Finance 475

Solutions to Problem Set #2

1)   With an inflation differential of 2% (3% in the US - 1% in Europe), we would expect the dollar to depreciate by 2% to $1.40(1.02) = $1.43.  Given the actual  depreciation of 7% (from 1.40 to 1.50), we end up with a real depreciation of 5% (US goods are 2% more expensive relative to Europe, but the dollar is 7% cheaper).

2) Assuming that PPP holds), the exchange rate should adjust so that there are no arbitrage opportunities (profits from buying low, selling high).

a)      With no transportation costs, taxes, tariffs, etc., the dollar price of roller skates should be the same everywhere. (e is the dollar price of Yen)

                                                          Prs = eP*rs


e = Prs /P* rs

   = $40/Y 4300

   = $.0093 /Yen


b)      Suppose there exists a $5 per skate cost of shipping. In order to insure that there are no chances to make profits either buying in the U.S. and selling in Japan or visa versa, we have the following two conditions (remember, profits = revenues -costs )

Profits from buying on the U.S. and selling in Japan: eP* rs - (Prs + $5)

Profits from buying in Japan and selling in U.S.: Prs - ( eP* rs + $5)

Setting the above expressions equal to zero and solving for s gives us the two exchange rates:

e = (Prs+$5)/P* rs

= ($45)/Y 4300 = Y .0105/ $

e = (Prs - $5)/P* rs

= ($35)/Y 4300 = Y .0081 $

Therefore, for any exchange rate between .0081 and .0105, no profitable

trades are possible.


a)      The CPI is defined as .5(Prs) + .5 (Psr) : Therefore,

CPI = .5(Prs) + .5 (Psr) = .5($40) + .5 ($10) = $25

CPI* = .5(P* rs) + .5 (P* sr) = .5(Y 4300) + .5 (Y 1075) = Y 2687.5

Therefore, as in (1), the nominal exchange rate should be:

e = CPI/CPI* = $25/Y 2687.5 = Y .0093 $

Note the real exchange rate is 1 (due to PPP)

b) Now, suppose that the Japanese price of roller skates rises to Y 4750:

To eliminate any profit opportunities, the new nominal exchange rate must be.

e = Prs/P*rs

= $40/Y 4750 = Y.0084 $ (a nominal depreciation of the Yen)

Note that this creates a profit opportunity in roller skating rinks, but we don't have to worry about this because roller skating rinks aren't traded. Also, note that with the new price of roller skates, the Japanese price rises to

CPI* = .5(Y 4750)+.5 (Y 1075) = Y 2912.50

 Given the new nominal exchange rate, and the new price levels, we can calculate   the real exchange rate.

RER = e(CPI)/CPI* = .0084(2912.5)/$25 = :9786 ( a real depreciation of the Yen)


a)      For the US, the price level is

P = .2(750) + .6(2,500) + .2(38) = $1657.60

Likewise, for Mexico

P = .2(7312.50) + .2(24,375) +.6(370.50) = p6559.80

b)      The nominal exchange rate as implied by the law of one price is p/p* if you use this with any of the commodities, you get (for example with computers)

e = 2,500/24,375 = .1026$/p  (or, equivalently 9.75 p/$). Note that the real exchange rate between the US and Mexico is                                                        RER = (eP*/P) = (.1026)(6559.8)/1657.6 = .4060

c)      If Al Gore nationalizes health care and consequentially increases the price of health care in the US to $1000:

        No Change is required of the exchange rate (health care is a non traded good)

        The Mexican price level is unaffected

        The US price level rises to P = .2(1000) + .6(2,500) + .2(38) = $1707.6

        The real exchange rate falls to RER = (eP*/P) = (.1026)(6559.8)/1707.6 = .3941 ( a real appreciation of 2.9%)

d)      If the price of oil rises 10% worldwide (Therefore, Po = 41.80, Po* = 407.55):

        Again, no change is required of the nominal exchange rate

        The US price level rises to 1708.36 (Iím assuming Medical Care is still $1000)

        The Mexican Price Level rises to 6582.03

        The real exchange rate rises to .3953 ( a real depreciation of .3%)

5)      The it is generally assumed  that an increase in output will appreciate a countryís currency (all else equal) in nominal terms.  However, this implicitly assumes a uniform rise in output over all sectors of the economy.  Why is this important?  When relative output of different sectors changes, there is generally a relative price change related with that event.  In this case, high tech has grown in size relative to manufacturing.  This can be a result of either a demand shift or a supply shift. If its from a demand shift, we would expect to see a rise in the relative price of high tech goods.  As the relative price of high tech rises (and high tech goods become a more important part of out economy) we would see a real dollar appreciation.  If the change is associated with a supply shift, the relative price of high tech goods falls and the US experiences a real depreciation