# 11 Exchange Rates

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## 11.1 Purchasing power parity.

In foreign exchange market, demand for home currency depends on the needs of either trade or international financial investment. Purchasing power parity focuses on how trade affects foreign exchange markets.

For the needs of trade, if we, as home country, export more, then the demand for home currency will be higher, which pushes home currency to appreciate.

1. Consider the real exchange of home currency, $$P\epsilon/P^{f}$$, where $$P$$ and $$P^{f}$$ are price levels of traded home and foreign baskets. If there is no disturbance in the markets, what will be the reasonable real exchange rate equilibrium level? What does a higher real exchange rate imply for the relative price of home to foreign baskets?

The price mechanism that brings import and export to equilibrium is their relative prices, which is real exchange rate here.

Suppose the equilibrium real exchange rate is $$k$$ (which is also the term of trade here). Real exchange rate higher than $$k$$ means that home export is too expensive relative to import. In this case, export will decrease and import will increase.

1. When $$P\epsilon/P^f>k$$ what would happen to import and export? What would happen to the foreign exchange market?

Suppose home central bank increases its currency supply to the foreign exchange market.

1. How would it affect the nominal exchange rate?

2. If import and export prices, $$P$$ and $$P^{f}$$, are sticky, how would it affect the real exchange rate?

3. If others things being equal, what would happen to home country’s import and export? With the change of import and export, how would it affect the nominal exchange rate?

4. Following the previous question, what happens to the real exchange rate? How would home country’s import and export adjust? Can such a depreciation policy boost home export in the long run?

5. What are other harms of a depreciation policy that you can think of?

## 11.2 Inflation exporting under fixed exchange rate

Assume that the real exchange rate $$P\epsilon/P^{f}$$ is a stable number. It implies that when home country adopts a fixed exchange policy, whenever $$P^{f}$$ increases, $$P$$ will increase eventually. Can you give a full story to argue why it is so? (We call this inflation exporting.)

## 11.3 Interest rate parity.

Another source of foreign exchange demand comes from international investment needs. If more foreigners want to invest in home country, then home country’s currency demand will increase in the foreign exchange market. Hence, home currency will appreciate.

1. Suppose home currency is NT and foreign currency is USD, and 1NT=$$\epsilon$$ USD. If saving 1NT gives you $$(1+i)$$NT tomorrow, while saving 1USD gives you $$(1+i^*)$$USD tomorrow, which country’s saving is a better deal given the expected exchange rate tomorrow to be $$\epsilon^e$$?

2. If home interest rate $$i$$ plus the expected home currency appreciation rate $$(\Delta\epsilon)^{e}/\epsilon$$ is larger than foreign interest rate $$i^{*}$$, which investment is a better deal? What would happen to home currency demand in the foreign exchange market? What would happen to the nominal exchange rate?

3. Suppose home central bank increases its money supply through bond purchasing. This will push down home interest rates. What would happen to home currency demand in the foreign exchange market? What would happen to the nominal exchange rate?

## 11.4 Big Mac Index

Every half year, the Economist computes the Big Mac indices based on the theory of Purchasing Power Parity (PPP).

1. Based on PPP, what does it mean to a country’s currency if its index is higher than one?

In the article, “The Big Mac index Our Big Mac index shows fundamentals now matter more in currency markets”, it says:

Measured against a basket of currencies, the dollar still looks dear. Only in three countries (Switzerland, Norway and Sweden) do burgers cost more, based on current exchange rates. But that is not necessarily a sign that depreciation is overdue in these countries.

1. Why might it not be a sign that depreciation is overdue in these countries?

2. When a country’s cost of a Big Mac rises due to its non-tradable input cost, how would it impact the country’s index?