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GSB 410 Economic Analysis • Dr. Jeff S. Hong • University of Bridgeport at Stamford, CT • Saturdays 09/07, 09/21, 10/05 & 10/19 8:30A.M.~5:00P.M. Demand & Supply • QXd = f(pX, Y, N, pZ, … etc.) • e.g.) Q = a+b1p+b2Y+b3N+b4pZ+e • QXs = f(pX, n, r, w … etc.) • e.g.) Q = a+b1p+b2n+b3r+b4w+e Bivariate Eqm Determination • QD = a + bP, where b<0. • QS = z + mP • Solve for Eqm Pe & Qe. • QD = a + bP = z + mP = QS • a - z = mP - bP • a - z = (m - b)Pe, where b<0. • Pe = (a - z)/(m - b) • Qe = a + bPe or Qe = z + mPe Qe & pe for Nike Shoes • The demand and supply curves for Nike tennis shoes are given by the following equations. • Q = 24,000 500p Q = 6,000 + 1,000p, where p is price in $ and Q is the # of pairs per month. • Find the eqm price and quantity. Economy in the Long-Run P SRAD LRAS SRAS LRAD Y Production Possibility Frontier YK (e.g. Car) PPF XL (e.g. Wheat) Why is PPF Bowed in? • Increasing (Opportunity) Cost (TC OC) - The opportunity cost of Y is increasing. • As we produce more of Y, we have to give up more of X for an additional unit of Y. • Technically, Marginal Rate of Substitution between X and Y (MRSXY) is increasing. Marginal Rate of Substitution XY X Y Opportunity Cost, Comparative Advantage & Int’l Trade • France Germany • Wine 50 bottles/labor 5 bottles/labor • Beer 25 bottles/labor 20 bottles/labor • Opportunity 1/2 beer 4 beer • Cost of Wine • Opportunity 2 wine 1/4 wine • Cost of Beer Import Tariff, Price Control, & Market Distortion P tariff = effective subsidy S Ptariff P* Shortage QD Q* QS D Q Long-Run Growth f(k), sf(k), k f(k) MPK = r = f'(k) = [f(k+1) f(k)]/k k r(MPK) sf(k) i = sf(k) > k i = s f(k )< k i* = sf(k*) = k* SS k* k Economy in the Long Run Y / L F ( K / L,1) y f (k ) f (k ) c i (1 s ) y i, where i sy sf (k ) & i I / L k i k sf (k ) k 0 sf (k *) k * in SS k * / f (k *) / s Business Cycle: Inflation P SRAD LRAS SRAD P SRAS LRAD Y Y Business Cycle: Recession P Boom Range of Accelerated Inflation Recovery Contraction/ Stagnation Recession Unemployment Trough Business Cycle - continued • At the height of economic boom, inflation is accelerating due to excessive D. • High price level & wage due to (inflation) increases production cost. • Firms downsize to reduce cost until p & w fall enough to make profit again. • When recession hits bottom, firms start expanding to take advantage of low p & w. • If >i, high discourages lending to the much needed investment. How to Measure Inflation? • CPI = P(retail goods)given year / P(retail goods)base year * 100 • PPI = P(wholesale ) given year / P(wholesale) base year * 100 • GDP deflator = P(all goods) given year / P(all goods) base year * 100 • or Nominal GDP / Real GDP *100, where Nominal GDP = Real GDP * . • i=r+ Unemployment • Frictional • Structural • Seasonal • Cyclical • Natural Rate of Unemployment (NAIRU) = Frictional + Structural + Seasonal • U = No. of Unemployed / (Total LF - No. of Discouraged Workers) * 100 Accounting for National Income • National Income Accounting Identity • Y = C + I + G + (X-M), where • Y = Output = Income = GDP • Sources = Uses • Balance of Payments Adjustments • Y C G = I + (X-M) • S(National Saving) = I + (X-M) • SI=XM • Capital Account = Current Account Accounting for Consumption • C = f(Yd, W, p, , r, Et[Yt+1]) • C = f(Yd, Ceteris Paribus), where • Yd = YT • C = a + bYd • b = MPC = C/Yd = (C2 C1)/(Yd2 Yd1) • Yd causes movement along the Consumption schedule. • in other variables shifts the entire C skdl. Marginal Propensity to Consume • MPC = C/Yd = (C2–C1)/(Y2–Y1) C C' C C2 C" C1 MPC < 1 W, , P Yd1 Yd2 Yd Accounting for Investment • I = f(r), where • r = i = i Pt/Pt-1 • An inflation would decrease r making it easier for businesses to borrow. K investments will increase. • A deflation would increase r making it difficult for businesses to borrow. K investments will decrease. Accounting for Net Export • G is exogenous. (regardless of T) • X M = f(YF/YH, e) • e = PriceH/PriceF • e Depreciation of home currency • e Appreciation of home currency National Income: AD Side Eqm • AD in Eqm if Y(GDP)=C+I+G+(X–M)=AD. Expenditure = C+I+G+(X-M) = C+u = bY+a = f(Y) MPC = 1 C+I+G+(X-M) P C+u = bY+a, where b = MPC < 1 and P u = I+G+(X-M) 45 Y* Y*' Y(GDP) Effect of Price & AD Curve P AD E" P" P E E' P Y" Y Y' Y Simple Algebraic Eqm Income Determination • Let C = a + bYd = a + b(YT) (1) • Y = C + I + G + (XM) (2) • Y = (a + bYd) + I + G + (XM) = a bT + bY + I + G + (XM) (3) • (1b)Y = a bT + I + G + (XM) (4) • a bT I G ( X M ) (5) Y 1 b Graphing AD Side Eqm • Y C I G XM • 3,600 3,100 240 120 40 • 3,700 3,200 240 120 40 • 3,800 3,400 240 120 40 • 3,900 3,600 240 120 40 • 4,000 3,700 240 120 40 Graphing AD Eqm - continued Expenditure Expenditure 3,800 E 3,800 Y(GDP) Circular Flow: Leakage & Injection • Yd+T = C+I+X–M+G • C+S+T = C+I+X–M+G • S+T+M = I+X+G • Leakage = Injection AD Eqm & Full Employment • Recessionary Gap & Inflationary Gap Expenditure E C+I+G+(X-M) Potential GDP Cool off EF Recessionary Gap Inflationary Gap (from using the slack in ER resource employment: NRU 4%~6%) YR YF Y Y(GDP) Consumption & Multiplier Effect • Induced C stems from Yd. Movement along C schedule. • Autonomous C results in shift of the entire C schedule w/o any Yd. (e.g. P) • Only autonomous C will have multiplier effect. Autonomous Consumption Expenditure Expenditure1 E1 Expenditure0 P E0 Y0 Y1 Y(GDP) Multiplier Effect • Assume initial consumption of $1Mil @MPC = .75. • C = 1Mil + .75*1Mil + .75*(.75*1Mil) + .75*[.75*(.75*1Mil)] … = i=0k .75^i*1Mil • C=1Mil(1+.75+.75^2+.75^3+ … +.75^k)…(1) • .75C=1Mil(.75+. 75^2+.75^3+ … +.75^k+1 (2) • In the limit where k, (1) – (2) • (1–.75)C = $1Mil C = $1Mil/(1–.75) • Multiplier = 1/(1–MPC) Multiplier is Oversimplified. • Multiplier ignores other factors that affect MPC negatively such as: • international trade (MCExpenditure skdl becomes flatter.Multiplier) i.e.) M = m(Y–T), where m = MPM If mb, since Yd=(b+m+s)Yd, where b+m+s =1 • inflation (C) • income tax (C) • financial system (Tight money policy money multiplier.) Algebra of Oversimplified Multiplier • From Income Determination a bT I G ( X M ) • Y (1) 1 b • Suppose any of the variables in the numerator increases by 1 unit: • a bT I G ( X M ) 1 (2) Y 1 b a bT I G ( X M ) 1 • Y = (1)–(2) 1 b a bT I G ( X M ) = 1 1 b 1 b Four Possible States of the Economy P P Inflation Deflation Y Perfect Growth Stagflation Y National Income: AS Side • AD = C+I+G+(X-M) = f(p, n, r, w, tech etc.) = AS • AS Y Q AS f ( p, n, MPK , MPL , tech, ) is sloped positively, because producers are motivated by (profit), where TR TC p * Q (w r ) * Q pQ(wL rK ) . Aggregate Supply Curve • Firms normally purchase K&L at fixed price (w & r, or MPL & MPK) in the SR. Thus, higher selling prices make production more profitable. p *Q ( w r ) * Q i.e.) • Wages account for more than 70% of all inputs. • If wAS (AS shifts in.) • If wAS (AS shifts out.) Shift in AS schedule • If price of K (r or MPK)/AS curve will shift in/out. • Technological breakthrough productivity, thus shifts As curve out. • If w is constant, productivity costs, thus Y. • As LF in both quantity and quality, and as the K stockthrough I, AS will shift out, more output (Y or Q) at given price ( p ). General Idea of Profit Max TR pQ (w r )Q TC p w r , Q Q Q Q where (TR TC) 0 Q Q Neoclassical Correction of Recession • Recessionary Gap is caused by inadequate C or by anemic I. • Cyclical unemployment. • Those employed eagerly hang on to the job. natural downward pressure on w w shifts AS curve out.p Recessionary gap. • Deflation erodes the recessionary gap, eventually leading to YF. • Conversely, inflationary gap is corrected by inflation (upward pressure on w & p). Self-Correcting Mechanism • The self-correcting mechanism does operate, if ever, only too slowly and weakly at heavy cost, thus giving rise to the need for gov't stabilization policy (AD vis-a-vis Structural Adjustment: AD). • Self-correcting mechanism works on the AS-side while expansionary/contractionary fiscal/monetary policies work on the AD- side. Critiques of Self-Correcting Mechanism • Deflationary Spiral: Businesses may be reluctant to hire more when they see no prospects of C increasing, as consumers, afraid of depleting their wealth, are unwilling to spend (cf. paradox of thrift). • i = r + r = i = i (Pt Pt-1)/Pt-1 • If (Pt Pt-1) < 0, then r > i Firms’ borrowingIY. • Keynesian Theory of Wage Rigidity (ratchet effect) Self-Correcting Critiques - continued • Psychological Factors/ Efficiency Wage: If wage, workers would either quit or devote less care to work (shirking). bad for morale To prevent moral hazard, pay high wages (efficiency wage). • Less Severe Biz Cycles after WWII: Recessions would not necessarily turn into depressions. Wait out rather than accept the w reductions. • Productivity Concerns: Productivity of individual workers are hard to identify. General wage cut might result in the loss of best employees. Pay efficiency wage to avoid adverse selection. • Minimum Wage Neoclassical Correction of Inflation • Inflation eventually erodes inflationary gap, and brings the economy to the EF. - i.e. • Rising prices purchasing power of consumers’ wealth cut back on C. • X, M . ( Ph/Pf > 1) • Eventually, AD is scaled back to YF, but the economy experience stagflation (p +Y) until the gap is eliminated. • EqmLR established w/ p and Y = YF. Two Types of Inflation • Demand-Pull Inflation: A brief period of stagflation is a natural course of adjustment/correction that comes after a demand-pull inflation. • Cost-Push Inflation or Stagflation: Adverse supply shocks cause a fall in output and acceleration in inflation. Inflation & Multiplier 1 • PH (X-M) & MPC (1 MPC ) • , prices will also rise. This will reduce net iff e , where in f (rh f ) exports (assuming no changee nominalre) and dampen consumer spending. "How much results from D" or "how much of the multiplier chain is cut off by " depends on the slope of the AS curve. • ADtptbtItADt+1 This also cuts the multiplier effect. Fiscal Policy • Fixed (lump-sum) Taxes: e.g.) property taxes do not depend on Y • Yd = YT C Expenditure • Yd = YT C Expenditure • Y Yd C = MPCYd • Since no MPC, FT shifts C down in parallel. Fiscal Policy (cont’d) • Variable Taxes (usually Progressive): • e.g.) personal/corporate income & sales taxes = f(Y) • Yd = YY = (1)Y, where T=Y • Yd = (1)Y C tilts down more sharply @YH than @YL. • Yd = (1)Y C tilts up more sharply @YH than @YL. • Y (1)Y=Yd C = MPC(1)Y = MPCVT Yd • tilts the C as it changes MPC by (1). Fiscal Policy (cont’d) • Effects of Fixed Tax Expenditure Fixed Tax CFT CVT Fixed Tax MPCFT>MPCVT Y Fiscal Policy (cont’d) • Effects of Variable Tax Expenditure Variable CV E Variable 45 Y Fixed Tax Multiplier Y a b[Y T ] I G ( X M ) a bY bT I G ( X M ) Y bY a bT I G ( X M ) (1 b)Y a bT I G ( X M ) a bT I G ( X M ) Y 1 b a b(T $1) I G ( X M ) Y ' 1 b b MPC Y 'Y Y 1 b 1 MPC Variable Tax Multiplier Let T Y Y a b(1 ) Y I G ( X M ) a I G (X M ) Y 1 b(1 ) a I G ( X M ) $1 Y ' 1 b(1 ) $1 1 Y 'Y Y 1 b(1 ) 1 MPC(1 ) Fiscal Policy - Tax Multiplier • Government purchases add to total expenditure directly through G in C+I+G+(XM). • Taxes reduce C. Depending on how much spending & taxing G may or Y. • Because they work indirectly via C, multipliers for tax changes are more complicated than multipliers for G. Fiscal Policy - G vs. T Multipliers Y Y • MultiplierGMultiplier G T ,T work indirectly by first changing Yd and then changing C. Since some Yd affects S rather than C, a $1 tax cut doesn’t pack as much punch as $1 of G. • If G & T by equal amounts, the effects don’t cancel out. Instead, Yeqm on AD side . If G and T by equal amounts, Yeqm level on AD side . • Fiscal policies that keep deficit the same (G = T) don’t necessarily keep AD the same. Besides, G=T won't crowd out I. Expansionary Fiscal Policy • Assuming P level is fixed, 3 options to raise GDP in the event of a recessionary gap: • i) G, ii) T or iii) Transfer Payments. e.g.) If YF=$7000, the economy is at recessionary gap w/ YE=$6000. If the Multiplier is 2.5, you can either i) G, ii) T, iii) Transfer Payments or iv) some combination of i) through iii) by only $400 to eliminate the recessionary gap. Contractionary Fiscal Policy • If inflationary gap, 3 options: • i) G, ii) T, iii) Transfer Payments or iv) some combination of i) through iii). • But if the economy is approximately at YF, this could rather cause unemployment. Gov’t Spending or Tax? • Any combo of G and T that produces the same AD, leads to the same Y and p. • Whether to G/T depends on how large a public sector policymakers want. • Advocates of big gov’t seek to AD thru G (to cure recession) and AD thru T (to cure inflation). • Advocates of small gov’t seek to AD by T and AD thru G. Why Balance the Budget? • Crowding Out Effect: G crowds out I i.e.) GT0 gov’t borrowing bank's credit to gov't i (cost of borrowing) I • (GT)ILR Growth. • G by bond sale isn't always preferred to G through T, b/c G by bond sale may lead to crowding-out of I. Should Government Intervene? • Liberal: pro-intervention, discretionary stabilization, coarse tuning is good enough. In the presence of long lags, attempts at stabilizing the economy can actually destabilize it. Democrat platform. • Conservative: min government intervention, automatic stabilizer () through fixed rules, criticize lags and uncertainties of stabilization policy, both fiscal and monetary. Republican platform Should Gov’t Intervene? (cont’d) • Automatic Stabilizer: automatically serves to support AD when it would otherwise sag and to hold down AD when it would otherwise surge ahead. reduces sensitivity to shocks. • e.g.) income tax, unemployment insurance, etc. multiplier. Banking & Monetary Policy • Definition of Money – Medium of Exchange – Unit of Account – Store of Value • Evolution of Money – Barter System: double coincidence of wants. – Commodity Money: intrinsic value (G&S coins) – Fiat Money: no intrinsic value, but backed • i) fully by gold & silver of equal value held in the issuer’s vault (full-bodied paper money) • ii) partially by gold & silver (19C bank notes) • iii) only by confidence (present day) Measuring Quantity of Money • M1 (Completely liquid) = Currency + Checkable Deposit balances in banks and savings institutions • M2 (liquid < M1) = M1 + Savings Account balances + shares in MMMF + small time deposits (CD) • M3 = M2 + large time deposits (CD) • Near Moneys: Liquid assets that are close substitutes for money, but not included in MS (e.g. short-term government bonds) – Liquidity refers to the ease w/ which it can be Money & K Markets and Banking • Money Market: Short-term, highly-liquid debt securities • Capital Market: Long-term debts & stocks • Fractional Reserve Banking: min reserve ratio required in the vault, while bank can – pursue profit by accepting deposits @ low i, but charge high i to loans. – have discretion over Ms. – be exposed to runs. • Bank Regulation – Deposit Insurance: e.g. FDIC Bank’s Balance Sheet Assets Liabilities & Net Worth Assets Liabilities Reserves @20% RR $ 1,000,000 Checking Deposits $ 5,000,000 Loans Outstanding 4500000 (4000000+N.W.) Total $ 55,000,000 Addendum: Bank Reserves Net Worth (=Accounting convention for d Actual Reserves $ 1,000,000 Stockholder's equity $ 500,000 Required Reserves $ 1,000,000 Excess Reserves $ - Total $ 5,500,000 Federal Reserve System Commercial Banks Federal Reserve Assets Liabilities Assets Liabilities Reserves 100 mil 4, T-Bills 100 mil 100 Bank Reserves mil T-Bills -100 mil 2, 1, buys/receives/collects pays/owes 3, Addendum: Changes in Reserves 100 Actual Reserves mil No Change Assume the bank already met RR before this transaction. Required Reserves 100 Excess Reserves mil Open Market Operation & Fed Balance Sheet • Fed buys U.S. gov’t securities. pays by creating new bank reserves w/ Fed. Ms (monetary expansion through money multiplier) • Fed sells U.S. gov’t securities. collects by reducing bank reserves w/ Fed. Ms Multi-Rounds of Banking & Money Creation Running Sums Reserves @20% Lent Out Reserves @20% Deposits Loans $ 20,000 $ 80,000 $ 20,000 $ 100,000 $ 80,000 $ 16,000 $ 64,000 $ 36,000 $ 180,000 $ 144,000 $ 12,800 $ 51,200 $ 48,800 $ 244,000 $ 195,200 $ 10,240 $ 40,960 $ 59,240 $ 295,200 $ 236,160 $ 8,192 $ 32,768 $ 67,232 $ 336,160 $ 268,928 continued continued continued continued continued $ 100,000 $ 500,000 $ 400,000 Multi-Rounds of Banking & Money Creation - continued D D0 1 R R R R 1 1 1 2 3 D 0 $100,000 $500,000, 1 R 1 (1 m) 1 .8 where m required reserve ratio L L0 1 R R R R 1 1 1 2 3 L 0 $80,000 $400,000 1 R 1 (1 m) 1 .8 D0 (1 R) R D0 (1 R) 1 R R R R 2 3 D0 , or D L $100,000 1 R Multiple Rounds of Money Creation • The chain of deposit creation ends only when there are no more excess reserves to be loaned out. (when the initial deposit is exhausted in loans.) • Since balance sheets must balance, the sum of all newly created assets (reserves + loans) must equal the sum of all newly created liabilities Oversimplified Deposit Multiplier 1 1 Deposit Re serve Re serve m 1 R • Restrictive Assumptions – Every recipient of cash must redeposit the cash into another bank rather than hold it. – Every bank must hold reserves no larger than the legal minimum. Need for Monetary Policy • During a recession, banks would Ms by excess reserves. Such a contraction of Ms would aggravate recession. • Banks will want to squeeze the max possible Ms out of cash reserves by keeping their reserves at the bare min when D for bank loans is buoyant, are high, and secure I opportunities abound. • During an economic boom, banks Ms, adding undesirable inflationary momentum to the boom. Need for Monetary Policy - continued • Bringing the money into analysis sheds a new light to explaining the biz cycle. – Inflationary gap: not due to exogenous I, but due to Ms money multiplier/ money illusion AD . – T (Fiscal) or i (Monetary) C & I AD . How Fed Controls Money Supply • OMO, Bond Prices, and Interest Rates – Bond sale Pb Rf i, since T-bond yield ≈ Rf return (i). If bond yield is Rf, banks must pay at least bond yield to attract deposit and charge higher i on the loan. – OMO bond purchase/sale not only Ms/ Ms, but also i/i. How Fed Controls MS - cont’d • Discount Rate/Bank Rate – Fed lends to commercial bank in trouble. c- bank’s deposit account w/ Fed Ms. – Fed can influence banks’ borrowing by manipulating i on these loans discount rate. – In the U.S., Fed relies primarily on OMO. Discount rate is secondarily and passively used to keep it in line w/ market i. • Reserve Requirements – R.R./R.R. Ms/Ms. – Fed no longer uses R.R. as a weapon of monetary control. Currently, R.R. is 10%. Money Supply Mechanism • Ms = f(i, Fed policy): i Banks loans & deposits Ms (mitigateMs). • However, the Fed can shift this relationship between i and Ms by employing either OMO, discount rate, or R.R.. • Sensitivity of Ms to i is rather weak. (For policy purpose, fix Ms or i.) IS-LM Model for Yeqm & r* i (r) LM r* IS Y* M/P, Y, I Money Demand on LM Side Md or L f (Y , i ) kY hi M h Y i if L M LM k k k M i Y h h Money Demand on IS Side Y a b(Y T ) (c dr ) G IS curve ac G b d T r IS eqn 1 b 1 b 1 b 1 b IS-LM Equilibrium Condition IS LM : ac G b d k M 1 Y T hY h P 1 b 1 b 1 b 1 b Cagan’s Money Demand Function L mt pt ( pt 1 pt ) mt pt 1 pt 1 pt ( 1) pt mt pt 1 1 pt mt pt 1 1 1 1 1 pt 1 mt 1 pt 2 1 1 1 1 pt mt mt 1 pt 2 1 1 1 1 1 1 2 mt mt 1 2 mt 2 3 mt 3 1 1 ( 1) ( 1) Interest Rates and Total Expenditure • i / i I & (XM) / I & (XM). (Since if i FLH C H ) e CF • I & (XM) / I & (XM) [C+I+G+(XM)] / [C+I+G+(XM)] Monetary Policy & AD • Fed targets @ stabilizing i by changing Ms. i Ms • Fed Policy Ms (where Md is fixed) &i I C+I+G+(X-M) Y • I C AD Ms Ms Multiplier Money and Price Level • Fiscal Policy: directly AD Firms Q (Output) P level mitigated Y • Monetary policy: Fed Ms i I AD P level mitigated Y • Fed Policy Ms (where Md is fixed) & i I C+I+G+(X-M) Y and P Two Reasons for Down-sloping AD Curve Revisited • PH Storage Value/PP of M & b mitigates C / (XM) AD. • PH or Avg transaction money cost Nominal GDP Md @ r given. • With Ms , Md i (the price of borrowing money) I /(XM) AD. • Now, the explanation is complete with C+I+(X-M) AD. Ms Shift in Broad Context • Although Ms = f(Fed Policy, i), Ms shift by i is not the immediate result of the Fed's monetary policy, but rather caused by the reaction of the commercial banks to the increase in i, - i.e.) i = f(Ms), which must clearly be distinguished from the increase in Ms by Fed's bond buyback. However, since people would rather not borrow at higher i, and rather keep their money in the bank, the intent of the commercial banks are partially cancelled. Ms Shift in Broad Context - cont’d – When Md, there's a natural pressure on i to . – i0 increases to i0' and Ms0 shifts out to Ms1. - i.e.) Ms = f(i). – This i-induced Ms shift is not by Fed, but by commercial banks. (Normally, Fed does it, but then Ms i - i.e.) i = f(Ms). When Fed does that, it's b/c Fed wants to fight the recession, so that Ms i concurs with the Fed's intent. In such a case, Md is assumed fixed.) – Eventually, this will be the new eqm. i Ms0 Ms1 What woul've been i1 if i were allowed to float. B/c Md may as transaction Md w/ Y, Ms cannot remain fixed if the target is to control i. i target Md1 M0 M1 Md0 M Fed’s Choice of Policy Target - continued i What would've been i1 if Ms were allowed to float. i1 (3) (2) Md shifts out as transaction Md w/ Y. Md1 i0 What would've been M1 if Ms were allowed to float. (1) M target Md2 Fed’s Choice of Policy Target i Ms0 Ms1 What woul've been i1 if i were allowed to float. B/c Md may as transaction Md w/ Y, Ms cannot remain fixed if the target is to control i. i target Md1 M0 M1 Md0 M Monetarism: Quantity Theory of Money • Equation of Exchange: PY=VM • Velocity: No. of times per year that an average dollar is spent on goods and services – If V is constant, Equation of Exchange can be used to determine nominal GDP. (Much simpler than the Keynesian Income- Expenditure model) Velocity from Equation of Exchange Total Value of Monetary Transations V Total Money Stock No min al Output (or GDP) M PY M How to Apply Velocity to Economic Planning • Log Transform the Equation of Exchange. Mt Vt Pt Yt M t 1 Vt 1 Pt 1 Yt 1 • Take the Natural Log on both sides. Mt Vt Pt Yt ln ln M t 1 Vt 1 Pt 1 Yt 1 Mt Vt Pt Yt ln ln ln ln M t 1 Vt 1 Pt 1 Yt 1 Log Transform - continued • By the properties of the logarithm ln M t ln M t 1 ln Vt ln Vt 1 ln Pt ln Pt 1 ln Yt ln Yt 1 %M %V %P %Y • If V is constant, i.e.) %V 0 , then Equation of Exchange can be used to determine % in nominal GDP. How much Ms has to be in/decreased. %M 0 %P %Y Velocity • In reality V is not constant at least in SR. • V1 (V of M1) is not constant in LR. • V2 (V of M2) is closer to constant, but not always. • V is a variable, not constant. Determinants of V: Monthly Pay Cycle Annual Income V Av g Cash Balance $24,000 ($2,500 $500) / 2 $24,000 16 $1,500 Determinant of V: Biweekly Pay Cycle Annual Income V Avg Cash Balance $24,000 24 $1,000 Determinant of Velocity • Efficiency of the payments mechanism – use of credit cards, use of wire transferetc. requires lower cash balances V. • interest rate – The higher the i, the lower the money holding. V. – However, this undermines the quantity theory b/c expansionary monetary policy (M) i V (counteracting M*V) mitigated. • Expected rate of inflation – High purchasing power money (PGDPMd) money holdings Quantity Theory of Money Modernized • V is predictable. – Study determinants of money growth and V predict growth rate () of nominal GDP. – Given understanding of V and control over Ms control over nominal GDP. • Keynesian: Money affects first i I AD (C+I+G+X-M) real GDP (Y). • Monetarist: Money affects i Ms & Md AD (MV) nominal GDP (PY). Time Series Forecasting Model p Yt 0 i Yt i t i 1 Deriving Time Series Model Yt 0 1Yt 1 t Yt 1 0 1Yt 2 t 1 Yt 0 1 [ 0 1Yt 2 t 1 ] t 0 0 1 Y 2 1 t2 1 t 1 t i * Y i 1 t i 1 t j j j 0 Random Walk in Time Series (1 1 L)Yt 0 t If (1 1 L) 0, 1 1 Random Walk dp(t ) dt dB(t ) Brownian Motion Regression Forecasting Model k Y 0 i Xi i 1 Compounding FV PV PV (1 r ) PV (1 r ) 2 PV (1 r ) n n PV (1 r ) i i0 Compounding m times for n years r mn Fn P1 m In the limit where m r mn lim P1 m m where 1 mn lim 1 e m m and log e X ln X Instantaneous Growth Rate X t X 0e gt ln X t ln X 0 gt ln X t 1 ln X 0 g (t 1) Xt ln ln X t ln X t 1 g X t 1 Net Growth Rate X dX (t ) 1 g X dt X 1 dX (t ) d log X d log X X , X dt dX dt dX (t ) where X X t X t 1 dt

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