Non Monotone Liquidity Under-Supply

We show that very little is needed to create liquidity under-supply in equilibrium: only the presence of credit constraints on demand. We show that the under-supply is a non-monotone function of the demand distortion that causes it, a result that may have interesting implications for emerging markets economies. Finally, we show that the inefficiency can be large, due to a liquidity under supply multiplier arising from the endogeneity of the credit constraint. We define liquidity as the flexibility to move goods (money) from one project (investment) to another. We show that credit constraints by themselves can cause investors to allocate too much capital to inflexible projects, and too little to flexible ones. Output can be improved, for example, by government taxation of returns from inflexible projects. This under-supply of liquidity arises without the uncertainty, intermediation, asymmetric information or complicated international financial framework used in other models in the literature. In this respect liquidity is like a commodity: according to our offsetting distortions principle, a distortion in the demand for any good can often be understood as an inefficiency of supply. We show that the liquidity under-supply is a non-monotone function of the credit constraint. The non monotonicity stems from the flexibility of liquid investments. The essence of liquidity is flexibility, so the presence of alternatives goes hand in hand with liquidity. The non monotonicity of the under-supply of liquidity is thus an inevitable consequence of its nature.This non monotonicity occurs for any commodity if we suppose that the central planner can affect only part of the supply curve: Second Best inefficiency is a non monotone function of the demand distortion. If we interpret the credit constraints as the degree of financial development in the economy, our second proposition suggests that when financial markets are very undeveloped, financial innovation may paradoxically make government intervention more necessary. It is difficult not to think about the financial innovation and simultaneous, dramatic, reduction of government participation in financial markets that took place in Latin American economies during the 90's. Numerous liquidity crises occurred in these economies during that period. We model the credit constraint by assuming that borrowers will default unless their promises are covered by collateral. Further, we assume that only an exogenous proportion �2 of one durable good can serve as collateral. This parameter �2 will represent the degree of financial development of the economy. We show that the magnitude of the under supply can be larger when the price of the collateral is endogenous, giving rise to a Liquidity Under Supply Multiplier. Any policy intervention that affects the interest rate in equilibrium will have two effects on the borrowing constraint: a direct effect, also present in the case when the credit constraint is exogenous, and an indirect effect through the price of the collateral. Finally, we explore our findings in a particular example in which utilities for the consumption good and the collateral are quadratic. In this context, we can be more precise about the effects on liquidity of the degree of financial development, �2 , and the marginal utility, λ, of collateral. First, in economies where the market value of collateral is low (because λ is low), there will always be liquidity under-supply, no matter how high �2 is. The government should intervene, for example, by taxing illiquid investments. Paradoxically, as �2 increases and the financial system becomes more efficient, the need for government intervention (taxation) increases. For higher values of λ, the liquidity under-supply is non-monotonic in �2 ,increasing for low values and decreasing for high values of �2 .Similarly, the liquidity under-supply multiplier is increasing in �2 for low values of λ and becomes non-monotonic in �2 for high values of λ.