# short questions please show your steps

Four question total need to making graphs and show steps.

1. [International trade] (20 points) (a) Use the FRED web site to plot the Japan/US foreign exchange rate from 2000 to 2019.

(b) Suppose an Apple Watch costs $329 in the US and the same model costs ￥36,800 in Japan. According to the law of one price (or equivalently the theory of purchasing power parity), what must be the exchange rate between dollar and yen (1 dollar equals how many yen)?

(c) Assume the exchange rate is 1 US dollar to 113 Japanese Yen. Suppose you can buy and sell any number of Apple Watch at its listed price in Japan or US with no transaction or transportation cost. Is there a way to arbitrage between these two markets (i.e. buy in one country and sell in another) so that you can make a profit? Explain your trading strategy.

(d) Suppose there is a transportation cost of $10 to import or export each Apple Watch. Will your strategy work?

(e) Suppose the exchange rate is 1 US dollar to 110 Japanese Yen. Will your strategy work?

2. [Exchange rate and optimal investment] (20 Points) (a) Consider the exchange rate between US dollar and British pound. Let CPI be the consumer price index, or equivalently the average price level in a country. Assume the ratio CPIUK/CPIUS =0.75. According to the law of one price, what must be the exchange rate between US dollar and British pound (i.e. 1 pound equals to how many dollars)?

(b) Use your answer from part (a) to compute the yield-to-maturity (i.e. nominal interest rate) of A, B and C. Which project has the highest yield-to-maturity?

(c) Find the range of exchange rate e such that Project A has the highest yield-to-maturity. Repeat the same calculation for B and C.

Let’s consider the problem in part (a) and (b) again, except now we include the inflation rates in the calculation. Again assume CPIUK/CPIUS =0.75 this year. Suppose the inflation rate in the US is 2% and that of UK is 0%.

(d) According to the law of one price, what must be the exchange rate between US dollar and British pound next year? What is the yield-to-maturity (i.e. nominal interest rate) of A, B and C if we take the inflation rates into account?

3. [Speculative attack] (10 Points) Assume Thailand unilaterally defends an exchange rate of 1 dollar to 24 baht with a foreign reserve of 40 billion US dollar. Suppose an investor wants to implement a speculative attack on baht.

(a) What is the minimum amount of baht that this investor should sell so that the Thai government will use all her foreign reserve to defend the exchange rate?

(b) Suppose the investor borrows just enough baht for the attack and the transaction cost for this borrowing is 800 million dollar. The investor sells all his baht in the foreign exchange market to buy US dollars (at the rate of 1 dollar to 24 baht). Suppose with probability 0.2 the attack is successful and the Thai government runs out of foreign reserve. If the attack is successful, then the Thai government devalues baht and the new exchange rate would be 1 dollar to 40 baht. Given this information, what is the investor’s expected profit from the speculative attack (in terms of US dollar)?

4. [Exchange rate and production] (30 points) Consider a double auction with two buyers and two sellers. The buyers are located in the US and the sellers are located in the UK. They each submit their bid in their local currency. Their demand and supply schedule are shown below:

Item Buyer 1 Buyer 2 Seller 1 Seller 2 1 $32

$35

£8

£5

2 $18

$25

£10

£9

3 $14 $21 £15 £12

Suppose the auctioneer earns zero profit and maximizes the volume of trade. Suppose the exchange rate is e=0.5, namely 1 dollar to 0.5 pound.

a) Solve for the equilibrium quantity and price(s).

b) How many units will each buyer purchase? How many units will each seller supply?

c) Suppose the dollar becomes weaker and the exchange rate falls to e=0.4. What is the equilibrium quantity and price(s)?

Now suppose the auctioneer always chooses the lowest price such that he earns zero profit and maximizes the volume of trade.

d) Suppose the Bank of England wants to export 5 units of goods to the US. What are the exchange rates that can induce this outcome?

e) Suppose the Bank of England wants to maximize the amount of US dollars earn from export. For example, if the UK exports 2 units to the US at the price of $3, then the total income is $6. What is the exchange rate e that the Bank of England should choose so that the amount of US dollars earned is maximized? Justify your answer.