ECOS3021 Business Cycles and Asset Markets University of Sydney
2021 Semester 1
Tutorial #4
1. Denote the price of a nominal bond that pays one dollar next period as St1. Now denote the price of a nominal bond that pays one dollar two periods from now as St2. Both bonds can be purchased today, but the first pays off next period while the second pays off two periods from now.
1.a) Write down an expression for the nominal rate of return on each bond as a function of the bond price. Rearrange this expression to express the bond prices as functions of the nominal rates of return.
1.b) Now write down expressions for the real rates of return on each bond as a function of the bond prices and current and future price levels. Use these expressions to find a Fisher Equation for each of the bonds.
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2. Consider the model from Lecture 4 for household choices over consumption, money holdings, and nominal bonds:
max logC1 +ωlog M +βlogC2 C1 ,C2 ,M,B P1
s.t. P1C1+M+B=P1Y1
P2C2 = P2Y2 + M + B(1 + rn)
In class, we showed that the Euler equation is:
1 =β(1+rn)P1 1 (1)
C1 P2 C2 And the money demand equation is given by:
M (rn)−1
P =ωC1 1+rn (2)
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2.a) Rewrite the money demand equation so that the nominal interest rate (i.e. the price) is expressed as a function of money demand (i.e. the quantity). Plot this money demand function on a graph with the interest rate on the y-axis, and money demand on the x-axis.
2.b) On a new graph, again plot the money demand curve from the previous question. Now add a money supply curve, such that the quantity of money supplied is constant/inelastic with respect to the interest rate. Be sure to label the equilibrium interest rate. On your graph, show what happen if there is a positive money demand shock, i.e. an increase in the parameter ω. Label the new equilibrium interest rate and quantity of money.
2.c) Combine budget constraints and the money demand equation (2) to find an expression for the bond- demand equation as a function of C1. As above, rewrite the equation to express the bond demand equation with the interest rate as a function of real bond holdings, B/P1. Why is the bond demand curve upward sloping? Use both math and economic intuition in your answer.
2.d) Draw the bond demand curve, with B on the x-axis, and rn on the y-axis. Now suppose a central bank P1
determines how many bonds are available in the bond market.1 The supply of bonds is constant/inelastic with respect to the interest. Illustrate equilibrium in the bond market, being sure to label the equilibrium interest rate.
2.e) Suppose the central bank increases the supply of bonds (i.e. by selling bonds into the market). What is the effect on the equilibrium nominal interest rate? Illustrate your answer. What is the effect of this policy on real money holdings? What does this suggest about the central bank’s ability to conduct monetary policy using either the money or bond supply?
1In practice, many fiscal, banking, and corporate institutions issue bonds. But central banks buy and sell large numbers of these bonds in order to influence the number available in the market for bondholders to purchase.
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