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 PSRAD 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

Y

X

Opportunity Cost, Comparative Advantage & Int’l Trade

• France Germany

• Wine50 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 DistortionP

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

skfk

SSinkksf

kksfkik

LIiksfsyi

whereiysickf

kfyLKFLY

/*)(/*

**)(0

)(

/&)(

,)1()(

)()1,/(/

Business Cycle: InflationPSRAD LRAS

SRAD

P

SRAS LRAD Y Y

Business Cycle: Recession

PBoom

Range of Accelerated Inflation

Recovery Contraction/Stagnation

Recession UnemploymentTrough

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)

• S I = X M

• 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 = 1C+I+G+(X-M)

P C+u = bY+a, whereb = MPC < 1 and

P u = I+G+(X-M)

45 Y* Y*' Y(GDP)

Effect of Price & AD CurveP

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)

• (5)b

MXGIbTaY

1

)(

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 - continuedExpenditure

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 GapExpenditure 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 ConsumptionExpenditure

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

• (1)

• Suppose any of the variables in the numerator increases by 1 unit:

• (2)

Y = (1)–(2) =

b

MXGIbTaY

1

)(

b

MXGIbTaY

1

1)(

b

MXGIbTa

1

1)(

b

MXGIbTa

1

)(

b1

1

Four Possible States of the EconomyP 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

• is sloped positively, because producers are motivated by (profit), where

.

),,,,,( techMPLMPKnpfQYAS AS

QrwQpTCTR *)(*

)( rKwLpQ

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.

i.e.)

• Wages account for more than 70% of all inputs.

• If wAS (AS shifts in.)

• If wAS (AS shifts out.)

QrwQp *)(*

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

0)(

,)(

Q

TCTR

Q

where

Q

TC

Q

Qrwrwp

Q

pQ

Q

TR

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

PH (X-M) & MPC , prices will also rise. This will reduce net exports

(assuming no change in nominal e) 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.

)1(

1

MPC

)(, fh rrfewhereeiff

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

MPC

MPC

b

bYYY

b

MXGITbaY

b

MXGIbTaY

MXGIbTaYb

MXGIbTabYY

MXGIbTbYa

MXGITYbaY

11'

1

)()1$('

1

)(

)()1(

)(

)(

)(][

Variable Tax Multiplier

)1(1

1

)1(1

1$'

)1(1

1$)('

)1(1

)(

)()1(

MPCbYYY

b

MXGIaY

b

MXGIaY

MXGIYbaY

YTLet

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• MultiplierGMultiplier , 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.

T

Y

G

Y

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 converted into cash

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 Examination– Minimum Required Reserves

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 discrepency)

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 Bank Reserves100 mil

T-Bills -100 mil 2, buys/receives/collects1, pays/owes 3,

Addendum: Changes in Reserves

Actual Reserves100 mil

Required ReservesNo Change Assume the bank already met RR before this transaction.

Excess Reserves100 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

000,100$,1

)1(1)1(

000,400$000,80$8.1

1

)1(1

1

1

11

,000,500$000,100$8.1

1

)1(1

1

1

11

0032

0

032

0

032

0

LDorDR

RDRRRRRDR

mL

RRRRRLL

ratioreserverequiredmwhere

mD

RRRRRDD

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

• 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.

serveR

servem

Deposit Re1

1Re

1

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

h

MY

h

ki

LMMLifik

h

k

MY

hikYiYfLorMd

),(

Money Demand on IS Side

eqnISrb

dT

b

b

b

G

b

ca

curveISGdrcTYbaY

1111

)()(

IS-LM Equilibrium Condition

Ph

MY

h

k

b

dT

b

b

b

G

b

caY

LMIS

1

1111

:

Cagan’s Money Demand Function

33

2

221

21

211

11

11

1

)1()1(1

1

1

1

11

1

11

1

11

1

11

1

1

)1(

)(

tttt

tttt

ttt

tttt

t

ttttt

tttt

mmmm

pmmp

pmp

pmpm

p

ppppm

pppmL

Interest Rates and Total Expenditure

• i / i I & (XM) / I & (XM). (Since if i FLH )

I & (XM) / I & (XM) [C+I+G+(XM)] / [C+I+G+(XM)]

eC

C

F

H

Monetary Policy & AD• Fed targets @ stabilizing i by changing Ms.

• Fed Policy Ms (where Md is fixed) & i I C+I+G+(X-M) Y

• AD Multiplier

Ms

i

Ms

I

Ms

C

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 , Md i (the price of borrowing money) I /(XM) AD.

• Now, the explanation is complete with C+I+(X-M) AD.

sM

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 cannotremain fixed if the target is to control i.i target

Md1

M0 M1 Md0 M

Fed’s Choice of Policy Target - continued

iWhat would've been i1 if Ms were allowed to float.

i1

(3) (2) Md shifts out as transactionMd w/ Y . Md1

i0What 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 cannotremain 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

M

PYM

GDPorOutputalNo

StockMoneyTotal

sTransationMonetaryofValueTotalV

)(min

How to Apply Velocity to Economic Planning

• Log Transform the Equation of Exchange.

• Take the Natural Log on both sides.

1111

t

t

t

t

t

t

t

t

Y

Y

P

P

V

V

M

M

1111

1111

lnlnlnln

lnln

t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

t

Y

Y

P

P

V

V

M

M

Y

Y

P

P

V

V

M

M

Log Transform - continued

• By the properties of the logarithm

• If V is constant, i.e.) , then Equation of Exchange can be used to determine % in nominal GDP. How much Ms has to be in/decreased.

YPVM

YYPPVVMM tttttttt

%%%%

lnlnlnlnlnlnlnln 1111

0% V

YPM %%0%

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

16500,1$

000,24$

2/)500$500,2($

000,24$

BalanceCashAvg

IncomeAnnualV

Determinant of V: Biweekly Pay Cycle

24000,1$

000,24$

BalanceCashAvg

IncomeAnnualV

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 V can meet Md, where GDP = Nominal Y.

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

tit

p

iit YY

10

Deriving Time Series Model

i

jjt

jit

i

ttt

tttt

ttt

ttt

Y

Y

YY

YY

YY

011

1122

1100

121010

12101

110

*

][

Random Walk in Time Series

MotionBrowniantdBdttdp

WalkRandomLIf

YL tt

)()(

1,0)1(

)1(

11

01

Regression Forecasting Model

i

k

ii XY

10

Compounding

n

i

i

n

rPV

rPVrPVrPVPV

FV

0

2

)1(

)1()1()1(

Compounding m times for n years

mn

n m

rPF

1

In the limit where m

mn

m m

rP

1lim

where

em

mn

m

11lim

and

XXe lnlog

Instantaneous Growth Rate

gXXX

X

tgXX

gtXX

eXX

ttt

t

t

t

gtt

11

01

0

0

lnlnln

)1(lnln

lnln

Net Growth Rate

1

)(

,loglog)(1

1)(

tt XXXdt

tdXwhere

dt

Xd

dX

Xd

dt

tdX

XX

Xdt

tdX

X

Xg