Download Practice Money Supply / Money Demand Problem

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Instructions: Please show all work or points will be taken off. Good luck!
1. (65 points total) Suppose the real money demand function is:
Md/P  1500  0.2 Y – 10,000 (r  e).
Assume M  4000, P  2.0, e  0.01, and Y  5000. Note: we are holding P and Y constant in this
problem until we get to case #2, see below.
a)
(5 points) What is the market clearing real interest rate?
For this, we want to solve for r by setting Md = Ms
Ms = M/P
Md/P = 1500 + .2Y – 10000(r+e)
Set them equal and plug in the values we know
M/P = 1500 + .2Y – 10000(r+e)
Assume M  4000, P  2.0, e  0.01, and Y  5000
So 4000/2 = 1500 + .2*5000 – 10000(r+.01) = 2000 = 2500 – 100 – 10000r
-400 = -10000r
r = -400/-10000 = 0.04 or 4%
Show your results on a real money supply, real money demand diagram and label this initial equilibrium
point as point A. Be sure to label your graph completely! Correctly drawn and completely labeled
diagram is worth 10 points total. Be sure to put relevant shift variables in parentheses next to the
appropriate function.
Case #1
b) (5 points) Suppose Bernanke and the Fed were successful in their campaign to raise inflationary
expectations to 4% (.04). Why would they want to do this? Use the Fisher equation to support
your argument.
They would want to do this if the real interest rate were too high. They would decrease the real
interest rate by increasing inflation to this level. This is because, by the Fisher equation, r is
inversely correlated with e. The Fisher equation states r = i - , meaning that when inflation rises,
r drops.
c) (5 points) Solve for the real interest rate that clears the money market given the change in inflationary
expectations. Please show work and Label this new point as point B on your diagram.
Use same equation as before, but plug in .04 instead of .01 for e
Ms = M/P
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Md/P = 1500 + .2Y – 10000(r+e)
Set them equal and plug in the values we know
M/P = 1500 + .2Y – 10000(r+e)
Assume M  4000, P  2.0, e  0.04, and Y  5000
So 4000/2 = 1500 + .2*5000 – 10000(r+.04) = 2000 = 2500 – 400 – 10000r
-100 = -10000r
r = .01 or 1%
d) (10 points) Explain how this strategy of raising inflationary expectations is supposed to stimulate
output. Recall that output is equal to C + I + G! Be very specific as this question is worth 10 points. Hint:
The price of current consumption in terms of future consumption and the user cost of capital most
definitely needs to be in your response.
Raising inflationary expectations stimulates output because when the real interest rate is low, the economy
is in expansion. This is due to a few reasons. First of all, the user cost of capital decreases when r decreases.
This is because the user cost of capital = r. Therefore, when r decreases, capital becomes cheaper. When
capital is cheaper, people borrow more as it is cheaper to rent capital. This increases investment, as there is
more capital being used in the market and it causes I to increase, because I depends on the user cost of
capital. Therefore, when it is cheaper to rent capital, people rent it more, and this increases investment.
Also, in relation to consumption, when the interest rate is low, current consumption is cheap relative to
future consumption. With a higher interest rate, consuming in the present costs a great deal, as there is a
large amount of money that is lost in the future due to consuming now, as Cfuture = (1+r) savingsnow.
Therefore, when interest rates are low, it is much cheaper to consume in the present, so this increases total
output in society as people are consuming more and saving less. It makes the opportunity cost of
consuming in the present decrease.
Case #2
e) (5 points) Let us return to our original conditions. Please redraw the original graph locating point A
(this is with e  0.01, we are holding expected inflation constant in case #2). We now experience some
economic growth so that Y = 6000. This is the only change. Resolve for the market clearing real rate of
interest and label on your diagram as point B. Please show all work. Correctly drawn and completely
labeled diagram is worth 10 points total. Be sure to put relevant shift variables in parentheses next to
the appropriate function.
Use same equation as before, but plug in 6000 instead of 5000 for Y
Ms = M/P
Md/P = 1500 + .2Y – 10000(r+e)
Set them equal and plug in the values we know
M/P = 1500 + .2Y – 10000(r+e)
Assume M  4000, P  2.0, e  0.01, and Y  6000
So 4000/2 = 1500 + .2*6000 – 10000(r+.01) = 2000 = 2700 – 100 – 10000r
-600 = -10000r
r = .06 or 6%
f) (5 points) Now explain exactly why the real rate of interest had to change the way it did to clear the
money market. Please be clear with the intuition being sure to refer to the bond market in your answer.
You should begin your response with "At the same real rate of interest, the money market is no longer
clearing. In particular money demand ....." you can finish the rest.
At the same real rate of interest, the money market is no longer clearing. In particular, money demand is
increasing, as money demand is correlated positively with Y. This means that when output is higher, the
demand for money is higher. This makes sense if we think about it, because if output in the economy is
higher, there people need more money in circulation to undertake all of these transactions. In order for this
demand for money to undertake these new transactions to be met, one of two things must happen. Either
the Fed must print more money to keep the interest rate at the same level, by finding a new equilibrium
with a higher money supply at the same interest rate, or not change the money supply and let the interest
rate rise. The rising interest rate will cause money to become more expensive, so people will demand less
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of it, as it is more expensive to undertake activities. Therefore, a rise in money demand in this way leads to
an increase in the real interest rate,
g) (5 points) Suppose the Fed wanted to keep real interest rates constant at their original level. Suppose
also that the money multiplier is 0.8, which is consistent with reality since the Fed began paying interest on
reserves beginning in October 2008. What exactly would the Fed have to do to keep real interest rates
constant at their original level? Be specific with regard to the type and quantity of open market operations
the Fed would need to conduct to be successful in keeping real interest rates constant at their original level.
The Fed would want to increase the amount of money in circulation to do this. In order to do this, the Fed
would want to conduct open market operations and buy existing bonds to influx money into the economy.
Similarly, they could reduce reserve requirements to influx money into society through an increase in
lendable money. Because the multiplier is .8, anything the Fed puts into society will be multiplied by 1+ .8
+.8^2,+.8^3…etc., because the money is spent multiple times. To find exactly how much money we would
need to influx, we use the equation from before except we are looking for M, not r.
For this, we want to solve for r by setting Md = Ms
Ms = M/P
Md/P = 1500 + .2Y – 10000(r+e)
Set them equal and plug in the values we know
M/P = 1500 + .2Y – 10000(r+e)
Assume M  ?, P  2.0, e  0.01, and Y  5000, r = .04
So M/2 = 1500 + .2*5000 – 10000(.04+.01) = 2000 = 2500 – 100 – 400
M/2 = 2000
M = 4000
M = MB(MM) MM= .8
MB = 4000/.8 = 5000. Therefore, there must be a total of 5000 in the monetary base in society.
h) (5 points) Finally, explain the movement to the new equilibrium in the money market given the Fed
expansion and show on your diagram as point C. Be sure to refer to the bond market as you did in part f).
In fact, you should start your response the same way.
The money supply increases like this because of the bond market. As interest rates go up, the price of bonds
go down and the supply of bonds decreases. In order to increase the amount of money in the market, the
Fed begins to demand more bonds, increasing the price of bonds and increasing the quantity supplied.
Because the price of the bond increases, the interest rate decreases, as they are inversely correlated. When
the interest rate returns to .04, the Fed stops buying bonds. Though this has happened, there is now more
money in the market, as buying bonds caused the Fed to send an influx of money into the economy as it
was buying bond.
2. (35 points total) During the video lectures in this lesson, I tried my best to emphasize the importance of
being able to identify shocks to money demand. During the Great Recession there was very much turmoil
in financial markets and as a result, money became more attractive relative to many non-monetary assets.
The graphic below is from a WSJ article from the fall of 2011. The left hand panel shows that the bid/ask
spread for stocks was increasing which suggests that stocks, the non-monetary asset we are focusing on in
this question, are becoming less liquid.1 The graphic on the right can be thought of as a measure of risk and
the implication in viewing the graphic is that stocks are becoming riskier. 2
1
The bid/ask spread is more of a money and banking/finance term and if you have never heard of it before,
no worries. If you want to learn more, see the Investopedia site for this term.
2
The VIX has received a great deal of attention throughout the Great Recession and the aftermath. To
learn more about the VIX, see the Investopedia entry about this index.
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a)
(10 points) Draw a money market diagram labeling the initial equilibrium as point A. Note that
this is a 'generic' graph meaning that there are no numbers. Now lets pretend that we have two
portfolio shocks to money demand, much like above so that 1) non-monetary assets become less
liquid (left hand panel) and 2) non-monetary assets become more risky (right hand panel). Show
exactly how your diagram is effected and explain exactly why real interest rates changed the way
they did. Label this new equilibrium as point B. Correctly drawn and completely labeled
diagram is worth 10 points total. Be sure to put relevant shift variables in parentheses next
to the appropriate function.
When both risk goes up and liquidity goes down in relation to non-monetary assets, the demand
for money increases. This is because money is a substitute for non-monetary assets and this is
because money is the safest asset, as it is very liquid and carries almost no risk. This increase in
demand causes the interest rate to increase as long as the Fed did not increase the money supply.
This is because demand exceeds supply for money, so the price of money increases to
accommodate this.
b) (5 points)Given that the economy is weak and the unemployment rate is much higher than that
associated with NAIRU, the Fed wants real rates to fall, not rise. Explain exactly what the Fed
would need to do. This is referred to as accommodating the shock to money demand. Label this
as point C on your diagram.
In order to accommodate this shock, the Fed would need to perform open market operations or
decrease the reserve requirement ratio to increase the amount of money in circulation. Only when
the amount of money in circulation is high enough will it create an equilibrium where the price of
money, rC is lower than it was at rA. This is because the demand for money can be met with more
money in circulation, and the price of money no longer has to rise to determine who gets it.
c) (10 points)Now explain how your answer would change if instead the shock to money demand was real.
That is, the same movement in the money demand curve from above was not caused by portfolio shocks
but was caused by a change in real output. Are the policy implications the same or are they different?
Explain. (hint: the term 'potential growth rate of the economy' should be in your answer).
If the shock to money demand was real, the total amount of money demanded in the long term would
increase because it would be demanded to purchase real goods, or more units of goods. This means that the
potential growth rate of the economy would increase, as now the economy has a greater capacity to create
more goods. This is similar to if there was a shift in Y. When this happens, the Fed would want to respond
in a way that permanently increased the amount of money in the economy, as now this shock to demand is
not temporary but is due to a fundamental change in the economy. To do this, the Fed would want to do
something like permanently decrease the reserve requirement ratio. This would ensure that there would
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always be a larger amount of money in the economy to offset this rising interest rate caused by structural
changes in the economy.
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