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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)
•   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
 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(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
        Graphing AD Side Eqm
•   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
    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=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:
•    international trade (MCExpenditure
    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
• 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 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,
    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’
  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
  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.
• ADtptbtItADt+1  This
  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
  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.) 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
  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 (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)]
         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 / (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
  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 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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