Exercise 2 At t 5 0, a foreign exporter sells you their merchandise. However, you will make the payment

(in foreign currency) for this product in time t 5 f =θ

2 . To guarantee the rate, the exporter offers you, at t 5 0, a future sales contract of foreign currency. The contract states the following: at time t 5 f =θ

2 , the exporter commits to sell you foreign currency at the exchange rate sðtÞ 5 θη 1 f ðtÞ

2 1 k, where θ . 0, η . 0, and k . 0. Your answer if you accept, or not, the proposed contract, occurs in time t 5 0. Possessing extensive knowledge regarding economics, you know (for sure) that the fundamentals will grow at a rate of θ, that is, f ðtÞ 5 θt until the end of time.

a. What is the exchange rate trajectory? Present its equation and illustrate your answer by means of a graph.

b. If k 5 0, do you accept, reject, or remain indifferent to the contract? How does your answer depend on the value of k?