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Linking Bond and Money Markets Economics 121 - Fall 2010 Pamela Labadie 1 Asset Demand Asset demand is the outcome of a decision problem solved by the household. The typical household is assumed to value consumption today and expected consumption over the rest of its life. The household starts period t with some wealth carried over from the past, call it W t - 1 . It receives its after-tax income Y - T and decides how much to consume and how much to save Y - T = C + S. Savings is added to existing wealth to determine the wealth to be allocated in the portfolio problem W t = W t - 1 + S. How should the household hold W t ? Specifically, should the household hold bonds, stocks or money? What kind of bonds - domestic or international? Government or corporate? The portfolio allocation problem is a complicated one and depends on things like expected returns, riskiness, and the correlation of an asset’s return with the rest of the portfolio. We will simplify the choice set dramatically by assuming that agents can hold money, which is non-interest bearing, and bonds, which bear interest. Hence, the wealth to be allocated W t is W t = B d t + M d t . (1) The supply of money is M s t and the supply of bonds is B s t . Money market equilibrium requires M d t = M s t , and bond market equilibrium requires B d t = B s t . Notice that the left side of (1) is the total demand for assets W t . The total demand equals total supply W t = B d t + M d t = B s t + M s t , 1

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which can be rewritten as M d t - M s t = B s t - B d t . The left side is the excess demand for money and the right side is the excess supply of bonds. If one market is in equilibrium, then the other market is necessarily also in equilibrium. This is a version of Walras Law : If there are n markets and n - 1 are in equilibrium, then the remaining market is necessarily in equilibrium. In our case, there are two asset markets (money and bonds) that are linked through the portfolio allocation problem. If one market is in equilibrium, then so is the other. If one market is in disequilibrium, then so is the other. 2 Bond Markets We simplify the model by assuming that the only interest-bearing asset is a bond. The issuer of supplier of the bond is a borrower while the buyer of the bond is a saver. To understand bond demand, let’s examine a one period discount bond. The expected return is equal to the yield to maturity i 1 ,t = R t +1 ,t = F - p 1 ,t p 1 ,t = F p 1 ,t - 1 . Notice that i 1 ,t and p 1 ,t are inversely related, given F . With this background, let’s list the factors that determine bond demand. Assumption 1 Assume that all bonds are one period discount bonds with the same face value. This assumption allows us to put the price on the vertical axis and quantity of bonds on the horizontal axis. Suppose that the equilibrium price is p 1 ,t = 1 , 000 and the equilibrium quantity is Q b = 100. Then the amount of lending through bond issue is p 1 ,t × Q b = \$100 , 000.
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