The U.S. and Mexico both produce orange juice. A gallon of orange juice sells in
ID: 2810783 • Letter: T
Question
The U.S. and Mexico both produce orange juice. A gallon of orange juice sells in the U.S. for USD 5.75. An equivalent gallon of juice sells in Mexico for MXN 70. The spot rate is .09 USD/MXN.
(a) According to purchasing power parity (PPP), what should be the USD/MXN exchange rate?
(b) Take the U.S. as the domestic country. Calculate the real exchange rate, Rt. Which country is more efficient?
(c) The Mexican GDP per capita is MXN 95,000. Translate this amount to (nominal) USD and to PPP USD prices.
(d) Suppose the price of a gallon of juice in Mexico decreases to MXN 63 over the next year, while the price of an equivalent U.S. gallon of orange juice increases to USD 6.05. According to the linearized version of relative PPP, what should be the USD/MXN exchange rate one-year from now?
(e) Next year, the exchange rate is 12.8 MXN/USD. Generate a trading signal based on PPP.
Explanation / Answer
(a) Current Spot Rate = 0.09 USD/MXN
A gallon of orange juice sells for 5.75 USD in the USA and for 70 MXN in Mexico. As per PPP, equivalent quality and quantity of the same good should have equal prices across countries.
Hence, by PPP :5.75 $ = 70 MXN
PPP Exchange Rate = (5.75/70) = 0.082 USD/MXN
(b) The real exchange rate is the ratio of the foreign price level to that of the domestic price level, where the foreign price level is converted at the current exchange rate into the domestic price level.
Foreign(MXN) price of juice = 70 MXN and Current Spot Rate = 0.09 USD/MXN
Therefore, real exchange rate = (70 x 0.09) / 5.75 = 1.096
A decrease in the real exchange rate would imply an increment in purchasing power of the $ over the consumption portfolio(juice) in Mexico. An increase would imply a decrease in pruchasing power of the $ over the consumption portfolio in Mexico. As the same good is costlier (in $ terms of (70 x 0.09) = 6.3 $) in Mexico as compared to in the US (good being a gallon of juice). the latter is more efficient as compared to the former.
(c)
Mexican GDP per Capita = 95000 MXN
Nominal Exchange Rate (Current Spot Exchange Rate) = 0.09 USD/MXN and PPP Exchange Rate = 0.082 USD/MXN
$ Denominated GDP per Capita (in Nominal Exchange Rate) = 95000 x 0.09 = $ 8550
$ Denominated GDP per Capita (in PPP Exchange Rate) = 95000 x 0.082 = $ 7790
(d) Relative PPP is a relationship that connects the forward (future PPP) exchange rate to the inflation prevalent in the two countries whose currencies are being considered through the exchange rates.
Change in Price in Mexico = (63-70) = - 7 MXN
% Change in Price = % Inflation = (-7/70) x 100 = - 10 %
Change in Price in the US = (6.05 - 5.75) = 0.3
% Change in Price = % Inflation = (0.3/5.75) x 100 = 5.23 %
Current PPP Rate = 0.082 $ / MXN
Therefore, USD/MXN exchange rate one year later = 0.082 x [1.0523/0.9] = 0.0958 $ /MXN or 0.096 $/MXN approximately.
NOTE: Please raise a separate qeury for the solution to the last sub-part.
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