Question

In an open economy Summerville, suppose capital inflow is $4 trillion, and domestic people buy $10 trillion foreign asset and domestically invest $10 trillion.

1. 1) Find national saving, and net capital outflow.

2. 2) If a Summerville CPI basket costs $100, a Winterville (another country) CPI basket costs 2,000 yen, and a dollar can buy 10 yen, find the nominal exchange rate and real exchange rate of yen.

3. 3) Assume CPI baskets in all countries are the same. According to purchasing power parity, the real exchange rate of yen will become 1 in the long run. Show an arbitrage plan that will make this change happen. Is there any possibility that the arbitrage might not be feasible in the practice? If so, explain with example.

Answer 1

1) (i) National Savings = Domestic people Investment in foreign asset + Domestic Investment
= $10 trillion + $10 trillion
= $20 trillion.

(ii) Net Capital Outflow = Capital Outflow - Capital Inflow
= Domestic people Investment in foreign asset + Domestic Investment
= $10 trillion + $10 trillion - Capital Inflow
= $10 trillion - $4 trillion
= $6 trillion.

2) If a Summerville CPI basket costs $100, a Winterville (another country) CPI basket costs 2,000 yen, and a dollar can buy 10 yen.

(i) The nominal exchange rate: 10 Yen per $.

(ii) The real exchange rate of yen:
= (10 * 100) / 2000
= 1000 / 2000
= 0.5

Thus, real exchnage rate of yen is 0.5 units of winterville basket for each unit of summerville basket.

3) Assume CPI baskets in all countries are the same. According to purchasing power parity, the real exchange rate of yen will become 1 in the long run.

As per the given prices, we can see that the prices of winterville basket is higher compared to summerville. There is an arbitrage plan if a person purchases this basket from summerville with 1000 yen and sells it in 2000 yen in winterville. Through this arbitrage plan, there will be an increase in the demand for summerville basket and supply of winterville baskets. This will result in an increase in the prices of summerville basket and a decrease in the prices of winterville basket, thereby resulting an increase in the real exchange rate to 1.

This arbitrage plan might not be feasible in practice because the basket may not have the exact same goods, imperfect mobility of capital and goods. Also, there exists transaction costs for purchasing and selling goods in the another country.