Consumption and Equilibrium Interest Rates in Stochastic Production Economies



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    • Graduate School of Business, Columbia University. I thank Jean Pierre Danthine, John Donaldson, David Modest, Krishna Ramaswamy, and Mark Rubinstein for their comments. Special thanks go to Doug Breeden, George Constantinides, Philip Dybvig, Jon Ingersoll, and Scott Richard for their suggestions. The comments and suggestions made by two anonymous referees were most helpful. Responsibility for errors remaining in this paper is mine. Faculty Research Fellowship from the Graduate School of Business, Columbia University partially supported this research.


In this paper, we analyze the behavior of equilibrium real interest rates in an identical consumer economy in which the preferences are represented by time additive logarithmic utility functions and production technologies are Cobb-Douglas with stochastic constant returns to scale. The following main results are established.

  • (i)When there is no relative price uncertainty, it is shown that the equilibrium interest rate exhibits a mean reverting tendency. A nontrivial steady state distribution is found to exist for the equilibrium interest rate. The properties of the equilibrium interest rate are also derived and discussed.
  • (ii)In a multigood economy, even with additive preferences across goods, the equilibrium interest rates depend explicitly on relative prices. The substitution possibilities in production technologies induce this result. This is in contrast to the findings of Richard and Sundaresan [11] who show that the analytical general equilibrium term structure of interest rates formula of Cox, Ingersoll, and Ross [5] is unaffected by the introduction of relative price uncertainty when the technologies are linear and hence involve no substitution.

Furthermore, we relate our results to those of Cox, Ingersoll, and Ross [5], Breeden [3], and Richard and Sundaresan [11] with special emphasis on stochastic production and realtive price uncertainty.