Exercise 11.5

A BOP Crisis with Linear Money Demand

⬅ Return

Problem

Consider an economy in which the demand for money is of the form

\[ L(\epsilon,c) = c-\frac{\epsilon_t}2, \]

where \(\epsilon_t\) denotes the devaluation rate, and \(c\) denotes a constant level of consumption. Suppose that \(c\) equals 2. Time is continuous, and the analysis starts at time 0. Let \(g\) denote a constant flow of government primary deficits. Suppose \(g=1.5\). At time 0, the government implements a currency peg. Let \(k_t\) denote the stock of (non-interest-bearing) foreign reserves held by the government. At time 0, and after any portfolio recomposition that the announcement of a currency peg might have caused, the level of reserves held at the central bank, \(k_0\), equals 10. The government is determined to defend the peg until it runs out of reserves. At that point, it switches to a constant rate of devaluation, high enough to finance the deficit.

  1. Calculate the rate of devaluation prevailing in this economy after the demise of the currency peg.

  2. Calculate the loss of reserves suffered by the government at the time of the BOP crisis.

  3. Calculate the length of the currency peg, denoted \(T\).

  4. Assume alternatively that at time 0 everybody understands that when the government runs out of reserves it will implement a fiscal reform whereby the primary deficit is fully eliminated. When does the government run out of reserves in this case? Is there a BOP crisis at time \(T\), that is, does the government lose a discrete amount of reserves at time \(T\)? Provide intuition.

Answer

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