The Monetary Approach to the Exchange Rate

1.    (12 points in total, 2 points for each sub question)

At time t = 0, the initial log values of the variables L, Y, and M are:

Table 1

What’s more, the continuous growth rate of real income gt  and of the money supply ut  are:

Table 2

Assume that households care about the opportunity cost of holding money, so that the demand for real money balances in both the U.S.A. and Australia is now given by:

ln  = 1 − 2i + lnY

Where i = ln (1 + i) is the log nominal interest rate. Prices are still fully flexible. For the values of

Y, M, gt, and utin Tables 1 and 2, calculate:

a)   The nominal interest rate in Australia and the U.S.A. (in log terms) if the log world real interest rate ln(1 + T∗) = 0.02 and real interest parity holds.

b)   The equilibrium natural log price levels lnP in Australia and the U.S.A. for t = 0;

c)    The equilibrium natural log price levels lnP in Australia and the U.S.A. for t = 1;

d)   The equilibrium natural log real money balances ln  in Australia and the U.S.A. for t = 0;

e)   The log of the equilibrium exchange rate lnSt,AUD/USD for t = 0; and

f)    The log of the equilibrium exchange rate lnSt,AUD/USD for t = 1.

2.    (13 points) Now assume that commencing at time t = 1, the Australian central bank                  announces an immediate increase to the (continuous) growth rate of the money supply, so      that ut = 0.1 inAustralia. Prices are fully flexible. Draw four graphs (including numerical values on axes) covering the period t = 0 through t = 2 that show:

a)    (2 points) The Australian log money supply, lnM; and

b)   (3 points) Australian log real money balances and nominal interest rate; and

c)    (2 points) The Australian log price level; and

d)   (2 points) The log exchange rate lnSt,AUD/USD .

e)  (4 points) Write an intuitive explanation for why there is a discrete jump in several of these graphs.

3.    (20 points) TNT model: Aging and the Real Exchange Rate (Lecture 9 slides)

It has been documented that as societies age, the demand for personal and health‐ care services, prime examples of nontradable goods, increases. To capture this phenomenon, suppose that there is an          increase in households’ preference for nontradable goods, which is reflected in an increase in 1 − γ, the exponent on nontradable consumption in the Cobb- Douglas function that aggregates consumption of   tradable and nontradable goods (Equation 9.2). Use the TNT model studied in lecture 9 based on            Section 9.1 of the S.U.W. text to answer the following questions:

a.    (5 points) What is the effect of this preference shock (decrease in γ or increase in 1 − γ ) on the

equilibrium consumption of tradable goods in periods 1 and 2? Explain. (Hint: You are given the expression of C1(T), which is equation 9.9. Derive the expression of  C2(T)(3 points). See        how/whether γ or 1- γ enters the expressions.)

b.    (5 points) What is the effect on the trade balance and the current account in periods 1 and 2? Explain.

c.    (6 points) Use a graphical approach to analyse the effect in period 1 of the preference shock on the relative price of nontradables and the real exchange rate.

d.    (4 points) The old‐ age dependency ratio is defined as the ratio of the number of people aged

65 or older to the number of people aged 15 to 64. Which countries would you expect to be    more expensive to live in: countries with high old‐ age dependency ratios or countries with low

old‐ age dependency ratios?  Briefly explain your answer.