Teoria y Politica Monetaria, Instructor: Marco Del Negro.

Problem set 7, Solutions

a) This is the same model seen in class: flexible exchange rates with 0 rate of money creation. If inflation abroad is constant, prices and the exchange rate are constant. Real money balances are m^*(0).
b) This is again the same model seen in class: flexible exchange rates with $\mu$ rate of money creation. If inflation abroad is constant, inflation and exchange rate depreciation are equal to $\mu$. Real money balances are $m^*(\mu)$.
c) To answer this part you should use the material discussed in the class ``Anticipated changes in monetary policy''. The first order condition with respect to money is as always:

$$\frac1{p_s}u_c(y,\frac{M^s_s}{p_s})=\frac1{p_{s+1}}\beta [u_c(y,\frac{M^s_{s+1}}{p_{s+1}})+u_m(y,\frac{M^s_{s+1}}{p_{s+1}})]$$

If you multiply both sides for M^s_s, and multiplying and dividing the right hand side for M^s_s+1, the above equation becomes:

$$\frac{M^s_s}{p_s}u_c(y,\frac{M^s_s}{p_s})=\frac{M^s_s}{M^s_{s... ...(y,\frac{M^s_{s+1}}{p_{s+1}})+u_m(y,\frac{M^s_{s+1}}{p_{s+1}})]$$

Since the rate of money creation is 0 before time t+T, that is, $\frac{M^s_s}{M^s_{s+1}}=1$, the above equation becomes

$$m_s u_c(y,m_s)=\frac{\beta}m_{s+1} [u_c(y,m_{s+1})+u_m(y,m_{s+1})]$$

for s<t+T.
We know that:
i) for s+1=t+T $m(s+1)=m^*(\mu)$
ii) the above equation is satisfied by m_s=m_s+1=m^*(0), which is the only point (if $m^*(\mu)$ is unique) where the function m_s+1=f(m_s) crosses the 45 degree line. From the figure you can see that real money balances jump down at the time of the announcement, and continue to decrease until they reach $m^*(\mu)$. Given that money supply is fixed, this implies that prices jump up, and continue to increase. Given the Law of One Price, the exchange rate follows the path of prices. d) With flexible exchange rates expectation of lax monetary policy in the future (lack of credibility) immediately lead to inflation and exchange rate depreciation. On the contrary, with fixed exchange rates the government can keep inflation under control until reserves run out, even if the current path is not sustainable in the long run.