n

g
a

Per Capita Effective Output in the Steady State:

~
ss
y  

1

s



n

g
a

8
Results from the steady state:
1.
Countries with higher saving rate have higher steady state level of
output and countries with lower saving rate have lower level of
output in the steady state.
2.
Countries with higher level of technology have higher level of output
and countries with lower level of technology have lower level of
output in the steady state.
3.
Countries with higher rate of population growth rate have lower level
of output in the steady state.
4.
Countries with higher capital share have higher output in the steady
state.
5.
Countries which differ in the initial capital stock eventually reach to
the same output level in the steady state.
6.
Growth of per capita income is zero in the steady state
9
Golden Rule for Saving and Capital Accumulation
y  k
y
Y
L
MPK  n  
k 1    n
i  n  k
C-max
S  sy  sk
Kg
Golden rule
Kss
k
K
L
Steady State
10
How High Should be the Saving Rate?
Saving Rate that Maximises Consumption
C-max = 1.25
y = 0.5*k0.5
y=2.5
k = 25
C
s1
s2
s*=0.5
s4
s5
Saving rate
11
How Human Capital Contributes to the
Economic Growth?
Thinking
New Ideas
Action
Better Tools
Application More and
High Quality
Products
Formula
Design
Software
Machines
Consultancy
Cars
Computers
Planes
Medicine
Trains etc.
12
How does the technological advancement affect the per
capita capital and per capita output in the steady state?
y  k
2 2
y2
Advanced Technology
i  n  k
2
2
S  sy  sk
2
2
2
Primitive Technology
y  k
1 1
y1
S  sy  sk
1
1
k1
k2
k
K
L
13
Endogenous Growth Model
Output:
Y K

ALY 

A = Stock of knowledge
L  L y  LA
Labour use:
The stock of knowledge rises if more people do research:

 

A   LA  A LA
A A LA
Growth rate of knowledge: g A  
A
A
Capital Accumulation:
K t  K t 1 1     I
t
Yt  Ct  I t
Market clearing:
Here technology is endogenous to efforts in production and
14
application of research.
Increase in Real Wage Rate with Human
Capital
w2
w1
Technological
advancement raises
wage rate but reduces
Work hours.
MPKh2
MPKh1
15
Constant Marginal Product of Capital with
Human Capital
r
MPKh3
MPKh1
k1
MPKh2
k2
k3
16
Meaning of Convergence and Divergence
Prediction of convergence
Solow Model: Catching up
under Growing apart
High income
High income
Y/P
Income
Y/P
Divergence
Low ncome
Low income
Time
Time
A poor country should grow
at faster rate than a rich
country as it has higher marginal
productivity of capital.
Evidence from African
Countries shows divergence.
17
Who Gain and Who Lose From Globalisation?
Capitalists in rich
countries and
workers in poor
countries gain.
rp
rR
MPKR
MPKP
wR
wR’
wp’
MPLR
MPLR’
wp
MPLP’
MPLP
18
Is this caused by the barriers to adopt a
good technology? Or by Lauddites?
19
Profit Maximisation Problem of Firms
Marginal Product of Capital = User Cost of Capital
y
y=f(k)
K


y
1


P
2 k
 P1k k 
Max  
1  r 
1 r
Subject to:
y  f (k )  k 
k
Investor Compare user cost of capital with its productivity
r     
K
1  r     K 
 1

k
MPK=
20
Analysis of Earnings (R) and Cost (C) from an Investment Project
K = 100000; d = 0.08; R (Earning) =18000
C =(r+d)*K
23,000
C>R
Cost
And
Earning
18,000
Break Even
Earning (R)
C<R
13,000
0.05
0.1
0.15
r
21
Role of Investment Tax Credit in Promoting Investment
Why Manufacturers Lobby for a Tax Credit?
MPK
r     
K
1  r     K 
MPK =
0
K1
K2
k
K
22
 1
Optimal Capital Stock for the Car Company
The user cost of capital :
i   
K
= 6% +3%-3% =6%
F K1   K 
Let
Marginal product of capital:
Optimal Investment condition:
F ' K1   K  1  0.75K 0.751

P.F ' K1   P1k i     k

80000.75K 0.751  20006%  3%  3%
8.0.75K
K
0.25
0.25
 3 


 0.06 
 26%
6K
K  50
0.25
 26%
4
= 6.25 million
23
Two Period Model of Consumption and Saving

U
C2
Max U C1 , C2   ln C1   ln C2
Subject to:
w2
W2
C2
  W1 
 C1 
1 r
1 r
c2
Borrowing
U
w1
c1

C1
24
Two Period Model of Consumption
Consumers’ problem:
Max U  C ,C   ln C   ln C
1
2
 1 2
Budget constraint in period 1:
C  b W
1
1
Budget constraint in period 2:
C1
: Consumption in period 1
C2
: Consumption in period 1
W1
C  b1 r W
2
2
 = subjective Discount factors
b = borrowing or lending
: Income in period 1
r = interest rate
W2 :Income
in period 12
U = utility
25
Life Cycle Model of Consumption and Saving
Modigiani-Ando-Brumberg life cycle hypothesis
Saving
C,S,Y
C-Smoothing
Borrowing
Dissaving
Young
Adult
Old
26
Smooth consumption and erratic income over life
Phillips Curve and
Expectation Augmented PC (NAIRU)
e
t
t
n
    bu  u
 t   e  but  un 
LPC



 t   e  but  un 
f
g
d
e
b
c
PC4
PC3
Un
Short run Phillip’s curve
PC
PC2
a
PC1
un
u
Natural rate of unemployment and a
vertical Phillip’s curves
27
Classical, Keynesian and New Keynesian Aggregate
Supply curves P  Pe  u  u  y  y
t t
t N
t
Classical Supply
New Keynesian Supply
PP
e
PP
e
PP
Pt  Pte  ut  u  yt  y
N
Pt  Pte  ut  u  yt  y
N
c
b
a



Y  Yn 10 P  Pe  Yn 10    e
Keynesian Supply
a1
Y = AD
d
AD2
e
AD1
0
y y
u  un
yy
u  un
yy
u  un
Output
28

Aggregate Supply, Inflation and the natural rate of
unemployment hypothesis
LAS
 
e
 
 
Summary:
SAS

y  y  10 p  pe
y  y  10    e
e
 t   te  ut  u  yt  y
N
e
 t   t  ut  u  yt  y
N
e
 t   t  ut  u  yt  y
N

 t   e  bu  un   s
e
o


yy yy
u  un u  un u  un
y y
u  un 
29
Supply Shock and Stagflation
LAS
 
e
Stagflation
 
 
e
AS1
AS=f(w,pe)
 a y  y  


t   e  
or
 s
 bu  u 
n 

e
AD =f(M,G, T)
o
yy yy
u  un u  un u  un
y y
30
Stabilisation: Table 1
ut  ut 1  0.5g yt  2%  t   t 1  ut  3% ; g yt
Year
Inflation Unemploy
Growth
ment rate
rate of
output
0
1
2
3
4
5
6
7
8
9
9
8
7
6
5
4
3
2
2
2
3
4
4
4
4
4
4
4
3
3
2
0
2
2
2
2
2
2
4
2
 g mt   t
Growth
rate of
money
supply
11
8
9
8
7
6
5
4
6
4
31
Macroeconomic Stabilisation Role of Tax and Spending
T = tY
G=T
Tax
and
G
Spending
T>G
Surplus in boom
G
T<G
Deficit in
recession
0
YF
Income
T
32
Balanced Budget Multiplier with Lump-Sum
Taxes
The real national income is given by the IS Curve:
1

Y
c0  I  G  c1T 
1  c1
Positive Government expenditure multiplier:
.
Negative tax multiplier:
Y
1

G 1  c1
c1
Y

T
1  c1
Y Y
=1/(1-c1) - c1/(1- c1) = 1

G T
A change of 100 in both G and T also raised income by 100.
Balanced change in G and T is not macro economically neutral. 33
The balanced budget multiplier:
Automatic Stabiliser with Proportional Taxes
C  c0  c1YD
Consumption:
Disposable income:
YD  Y  T
T  t 0  t1Y
Tax Revenue
Income (IS curve):
0  c1  1
0  t1  1
Y = c0 + c1YD + I + G
1
Y
* [c0 - c1 t 0  I  G]
(1 - c1  c1 t 1 )
The multiplier = 1/(1-c1+c1t1) <1/(1- c1),
so the economy responds less to changes in
autonomous spending when t1 is positive.
High T when Y is high.
Low T when Y is low.
34
How much should be the tax rate to maximise the government revenue ?
Tax compliance
R-max
Tax avoidance
Tax evasion
Revenue
R-low
Revenue=F(t)
t-Low
t-Rmax
tH
Tax rate
35
Laffer Curve Model:A Numerical Example
Rt  50t  2t 2
Where R is revenue in billion of pounds, t is the tax rate.
The tax rate that maximises the revenue is given by
Rt
 50  4t  0  t = 12.5
t
There are two tax rates that can raise the same revenue.
200  50t  2t 2 
2  4(100)

(

25
)

(

25
)
t 2  25t 100  0 ; t1 
=
2
t  2515  5,20
1
2
36
Debt Dynamics: Determinants of Debt/GDP Ratio
B
 B  G T
(5)
  
 r  g 
Y
Y
Y 
• Higher the interest rate causes a rise in B/Y
• Lower the growth rate of output causes a rise in B/Y
• Higher the current deficit (G -T) leads to higher B/Y
• Higher initial B/Y implies higher B/Y in subsequent
years
Example
Debt ratio = 100% r = 3% g = 2%
T-G = 1% is required to keep B/Y constant
37
Revenue from Inflation Tax and Its Limitations
Inflation rate equals
growth rate of money
supply in the steady state.
Seigniorage
S-Max
S-low
S = F()
-low
-max
-high
Inflation tax
38
Seigniorage (Inflation Tax) : A Numerical Example
Seigniorage

Si
40
1000
0
0
30
905
0.01
9.05
20
819
0.02
16.38
607
0.05
30.35
368
0.1
36.8
135
0.2
27
82
0.25
20.5
7
0.5
3.5
10
5
0.
25
2
0.
Inflation
0.
1
0.
05
0.
02
0.
0.
01
0
0
Seigniorage revenue
M/P
39
Basic Proposition of the Ricardian Equivalence
Tax or Borrowing Does not Make Any Difference
Tomorrow
C2
Before Borrowing
Budget Constraint
After borrowing
budget constraint
C1 
C1 
C2
 w2 
 w1   

1 r
1

r


C2
 
 w
 w1   1    2  2 
1 r
1 r 1 r 
C1
Today
40
Bank of England’s View on Transmission Mechanisms of Monetary
Policy: How Does Money Supply Affect the Price Level?
i,r,er,Pe
Market
rate
Official
rate
MS
Domestic
demand
Y
Domestic
inflationary pressure
Total demand
Asset
prices
Expectations
and confidence
P
C+I+G
Inflation
Net external
demand
X,M
π
Import
prices
Exchange
rate
Two Conditions to have real effect of Monetary policy
Central bank controls monetary base M1 = R + Cu
Prices do not adjust instantaneously
M
M  i, r  C , I , X , G  Y  P   
 i, r 
P
41
An Increase in Money Supply Can Lower Real
and Nominal Interest Rates in the Short but not in the Long Run
M
M  i, r  C , I , X , G  Y  P   
 i, r 
P
iT  rn  
Fisher Equation
i
i0  rn
r
0
t0
T
time
Monetary policy can have some real effect in the short run but not in the long run.
Short runs become shorter with more accurate expectations
42
Link Between Financial System and the Economy
Y= F(K,L)
C
T
S
Funds
K
Profit
FA
Equity
Treasury
Bonds
Deposit
Banks
Pension Funds
43
Financing of an Investment Project
Demand
for output
Self
Finance
Bequests
Maturity
Need for Capital
Financing an
Investment
Project
Bonds:
Debt Finance
Banks, Building
Society, Insurance
Risks
AAA
BBB
CCC
Instalment Repayment
Method
Method
No
Risk
Equity Finance
Stock Market
(LSE)
Risk
High
Risk
44
Market Price of a bond (console)
What is the market price (value) of a console that
pays 100 each year forever at the interest rate, r?
PV  100  100  100 ........... 100n
1 
2 
3
1 r 
1 r 


1 r 
1 r 



















1
1
PV 
100
1
1 r 



n1
1 r 
1 1
1 r














as n  
1
n1

1 r 


1 r  100 100
100

=
=
=1000.
PV 
r 0 .1
 r 
1
1 r 


0
45
Price of a Stock: An example





D
P
 r  g  x 
Share

PShare = Price of a Stock
D = expected Dividend
r = interest rate
g = growth rate of dividend
x = risk premium
D = 1000 and r =5% and g=3% has a risk x =0;




 1000
1000

P

 50,000

Share 0.05  0.03  0  0.02
If r =8%




 1000
1000

P

 20,000

Share 0.08  0.03  0  0.05
46
Observations From the above Analysis of Stock Markets
•
Lower the market interest rate, higher is the value of stock.
Because future earnings are discounted at lower rate.
•
Higher the growth rate of dividend higher the value of stock. As
dividend grows earning from the share rises and hence price rise.
•
Higher the risk premium lower is the value of the share. A
decrease in the risk premium will increase the market value of a
stock.
•
Arbitrage implies same rate of risk adjusted returns in both stocks
and bonds.
•
(in the short run) Higher the resale value of the stock higher is its
price.
47
Income, Saving and Outstanding Asset or Debt in Life Cycle Model
Debt and Savings in Life Cycle Model
1400000
1200000



 
S  1 X  X
 
2
 ....  X

n

1 X
1 X
2
36
e
e
V YLt  Tt  0.75 1  1.03  1.03  ...  1.03
£40000 =1985227.
Debt/Credit
1000000
Working life: 21-65
Consumption life: 22 -90
:
Life time income: 2958727
Smooth consumption: 42880
Growth rate of income: 5%
=1985227
Initial income:20000
600000
400000
200000
89
86
83
80
77
74
71
68
65
62
59
56
53
50
47
44
41
38
35
32
29
26
23
0
ag
e
Debt or Savings
800000
;t
-200000
-400000

n 1

e  T e  1  t 1  1  g   1  g 2  ...  1  g 36 Y
V YLt
t

 0
Age
48
Interest Determination Rule to Achieve the Inflation Target: Taylor Rule
yt  yt *  d  i  i* 
 t 1 t 1 
where
d 0
yt is actual output yt* is trend output, it
(9)
is the actual
*
i
interest rate and t the basic interest rate,
One period lag is assumed between the interest rate decision
and the change in the output.
 t   t*  c y

where  t
 y* 
t 1 t 1
(10)
*

and t are actual and target inflation rates.
Interest rate rule:
it  it*  a yt  yt*   b t  t* 

c0



a  0;b  0
(11)
49
Reduced Form Equation of the Interest Determination
Model
yt  yt *  d  i  i* 
 t 1 t 1 


*
*
 t   t  c y  y 
t 1 
 t 1
it  it*  a yt  yt*   b t  t* 




a  0;b  0
(11)
Substituting the output and inflation equations in the interest
rate rule:




it  it*  a  d  i  i*    b  cd  i  i*  
t 2  
 t 1 t 1 
 t 2


it  it*  ad  i  i*   bcd  i
 i* 
 t 1 t 1 
 t 2 t 2 
it  adi  bcdi
 it*  adi*  bcdi*
t 1
t 2
t 1
t 2
(12)
50
Why Should the Central Bank Be Independent?
Inflation Biases of a Government and a Central
Bank
Figure 1
Preference of government and a conservative central bank regarding inflation and output
AS
Preference of Government (GP)
Inflation
A
AS1
B
O
Preference of a CB (CP)
Yn
Output
G
51
An Example of an Open Economy Model

Y  CY  T   I i     G  NX Y , Y f , 
National Income
Consumption
Investment
Tax and Spending
C  200 0.8Y  T 
I  50  200i   
T =100 G = 100
NX  10  0.3Y f  0.1Y  20
Net exports
Real exchange rate
Financial integration
Demand for Money
Parameters

Y  500
f
EP *

P
i  i  5%
*
M
 200  50i  0.5Y
P
  0.02
P 2 P2
*
52
Three GAPs: Investment-Saving, Government Budget and
Trade Gaps in a Keynesian Model
SI
S(Y)
Trade Surplus
NX  0
S  I   T  G   X  M
 NX  Cap Flow
K-outflow
i
T G  0
i
Private saving +public saving
= net export
SI
I(r)
Trade deficit
K-inflow NX  0
0
Saving and Investment
Re call : Y  C  S  T  M  C  I  G  X  rK  wL  Tr
53
IS-LM Model in an Open Economy: Mundell-Fleming Model
Exchange
Rate
LM (y, i)
Assumption:
Money supply does not
depend on exchange rate
e*
IS*
o
y
Output
54
Impact of Fiscal Policy under Fixed and Flexible Exchange Rate Systems
Flexible Exchange Rate System
Fixed Exchange Rate System
LM
LM1
LM2
e2
IS*’
e
IS*’
e1
IS*
IS*
Y
No Impact of Fiscal Policy
Y1
Y2
Full Impact of Fiscal Policy
55
Impact of Monetary Policy under Fixed and Flexible Exchange Rate Syste
Flexible Exchange Rate System
Fixed Exchange Rate System
LM
LM1
LM2
e2
IS*’
e
e1
IS*
IS*
Y1
Y2
Full Impact of Monetary Policy
Y1
Y2
No Impact of Monetary Policy
56
IS-LM and Uncovered Interest Parity Model
LM
2
1
i
i
IS1
IS
0
Y0
Y1
UIP
0
E0
E1
Appreciation
Exchange rate
57
J-Curve Hypothesis: Impact of Devaluation on Net Exports
Export creation and
Import substitution or
demand switching takes time
Net
Exports
o
Time
58
Marshall-Lerner condition
Devaluation is effective if
ex  em  1
Devaluation is ineffective if
ex  em  1
Devaluation has no effect in trade balance
ex  em  1
ex
em
is elasticity of export
is the elasticity of imports
59
t
e
*




Purchasing Power Parity: e
t
t
t
Uncovered Interest Parity:
et
it  i 
et
*
t
(1)
(2)
Using the Fisher equation (2) becomes
et
 t  rt    r 
et
*
t
*
t
(3)
Slight rearrangement:
et
 t     rt   rt*
et
*
t
et
0
t  
From PPP
et t
*
t

(4)
rt  r
*
t
When both PPP and UIP hold exactly the domestic and foreign real
interest rates are equal.
60
Triangular Exchange Rates and Appreciation
and Depreciation with respect to the Third Currency
Initial exchange rates
1.11
£0.69
2001
$1
End of 2002
0.98
0.78
£0.63
$1
2002
£0.53
$1
2004
0.53
In 2004 one dollar in terms of pound and Euro is 0.78  0.68
0.63
In 2002 one dollar in terms of pound and Euro is 0.98  0.64
0.69
In 2001 one dollar in terms of pound and Euro is 1.11  0.621
0.68  0.62
 0.0968  9.7%
Appreciation of  against £ (2001-04) =
0.62
61
Cooperation or non-Cooperation?
...............................
Advanced Countries

Developing Countries  NC
 C
NC
4,4
3,6
C
6,3
5,5
Nash Solution is non-cooperation (NC,NC) =(4,4)
...............................
Advanced Countries

Developing Countries  NC
 C
C
4, 4 6,3
3, 6 5,5
NC
Cooperative Solution (C,C) =(5,5)
Cooperative solution Pareto dominated Non-cooperative solution.
Pareto efficiency: at least one party gains without hurting the other.
62
Extensive Form of International Cooperation Game
NC
NC
(4,4)
Advanced
economies
C
(6,3)
(3,6)
Developing
Economies
NC
C
Advanced
economies
C
(5,5)
63
Dynamics of International Policy Cooperation Game: Solution by Backward Induction
NC
NC
(4,4)
Advanced
economies
C
(6,3)
(3,6)
Developing
Economies
NC
C
Advanced
economies
C
(5,5)
64
Solution for the Discount Factor of the Game
PV (C , C )  5  5  5 2  5 3  ...  5 n 
Lim n 
5
1 
PV (cheat)  6  4  4 2  4 3  ...  4 n
PV (cheat)  6  4 2  4 3  ...  4 n1
1   PV (cheat)  6  6  4
PV (cheat)  6  4
lim n 

1   
5

 6 4
1   
1
5  61     4
 n 1  0
6  5  2
1
 
2
65
Fiscal and Monetary Policy Game in a
Diagram
M
(Nardhaus (1994) Model)
Budget
Surplus, S
+
Monetary Bliss (MB)
F
0
Interest rate, r
Budget
Deficit,
D
Nash equilibrium (N)
Fiscal Bliss (FB)
M
F
66

Discretion
ASd
d
ASr
Policy Rule, Discretion, Cheating and Time Inconsistency in Economic Policy
Making
ch
Cheating
ASd
r =0
Bliss
1 y = y*
yT
Policy rule
y-y*
2
1,2,3,4 Iso social cost functions
3
ASr
4
Kydland and Prescott (1977)
PR
67
Budget surplus : fiscal policy Instrument
Adjustment of Budget Surplus or Interest Rate for Internal and External
Stability
Two objectives:
Internal Stability: Full Employment
External Stability: Trade Balance
Two instruments:
Budget surplus or deficit and interest r
BOP Surplus
a
b
d
Inflation: Boom
c
e
i
Unemployment: Recession
h
g
f
Internal Balance
BOP Deficit
External Balance
0
Interest rate: Monetary Policy instrument
68
Assignment Problem in the Mundell-Fleming Model
LM2
+
-
i
c
BOP
Targets
Internal stability y*
External stability BOP
Instruments:
Monetary policy (i)
Fiscal policy (G,T)
b
a
IS2
IS1
LM1
0
y*
y
a: initial point of internal balance but external imbalance (IS1=LM1)
b: use of monetary policy (LM2) for external balance creates internal imbalance
c: accommodative fiscal policy (IS2) restores the balance
69
General Equilibrium Set-up of Household and Firms’ Problem
Household’s Problem:
Max U  c l 1
Subject to:
s
i. l  h  1
s
ii. wh    pc
time constraint
budget constraint
s
c

0
;
l

0
;
h
 0 non-negativity constraint
iii.
(1)
Firm’s problem
Max   py  wh d
subject to :
 
i. y  h
d 
technology constraint
d
y

0
;
h
 0 non negativity constraint
ii.
(2)
70
Derivation of Labour Supply, Consumption and Leisure Demand Functions
  
s w
 1  h
c  
p
1  
  

s w
s w
 1  h
h
  c  
p p
p
1  



w    
s w
 1  h
h
  
p p 1  
p
s


w 


   1    
  
w
p p

 1 
c  
p
w
 1   


p


(7)

(8)
w
w 
h
   1   
p
p p
(9)
s

(10)
l  1 hs  1
w 
 1   
p p
(11)
w
p
71
 
max   py  wh  p h
d

d

p

h
h d
 

p
 yw
d
 
h
 hd
p
 1 w

h d  
 p 
1
 1


 1
d 
 1 w

h  
 p 
w0
w d  1 w

h  
p
 p 

 1

w  1 w


p  p 
 wh
d
1
 1
 w
  
 p
w  w
   
w 
  1   
p  p
p
p
 hs 

w
p

 1

 1
(12)
d
1
 1
(13)

1


 1
 1
1
1




     
  
  



1




1


1
1
1
      1   
  
  


w
p
(14)
(15)
72
Real wage rate, profit and output in Equilibrium
 1

w

 1
1

p 

 1
 1
1
1




1         

  
 



p
 yw
d
 
h
 hd
p


w d  1 w

h  
p
 p 



1
yˆ  





 1

w  1 w


p  p 
1
 1
 w
  
 p




  1



1

1

 


1


1
1    1     1   

 
    

 

 1

 1
(16)

1


 1
 1
1
1




     
  
  


(17)
(18)
73
Leisure, Labour Supply and consumption in Equilibrium




ˆl  1  hˆ s  1   1








  1

 1

1





1


1
1
1
 

1    
   


 
  






1
d
s
hˆ  hˆ  







 
 
    1
1  
cˆ  
1



  
 
 
 

1
 1




  1



1

1

 


1


1
1    1     1   

   1      

 
  1 



  1

 1

1

 


1


1
1
1
1          

 
    

 
(19)
1
 1
(20)



  1

 1

1


1  1
1  1
 1         

 
  



(21)
74
Business rates, 19, 4%
Public Revenue 2004: £455bn
Source HM Treasury
Other receipts, 62, 14%
Value-added tax, 73, 16%
Council tax, 20, 4%
Corporation tax, 35, 8%
Income tax, 128, 28%
Excise duties, 40, 9%
National Insurance, 78, 17%
75
Public Spending 2004. £487
Source: HM Treasury
Other expenditure, 49, 10%
Education, 63, 13%
Debt interest, 25, 5%
Transport, 16, 3%
Industry and agriculture, 20, 4%
Health, 81, 17%
Housing and other environment, 17,
3%
Law and protective services, 29, 6%
Defence, 27, 6%
Other health and personal services, 22,
5%
Social protection, 138, 28%
76
Household Problem in Presence of Consumption and Income Taxes
Max U  c l 1
l  hs  1
p1  tc c  w1  tl h    R
s
ptc c  wt l h s  R
c  0; l  0; h  0
(1’)
s
p1  tc c  w1  tl h    R
s

Lc, l ,    c 1  h


s 1

wh    pc
s
  w1  t l h s    R  p1  t c c
(2’)

(3’)
77
Determination of Real Wage Rate in the Presence of Taxes
 1 w

h d  
 p 
 w
 
 p
1
 1
1
 1


1





1
   w  1  t l    w   1   1  1   1  
    

 
   


1


p
1

t
p
 
  

 

c  



 hs 
w    1  t l  

 1
p  1    1  t c  
   1  t l 



 1    1  t c 

1

1







1


1


1


1

t

1
1
1


l
  

  1       
    1    1  t c     
   









w 

1
p 
 1   1  

   
     1  

   1  t l 



 1    1  t c 


 1  t l    1   1

  1   

 1  t c     






1


 1   1 
    
    
 
 1
78
Leisure and Consumption in the Presence of Taxes




   1  t l 
1 





 1    1  t c 
ˆl  1   1   1 


1

1

  


 1   1    1  t l    1   1  1   1 

 1        
   




1


1

t
    
c 

   
   
 







   1  t l 

1 




1    1  t c 
     1   1 
  w1  t l 

 1    
cˆ  
  p1  t 
1

1
1











c
  1   1    1  t l    1   1  1   1   



  1         

   

     

     1    1  t c     

  


 ˆ1
ˆ
U  cˆ l
79
Efficiency Gains in the UK from elimination of all taxes and transfers
(Measured as a percent of benchmark utility level of a representative
household)
Equivalent Variation
=
3.715
Compensating Variation
=
-3.582
Efficiency Gains from Switching to Labour income Taxes
Equivalent Variation
=
-0.693
Compensating Variation
=
0.697
Efficiency Gains from Switching to Consumption Taxes
Equivalent Variation
=
2.967
Compensating Variation
=
-2.882
80