Credit and inflation under borrowerʼs lack of commitment

Abstract

Here we investigate the existence of credit in a cash-in-advance economy where there are complete markets but for the fact that agents cannot commit to repay their debts. Defectors are banned from the credit market but they can use money balances for saving purposes. Without uncertainty, deflation crowds out credit completely. The equilibrium allocation, however, is efficient if the government deflates at the time preference rate. Efficiency can also be restored with positive inflation. For any non negative inflation rate below the optimal level, the volume of credit and the real interest rate increase with inflation. Our results hold when idiosyncratic uncertainty is introduced and households are sufficiently impatient but in one instance: efficiency cannot be restored if the deflation rate is nearby the rate of time preference. Our numerical examples suggest that the optimal inflation rate is not too large for reasonable levels of patience and risk aversion. Finally, we present a framework where the use of money arises endogenously and show that it is tantamount to our cash-in-advance framework. Our results hold in this modified environment.

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