Question

can you please do all work in steps on a paper if possible

Exercises: Parity conditions in real markets and financial markets EXERCISE 4 (Purchasing Power Parity) We live in a four-country world where people only grow and eat coconuts. We have the following data: Brazil a Mexico Argentina United States Price of one BRL 2,000 MXN 5 ARS 1.5 USD 1.4 coconut Exchange rate MXN/BRL 400 ARS/BRL 1,200 USD/BRL 1,400 a) Does Purchasing Power Parity hold for the BRL with respect to the MXN, ARS, and the USD? b) Are the currencies overvalued or undervalued relative to the BRL according to PPP standards? c) Is the cost of living in Brazil lower or higher than in Mexico, Argentina, and the US? d) Expected annual inflation is 100 percent in Brazil, 12 percent in Mexico, 25 percent in Argentina, and 6 percent in the United States. According to Relative PPP, what are the expected spot rates (in BRL) one year from now? Can we expect an appreciation or depreciation of BRL?

Answer 1

Purchasing Power Parity is a theory which states that exchange rates between currencies are in equilibrium when their purchasing power is same in each of the two countries.

a) Price of one coconut in Brazil is BRL 2,000

• Price of coconut in Mexico is MXN 5. MXN 1 = BRL 400, hence price of one coconut in Mexico is MXN 5 * BRL 400 = BRL 2,000.
• Price of coconut in Argentina is ARS 1.5. ARS 1 = BRL 1,200, hence price of one coconut in Mexico is ARS 1.5 * BRL 1,200 = BRL 1,800.
• Price of coconut in USA is USD 1.4. UDS 1 = BRL 1,400, hence price of one coconut in Mexico is USD 1.4 * BRL 1,400 = BRL 1,960.

From above, we can see that price of coconut in Brazil & Mexico is same i.e. BRL 2,000 and it is different in Argentina & USA, hence Purchasing Power Parity holds for BRL with respect to MXN but it does not hold with respect to ARS & USD.

b) Calculation of overvalued or undervalued currency relative to BRL-

• Mexico- Spot price MXN/BRL = 400, according to PPP 400=2000/Price in Mexico : 400=2000/5 : 400=400 hence MXN is correctly valued relative to BRL
• Argentina- Spot Price = 1200, as per PPP 1200=2000/Price in Argentina : 1200=2000/1.5 : 1200=1333.33. This means that ARS is undervalued and it should be correctly valued at ARS1 = BLR 1333.33
• USA- Spot price = 1400, as per PPP 1400=2000/Price in USA : 1400=2000/1.4 : 1400=1428.57. This means that USD is undervalued and it should be correctly valued at USD 1 = BRL 1428.57.

c) Cost of living in Brazil is equal to cost of living in Mexico but is higher as compared to Argentina and USA. The main reason for higher cost of living in Brazil could be due to inflation caused by rising cost of housing, etc.

d) The prediction for spot rates are as follows:

Mexico- 400*2/1.12=714.28 BRL

Argentina- 1200*2/1.25=1920 BRL

USA- 1400*2/1.06=2641.51 BRL

Formula - Spot rate * (1+BRL Inflation rate)/(1+Foreign Inflation rate)=Future Rate