An Axiomatic Analysis of the Optimal Rate of Interest in the Bewley Models

Document Type : Original Article


1 Assistant Professor of Economics, Faculty of Humanities, Yasouj University

2 Associate Professor of Economics, Faculty of Administrative Sciences and Economics, University of Isfahan

3 Associate Professor of Statistics, Faculty of Statistics, University of Isfahan


The main question of this study is that in an environment that we have only precautionary demand for money and assets, which rate of interest assures existence and optimality of equilibrium. This economic environment has two essential properties: heterogeneous agents that face to idiosyncratic risk, and incomplete markets without possibility of complete insurance by means of lending for hedging this risks. In this environment, agents hold precautionary savings in the form of a single asset such as fiat currency, credit, and capital for self-insurancing themselves against idiosyncratic income fluctuations. Bewley models are formed in this environment. In this paper, by using the axiomatic method, we will prove that when agents have access to the two forms of assets for self insurancing, i.e. fiat currency and credit, the necessity of decreasing the interest rate (more than time preference rate) for convergence of consumption and asset and the existence of monetary equilibrium are still true.


- Aiyagari, S. R. (1994). Uninsured Idiosyncratic Risk and Aggregate Saving. The Quarterly Journal of Economics, 109(3), 659-684.
- Athreya, K. & Lahiri, S.N. (2006). Measure Theory and Probability Theory. Springer.
- Bailey, M.J. (1956). The Welfare Cost of Inflationary Finance. Journal of Political Economy, 64(2), 93-110.
- Bewley, T. (1980). The Optimum Quantity of Money. in Karekan, J. & Wallace, N. (1980). Models of Monetary Economics. Minneapolis, Minnesota. Federal Reserve Bank, 169-210.
- Bewley, T. (1983). A Difficulty with the Optimum Quantity of Money. Econometrica, 51(5), 1485-1504.
- Blackwell, D. (1965). Discounted Dynamic Programming. Annals of Mathematical Statistics, 36, 226-235
- Cagan, P. (1958). The Demand for Currency Relative to the Total Money Supply. Journal of Political Economy, 66(4), 303-328.
- Cesarano, F. (1998). Providing for the Optimum Quantity of Money. Journal of Economic Studies, 25(6), 441-449.
- Chamberlain, G., & Wilson, C. (2000). Optimal Intertemporal Consumption Under Uncertainty. Review of Economic Dynamics, 3(3), 365–395.
- Davoudi, P. & Hadian, M. (2011). Money Interast Rate and Financial Crisis. Journal of Economics and Modelling, 2 (5-6), 39-68 (In Persian).
- Debreu, G. (1959). Theory of Value: An Axiomatic Analysis of Economic Equilibrium. Yale University Press. New Haven.
- Friedman, M. (1969). The Optimum Quantity of Money. in Friedman, M. (1969). The Optimum Quantity of Money and Other Essays. Chicago. Aldine, 1-50.
- Friedman, M. (1953). The Methodology of Positive Economics. in Friedman, M. (1953). Essays in Positive Economics. Chicago. Chicago University Press.
- Frisch, R. (1959). A Complete Scheme for Computing all Direct and Cross Demand Elasticities in a Model with Many Sectors. Econometrica, 27, 177–196
- Gong, G. & Semmler, W. (2004). Stochastic Dynamic Macroeconomics: Theory, Numerics and Empirical Evidence.
- Grandmont, J.M. & Laroque G. (1973). Money in the Pure Consumption Loan Model. Journal of Economic Theory, 6, 382-95
- Hellwig, M. F. (1993). The Challenge of Monetary Theory. European Economic Review, 37(2-3), 215-242.
- Hildenbrand, W. (1974). Core and Equilibria of a Large Economy. Princeton. Princeton Univercity Press.
- Huggett, M. (1993). The Risk Free Rate in Heterogeneous-Agent, Incomplete-Insurance Economies. Journal of Economic Dynamics and Control, 17(5-6), 953–969.
- Imrohoroglu, A. (1992). The Welfare Cost of Inflation Under Imperfect Insurance. Journal of Economic Dynamics and Control, 16(1), 79–92.
- Ireland, P.N. (2003). Implementing the Friedman Rule. Review of Economic Dynamics, 6, 120–134.
- Kocherlakota, N. & Cole, H.L. (1998). Zero Nominal Interest Rates: Why They’re Good and How to Get Them. Federal Reserve Bank of Minneapolis Quarterly Review, 22(2), 2–10.
- Krusell, P. & Smith, A. (1998). Income and Wealth Heterogeneity in the Macroeconomy. Journal of Political Economy, 106(5), 867–896.
- Lucas Jr., R.E. and Prescott, E.C. & Stokey N. (1989). Recursive Methods in Economic Dynamics. Cambridge. Harvard University Press.
- Mehra,  R.  &  Prescott, E.C. (1985).  The  Equity  Premium:  A  Puzzle. Journal  of  Monetary  Economics, 15,  145-162.
- Meyer, P. A. (1966). Probability and Potentials. Waltham. Blaisdell.
- Samuelson, P.A. (1963).  D. H. Robertson (l890-1963). Quarterly Journal of Economics, 77, 517-36.
- Samuelson, P.A. (1968).  What Classical and Neoclassical Monetary Theory Really Was. Canadian Journal of Economics, 1, 1-15.
- Samuelson, P.A. (1969). Nonoptimality of Money Holding under Laissez Faire. Canadian Journal of Economics, 2, 303-8.
- Sargent, T.J. & Ljungqvist, L. (2013). Recursive Macroeconomic Theory (Third Ed.). MIT Press.
- Tobin, J. (1965). Money and Economic Growth. Econometrica, 33(4), 671-68.
- Townsend, R.M. (1980). Models of Money with Spatially Separated Agents. in Karekan, J. & Wallace, N. (1980). Models of Monetary Economics. Minneapolis, Minnesota. Federal Reserve Bank, 65–303.
- Woodford, M. (1990). The Optimum Quantity of Money. in Friedman, B.M. and Hahn, F.H. (1990). Handbook of Monetary Economics, 2, New York. North-Holland.