A Dynamic equilibrium with small fixed transactions costs

This paper studies a dynamic equilibrium with small fixed transactions costs. We consider an overlapping generations economy with two assets of different liquidity. Trading the liquid asset does not involve transactions costs while trading the illiquid asset requires a fixed transaction fee. Both assets cannot be sold short. Agents receive an exogenous income. We look at the equilibrium rates of return of the two assets when the transaction fee is small, under two scenarios: when the number of illiquid assets is constant and the rate of return of liquid assets is zero, and when the number of illiquid assets is constant and a financial intermediary issues a quantity of liquid assets proportional to the liquidity premium (the difference between the rates of return of the two assets). We find that the optimal policy for a young agent is to accumulate the liquid asset in order to convert it into the illiquid asset at successive points in time. An old agent does the opposite and converts a portion of his holding of illiquid assets back into the liquid asset each time he has consumed all his stock of the latter. The liquidity premium is larger in the second scenario where it is proportional to the cubic root of the transaction fee. It is smaller in the first scenario where it is proportional to the square root of the fee.