Econ 302 Exercise Set 6 Answer Outlines

Course Instructor: Leigh Tesfatsion
Date Assigned: 18 April 1996


                        ANSWER OUTLINE

SIXTH TAKE-HOME EXERCISE SET [14 Points Total]       L. Tesfatsion
DUE DATE:  Tuesday, April 30, 9:30 A.M.         Econ 302/Spring 96
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EXERCISE 6.1  [6 Points Total].  This exercise extends the
previously assigned "balanced budget" exercise 3.4 on the Third
Exercise Set.  Consider an economy described by the following six
relations, where D denotes an exogenously set target level for
the government budget deficit:
     (1) Y = C + I + G + NE
     (2) C = a + b[1-t]Y
     (3) I = e - dR
     (4) NE = g - mY - nR
     (5) M/P = kY - hR
     (6) G - tY = D
Period T endogenous variables:  Y, C, I, NE, R, G
Exogenous variables (positive): a,b,t,e,d,g,m,n,M,P,k,h,D,
                                with t,b less than 1

Part A: Define what is meant by an IS curve for the economy
described by relations (1) thru (6).  Derive an algebraic
expression for the IS curve for this economy and illustrate this
curve graphically.  Determine whether or not an increase in D
affects the IS curve, and illustrate any effects graphically.

Part B: Define what is meant by an LM curve for the economy
described by relations (1) thru (6).  Derive an algebraic
expression for the LM curve for this economy and illustrate this
curve graphically.  Determine whether or not an increase in D
affects the LM curve, and illustrate any effects graphically.

Part C:  Using Parts A and B, graphically determine how an
increase in D affects the IS-LM equilibrium values Y^o and R^o
for GDP Y and the real interest rate R.  Provide an economic
interpretation for your findings.  In particular, do your
findings suggest that an increase in D (i.e., an increase in the
size of the government budget deficit) has negative short-run
implications?  negative long-run implications?  Explain
carefully. ------------------------------------------------------

EXERCISE 6.2  [4 Points Total]. Hall and Taylor, Chapter 9,
ANALYTICAL exercise 9, page 262. #Be sure to justify your
assertions and label all graphs carefully.#
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EXERCISE 6.3 [4 Points Total]. Hall and Taylor, Chapter 9,
MACROSOLVE exercise 5, page 264. #Be sure to justify your
assertions and include with your answer any MacroSolve data
referred to in your answer#.
    NOTE: The "price shock" referred to in part b is a term Z(T)
appended to the usual expectations augmented Phillips curve that
is treated as an exogenous variable (a disturbance to the economy
from "outside"):
     INF(T,T+1) = INF^e(T,T+1)  + [Y(T)-Y*(T)]/Y*(T)  +   Z(T) .
The effect of Z(T) is to cause a sudden change in P(T+1) not due
to either inflationary expectations or GDP gap pressures.
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ANSWER OUTLINE FOR EXERCISE 6.1: [6 Points Total]

ANSWER OUTLINE FOR PART A: [2 Points]

     The IS Curve shows all combinations of the real interest
rate R and real GDP Y that are consistent with product market
equilibrium, in the sense that demand for newly produced goods
and services equals supply and all expectations are fulfilled.

     For the economy at hand, the relations dealing with the
product market are relations (1), (2), (3), (4), and (6)---that
is, all relations except the money market relation (5).  As
explained in HT7, these relations can be interpreted as the
partially reduced down expressions for demand, supply, and
equilibrium relations in the product market.  The only difference
between the product market relations for the HT7 economy and the
product market relations for the economy at hand is relation (6),
which specifies that G is an endogenous variable for the economy
at hand.  [REMARK:  Specifically, G takes on whatever value is
necessary in order to guarantee that the current government
budget deficit stays at the exogenously given target level D.
Note that the tax rate t is still given as an exogenous variable,
but of course the amount tY of total tax **revenues** is
determined endogenously.]

     The IS curve is obtained from the product market relations
(1)-(4) and (6) as follows.

-------------
#Step 1#:  Reduce down relations (1)-(4) and (6) to one equation
in the two unknowns R and Y by substituting out for the other
endogenous variables C, I, G, and NE that appear in these relations.

    Y = (a + b[1-t]Y) + (e - dR) + (D + tY) + (g - mY - nR)
-------------

#Step 2#: Collect terms in Y and in R

    (1 - b[1-t] - t + m) x Y  =  (a + e + D + g)   -  (d+n) x R

or equivalently

    (d+n) x R   =   (a + e + D + g)  -  (1-b[1-t] - t + m) x Y

                =   (a + e + D + g)  -  ([1-t] - b[1-t] + m) x Y

                =   (a + e + D + g)  -  ([1-t][1-b] + m) x Y
                 
--------------
#Step 3#: Solve for R as a function of Y (slope-intercept form)
.ls 2

             (a + e + D + g)          ([1-t][1-b] + m)
       R  =  ---------------     -   -----------------  Y
                  (d+n)                     (d+n)
                                 
              ...............    .....................
              R-Intercept (+)       Slope dR/dY (-)
                                
---------------

#Graphical Illustration#:

         R
         |
(a+e+D+g)|                 
---------.is
  (d+n)  |    is
         |         is                    
         |              is <-------------IS Curve for any given D
         |                   is
         |                        is
         |                            is
         |                                  is
         |-----------------------------------------------   Y
         0


  IS Curve with positive R-intercept and negative slope dR/dY.


#Effects of an Increase in D#:

     The exogenous target deficit level D enters into the
numerator of the R-intercept for the IS curve with a positive
sign, but it does not enter into the expression for the slope of
the IS curve.  Consequently, an increase in D increases the
R-intercept without changing the slope.  It follows that the IS
curve undergoes a parallel **upward** shift, so that the new IS
curve yields a higher level of R for each level of Y.  This
upward shift of the IS curve should be graphically depicted.


ANSWER OUTLINE FOR PART B: [2 Points]

     The LM Curve shows all combinations of the real interest
rate R and real GDP Y that are consistent with money market
equilibrium, in the sense that the demand for money equals the
supply of money and all expectations are fulfilled.

     For the economy at hand, the only relation dealing with the
money market is relation (5). As explained in HT7, this relation
can be interpreted as the partially reduced down expression for
demand, supply, and equilibrium relations in the money market.
The only difference between the money market relations for the
HT7 economy and the money market relation for the economy at hand
is that the expected inflation rate does not enter into this
money market relation.  (Money demand is assumed to depend on the
real interest rate R rather than the nominal interest rate R+INF.)

     The LM curve is obtained from the money market relation
(5) as follows.

-------------
#Step 1#:  Relation (5) is already one relation in the two
endogenous variables of interest, Y and R; no other endogenous
variables appear in relation (5).

-------------

#Step 2#: Collect terms in Y and in R

    hR  =  - M/P  +  kY

--------------

#Step 3#: Solve for R as a function of Y (slope-intercept form)


       R   =      - M/hP           +   (k/h)    x   Y
              ...............   ...............
              R-Intercept (-)   Slope dR/dY (+)

---------------
.ls 2
#Graphical Illustration#:

         R
         |
         |
         |                                      lm
         |                                   lm
         |                                lm
         |                             lm
         |                          lm
         |                       lm
         |                    lm
         |                 lm
         |--------------lm---------------------------------   Y
         0          lm
         |       lm
         |    lm
   -M/hP . lm
         |


  LM Curve with negative R-intercept and positive slope dR/dY.


#Effects of an Increase in D#:

     The exogenous target deficit level D does not appear
anywhere in the algebraic expression for the LM curve.  It
follows that the placement of the LM curve is **unaffected** by
changes in D.


ANSWER OUTLINE FOR PART C: [2 Points]

     From Part A and Part B, above, an increase in D shifts
upward the IS curve but leaves the LM curve unchanged.  It
follows that the IS-LM equilibrium values for Y and R in the
current period are **both increased** as a result of this
increase in D.  This should be illustrated graphically.

#Economic Interpretation#: 

    The increase in the IS-LM equilibrium level for real GDP Y in
the current period T implies an increase in employment (a reduction
in unemployment) in period T, which is a good short-run implication.

     However, the increase in the IS-LM equilibrium value for the
real interest rate R decreases the period T investment level
I(T).  Economic agents are now buying more government bonds and
putting less money into capital investment.  [Recall that an
increase in the government budget deficit will generally be
financed by an increase in DB, i.e., an increase in the rate at
which **newly** issued bonds are being sold to the HC private
sector and to ROW in exchange for money.]

     Consequently, it follows from the identity

   K(T+1) = K(T) + I(T) - (Period T Capital Depreciation Expenditure)

that the capital stock K(T+1) in the next period T+1 will be
lower than it otherwise would have been.  This in turn implies
that potential GDP in period T+1,

     Y*(T+1)  =  F(N*(T+1),K(T+1),A) ,

will be lower than it otherwise would have been, a bad longer-run
implication for the economy.

     This bad longer-run implication is the kind of prediction
made by those who worry about growing government budget deficits.
Note, however, that this negative impact on private investment
could in principle be prevented by an appropriately accommodating
monetary policy---an increase in the money supply M engineered by
the Fed via an open market operation in which **existing** bonds
currently in the hands of the private sector are purchased from
the private sector in exchange for money.  This increase in M could
shift down the LM curve to prevent the rise in R.  If the economy
is currently in a state such that Y is less than Y*, then these
accommodating downward shifts in the LM curve might be able to
prevent rises in the real interest rate without causing inflationary
pressures---that is, without causing Y to rise above Y*.

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ANSWER OUTLINE FOR EXERCISE 6.2: [4 points total]

When the Reagan administration came into power in 1981, three of
its primary objectives were to reduce inflation, lower taxes, and
increase defense spending.

ANSWER OUTLINE FOR PART A: [2 Points]  Explain why the achievement
of all three goals required an extremely restrictive monetary policy.

     Lowering income tax rates and increasing government defense
expenditures are each **expansionary** fiscal policies in the
sense that they rotate and shift upwards the IS curve, respectively,
resulting in a higher IS-LM equilibrium level for real GDP Y.  On
the other hand, to keep inflation in check, it follows from a
Phillips curve argument that it is generally necessary to ensure
that real GDP Y stays below or at potential real GDP Y*.

     As seen in Figure 9-12 in HT Chapter 9, the U.S. economy was
close to potential GDP when Reagan was inaugurated in 1981.  Thus,
to reduce the inflation rate while at the same time cutting taxes
and increasing defense expenditures required an extremely restrictive
monetary policy to ensure that Y did not rise above Y*.

     In actuality, attempts were made by the Fed in 1981-2 to keep
the **growth rate** of the money supply in check while the Reagan
Administration increased the **growth rate** of defense expenditures
and pushed through changes in the tax code that resulted in deep
cuts in income tax rates across all income brackets.  But the
general qualitative implications of these policy choices can be
captured within the HT8 IS-LM model by considering the combined
effects of a sharp decrease in the money supply M, a sharp decrease
in the tax rate t, and a a sharp increase in the level of government
expenditures G, starting from a position of internal balance (IS=LM
and Y=Y*) with a high but correctly predicted inflation rate (INF = INF^e).

     The big decrease in t rotates **up** the IS curve (higher R for
each Y) and the big increase in G shifts **up** the IS curve (higher
R for each Y); the LM curve is unaffected by the decrease in t
and the increase in G.  Thus the new IS-LM equilibrium point
occurs at a level of Y that is sharply higher than Y*, so a
large positive GDP gap opens up.  It follows from the form of the
expectations-augmented Phillips curve that the inflation rate
will then increase unless there is an appropriately large
offsetting **decrease** in the money supply M to push the LM
curve **up** (higher R for each Y).  Pushing the LM curve up
means that the IS-LM intersection point is pushed back to a lower
Y level; but note that the real interest rate is then at an even
higher level than before.  

     ADDITIONAL REMARKS:  Hall and Taylor argue (pages 558-559)
that there was a monetary policy error on the part of the Fed in
1982: they argue that the monetary policy followed by the Fed was
too restrictive and resulted in unnecessarily high interest rates
and an unnecessarily severe recession.  You may want to take a
look at this discussion; see also the empirical data reported in
HT Chapter 13, in particular figure 13-5.
     Many Democrats have argued that it was the Reagan Administration's
sharply expansionary fiscal policy in 1981 that was the primary
policy mistake because this is what forced the Fed into a restrictive
monetary policy stance.  The short-run outcome was the severe
1981-82 recession and the longer-run outcome was the twin deficit
problem---the simultaneous opening up of a large and persistent
government budget deficit together with a large and persistent
current account deficit.  (Why?)  Republicans counter that the
primary policy mistake was the failure of the Democratically
controlled Congress to enact other types of spending cuts to
offset the effects of the reduced tax rates and increased defense
expenditures.


ANSWER OUTLINE FOR PART B: [2 Points]  Could the same disinflation
have been achieved with a less restrictive monetary policy and a
more restrictive fiscal policy?  If not, why not? If so, explain
how the following variables would have been affected during the
1981-1984 period: output, inflation, interest rates, consumption,
investment, the trade deficit, and the government budget deficit.

     Yes, according to the basic HT8 IS-LM model.  By reducing
the extent of the increase in G while at the same time reducing
the extent of the decrease in t and reducing the extent of the
decrease in M, the **same** real GDP level Y could be achieved
(hence the same rate of disinflation) at a **lower** real interest
rate.  Comparing the effects of this milder course of policy
action relative to the initial sharp increase in G and sharp
decreases in t and M, one finds that:

   Output (real GDP) would be the **same**;

   Inflation would be the **same** because the real GDP gap
       would be the same;

   The real interest rate would be **lower**;

   Consumption would be **lower** due to higher t at the same
       level of Y;

   Investment would be **higher** due to lower R at the same
       level of Y;

   The trade deficit (Imports-Exports) would be **smaller** because
       of the lower R and the same level of Y (hence the higher
       level of exports with unchanged imports);

   The government budget deficit G-tY would be **smaller** due to
       higher t and lower G at the same level of Y.

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ANSWER OUTLINE FOR MACROSOLVE EXERCISE 6.3: [4 Points Total]

**NOTE**** See the closed reserve version of this answer key
(Reading Room, Heady 368) for the MacroSolve data figures and
tables that supports the answer outlines given below.  Note also
that, in all MacroSolve exercises with the AD/PA, Closed Econ
model, the default parameter settings for M and P are M=900 and
P=1.  Also, the economy begins in internal balance and stays in
internal balance at Y=Y*=6000, where potential GDP Y* remains
constant at 6000 in each time period.

Suppose the Fed adopts a policy to fight inflation.  What should
it do in response to an increase in government expenditure?
Select the "AD/PA, Closed Econ" model and increase government
spending by $50 billion.

ANSWER OUTLINE FOR PART A: [2 Points]  What change in the money
supply is required to maintain stability of the price level?

     Let us first examine what happens when G is increased by $50
billion in period 1 with **no** change in the money supply.  Data
generated for the resulting economy are presented in Table 1 and
graphically depicted in Figure 1.

     As seen during the dynamic display of Figure 1, the increase
in G by $50 billion in period 1 shifts **up** the IS curve
(higher R for each Y) in period 1 but does not affect the LM
curve in period 1.  Consequently, both Y and R increase in period
1.  Because the economy was originally in internal balance with
Y=Y*=6000, the increase in Y in period 1 opens up a positive GDP
gap in period 1 and puts upward pressure on the price level for
period 2 through the expectations-augmented Phillips curve.  As
seen in Table 1, the price level ultimately increases from its
original value of 1.0 to a final value of 1.03, attained when the
GDP gap once again is zero; and the LM curve has shifted up in
response to the increase in P.  Consequently, the new IS-LM
equilibrium is at the same Y level (Y=Y*=6000) but at a higher
real interest rate R.

     A cut of $25 billion in the money supply M in period 1, the
same period that G increases by $50 billion, shifts the LM curve
**up** (higher R for each Y) and just offsets the effects on Y
of the increase in G.  That is, as seen in Figure 2 and Table 2,
Y remains equal to Y*, implying that the GDP gap remains equal to
zero.  Consequently, there is no pressure on the price level to
change.  As seen in Figure 2, however, the cut in M in response
to the increase in G does result in a higher real interest rate R.

     The fact that a cut in M of $25 billion is needed to
maintain Y equal to Y*, and hence a constant price level,
subsequent to a $50 billion increase in G can be determined either
by trial and error or by doing an offsetting multiplier
calculation along the lines of the previously assigned MacroSolve
Exercise 1 (HT, p. 207) on the Fourth Exercise Set.


ANSWER OUTLINE FOR PART B: [2 Points]  Now suppose the economy
suffers a 5 percent price shock (as opposed to the increase in
government spending):

(*)  INF(0,1)  =  INF^e(0,1)  +  [Y(0) - Y*]/Y*   +   .05

How should you respond according to the inflation-fighting policy?
What is the impact of your response on output?  Are GDP fluctuations
larger or smaller?

     It follows from relation (*) above that the 5 percent price
shock at the end of period 0 (or equivalently, at the beginning
of period 1) increases the price level P(1) in period 1.  Thus,
the real money supply M/P(1) in period 1 is smaller and the LM
curve shifts **up** (higher R for each Y); the IS curve is not
directly affected by price shocks.  Consequently, IS-LM equilibrium
in period 1 is re-established at a smaller level of Y.  This
opens up a negative GDP gap which puts downward pressure on the
price level.

    The ultimate effects of the 5 percent price shock, assuming
no policy response, are seen in Figure 3 and Table 3.  Note, in
particular, from Figure 3, that the price level does not start to
decrease until period 3.

     **Cutting** the money supply M in period 1 shifts up the
LM curve even further, thus opening up an even larger negative
GDP gap and putting additional downward pressure on the price
level.  Consequently, the price level adjust back down more
quickly if M is cut.  See Figure 4 and Table 4, for example,
which depict what happens when M is cut by $50 in period 1.  Note
that P now starts to decrease in period 2.

     Nevertheless, this faster downward adjustment of the price
level due to a cut in M comes at the cost of greater volatility
in GDP, in the sense that Y undergoes a more negative change than
in Part A before finally returning once more to Y* as the price
level drops.  Note that Y in Figure 3/Table 3 drops only to 5867
whereas Y in Figure 4/Table 4 drops all the way down to 5773.

     Moreover, to the extent that M is cut, the price level will
fall to a **lower** level than its original default value P=1.
See Figure 4/Table 4, for example.

     The reason for this is that the 5 percent price shock shifts
up the LM curve but leaves the IS curve unaffected.  Consequently,
in order for internal balance to be reestablished, the LM curve
must return to its **original** position (so that the IS and LM
curves again intersect at Y=Y*).  But the LM curve will only
return to its original position if the real money supply M/P
returns to its original level---which is 900 under the MacroSolve
default values M=900 and P=1.  If M=900 is unchanged, this means
that P must return to its original default value P=1.  But if M
is decreased to 850, then P must decrease to 850/900 = 0.9444...
in order for the real money supply M/P = 850/P to again equal its
original value 900.