Consider an economy characterized by a demand for money of the form: MD =PYe?
Where P is the price level, Y is the country’s aggregate output and i is the nominal interest rate. Here the parameters and are positive constants. The symbol e indicates the ‘natural” number, i.e. the base of the natural logarithm. (i.e. ln(e) = 1). This functional form is widely used in empirical studies of the demand for money.
The supply of money (MS) is controlled by the Central Bank and as seen in class, the equilibrium in the money market is given by the equality of the demand for and supply of money.
Assume that Y = 2, P = 1, ? = 2, = 0.8. Assume also that Ee = 1.1 and that the foreign interest rate is i? = 0.1 = 10%.
1. Imagine that the Central Bank aims to maintain the domestic interest rate at 8% (i.e.: i = 0.08). What should be the money supply needed to achieve that as the equilibrium in the money market? Assuming that the Uncovered Interest Rate parity holds, what would be the equilibrium exchange rate?
2. Can the Central Bank simultaneously hold the exchange rate at E = 1.05 and i = 8%? If so, explain how. If not, explain why.
3. Now, imagine that the economy is initially in the equilibrium described in the first item of this question but domestic output rises to Y = 2.5. Describe the new equilibrium of the economy if:
a The Central Bank insists in keeping the money supply at the original (initial) level. b The Central Bank insists in holding the equilibrium interest rate at i = 8%.