Introduction to Macroeconomics

							Department of Economics                                                University of Pennsylvania


             Introduction to Macroeconomics
        ECON 002 – 218 & 219 (Departmental Honors)
                       Spring 2002

                2nd Midterm Exam Make-up Solutions
                                        April 1st, 2002

                            Instructor: Prof. John Knowles

                        (Teaching Assistant: Marco Airaudo)

Instructions:

       Answer all sections of this test. This is a 60 minute exam; 50 minutes have been assigned to
        questions. You have 10 minutes for review and prayer.

       Write all answers in the blue books provided. Show all work. Use diagrams where
        appropriate and label all diagrams carefully.

       Use blue or black ink pen. Pencils are allowed only if you need to draw a graph. Full credit
        will not be given if you just guess right.

       Write your name and your Recitation Instructor’s name in every blue book that you use.

       This exam is given under the rules of Penn’s Honor System.

       All bluebooks, blank or filled, must be handed in at the end of this exam. No blue books may
        be taken from the room.
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Note: the exam is not as long as you might think. You are supposed to write brief
but meaningful answers. Try to stick with the time recommendations at the
beginning of each question.

Question 1: inflation in the AS-AD model

Recommended time: 10 minutes (20 points)

The standard AS-AD framework is well suited to describe how inflation can arise in
general equilibrium.
   1) List and describe the two main types of inflation. How can inflation be a very
       persistent phenomenon (in other words, how can inflation spirals arise)? Describe
       accurately. 10 points
   2) Can we devise any kind of fiscal policy able to at least reduce such inflationary
       effects, for both types of inflation? What could be side effects of such policies on
       the government budget? 10 points

Answer

   1) They are demand-pull and cost-push inflation. If inflation is demand pull, then it
      could be persistent if fiscal shocks are persistent (ex: long lasting war). The self
      adjustment of AS would push inflation even higher, new increases in public
      expenditure occur, new adjustements..and so on. The self adjustment of AS is due
      to the equilibrium adjustment in the labor market. If inflation is cost-push, then
      inflation can be persistent if shocks to inputs costs are persistent. For instance the
      „70s oil crises. After each supply shift, the government follows expansionary
      fiscal policies to close output gaps, then new shocks occur and so on. Of course,
      the government might simply stay still and wait for the equilibrium adjustment of
      AS. However we know that AS rarely moves down by itself (sticky wages
      downward). So it seems that some fiscal action is needed. See graphs in lecture
      notes. We have the so called inflation spirals.
   2) Demand-pull inflation. Any time G goes up, the government might want to
      immediately increase taxes to bring AD back Is this a good policy? It depends. A
      side affect is that people (also voters) do not like tax increases, so government
      might be worried of outcomes of future elections if they do that. Cost-push
      inflation. Maybe some kind of supply side fiscal policy, such as corporate tax
      cuts. In that way, once the cost of inputs goes up (AS shift to the left), the
      government might want to subsidize production by lowering corporate taxes and
      capital gains taxes. AS (if the policy is effective) would shift to the right again.
      No big fiscal expansions would be needed. A side effect (as well known) is
      possible budget deficits.


Question 2: monetary policy

Recommended time: 15 minutes (30 points)
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Consider the following set up:
    Aggregate supply (AS) is perfectly flat;
    Let “r” be the real interest rate;
    Taxes are lump sum: T=70;
    C = 120-P + 0.9*DI;
    G = 70, NX = 0;
    I = 60 – 2.5*r;
    Money supply is: M = 50;
    Money demand is: M = 100 – 5*r;

Answer the following questions:
   1) Suppose that the output gap (the difference between full employment and
      equilibrium output) is 100. The Fed‟s target is to make the gap equal to zero.
      Should the Fed increase or decrease the money supply? By how much? Show
      your work. 15 points
   2) Suppose now that aggregate supply is upward sloping. Its function is: P = 50+Y.
           Would the policy you found at 1) be enough to close the output gap?
              Explain. 5 points
           Find the relationship between equilibrium output and the real interest rate
              in this new AD-AS set up. In other words you have to find an expression
              of Y* as a function of “r”. Hint: you need to get the function of AD first.
              10 points.

Answer

The answer to this question was shorter than you probably thought. You just had to use
the multiplier formula and a couple of steps in 1). To answer to 2), only a substitution
was necessary.

Part 1

Let‟s go by steps. What is the intuition? We know that AS is flat, meaning that the shift
of AD we need is equal to the gap (50). We want to use monetary policy to do that. We
know that investments are negatively affected by the interest rate “r” and that the interest
rate is negatively affected by the money supply. First get the general multiplier formula:

                 Y = (1/1-b)*(C+I+G)                                   (1)

Note that (1/1-b) = 10. Since we want to affect investments, it must be:

                                    Y = 10*I
Y must be 100, therefore I = 10. We need “I” to go up by 10 to close the gap. Using
the investment demand equation:

                                       I = -2.5*r
Department of Economics                                          University of Pennsylvania



Plug in I = 10, to get the necessary change in “r”: r = -4 (decrease by 4%).
Last step is to find by how much money supply has to increase in order to make “r” 4%
lower. From the money market equilibrium (money demand equal to money supply):

                                         100-5*r = 50

We do not even need to know what money supply is. So let‟s put a general value MS
instead of 50, such that 100-5*r = MS. This implies that:

                                         MS = -5*r

Plug in r = -4 to get MS = 20. Money supply has to increase by 20 in order to make
output gap equal to zero.

Note: there was no need to go through messy algebra or additional computation. The
point was to understand how the multiplier effect works. We had a similar exercise in one
of the past quizzes, though it was about fiscal policy.

Part 2

From part 1, the equation for AD is (just plug in numbers in (1) above)

                      Y = (1/1-0.9)*[120+70+60-0.9*70 – P – 2.5*r]
                                   =3130 – 10*P – 25*r

Write P as a function of Y:

                     P = 313 –2.5*r – 0.1*Y                        (2)

On equilibrium AD = AS, so just equate (2) to the AS function:

                                  313 –2.5* r – 0.1*Y = 50 + Y

Solve for Y as a function of r:


                                      Y = (263-2.5*r)/1.1

As expected, equilibrium output is negatively affected by the interest rate. The higher “r”,
the lower Y, and viceversa.
Department of Economics                                        University of Pennsylvania


Question 3: open market operations

Recommended time: 15 minutes (30 points)

There is an extra credit question here

An indirect way used by the Fed to control money supply is by open market operations.
Namely the Fed buys/sells bonds in exchange for some monetary aggregate in order to
affect the equilibrium interest rate. Bonds are basically promises by the Fed (or Treasury)
to pay back some known amount of money in the future for a given price today. Consider
the following set up:
     Bonds supply is vertical: B = 60;
     Let Pb be the price today of 1 bond promising to pay 100$ tomorrow;
     Bonds demand by consumer is: B = 150 – Pb
     Let R (the required reserve ratio) be 0.25 (25%)
     Let M be a monetary aggregate, including deposits held at commercial banks
     Only banks hold bonds
     People hold deposits at commercial banks
    1) What is the equilibrium price of the bond? What the related interest rate? You
        need to compute both of them. 10 points
    2) Suppose that the Fed buys $1 million worth of bonds. The Fed pays the purchase
        by increasing deposits held by commercial banks by $1 million. What is the
        quantitative change in the supply of M? 10 points
    3) Extra credit. Suppose that suddenly US residents become worried that the
        government would not be able to pay back its debt (namely its bond promises)
        and as a consequence that banks would not be able to give back deposits (since
        banks hold government bonds). How would the shape of bonds demand change
        with respect to the Pb? What could be an immediate policy the Fed should
        implement to reduce the risk of such “banking panics” (or sometimes “runs”)? 10
        points.

Answer

   1) Just equate bond supply and bond demand: 60 = 150 – Pb. Such that Pb = 90 and
      the interest rate is (100-90)/90. You were supposed to draw a graph for the
      bond market to make the argument clearer.
   2) Use the deposit multiplier: total change in deposits is equal to the initial change
      ($1 million) divided by the reserve ratio (0.25), therefore a total of $4 millions.
      This because of the fact that we are assuming that M includes deposits. As
      you know some aggregates do not.
   3) Since now there is some risk on bonds, banks will react more elastically to
      changes in the price of those. So the demand for bonds will become flatter, i.e. for
      small changes of the price Pb, the quantity demanded will change much more. In
      technical words, people require risk premia on debt. Second, if the risk of bank
      runs has to be reduced, the Fed should probably increase the R ratio such that
      depositors will feel that their money is safer even with default risk by the
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       Treasury. Of course doing this too late will not change the consumer perception of
       default risk.

Question 4: monetarism, quantity theory and monetary policy

Recommended time: 15 minutes (30 points)

Answer the following questions (answers are supposed to be brief but meaningful).

   a) What is the basic equation on which the quantity theory of money is based? What
      is it basically saying in terms of monetary policy?
   b) Monetary policies supported by either the Monetarist or the standard Keynesian
      economists can be distinguished by one main point. The former thought that the
      best policies should be “fixed rules, independent from the state of the economy”.
      The latter instead believed that policies had to be based on the state of the
      economy (so called “feedback rules”). Do you agree with such distinction?
      Briefly explain 5 points
   c) Though the quantity theory of money was very popular in the „80s, central banks
      (the Fed too) started to look at other monetary policy targets and tools from then
      on. Why? 5 points
   d) Would going back to money growth targeting be a good policy right now
      according to the recent studies by the Fed? Briefly explain. 5 points
   e) Can the ongoing introduction of new financial instruments for transactions in the
      market be a problem for such a policy? Briefly explain. 5 points
   f) Consider the two following facts: printing money is basically costless;
      expansionary monetary policy creates more output. If these facts are true, why do
      governments sometimes prefer expansionary fiscal policies (creating deficits) than
      expansionary monetary policies? 5 points.

Answer

   1) The basic equation is called the “equation of exchange”: M*V = P*Y. It basically
      states that if velocity is constant (or at least predictable), then by controlling the
      growth rate of money we can affect equilibrium nominal GDP. In the long run
      (since real GDP growth is almost zero, being stuck at the full employment level),
      money growth directly affects inflation (growth rate of P).
   2) You should quite agree for the following reasons. For what stated in 1), monetary
      policy should follow indeed fixed rules according to Monetarists. The equation of
      exchange in fact states that the Fed should control the growth rate of money to
      affect long run inflation, independently from what equilibrium output is.
      Keynesian economists, instead, always state that the interest rate should be cut
      (and then money supply expanded) if output is below full employment, and raised
      if above. They are then following feedback rules, since monetary actions are
      different according to the state of the economy.
   3) The reason is simple: velocity started to be difficult to predict due to high
      financial instability. If that was the case, indeed the effect of money growth on
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      inflation and GDP was much more difficult to assess. We might also say that in
      the same period money demand became more difficult to estimate too. So, also
      Keynesian economists were in trouble when trying to predict the effects of money
      supply on the interest rate. Both school started to look at other monetary tools,
      such as a direct interest rate target.
   4) It looks like that velocity is more stable and that money demand can be estimated
      more accurately again. If that is the case, controlling MS can be effective to
      control the interest rate.
   5) That will always be, no matter what school you believe in. If you are a
      Monetarist, indeed you will have to deal with highly unstable velocity, since
      people will probably switch to new media of exchange when available (credit
      cards and stuff like that). If you are a Keynesian too, since money demand is the
      first to suffer such innovations. Why holding non interest bearing notes and coins
      when we can use cards linked to interest bearing deposits? Consider also the fact
      that transaction costs are diminishing and that credit cards services are improving.
   6) One reason: inflation. If the economy grows at a slower rate than the amount of
      money injected, and if velocity is roughly constant, the price level has to increase.
      This is clear from M*V = P*Y, but applies also in the standard Keynesian
      framework.