ECOS3010: Tutorial 5 (Answer Key)
Question 1-5. Answer True, False or Uncertain. Brieáy explain your answer.
1. The Lucas Critique stresses that the government cannot design policy purely based on the reduced form correlation from the data.
True. The Lucas Critique points out that the reduced form correlations are subject to change when the government changes its policies and thus the rules under which decision makers operate. It implies that while econometric policy evaluation is useful, we also need a theory to help us understand how people react to di§erent government policies. It is not su¢ cient just to look at the data.
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2. In an OLG model with two countries and two monies/currencies, people would like to hold both currencies no matter what the values of these currencies are.
False. When people are free to hold and use any currency, people would choose to hold the currency (or currencies) that can help them buy the most goods. In equilibrium, only when the exchange rate satisÖes et = vta=vtb, both currencies are valued and held by people. For example, if et > vta=vtb, no one would like to hold country a currency. On the other hand, if et < vta=vtb, no one would like to hold country b currency.
3. In an OLG model with two countries and two currencies, suppose that foreign cur- rency controls are in e§ect. The government cannot choose to both Öx the exchange rate and acquire its preferred level of seigniorage.
True. When foreign currency controls are in e§ect, the government has to set its growth rate of money supply according to za = zbna=nb to keep a Öxed exchange rate. In this case, the government cannot freely choose its preferred level of seigniorage. If the government wants to choose za to generate a certain level of seigniorage, the exchange rate cannot be Öxed. Overall, it is not possible to both Öx the exchange rate and acquire a preferred level of seigniorage when foreign currency controls are in e§ect.
4. The áuctuations in exchange rates can always be attributed to changes in economic fundamentals.
False. From the data on exchange rate áuctuations, we can see a lot of extreme áuc- tuations cannot be tied to any changes in real economic conditions. Neither the change in money supply nor the change in money demand can explain the change in exchange rate. Fluctuations in exchange rates cannot always be attributed to changes in economic fundamentals.
5. In an OLG model with international currency traders, there exist two money market clearing conditions for the two monies. Therefore, the exchange rate is no longer indeter- minate.
False. Even if there are two money market clearing conditions, exchange rate is still indeterminate as long as international currency traders can freely adjust its holding of di§er- ent currencies. Basically, whenever international currency traders changes the composition of their currency portfolios, it will change the exchange rate.
6. Suppose that the United States (country a) and Great Britain (country b) have foreign currency controls in e§ect. The demand for money is growing at 10.25 percent in the United States and at 2 percent in Great Britain (net rates) each period. The money supplies in the United States and Great Britain are growing at 5 and 6.25 percent (net rates) in each period, respectively.
(a) DeÖne the exchange rate (et) as in our lectures, what are the units in which the exchange rate is measured, U.S. dollars per British pound or British pounds per U.S. dollar?
We deÖne exchange rate et as
et = value of U.S. dollar = units of British pounds:
value of British pound units of U.S. dollar
The exchange rate et is measured as British pounds per U.S. dollar.
(b) What is the rate of return on money in the U.S.? In Great Britain? The rate of return on money in the U.S. can be expressed as
va na 1 + 10:25%
t+1 = = =1:05: vta za 1+5%
The rate of return on money in Great Britain can be expressed as
vtb+1 nb 1 + 2%
vtb =zb =1+6:25%=0:96:
The U.S. is experiencing deáation and Great Britain is experiencing ináation.
Note that here we use the expression for the rate of return on money directly. You can also derive it by yourself following the steps that we use in class: deriving the value of money in period t from the money market clearing condition and also deriving the value of
money in period t + 1.
(c) In a system of áexible exchange rate, what is the time path of the exchange rate
between the U.S. and Great Britain (et+1=et)?
With foreign currency controls, the time path of the exchange rate is
et+1 vta nz 1:05
=b =ab= =1:094:
The exchange rate is increasing over time, since the real value of U.S. dollar is increasing over time whereas that of British pounds is decreasing over time. It implies that the relative value of the U.S. dollar to the British pound is increasing over time.
(d) Suppose the U.S. desires to Öx the exchange rate. How can the U.S. government set its growth rate of money supply za to accomplish this goal?
If the U.S. government wants to Öx the exchange rate, it has to set its growth rate of
money supply za as
a na b 1:1025
z = nbz = 1:02 1:0625=1:148:
et vt+1 z n 0:96 vtb
The growth rate of the U.S. money supply must increase to lower the rate of return on U.S. dollars.
7. Suppose that Germany (country a) and France (country b) do not have foreign currency controls in e§ect. The total demand for money is always 2,000 goods in Germany and 1,000 goods in France. The money supplies are 100 marks in Germany and 300 francs in France. Find the value of each countryís money if the exchange rate et (as deÖned in our lectures) is 3. Do the same if et = 1. Is one exchange rate more likely than the other? Explain.
The world money market clearing condition is
vtaMta + vtbMtb = Nta ya ca1;t + Ntb yb cb1;t : 2
We know that
Nta ya ca1;t=2000 and Ntbyb cb1;t=1000: We also know that
Mta = 100 and Mtb = 300:
If we substitute these numbers into the world money market clearing condition, we have
100vta + 300vtb = 3000: When the exchange rate et is 3, it implies that
We can solve for vtb from It follows that
vta ab et=vtb=3 or vt=3vt:
1003vtb +300vtb =3000 ! vtb =5: vta = 3vtb = 15:
When the exchange rate is 1, we have
et=vtb=1 or vt=vt: 100vtb +300vtb =3000 ! vtb =7:5:
v ta = v tb = 7 : 5 :
It is important to note that either exchange rate "works as well" as the other and neither is more likely than the other. In fact, we could have picked any exchange rate we wanted. This is what is meant by the "indeterminacy of the exchange rate".
8. Suppose that there are three types of people in our model of two countries and two currencies. Type a people can hold only the money of country a, type b can hold only the money of country b, and type c can hold the money of either country. Every individual wants to hold 10 goods worth of money when young. There are 300 type a people, 200 type b people, and 100 type c people. There are 100 units of country a money and 200 units of country b money.
(a) Find the range of stationary equilibrium values for vta, vtb and et.
With international currency traders, the value of country a money and the value of country b money are
va = Nta ya ca1;t+tNtc yc cc1;t;
vtb = Ntb yb cb1;t+(1 t)Ntc yc cc1;t:
We can then solve for vtb from It follows that
The exchange rate can be expressed as
Nta (ya ca1;t )+t Ntc (yc cc1;t ) (yb cb1;t )+(1 t )Ntc (yc cc1;t ) Mtb
vtb From the question, we know that
Na = 300; Nb =200andNc =100; ya ca1;t = yb cb1;t =yc cc1;t =10;
Mta = 100andMtb=200:
Substituting these values into the expression of vta; vtb and et, we have
vta = 3000 + 1000t = 30 + 10t; 100
vtb = 2000+1000(1 t) =15 5t; 200
3000+1000t 6 + 2t et= 100 = :
2000+1000(1 t) 3 t 200
Given that t ranges from 0 to 1, the value of vta ranges from 30 to 40. The value of vtb ranges from 10 to 15. The value of et ranges from 2 to 4.
(b) Now suppose that 100 type a people and 100 type b people become type c people. Now Önd the range of stationary equilibrium values for vta, vtb and et. Has the range of equilibrium exchange rates expanded or contracted? Explain this change.
When 100 type a people and 100 type b people become type c people, the populations of the three types of people are
Na =200; Nb =100andNc =300: we need to update our expressions as
vta = 2000 + 3000t = 20 + 30t; 100
vtb = 1000+3000(1 t) =20 15t; 200
2000+3000t 4 + 6t et= 100 = :
1000+3000(1 t) 4 3t 200
As t ranges from 0 to 1, the value of vta ranges from 20 to 50. The value of vtb ranges from 5 to 20. The value of et ranges from 1 to 10. Since more multinational people who can freely switch between the holding of the two currencies, the range of the exchange rate expands.
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