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. 52

2. $18. $25. 10. 93

3. $14. $21. 15. 12

Suppose the auctioneer earns zero profitand 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 thedollar 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 pricesuch 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 chooseso that the amount of US dollars earned is maximized?Justify your answer.