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

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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 Market price (p) and wage rate (w) such that: Y = C LD = LS LS +l = L Micro-Foundation to Macro Variables General Equilibrium with a representative household and firm Question: List 10 different things missing from this model.

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3 Population, total2000 East Asia & Pacific1,855,200,000 Europe & Central Asia474,310,000 European Monetary Union303,980,000 Middle East & North Africa295,180,000 South Asia1,355,100,000 Sub-Saharan Africa658,940,000 Latin America & Caribbean515,710,000 United States281,550,000 Others317,330,000 Heavily indebted poor countries (HIPC)632,160,000 Low income2,459,800,000 High income902,850,000 Low & middle income5,154,400,000 High income nonOECD50,794,000 High income OECD852,060,000 Least developed countries (UN classification)660,030,000 Lower middle income2,047,600,000 Middle income2,694,600,000 Upper middle income647,010,000 World6,057,300,000

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4 GDP (current US$)2, East Asia & Pacific2,059,100,000, Europe & Central Asia942,080,000, European Monetary Union6,048,400,000, Latin America & Caribbean2,000,500,000, Middle East & North Africa659,690,000, Sub-Saharan Africa322,730,000, United States9,837,400,000, United Kingdom1,414,600,000, South Asia596,790,000, World31,493,000,000, Heavily indebted poor countries (HIPC)200,880,000, High income24,927,000,000, High income nonOECD857,350,000, High income OECD24,073,000,000, Least developed countries (UN classification)190,520,000, Low & middle income6,560,600,000, Low income1,048,300,000, Lower middle income2,347,200,000, Middle income5,513,200,000, Upper middle income3,170,500,000,000.00

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5 Solow Growth Model Production function with capital and labour as its inputs. Closed Economy without Government. Market clearing: Households Saving Decision: Investment requirement: Closure rule in the model: Dynamics: Capital accumulation: Firms Production Function

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

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7 Growth Accounting Take log of both sides: Differentiate with respect to time :

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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:

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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

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

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11 Saving rate C-max = 1.25 Consumption s*=0.5 y=2.5 k = 25 y = 0.5*k 0.5 s1s2 s4 s5 How High Should be the Saving Rate? Saving Rate that Maximises Consumption C

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12 How Human Capital Contributes to the Economic Growth?

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

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14 Endogenous Growth Model

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15 MPKh1 MPKh2 w1 w2 Increase in Real Wage Rate with Human Capital Technological advancement raises wage rate but reduces Work hours.

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16 r MPK h1 MPK h2 MPK h3 k3k2k1 Constant Marginal Product of Capital with Human Capital

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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.

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18 Who Gain and Who Lose From Globalisation? MPL R MPL P wpwp wpwp wRwR wRwR MPK R MPK P rprp rRrR Capitalists in rich countries and workers in poor countries gain.

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

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

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

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22 Role of Investment Tax Credit in Promoting Investment Why Manufacturers Lobby for a Tax Credit? MPK = K1K2 0 K MPK

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

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

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25 Two Period Model of Consumption Consumers problem: = subjective Discount factors : 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:

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

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27 Phillips Curve and Expectation Augmented PC (NAIRU)

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28 Classical, Keynesian and New Keynesian Aggregate Supply curves Keynesian Supply Classical Supply New Keynesian Supply Y = AD 0Output AD1 AD2 a b c d a1

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

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

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31 Stabilisation: Table 1

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32 Macroeconomic Stabilisation Role of Tax and Spending Tax and Spending GG T T = tY Income YFYF G = T T > G Surplus in boom T < G Deficit in recession 0

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33 Balanced Budget Multiplier with Lump-Sum Taxes. =1/(1-c 1 ) - c 1 /(1- c 1 ) = 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.

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34 Automatic Stabiliser with Proportional Taxes Consumption: Disposable income: Tax Revenue Income (IS curve):Y = c 0 + c 1 Y D + 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.

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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 avoidance Tax evasion Revenue=F(t) Tax compliance

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36 Laffer Curve Model:A Numerical Example

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

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38 Inflation tax S-Max Seigniorage -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.

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39 M/P Si Seigniorage (Inflation Tax) : A Numerical Example

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40 Basic Proposition of the Ricardian Equivalence Tax or Borrowing Does not Make Any Difference C1 C2 Before Borrowing Budget Constraint After borrowing budget constraint Today Tomorrow

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

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42 time t0 0 r i T An Increase in Money Supply Can Lower Real and Nominal Interest Rates in the Short but not in the Long Run 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

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

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

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45 Market Price of a bond (console)

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46 Price of a Stock: An example P Share = 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%

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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.

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48 ; t : = = Income, Saving and Outstanding Asset or Debt in Life Cycle Model

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

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50 Reduced Form Equation of the Interest Determination Model

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

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

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53 Three GAPs: Investment-Saving, Government Budget and Trade Gaps in a Keynesian Model i Saving and Investment I(r) S(Y) Private saving +public saving = net export Trade Surplus Trade deficit 0 i K-outflow K-inflow

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

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55 Impact of Fiscal Policy under Fixed and Flexible Exchange Rate Systems IS* e1 e2 Y No Impact of Fiscal Policy LM LM1 LM2 Fixed Exchange Rate System Y1Y2 e IS* Flexible Exchange Rate System Full Impact of Fiscal Policy

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56 Impact of Monetary Policy under Fixed and Flexible Exchange Rate Systems IS* e1 e2 Full Impact of Monetary Policy LM LM1 LM2 Fixed Exchange Rate System Y1Y2 e IS* Y1Y2 Flexible Exchange Rate System No Impact of Monetary Policy

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57 Exchange rate i LM IS Y0 00 i IS-LM and Uncovered Interest Parity Model Y1E0E1 1 2 Appreciation UIP IS1

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

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59 Marshall-Lerner condition

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

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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.

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

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

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65 Solution for the Discount Factor of the Game

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

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67 y = y* Bliss y-y* yTyT 1,2,3,4 Iso social cost functions ASr 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)

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68 Adjustment of Budget Surplus or Interest Rate for Internal and External Stability Internal Balance External Balance Budget surplus : fiscal policy Instrument Interest rate: Monetary Policy instrument 0 BOP Surplus BOP Deficit Unemployment: Recession Inflation: Boom Two objectives: Internal Stability: Full Employment External Stability: Trade Balance Two instruments: Budget surplus or deficit and interest rate a b c d e f g h i

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69 Assignment Problem in the Mundell-Fleming Model i y y* 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 imbalance c: accommodative fiscal policy (IS2) restores the balance b Targets Internal stability y* External stability BOP Instruments: Monetary policy (i) Fiscal policy (G,T) + -

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70 General Equilibrium Set-up of Household and Firms Problem

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

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

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

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

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

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78 Determination of Real Wage Rate in the Presence of Taxes

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79 Leisure and Consumption in the Presence of Taxes

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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 =

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