1

Economic Modelling

Review: Lectures 1-22

March 29, 2004

2

Economy(p, w, y, c, l, L)

Firms (producers) Max π(LS)

Households (consumers)Max U(C,L)

Labour supply, L

Wage payment, wL

Supply of Goods

Payments for goods, p.y

1lcUMax1 LSlwLSpc

0;0;0 LSlc

wLDpyMax LDy

0;0 LDy

Market price (p) and wage rate (w) such that:Y = CLD = LSLS +l = L

Micro-Foundation to Macro VariablesGeneral Equilibrium with a representative household and firm

Question: List 10 different things missing from this model.

3

Location of Population across the Globe, 2000 (out of six billion)

31

8

55

22

11

9

55

East Asia & PacificEurope & Central AsiaEuropean Monetary UnionMiddle East & North AfricaSouth AsiaSub-Saharan AfricaLatin America & CaribbeanUnited StatesOthers

Population, total 2000

East Asia & Pacific 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 1,355,100,000

Sub-Saharan Africa 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

Low & middle income 5,154,400,000

High income nonOECD 50,794,000

High income OECD 852,060,000

Least developed countries (UN classification) 660,030,000

Lower middle income 2,047,600,000

Middle income 2,694,600,000

Upper middle income 647,010,000

World 6,057,300,000

4

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 322,730,000,000.00

United States 9,837,400,000,000.00

United Kingdom 1,414,600,000,000.00

South Asia 596,790,000,000.00

World31,493,000,000,000.0

0

Heavily indebted poor countries (HIPC) 200,880,000,000.00

High income24,927,000,000,000.0

0

High income nonOECD 857,350,000,000.00

High income OECD24,073,000,000,000.0

0

Least developed countries (UN classification) 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

Distribution of the Global Income, 2000 (31 Trillion $)

0.07

0.03

0.19

0.060.020.01

0.31

0.04 0.02

East Asia & Pacific

Europe & CentralAsiaEuropeanMonetary UnionLatin America &CaribbeanMiddle East &North AfricaSub-SaharanAfricaUnited States

United Kingdom

South Asia

5

Solow Growth ModelProduction function with capital and labour as its inputs.Closed Economy without Government.

tLtKtAtY

tItCtY

Market clearing:

tsYtS

tKntI

tItS tIt

KtK 1

1

Household’s Saving Decision:

Investment requirement:

Closure rule in the model:

Dynamics: Capital accumulation:

Firm’s Production Function

6

Per Capita Output and Per Capita Capital Stock in the Steady State

ky

L

Yy

L

Kk

sksyS

kni

0.5ks ks

SST

7

Growth Accounting

1LAKY

LKAY ln1lnlnln

LL

KK

AA

YY 1

LgKggYgYY

A 1

Take log of both sides:

Differentiate with respect to time :

8

Capital Stock and output in the Steady State in the Solow Model with technical progress

Fundamental equation of economic growth: agn

k

kdks 1~

~

~

In steady state 0~

~

k

kd agnks 1~

11

~

agnsssk

1~

agnsssy

Per Capita Effective Capital Stock in the Steady State:

Per Capita Effective Output in the Steady State:

9

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

10

Golden Rule for Saving and Capital Accumulation

ky

L

Yy

L

Kk

sksyS

kni

KssKg

C-max

nMPK

nk 1

Golden rule Steady State

11

Saving rate

C-max = 1.25

Con

sum

ptio

n

s*=0.5

y=2.5

k = 25

y = 0.5*k0.5

s1 s2 s4 s5

How High Should be the Saving Rate? Saving Rate that Maximises Consumption

C

12

How Human Capital Contributes to the Economic Growth?

Thinking New Ideas Formula Design Software

Action Better Tools Machines Consultancy

Application More and High Quality Products

Cars Computers Planes Medicine Trains etc.

13

How does the technological advancement affect the per capita capital and per capita output in the steady state?

11

sksyS

22

ky

1y

L

Kk

222

sksyS

22

kni

2y

1k 2k

Primitive Technology

Advanced Technology

11

ky

14

Output: YALKY

A = Stock of knowledge

Labour use: Ay LLL The stock of knowledge rises if more people do research:

AA LALA

Growth rate of knowledge: A

LA

A

Ag A

A

Capital Accumulation:

t

ItKtK 11

Market clearing: ttt ICY Here technology is endogenous to efforts in production and application of research.

Endogenous Growth Model

15

MPKh1

MPKh2w1

w2

Increase in Real Wage Rate with Human Capital

Technologicaladvancement raises

wage rate but reducesWork hours.

16

r

MPKh1 MPKh2

MPKh3

k3k2k1

Constant Marginal Product of Capital with Human Capital

17

Prediction of convergence underSolow Model: Catching up

High incomeIncomeY/P

Low income

Time

Growing apart

High income

Y/P

Divergence

Low ncome

Time

Meaning of Convergence and Divergence

A poor country should growat faster rate than a rich country as it has higher marginal productivity of capital.

Evidence from African Countries shows divergence.

18

Who Gain and Who Lose From Globalisation?

MPLR

MPLR’

MPLP

MPLP’wp

wp’

wR

wR’

MPKR MPKP

rp

rR

Capitalists in rich countries and workers in poor countries gain.

19

Is this caused by the barriers to adopt a good technology? Or by Lauddites?

20

k

y y=f(k)

k*

MPK=

Profit Maximisation Problem of FirmsMarginal Product of Capital = User Cost of Capital

r

kPkP

r

y Kk

1

1

12

1

Max

Subject to:kkfy )(

Kr

Kr 11k

Investor Compare user cost of capital with its productivity

21

C =(r+d)*K

0.05 0.1 0.15 r

Earning (R)18,000

13,000

23,000

Break Even

Analysis of Earnings (R) and Cost (C) from an Investment Project

CostAndEarning

C < R

C > R

K = 100000; d = 0.08; R (Earning) =18000

22

Role of Investment Tax Credit in Promoting InvestmentWhy Manufacturers Lobby for a Tax Credit?

Kr 1

Kr

MPK =

K1 K20

1k

K

MPK

23

Optimal Capital Stock for the Car Company

Ki = 6% +3%-3% =6% The user cost of capital :

KKF 1Let

175.011 75.0' KKKF Marginal product of capital:

kk iPKFP 11'.Optimal Investment condition:

%3%3%6200075.08000 175.0 K

%6275.0.8 25.0 K %626 25.0 K

06.0

325.0K 450K = 6.25 million

24

C1

C2

r

CC

r

WW

112

12

1

2121 lnln, CCCCUMax

w1 c1

c2

w2

Two Period Model of Consumption and Saving

Borrowing

Subject to:

U

U

25

Two Period Model of Consumption

2ln

1ln

2,

1CCCCUMax

Consumers’ problem:

11WbC

2

12

WrbC

1C

2C

1W

2W

= subjective Discount factors: Consumption in period 1

: Consumption in period 1

: Income in period 1

:Income in period 12

b = borrowing or lending

r = interest rate

U = utility

Budget constraint in period 1:

Budget constraint in period 2:

26

C-Smoothing

Young Adult Old

Saving

Borrowing

Dissaving

C,S,Y

Life Cycle Model of Consumption and SavingModigiani-Ando-Brumberg life cycle hypothesis

Smooth consumption and erratic income over life

27

Phillips Curve and Expectation Augmented PC (NAIRU)

nt

et uub

Un Short run Phillip’s curve PC

LPC nte

t uub

f g d e PC4 b c PC3 a PC2 u un PC1 Natural rate of unemployment and a vertical Phillip’s curves

nte

t uub

28

Classical, Keynesian and New Keynesian Aggregate Supply curves

Keynesian Supply

Classical Supply

New Keynesian Supply

en

en YPPYY 1010

Y = AD

0 Output

AD1

AD2

a

b

c

d

a1

yy yy yy nuu nuu nuu

ePP

ePP

ePP

yty

yty

yty

NutuetPtP

NutuetPtP

NutuetPtP

29

suub ne

t

e e

e

yy yy yy o

LAS

Aggregate Supply, Inflation and the natural rate of unemployment hypothesis

nuu nuu nuu

nuu

SAS

eyy 10

eppyy 10

yty

yty

yty

Nutuett

Nutuett

Nutuett

Summary:

30

s

uub

or

yya

n

et

AS=f(w,pe)e

e

e

yy yy yy o

LAS

Supply Shock and Stagflation

nuu nuu nuu

AD =f(M,G, T)

Stagflation

AS1

31

%25.01 yttt guu %31 ttt u ; tmtyt gg Year Inflation Unemploy

ment rate Growth rate of output

Growth rate of money supply

0 9 3 2 11 1 8 4 0 8 2 7 4 2 9 3 6 4 2 8 4 5 4 2 7 5 4 4 2 6 6 3 4 2 5 7 2 4 2 4 8 2 3 4 6 9 2 3 2 4

Stabilisation: Table 1

32

Macroeconomic Stabilisation Role of Tax and Spending

Taxand Spending

G G

T

T = tY

IncomeYF

G = T

T > GSurplus in boom

T < GDeficit in recession

0

33

Balanced Budget Multiplier with Lump-Sum Taxes

TcGIcc

Y 1011

1

11

1

cG

Y

1

1

1 c

c

T

Y

.

T

Y

G

Y

=1/(1-c1) - c1/(1- c1) = 1

The real national income is given by the IS Curve:

Positive Government expenditure multiplier:

Negative tax multiplier:

The balanced budget multiplier:

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.

34

Automatic Stabiliser with Proportional Taxes

10 1 t

DYccC 10

TYYD

YttT 10

]tc-[c*)tcc-(1

1010

111

GIY

10 1 cConsumption:

Disposable income:

Tax Revenue

Income (IS curve): Y = c0 + c1YD + I + G

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.

35

How much should be the tax rate to maximise the government revenue ?

Revenue

R-max

t-Rmaxt-Low tH Tax rate

R-low

Tax avoidanceTax evasion

Revenue=F(t)

Tax compliance

36

Laffer Curve Model:A Numerical Example

2250 tttR W h e r e R i s r e v e n u e i n b i l l i o n o f p o u n d s , t i s t h e t a x r a t e .T h e t a x r a t e t h a t m a x i m i s e s t h e r e v e n u e i s g i v e n b y

0450

tttR

t = 1 2 . 5

T h e r e a r e t w o t a x r a t e s t h a t c a n r a i s e t h e s a m e r e v e n u e .2250200 tt

0100252 tt ;2

)100(42)25()25(1

t =

20,52

15251 t

37

Debt Dynamics: Determinants of Debt/GDP Ratio

Y

Bgr

Y

TG

Y

B

• 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

yearsExample Debt ratio = 100% r = 3% g = 2% T-G = 1% is required to keep B/Y constant

(5)

38Inflation tax

S-Max

Sei

gnio

rage

-max

Revenue from Inflation Tax and Its Limitations

S = F()

-low -high

S-low

Inflation rate equals growth rate of money supply in the steady state.

39

M/P Si

1000 0 0

905 0.01 9.05

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

Seigniorage

0

10

20

30

40

Inflation

Sei

gn

iora

ge

reve

nu

eSeigniorage (Inflation Tax) : A Numerical Example

40

Basic Proposition of the Ricardian EquivalenceTax or Borrowing Does not Make Any

Difference

r

ww

r

CC

112

12

1

rr

ww

r

CC

11122

112

1

C1

C2

Before Borrowing Budget Constraint

After borrowing budget constraint

Today

Tomorrow

41

Officialrate

Marketrate

Assetprices

Exchangerate

Expectationsand confidence

Domesticdemand

Net externaldemand

Domesticinflationary pressure

Importprices

Inflation

Total demand

Bank of England’s View on Transmission Mechanisms of Monetary Policy: How Does Money Supply Affect the Price Level?

Two Conditions to have real effect of Monetary policyCentral bank controls monetary base M1 = R + CuPrices do not adjust instantaneously

riP

MPYGXICriM ,,,,,

YC+I+G

i,r,er,Pe

π

P

X,M

MS

42

nT ri

nri 0

timet00

r

i

T

An Increase in Money Supply Can Lower Real and Nominal Interest Rates in the Short but not in the Long Run

riP

MPYGXICriM ,,,,,

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

Fisher Equation

43

Y= F(K,L)

SC T

Funds

K FA

EquityTreasury

Bonds

DepositBanks

Pension FundsProfit

Link Between Financial System and the Economy

44

Financing an Investment

Project

Self FinanceBequests

Bonds:Debt Finance

Banks, BuildingSociety, Insurance

Equity FinanceStock Market

(LSE)

NoRisk Risk

HighRisk

MaturityInstalment

MethodRepayment

Method

Financing of an Investment Project

Demand for output

Need for Capital

RisksAAABBBCCC

45

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?

nrrrr

PV

1100...........

31

1002

1

1001

1

100

r

nr

rPV

111

11

11

11

100 as n 0

11

1

n

r

r

r

rPV 1

11

100 = r100=

1.0100=1000.

46

Price of a Stock: An example

xgrD

ShareP

PShare = Price of a StockD = expected Dividendr = interest rate g = growth rate of dividend x = risk premium

D = 1000 and r =5% and g=3% has a risk x =0;

000,5002.0

1000003.005.0

1000

ShareP

000,2005.0

1000003.008.0

1000

SharePIf r =8%

47

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.

48

Debt and Savings in Life Cycle Model

-400000

-200000

0

200000

400000

600000

800000

1000000

1200000

1400000

Age

Deb

t or S

avin

gs

Debt/Credit

Working life: 21-65Consumption life: 22 -90Life time income: 2958727 Smooth consumption: 42880Growth rate of income: 5%Initial income:20000

0

361...21111 YgggtetTe

LtYV

;

X

nXn

XXXS

1

11

....2

1

t

:

40000£36

03.1...2

03.103.1175.0 e

tTeLtYV

=1985227

=1985227.

Income, Saving and Outstanding Asset or Debt in Life Cycle Model

49

*11

*ti

tidtyty 0d (9)

where tyis actual output

*ty is trend output, ti is the actual

interest rate and *ti the basic interest rate,

One period lag is assumed between the interest rate decision and the change in the output.

*11

*t

yt

yctt 0c (10)

where t and *t are actual and target inflation rates.

Interest rate rule:

***ttbtytyatiti 0a ; 0b (11)

Interest Determination Rule to Achieve the Inflation Target: Taylor Rule

50

Reduced Form Equation of the Interest Determination Model

*11

*ti

tidtyty

*11

*t

yt

yctt

***ttbtytyatiti 0a ; 0b

(11)

Substituting the output and inflation equations in the interest

rate rule:

*

22*

11*

ti

ticdb

ti

tidatiti

*22

*11

*titibcdtitiadtiti

*2

*1

*21 tbcditadititbcditaditi (12)

51

Why Should the Central Bank Be Independent?Inflation Biases of a Government and a Central

Bank Figure 1

G

Preference of government and a conservative central bank regarding inflation and output AS Preference of Government (GP)Inflation A

AS1

B Preference of a CB (CP)

O Yn Output

52

TYC 8.0200 iI 20050

201.03.010 YYNX f

P

EP*

%5* ii

T =100 G = 100

,, fYYNXGiITYCY

YiP

M5.050200

National Income

Consumption

Investment

Tax and Spending

Net exports

Real exchange rate

Financial integration

Demand for Money

An Example of an Open Economy Model

500fY 02.0 2* P 2PParameters

53

Three GAPs: Investment-Saving, Government Budget and Trade Gaps in a Keynesian Model

i

Saving and Investment

I(r)

S(Y)

TrwLrKXGICMTSCYcall :Re

FlowCapNX

MXGTIS

IS

Private saving +public saving = net export

IS

0NXTrade Surplus

Trade deficit0NX

0

i

0 GTK-outflow

K-inflow

54

IS-LM Model in an Open Economy: Mundell-Fleming Model

IS*

e*

LM (y, i)

Output

Exc

hang

e R

ate

o y

Assumption:Money supply does not depend on exchange rate

55

Impact of Fiscal Policy under Fixed and Flexible Exchange Rate Systems

IS*

IS*’

e1

e2

YNo Impact of Fiscal Policy

LM LM1LM2

Fixed Exchange Rate System

Y1 Y2

e

IS*IS*’

Flexible Exchange Rate System

Full Impact of Fiscal Policy

56

Impact of Monetary Policy under Fixed and Flexible Exchange Rate Systems

IS*

IS*’

e1

e2

Full Impact of Monetary Policy

LM LM1LM2

Fixed Exchange Rate System

Y1 Y2

e

IS*

Y1 Y2

Flexible Exchange Rate System

No Impact of Monetary Policy

57

Exchange rate

i

LM

IS

Y00 0

i

IS-LM and Uncovered Interest Parity Model

Y1 E0 E1

1

2

Appreciation

UIP

IS1

58

Time

J-Curve Hypothesis: Impact of Devaluation on Net Exports

Net Exports

o

Export creation and Import substitution or demand switching takes time

59

Marshall-Lerner condition Devaluation is effective if

1 mx ee

Devaluation is ineffective if

1 mx ee

Devaluation has no effect in trade balance

1 mx ee

xe is elasticity of export

me is the elasticity of imports

60

Purchasing Power Parity: *tt

tete

(1)

Uncovered Interest Parity: t

ttt e

eii

*

(2)

Using the Fisher equation (2) becomes

t

ttttt e

err

**

(3)

Slight rearrangement:

**tt

t

ttt rr

e

e

(4)

From PPP 0*

tt

ttt e

e

*tt rr

When both PPP and UIP hold exactly the domestic and foreign real interest rates are equal.

61

Initial exchange rates End of 2002 1.11 0.98 0.78 £0.69 $1 £0.63 $1 £0.53 $1

2001 2002 2004

In 2004 one dollar in terms of pound and Euro is 68.078.0

53.0

In 2002 one dollar in terms of pound and Euro is 64.098.0

63.0

In 2001 one dollar in terms of pound and Euro is 621.011.1

69.0

Appreciation of against £ (2001-04) = %7.90968.062.0

62.068.0

Triangular Exchange Rates and Appreciation and Depreciation with respect to the Third Currency

62

5,56,3

3,64,4

...............................

C

NC

CNC

CountriesDeveloping

CountriesAdvanced

5,56,3

3,64,4

...............................

C

NC

CNC

CountriesDeveloping

CountriesAdvanced

Cooperation or non-Cooperation?

Nash Solution is non-cooperation (NC,NC) =(4,4)

Cooperative Solution (C,C) =(5,5)

Cooperative solution Pareto dominated Non-cooperative solution.

Pareto efficiency: at least one party gains without hurting the other.

63

Developing

Economies

Advanced economies

Extensive Form of International Cooperation Game

NC

C

NC

C

NC

C

(4,4)

(6,3)

(3,6)

(5,5)

Advanced economies

64

Developing

Economies

Advanced economies

Dynamics of International Policy Cooperation Game: Solution by Backward Induction

NC

C

NC

C

NC

C

(4,4)

(6,3)

(3,6)

(5,5)

Advanced economies

65

1

55...5555),( 32 n

nLimCCPV

ncheatPV 4...4446)( 32

132 4...446)( ncheatPV

466)(1 cheatPV 0lim

1

n

n

1

46)(cheatPV

146

1

5

4165 256 2

1

Solution for the Discount Factor of the Game

66

Monetary Bliss (MB)

Fiscal Bliss (FB)Nash equilibrium (N)

BudgetSurplus, S

BudgetDeficit, D

0

+

-

M

M

F

F

Interest rate, r

Fiscal and Monetary Policy Game in a Diagram

(Nardhaus (1994) Model)

67

y = y*

Bliss

y-y*yT

1,2,3,4 Iso social cost functions

1

2

3

4

ASr

ASr

ASd

ASd

d

ch

r =0

PR

Policy Rule, Discretion, Cheating and Time Inconsistency in Economic Policy Making

Policy rule

Discretion

Cheating

Kydland and Prescott (1977)

68

Adjustment of Budget Surplus or Interest Rate for Internal and External Stability

Internal Balance

External Balance

Bud

get s

urpl

us :

fisc

al p

olic

y In

stru

men

t

Interest rate: Monetary Policy instrument

0

BOP Surplus

BOP Deficit

Unemployment: RecessionInflation: Boom

Two objectives:Internal Stability: Full EmploymentExternal Stability: Trade BalanceTwo instruments:Budget surplus or deficit and interest rate

a b

cd

e

fghi

69

Assignment Problem in the Mundell-Fleming Model

i

yy*0

LM1

LM2

IS1

IS2

BOP

a

c

a: initial point of internal balance but external imbalance (IS1=LM1)b: use of monetary policy (LM2) for external balance creates internal imbalancec: accommodative fiscal policy (IS2) restores the balance

b

TargetsInternal stability y*External stability BOPInstruments:Monetary policy (i)Fiscal policy (G,T)

+

-

70

Household’s Problem:

1lcUMax

Subject to:

i. 1 shl time constraint

ii. pcwh s budget constraint

iii. 0;0;0 shlc non-negativity constraint (1)

Firm’s problem dwhpyMax

subject to :

i. dhy technology constraint

ii. 0;0 dhy non negativity constraint (2)

General Equilibrium Set-up of Household and Firms’ Problem

71

p

whc s

11

p

whc

pp

wh ss

11

p

wh

pp

wh ss

11 1

pp

w

p

wh s

p

w

p

wpp

w

c

1

11

p

wpp

w

hl s

1

11

Derivation of Labour Supply, Consumption and Leisure Demand Functions

(7)

(8)

(9)

(10)(11)

72

ddd whhpwhpy max

01

whph

dd

1

1

1

p

whd

1

1

111

1

1 1111

p

w

p

w

p

w

p

wh

p

wh

p

hwy

pdd

d

p

w

p

w

p

w

p

wpp

w

hp

wh sd

111

11

1

1

11

1

1

(12)

(13)

(14)

(15)

73

1

1

1

1

1

111

p

w

1

1

1

1

1

1

111

1ˆ

y

Real wage rate, profit and output in Equilibrium

1

1

111

1

1 1111

p

w

p

w

p

w

p

wh

p

wh

p

hwy

pdd

d

(16)

(17)

(18)

74

1

1

1

1

1

1

1

111

11ˆ1ˆ

shl

1

1

1

1

1

1

1

111

1ˆˆ

sd hh

Leisure, Labour Supply and consumption in Equilibrium

1

1

1

1

1

1

1

1

1

1

1

1

111

111

11

1ˆ

c

(19)

(20)

(21)

75

Public Revenue 2004: £455bn Source HM TreasuryBusiness rates, 19, 4%

Value-added tax, 73, 16%

Corporation tax, 35, 8%

Excise duties, 40, 9%

National Insurance, 78, 17%

Income tax, 128, 28%

Council tax, 20, 4%

Other receipts, 62, 14%

76

Public Spending 2004. £487Source: HM Treasury

Education, 63, 13%

Health, 81, 17%

Social protection, 138, 28%Other health and personal services, 22,

5%

Defence, 27, 6%

Law and protective services, 29, 6%

Housing and other environment, 17, 3%

Industry and agriculture, 20, 4%

Transport, 16, 3%

Debt interest, 25, 5%

Other expenditure, 49, 10%

77

1lcUMax

1 shl

Rhtwctp slc 11

Rhwtcpt slc

0;0;0 shlc

Rhtwctp slc 11 pcwh s

ctpRhtwhclcL cs

ls

111,,1

(1’)

(2’)

(3’)

Household Problem in Presence of Consumption and Income Taxes

78

11

1

1

11

1

1

11

1

1

11

1

1

c

l

c

l

sd

t

t

p

w

p

w

t

t

p

w

hp

wh

1

1

11

1

1

1

111

1

1

1

1

1

1

1

c

l

c

l

t

t

t

t

p

w

1

1

1

11

1

111

1

1

1

1

1

1

1

c

l

c

l

t

t

t

t

p

w

Determination of Real Wage Rate in the Presence of Taxes

79

1

1

11

1

1

1

111

1

1

1

1

1

1

111ˆ

c

l

c

l

t

t

t

t

l

c

l

c

l

c

l

tp

tw

t

t

t

t

c

1

1

111

1

1

1

1

1

1

111

1ˆ

1

1

11

1

1

1

1ˆˆˆ lcU

Leisure and Consumption in the Presence of Taxes

80

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 TaxesEquivalent Variation = -0.693

Compensating Variation = 0.697 Efficiency Gains from Switching to Consumption Taxes

Equivalent Variation = 2.967 Compensating Variation = -2.882