Pauta Ayudantia 3

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Pontificia Universidad Católica de Chile
Instituto de Economía
Segundo Semestre 2017
Pauta Ayudantía 3
Macroeconomía II
Caio Machado
Ayudantes:
Cristóbal Ojeda: ctojeda@uc.cl
Sofia Gillet: msgillet@uc.cl
True or False
(a) The demand for money is determined by income but not by interest rates. (F)
(b) The central bank can either increase the money supply or raise interest rates to boost GDP growth in
the economy. (true)
(c) The propensity to consume has to be positive, but other- wise it can take on any positive value. (False.
The propensity to consume must be less than one for our model to make sense.)
(d) If there is more preferences for liquidity, bigger the money multiplier will be. Falso. A mayor preferencia
por liquidez, mayor la cantidad de efectivo que las personas mantienen y luego menores los depósitos.
Dado ello menores los fondos que los bancos tienen para prestar y menor el multiplicador. Derivar
multiplicador respecto a cr.
(e) An increase of one unit in government spending leads to an increase of one unit in equilibrium output.
(F, multiplier)
Question 1
To increase tax revenue, the U.S. government in 1932 imposed a 2-cent tax on checks written on bank account
deposits. (In today’s dollars, this tax would amount to about 34 cents per check.)
(a) How do you think the check tax affected the currency-deposit ratio? Explain.
R: This makes people more reluctant to use checking accounts as a means of exchange. Therefore, they hold
more cash for transactions purposes, raising the currency–deposit ratio cr.
(b) Use the model of the money supply under fractional-reserve banking to discuss how this tax affected the
money supply.
R: The money supply falls because the money multiplier, cr+1cr+rr , is decreasing in cr. The higher the currency–de-
posit ratio, the lower the proportion of the monetary base that is held by banks in the form of reserves and, hence,
the less money banks can create.
(c) Many economists believe that a falling in the money supply was in part responsible for the severity of the
Great Depression of the 1930s. From this perspective, was the check tax a good policy to implement in the middle
of the Great Depression?
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R: The contraction of the money supply shifts the LM curve upward, raising interest rates and lowering output.
Figure 1: Graph
Question 2
Automatic stabilizers In this chapter we have assumed that the fiscal policy variables G and T are independent of
the level of income. In the real world, however, this is not the case. Taxes typically depend on the level of income
and so tend to be higher when income is higher. In this problem, we examine how this automatic response of
taxes can help reduce the impact of changes in autonomous spending on output. Consider the following behavioral
equations:
C = c0 + c1Yd
T = to + t1Y
Yd = Y − T
G and I are both constant. Assume that t1 is between 0 and 1.
(a) Solve for equilibrium output.
R: Se que Y = C + I +G , reemplazo y obtengo el output.
(b) What is the multiplier? Does the economy respond more to changes in autonomous spending when t1 is 0
or when t1 is positive? Explain.
R: Multiplier = 11−c1−t1 . Increases in autonomous spending now create a multiplier effect through consumption
and tax.
(c) Why is fiscal policy in this case called an automatic stabilizer?
R: Makes it clear that any change in autonomous spending from a change in investment, to a change in govern-
ment spending, to a change in taxes will have the same qualitative effect: It will change output by more than its
direct effect on autono- mous spending.
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Question 3
The following are the money demand and money supply functions in an economy.
Ms = 8, 000
Md = 40, 000(0.25− i)
(a) Calculate the equilibrium interest rate.
R: 20 = Md = 100(0.25− i), i = 5%. Graph.
(b) Suppose the central bank raises the equilibrium interest rate to 10%, will there be excess money supply or
money demand? What monetary policy should be followed to reach the new equilibrium interest rate?
R: Change in money demand. We have to ajust the money supply. Graph
Question 4
Tools of monetary policy Suppose that the household nominal income in an economy is £5,000 billion and the
demand for money is given by:
Md = Y (0.08− 0.4i)
(a) If the money demand is equal to £100 billion what is the interest rate?
R: $100B = 0.1($5,000B)(.8-4i) i=15%
(b) What should the central bank do to interest rates if it wants to increase the money supply to £300 billion?
R: If H increases to $300B the interest rate falls to 5%.
(c) If the central bank decides to expand money supply to £300 billion, should it change the interest rate or
implement open market operations?
Monetary policy in a liquidity trap. Now suppose that money demand holds as long as interest rates are positive.
Answer the following questions when the interest rate is equal to zero:
(a) What is the demand for money when the central bank sets the interest rate at zero?
R: Replace i=0 and Y=5000
(b) If the central bank cuts interest rate to −0.5%, what is the effect on the demand for money?
R: Replace i=-0,5.
(c) Which central banks have adopted a zero or a sub-zero interest rate policy?
R: Japan, USA.
(d) Can you justify the reasons behind the negative interest rate policy? Do these reasons always hold in
practice?
(e)(Proposed) Bank of Japan has been using negative interest rates for a long period of time. Go to the
Web site of the Bank of Japan and check the statistical database (https://www .stat-search.boj.or.jp) to trace the
interest rates. Identify the periods when Bank of Japan followed a zero and sub- zero interest rate policy. Check
from the same database how interest rates affect money stock.
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Question 5
Suppose that a person’s wealth is $50,000 and that her yearly income is $60,000. Also suppose that her money
demand function is given by
Md = Y (0.35− i)
(a) Derive the demand for bonds. Suppose the interest rate increases by 10 percentage points. What is the
effect on her demand for bonds?
R: Bd = 50,000 - 60,000 (0.35-i) If the interest rate increases by 10 percentage points, bond demand increases
by $6,000.
(b) What are the effects of an increase in wealth on her demand for money and her demand for bonds? Explain
in words.
R: An increase in wealth increases bond demand, but has no effect on money demand, which depends on income
(a proxy for transactions demand).
(c) What are the effects of an increase in income on her demand for money and her demand for bonds? Explain
in words.
R: An increase in income increases money demand, but decreases bond demand, since we implicitly hold wealth
constant.
(d) Consider the statement “When people earn more money, they obviously will hold more bonds.” What is
wrong with this statement?
R: First of all, the use of “money” in this statement is colloquial. “Income” should be substituted for “money.”
Second, when people earn more income, their wealth does not change right away. Thus, they increase their demand
for money and decrease their demand for bonds.
Question 6 (Proposed)
Greece’s usage of fiscal policy to avoid the meltdown and the debt crisis. As a result of the combined effects of the
global financial crisis and the sovereign debt crisis, the GDP of Greece declined from €281.44 billion in 2008 to
€176.5 billion in 2015.
(a) What is the percentage change of GDP during this period?
R:
(b) By how much should autonomous expenditure have risen in order to prevent the slide in the GDP of Greece,
given that marginal propensity to consume is 0.6?
R:
(c). In reference to your reply to part (b), explain why the Greek Parliament refused the austerity measures
that lender na- tions sanctioned for Greece.
R:
(d) The Greek reform program aimed to improve incentives to private investors. By how much do these incentives
alone improve GDP if they have increased investment by €15.5 billion?
R:
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