Exercise 11.6

BOP Crisis: A Numerical Example

⬅ Return

Problem

Consider the model of BOP crises of Section 11.5. Suppose \(c^T=y^T\), where \(y^T\) denotes output, assumed to be constant. Suppose that the initial stock of foreign reserves, \(k_0\), is 10 percent of output; the lower bound on reserves, \(k_L\), is 0; the fiscal deficit, \(g\), is 2 percent of output; and the money demand function is given by \(c^T(a-bi)\), with \(a=0.2\) and \(b=0.25\). Find the date of the BOP crisis, denoted \(T\), and the devaluation rate post BOP crisis, denoted \(\epsilon^H\).

Answer

The post BOP crisis devaluation rate is given by

\[ \epsilon^H(0.2-0.25\epsilon^H)=0.02 \]

Solving this quadratic polynomial for the smallest root (for we want to be on the upward-sloping side of the Laffer curve) yields

\[ \epsilon^H=11\%. \]

Then \(T\) is given by

\[ \begin{eqnarray*} T &=& \frac{(k_0-k_L)-yb\epsilon^H}{g} \\ &=& \frac{0.1-0.25\cdot 0.11}{0.02} \\ &=&3.6 \mbox{ years}. \end{eqnarray*} \]