Financial Crashes versus liquidity trap: the dilemma of monetary policy

This paper considers a two-period monetary double auction with incomplete markets of securities and derivatives. Players may share heterogenous beliefs. Short positions in derivatives are constrained by collateral requirements. A central Bank stands ready to lend money or engage in unconventional monetary policy such as quantitative easing. In sharp contrast with the usual picture of equilibrium properties, I show that only three scenarios are compatible with Nash equilibrium condition: 1) either the economy enters a liquidity trap in the first period; 2) or the money injected by the Central Bank fuels a financial inflation driven by "rational exuberance", whose burst leads to a global crash in the next period, 3) else a significant inflation of commodity prices accompanies the functioning of markets. In particular, neither Friedman's golden rule, nor the Taylor rule turn out to be compatible with the third scenario: Both inevitable lead to a liquidity trap. An example shows that quantitative easing does not provide, in general, any escape from the monetary dilemma