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**Review: Lectures 1-22 March 29, 2004**

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

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**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.

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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

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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

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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:

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

SST 0.5ks ks

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**Growth Accounting Take log of both sides:**

Differentiate with respect to time :

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**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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**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

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**Golden Rule for Saving and Capital Accumulation**

C-max Kg Kss Golden rule Steady State

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**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

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**How Human Capital Contributes to the Economic Growth?**

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

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**Endogenous Growth Model**

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**Increase in Real Wage Rate with Human Capital**

MPKh2 w1 MPKh1 Technological advancement raises wage rate but reduces Work hours.

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**Constant Marginal Product of Capital with Human Capital**

MPKh3 MPKh1 MPKh2 k1 k2 k3

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**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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**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

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**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?

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**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*

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**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

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**Role of Investment Tax Credit in Promoting Investment **

Why Manufacturers Lobby for a Tax Credit? MPK MPK = K1 K2 K

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**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

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**Two Period Model of Consumption and Saving**

C2 w2 Subject to: c2 Borrowing U c1 w1 C1

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**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

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**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

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**Phillips Curve and Expectation Augmented PC (NAIRU)**

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**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

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**Aggregate Supply, Inflation and the natural rate of unemployment hypothesis**

LAS SAS o Summary:

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**Supply Shock and Stagflation**

LAS AS1 AS=f(w,pe) Stagflation AD =f(M,G, T) o

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Stabilisation: Table 1

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**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

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**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.

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**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.

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**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

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**Laffer Curve Model:A Numerical Example**

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**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

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**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

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**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

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**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

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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

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**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

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**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

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**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

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**Market Price of a bond (console)**

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**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%

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

= : t ; =

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

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**Reduced Form Equation of the Interest Determination Model**

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**Why Should the Central Bank Be Independent**

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

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**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

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**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

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**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

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**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

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**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

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**IS-LM and Uncovered Interest Parity Model**

2 1 i i IS1 IS UIP Y1 E0 E1 Y0 Appreciation Exchange rate

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**J-Curve Hypothesis: Impact of Devaluation on Net Exports**

Export creation and Import substitution or demand switching takes time Net Exports o Time

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**Marshall-Lerner condition**

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**Triangular Exchange Rates and Appreciation**

and Depreciation with respect to the Third Currency

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**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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**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)

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**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)

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**Solution for the Discount Factor of the Game**

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**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

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**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)

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**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

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**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

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**General Equilibrium Set-up of Household and Firms’ Problem**

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**Derivation of Labour Supply, Consumption and Leisure Demand Functions**

(7) (8) (9) (10) (11)

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

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**Real wage rate, profit and output in Equilibrium**

(16) (17) (18)

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**Leisure, Labour Supply and consumption in Equilibrium**

(19) (20) (21)

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**Household Problem in Presence of Consumption and Income Taxes**

(1’) (2’) (3’)

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**Determination of Real Wage Rate in the Presence of Taxes**

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**Leisure and Consumption in the Presence of Taxes**

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**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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The Solow Model and Beyond

The Solow Model and Beyond

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