# Reocities

Document Sample

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

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
•                 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
P

P

Y        Y
P
Boom

Range of Accelerated Inflation

Recovery                  Contraction/
Stagnation
Recession  Unemployment
Trough
• 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
•   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 = YT
• 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
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

E"
P"

P                  E

E'
P
Y"      Y       Y'          Y
Simple Algebraic Eqm Income Determination

• Let C = a + bYd = a + b(YT)     (1)
• Y = C + I + G + (XM)            (2)
• Y = (a + bYd) + I + G + (XM)
= a  bT + bY + I + G + (XM) (3)
• (1b)Y = a  bT + I + G + (XM) (4)
•       a  bT  I  G  ( X  M ) (5)
Y
1 b
•   Y       C       I     G     XM
•   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
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
• 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=0k .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:
skdl becomes flatter.Multiplier)
i.e.) M = m(Y–T), where m = MPM
If mb, 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
= 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 wAS (AS shifts in.)
• If wAS (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 stockthrough 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,
•   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
• 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’
borrowingIY.
• 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
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.
also cuts the multiplier effect.
Fiscal Policy
• Fixed (lump-sum) Taxes: e.g.)
property taxes do not depend on Y
• Yd = YT  C  Expenditure
• Yd = YT  C  Expenditure
• Y  Yd  C = MPCYd
• 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 = YY = (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+(XM).
• 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
• MultiplierGMultiplier    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
. If G and T  by equal amounts, Yeqm
•  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
• Whether to G/T depends on how large a
public sector policymakers want.
G (to cure recession) and  AD thru T
(to cure inflation).
T and  AD thru G.
Why Balance the Budget?
• Crowding Out Effect: G crowds out I
i.e.) GT0  gov’t borrowing 
bank's credit to gov't  i (cost of
borrowing)  I
• (GT)ILR 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
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,
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,
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
– T (Fiscal) or i (Monetary)  C & I 
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 (mitigateMs).
• 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
ac   G    b     d
              T      r  IS eqn
1 b 1 b 1 b    1 b
IS-LM Equilibrium Condition

IS  LM :
ac 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 & (XM) / I & (XM).
(Since if i  FLH  C H           )
e
CF 
• I & (XM) /  I & (XM) 
[C+I+G+(XM)] / [C+I+G+(XM)]
• Fed targets @ stabilizing i by changing Ms.
i
 Ms

• Fed Policy        Ms (where Md is fixed)
&i     I    C+I+G+(X-M)  Y
 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
• PH  Storage Value/PP of M & b 
mitigates C / (XM)  AD.
• PH or Avg transaction money cost 
Nominal GDP  Md @ r given.
• With Ms , Md  i (the price of
borrowing money)  I /(XM) AD.
• Now, the explanation is complete with
• 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 transferetc. 
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 
(PGDPMd) 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 t2        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

i0
Compounding m times for n years

   r
mn

Fn  P1  
 m
In the limit where m

   r
mn

lim P1  
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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