Exercises 2—Currency boards
Haakon O.Aa. Solheim∗
April 30, 2002
Exercise
1. Given the data given in the exercise, compute the values of the money
supply and the monetary base.
Solution: Money supply: 9750, money base: 900
2. Next, assume that the Argentinean real exchange rate appreciates visa-vis USD. Provide one or two sentences to say what this means. This
question should be answered abstractly, without references to the above
data. Your answer should be expressed in intuitive terms, using plain,
jargon-free language.
3. Now suppose that, because of the ARP real appreciation, an Argentinean importer wants to import some U.S. goods. Specifically, she
wants to import 18 dollars worth of machines. This means that she
needs to obtain USD 18.
(a) First, suppose the importer goes to her commercial bank and asks
for USD 18. The commercial bank turns to a trader in an American bank, and asks him to sell it USD 18 in return for ARP 18.
Assume the trade goes through, and the importer receives USD
18 from its bank in return for ARP 18. What is the effect on the
Argentinean monetary base?
Solution: This transactions does not involve the currency board.
The money base is not affected.
(b) Second, suppose that, because of the overvaluation, the trader at
the American bank will not sell USD for ARP at 1:1. He might sell
each USD for 1.2 ARP, but if he did then the fixed exchange rate
∗
Norwegian School of Management (BI). email: haakon.o.solheim@bi.no. This exercise
is adopted from Chris Telmer, GSIA, Carnegie Mellon University.
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would have de facto collapsed. The good news for the Argentinean
importer is that the currency board is obliged to sell her USD at
1:1. The commercial bank will trade ARP 18 for USD 18 by
sending a request to the currency board.
What is the currency board supposed to do with the pesos it
receives for these USD? If the currency board does this, what is
the effect on the Argentinean monetary base?
Solution: The currency board is supposed to burn the ARPs it
receive. To keep the balance sheet in balance, the amount of ARP
issued must match the reserve holdings of USD. If reserves are
reduced with 18, the amount of money issued must be reduced by
18.
(c) According to the quantity theory of money, money (M ) times the
number of transactions conducted with money (velocity, V ) should
equal the price level, P , times the number of transactions in the
economy, T , or
M · V = P · T.
(1)
We can simplify by assuming that velocity is constant, and that
T can be set equal to to total production in the economy, Y .
Do you think the actions by the currency board described above
will alleviate the overvaluation of the Argentinean peso? Why?
Solution: According to the QTM a contraction of the money base
should lead to lower prices. It the Argentinean price level falls,
the real exchange rate of Argentina devalues. This will alleviate
the overvaluation.
(d) What will happen if, for some reason, this process continues? That
is, what will happen if Argentineans try to convert all their ARPdenominated bank deposits into USD?
Solution: If the process continues, the currency board will run
out of USD. At this point Argentina must either float the peso or
impose capital controls. If the process continues further the banks
will collapse. The reason is that the holdings of the currency board
only back-up the currency, not the entire monetary supply.
4. Given the transaction by the Argentinean importer, what will happen
to the Argentinean current account once this transaction occurs? Will
there be change in the direction of trade flows? How will capital flows
be affected?
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Solution: If the overvaluation in Argentina is alleviated, Argentine
goods become more attractive in foreign markets, and foreign goods
less attractive in Argentina. The Argentinean trade deficit will be
reduced. Capital flows that are necessary to finance the trade deficit
will abate.
5. Once the Argentinean importer has obtained the USD 18, you should
find that the system of balance sheets are no longer ‘in equilibrium’.
That is, the two ratios discussed above are no longer 12 and 60. Use
the four linear equations described in the appendix to compute the new
equilibrium. What is the new money supply? Is this new value for the
money supply consistent with alleviating the overvaluation problem?
Solution: The four equations can be expressed as:
C =
60H
12 + 60
R = H −C
L = (60 − 1)R
D = 12C.
H is given as 900 − 18 = 882. We then find that
C = 735
R = 147
L = 8673
D = 8820.
The new money supply will be 9555, which is less than 9750. This is
consistent with alleviating the overvaluation. The money supply has
decreased, which will decrease prices and make the real value of ARP
fall.
The economics behind this might go as follows. Upon seeing reserves
fall below a safe level, commercial banks start to call in loans. This
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causes interest rates to rise. The increase in interest rates induces a fall
in the level of economic activity and a drop in national income. The
latter reduces the demand for goods, as well as money, thereby pushing
the domestic price level down. The reduction in domestic demand, in
addition to the depreciation of the real exchange rate, tends to push
the current account balance toward surplus.
6. The money multiplier is defined as the ratio of the reduction in the
money supply to the reduction in the monetary base. The money multiplier tells us how fast the supply of money grows if another unit of
monetary base is created. What is the money multiplier here? If the
central bank prints one more piece of currency, how much will the total money supply grow, and therefore how much will the price level
increase (if V and Y is constant)?
Solution: The money multiplier is
9750 − 9555
= 10.83
18
(2)
The important point in the example above is to show that a currency
board has a ‘self-correcting’ aspect to it. Excessive inflation (relative to the
reserve country) and/or real exchange rate overvaluation should be corrected
if the currency board does what it is supposed to do. In addition, the example
points out that a county with a currency board has effectively given up
any sort of active monetary policy. Monetary policy becomes a currency
printing/burning robot.
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