1. Review: Lectures 1-22 March 29, 2004
Economic Modelling
Review: Lectures 1-22
March 29, 2004

2. 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
Wage payment, wL
Labour supply, L
Economy
(p, w, y, c, l, L)
Households
(consumers)
Max U(C,L)
Firms
(producers)
Max π(LS)
Payments for goods, p.y
Supply of Goods
Question: List 10 different things missing
from this model.

3. 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
World
31,493,000,000,000.00
Heavily indebted poor countries (HIPC)
200,880,000,000.00
High income
24,927,000,000,000.00
High income nonOECD
857,350,000,000.00
High income OECD
24,073,000,000,000.00
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

5. 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:
Closure rule in the model:
Dynamics: Capital accumulation:

6. Per Capita Output and Per Capita Capital Stock in the Steady State
SST
0.5ks ks

7. Growth Accounting 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:
Per Capita Effective Capital Stock in the Steady State:
Per Capita Effective Output in the Steady State:

9. Results from the steady state:
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.
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.
Countries with higher rate of population growth rate have lower level of output in the steady state.
Countries with higher capital share have higher output in the steady state.
Countries which differ in the initial capital stock eventually reach to the same output level in the steady state.
Growth of per capita income is zero in the steady state

10. Golden Rule for Saving and Capital Accumulation
C-max Kg
Kss
Golden rule
Steady State

11. How High Should be the Saving Rate
How High Should be the Saving Rate? Saving Rate that Maximises Consumption
C-max = 1.25
y = 0.5*k0.5
y=2.5
Consumption
k = 25 C s5 s4 s1 s2
s*=0.5
Saving rate

12. How Human Capital Contributes to the Economic Growth?

13. How does the technological advancement affect the per capita capital and per capita output in the steady state?
Advanced Technology
Primitive Technology

14. Endogenous Growth Model

15. Increase in Real Wage Rate with Human Capital
MPKh2 w1
MPKh1
Technological
advancement raises
wage rate but reduces
Work hours.

16. Constant Marginal Product of Capital with Human Capital
MPKh3
MPKh1
MPKh2 k1 k2 k3

17. Meaning of Convergence and Divergence
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.

18. Who Gain and Who Lose From Globalisation?
Capitalists in rich countries and workers in poor countries gain. rp rR
MPKR
MPKP wR
wp’
wR’
MPLR
MPLP’ wp
MPLR’
MPLP

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

20. y=f(k) y Max Subject to: k MPK= k*
Profit Maximisation Problem of Firms
Marginal Product of Capital = User Cost of Capital
y=f(k) y
Max
Subject to: k
Investor Compare user cost of capital with its productivity
MPK= k*

21. Analysis of Earnings (R) and Cost (C) from an Investment Project
K = ; d = 0.08; R (Earning) =18000
C =(r+d)*K
23,000
C > R
Cost
And
Earning
Break Even
18,000
Earning (R)
C < R
13,000
0.1
0.15 r
0.05

22. Role of Investment Tax Credit in Promoting Investment
Why Manufacturers Lobby for a Tax Credit?
MPK
MPK = K1 K2 K

23. Optimal Capital Stock for the Car Company
The user cost of capital :
= 6% +3%-3% =6%
Let
Marginal product of capital:
Optimal Investment condition:
= 6.25 million

24. Two Period Model of Consumption and Saving C2 w2
Subject to: c2
Borrowing U  c1 w1 C1

25. Two Period Model of Consumption
Consumers’ problem:
Budget constraint in period 1:
Budget constraint in period 2:
: Consumption in period 1
 = subjective Discount factors
: Consumption in period 1
b = borrowing or lending
: Income in period 1
r = interest rate
:Income in period 12
U = utility

26. Life Cycle Model of Consumption and Saving
Modigiani-Ando-Brumberg life cycle hypothesis
Saving
C,S,Y
C-Smoothing
Borrowing
Dissaving
Old
Young
Adult
Smooth consumption and erratic income over life

27. Phillips Curve and Expectation Augmented PC (NAIRU)

28. Classical, Keynesian and New Keynesian Aggregate Supply curves
Classical Supply
New Keynesian Supply c b
Keynesian Supply a a1
Y = AD d
AD2
AD1
Output

29. Aggregate Supply, Inflation and the natural rate of unemployment hypothesis
LAS
SAS o
Summary:

30. Supply Shock and Stagflation
LAS
AS1
AS=f(w,pe)
Stagflation
AD =f(M,G, T) o

31. Stabilisation: Table 1

32. Macroeconomic Stabilisation Role of Tax and Spending
T = tY
T > G
Surplus in boom
G = T
Tax
and
Spending G G
T < G
Deficit in
recession YF
Income T

33. Balanced Budget Multiplier with Lump-Sum Taxes
The real national income is given by the IS Curve:
Positive Government expenditure multiplier: .
Negative tax multiplier:
The balanced budget multiplier:
=1/(1-c1) - c1/(1- c1) = 1
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
Consumption:
Disposable income:
Tax Revenue
Income (IS curve):
Y = c0 + c1YD + I + G
High T when Y is high.
Low T when Y is low.
The multiplier = 1/(1-c1+c1t1) <1/(1- c1),
so the economy responds less to changes in
autonomous spending when t1 is positive.

35. How much should be the tax rate to maximise the government revenue ?
Tax compliance
R-max
Revenue
Tax avoidance
Tax evasion
R-low
Revenue=F(t)
Tax rate tH
t-Low
t-Rmax

36. Laffer Curve Model:A Numerical Example

37. Debt Dynamics: Determinants of Debt/GDP Ratio
(5)
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

38. Revenue from Inflation Tax and Its Limitations
Inflation rate equals
growth rate of money
supply in the steady state.
S-Max
Seigniorage
S-low
S = F()
-max
Inflation tax
-low
-high

39. Seigniorage (Inflation Tax) : A Numerical Example Si
1000
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

40. 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
Today

41. Bank of England’s View on Transmission Mechanisms of Monetary Policy: How Does Money Supply Affect the Price Level?
i,r,er,Pe P
C+I+G MS Y π
X,M
Two Conditions to have real effect of Monetary policy
Central bank controls monetary base M1 = R + Cu
Prices do not adjust instantaneously

42. An Increase in Money Supply Can Lower Real
and Nominal Interest Rates in the Short but not in the Long Run
Fisher Equation i r T
time t0
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

43. Link Between Financial System and the Economy
Y= F(K,L) C T S
Funds K FA
Deposit
Banks
Pension Funds
Treasury
Bonds
Profit
Equity

44. Financing of an Investment Project
Need for Capital
Demand
for output
Financing an
Investment
Project
Self
Finance
Bequests
Bonds:
Debt Finance
Banks, Building
Society, Insurance
Equity Finance
Stock Market
(LSE)
Risks
AAA
BBB
CCC
Maturity
Instalment
Method
Repayment
Method No
Risk
Risk
High
Risk

45. Market Price of a bond (console)

46. Price of a Stock: An example
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;
If 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. Income, Saving and Outstanding Asset or Debt in Life Cycle Model= : t ; =

49. Interest Determination Rule to Achieve the Inflation Target: Taylor Rule

50. Reduced Form Equation of the Interest Determination Model

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

52. An Example of an Open Economy Model
National Income
Consumption
Investment
Tax and Spending
T =100 G = 100
Net exports
Real exchange rate
Financial integration
Demand for Money
Parameters

53. Three GAPs: Investment-Saving, Government Budget and
Three GAPs: Investment-Saving, Government Budget and Trade Gaps in a Keynesian Model
S(Y)
Trade Surplus
K-outflow i
Private saving +public saving
= net export i
I(r)
Trade deficit
K-inflow
Saving and Investment

54. IS-LM Model in an Open Economy: Mundell-Fleming Model
LM (y, i)
Exchange Rate
Assumption:
Money supply does not
depend on exchange rate e*
IS* o
Output y

55. Impact of Fiscal Policy under Fixed and Flexible Exchange Rate Systems
Fixed Exchange Rate System LM
LM1
LM2 e2
IS*’ e e1
IS*’
IS*
IS* Y1 Y2 Y
No Impact of Fiscal Policy
Full Impact of Fiscal Policy

56. Impact of Monetary Policy under Fixed and Flexible Exchange Rate Systems
Fixed Exchange Rate System LM
LM1
LM2 e2 e
IS*’ e1
IS*
IS* Y1 Y2 Y1 Y2
Full Impact of Monetary Policy
No Impact of Monetary Policy

57. IS-LM and Uncovered Interest Parity Model2 1 i i
IS1 IS
UIP Y1 E0 E1 Y0
Appreciation
Exchange rate

58. J-Curve Hypothesis: Impact of Devaluation on Net Exports
Export creation and
Import substitution or
demand switching takes time
Net
Exports o
Time

59. Marshall-Lerner condition

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

62. 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. Extensive Form of International Cooperation Game
(4,4) NC
Advanced
economies NC C
(6,3)
(3,6)
Developing
Economies NC
Advanced
economies C C
(5,5)

64. Dynamics of International Policy Cooperation Game: Solution by Backward Induction
(4,4) NC
Advanced
economies NC C
(6,3)
(3,6)
Developing
Economies NC
Advanced
economies C C
(5,5)

65. Solution for the Discount Factor of the Game

66. Fiscal and Monetary Policy Game in a Diagram
(Nardhaus (1994) Model)
Budget
Surplus, S +
Monetary Bliss (MB) F
Interest rate, r -
Nash equilibrium (N)
Budget
Deficit, D
Fiscal Bliss (FB) M F

67. 1,2,3,4 Iso social cost functions 3 ASr 4 PR
ASd d
ASr
Discretion
Policy Rule, Discretion, Cheating and Time Inconsistency in Economic Policy Making
ch
Cheating
ASd
r =0
Bliss 1
y = y* yT
y-y*
Policy rule 2
1,2,3,4 Iso social cost functions 3
ASr 4 PR
Kydland and Prescott (1977)

68. BOP Surplus a b d c e h i g f BOP Deficit
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 rate
BOP Surplus a b d
Inflation: Boom c e
Unemployment: Recession
Budget surplus : fiscal policy Instrument h i g f
Internal Balance
BOP Deficit
External Balance
Interest rate: Monetary Policy instrument

69. Assignment Problem in the Mundell-Fleming Model
LM2 +
BOP i - c
Targets
Internal stability y*
External stability BOP
Instruments:
Monetary policy (i)
Fiscal policy (G,T) b a
IS2
IS1
LM1 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

70. General Equilibrium Set-up of Household and Firms’ Problem

71. Derivation of Labour Supply, Consumption and Leisure Demand Functions
(7)
(8)
(9)
(10)
(11)

72. (12)
(13)
(14)
(15)

73. Real wage rate, profit and output in Equilibrium
(16)
(17)
(18)

74. Leisure, Labour Supply and consumption in Equilibrium
(19)
(20)
(21)

77. Household Problem in Presence of Consumption and Income Taxes
(1’)
(2’)
(3’)

78. Determination of Real Wage Rate in the Presence of Taxes

79. 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 =
Compensating Variation =
Efficiency Gains from Switching to Labour income Taxes
Equivalent Variation =
Compensating Variation =
Efficiency Gains from Switching to Consumption Taxes
Equivalent Variation =
Compensating Variation =