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Finance, Economics, and Mathematics by Robert C. Merton, Oldrich A. Vasicek

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Chapter 11The Economics of Interest Rates

Journal of Financial Economics, 76 (2)(2005), 293–307.

Abstract

The paper looks at the behavior of investors in an economy consisting of a production process controlled by a state variable representing the state of technology. The participants in the economy maximize their individual utilities of consumption. Each participant has a constant relative risk aversion. The degrees of risk aversion, as well as the time preference functions, differ across participants. The participants may lend and borrow among themselves, either at a floating short rate or by issuing or buying term bonds. We derive conditions under which such an economy is in equilibrium, and obtain equations determining interest rates.

Introduction

What determines interest rates? Intuitively, it seems that interest rates should be set by supply and demand for borrowing and lending, given the production opportunities in the economy (both current and as they may change in the future depending on technological developments), the time preference for consumption and the attitude toward risk and return of the participants in the economy, and the distribution of wealth across the participants. This would necessitate a general equilibrium model of the economy under the optimal consumption and investment decisions of the players. So far, however, such a model does not seem to have been developed in sufficient generality.

Cox, Ingersoll, and Ross (1985a, 1985b) postulate an economy ...

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