Exercise 5 Consider an economy that adopts a fixed exchange rate regime and that possesses the volume of reserves R . 0, administered by the central bank with the objective of defending exchange rate parity. Assume that the central bank assets, denoted in the currency to which the parity was established, are represented by WCB and the liabilities are denoted by BCB.

Also assume that WCB , BCB. There are J investors, being M small investors, each of which possesses one unit of domestic currency, and a large investor who alone possesses N units of domestic currency. Consider a noncooperative game in one period when the investors decide whether to speculate against the domestic currency or to maintain their position in this asset, and the central bank decides if it keeps the parity or allows the domestic currency to depreciate. When the investors decide to “attack,” selling their domestic currency, they must pay a transaction cost of c . 0 monetary units for each unit of domestic currency sold.

The nominal exchange rate, S, is measured as the price of the foreign currency with which parity was established. This game is represented, in normal form, as follows:

Central Bank Defend ðΔS 5 0Þ Depreciate ðΔS . 0Þ

Investors Attack 2c; 2 R=ðM 1 NÞ ΔS 2 c; ΔSðWCB 2 BCBÞ

Maintain 0; 0 2ΔS; ΔSðWCB 2 BCBÞ

a. What condition must be met for a speculative attack, in the self-fulfilling prophecy form, for there to be equilibrium of pure strategies for this game?

b. Explain under what conditions a speculative attack becomes the optimum answer for any small investor when they observe the large investor sell N units of domestic currency while the other M
1 small investors maintain their positions?

c. Assume that N 5 0 and that one small investor anticipates that the other small investors intend to hold a speculative attack. What equilibria are possible?

d. If you were an economic policymaker in this country, what regulatory instrument would you adopt to reduce the propensity of investors to hold a speculative attack? Explain your answer.