Existence of a Radner equilibrium in a model with transaction costs

TL;DR

This paper proves the existence of a Radner equilibrium in a model with transaction costs, showing how these costs influence the interest rate and welfare in a dynamic setting.

Contribution

It establishes the existence of a Radner equilibrium with transaction costs and derives an explicit formula for the equilibrium interest rate.

Findings

Transaction costs affect the equilibrium interest rate.

Discrete-time equilibrium converges to continuous-time model.

Explicit formula links transaction costs to interest rate.

Abstract

We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon and analyze the effect of transaction costs on the endogenously determined interest rate. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity. After establishing the existence of a discrete-time equilibrium, we show that the discrete-time equilibrium converges to a continuous-time equilibrium model. The continuous-time equilibrium provides an explicit formula for the equilibrium interest rate in terms of the transaction cost parameter. We analyze the impact of transaction costs on the equilibrium interest rate and welfare levels.