Optimal Monetary Policy in a Model of Money and Credit

Abstract

We investigate the extent to which monetary policy can enhance the functioning of the private credit system. Specifically, we characterize the optimal return on money in the presence of credit arrangements. There is a dual role for credit: it allows buyers to trade without fiat money and also permits them to borrow against future income. However, not all traders have access to credit. As a result, there is a social role for fiat money because it allows agents to self‐insure against the risk of not being able to use credit in some transactions. We consider a (nonlinear) monetary mechanism that is designed to enhance the credit system. An active monetary policy is sufficient for relaxing credit constraints. Finally, we characterize the optimal monetary policy and show that it necessarily entails a positive inflation rate.

Optimal monetary interventions in credit markets

“…According to (11), y 1 = y m 1 , and round-1 DM consumption is identical to that in the no monitoring economy. According to (12), if D is relatively high and the expected marginal surplus using debt alone is lower than the real interest rate, the buyer has no incentive to bring money to use in round-2 DM. In this case, he consumes up to the available debt limit and y 2 > y m 2 .…”

“…where y 2 is given by (12) and z 2 = ρ 2 y 2 − D. Note that we did not include the cost of holding money and the trade surpluses from round-1 DM on both sides as they are not affected by the bad record. Note also that the presence of z 2 reflects the possibility that the buyer also uses money in the monitored round.…”

On the optimal quantity of liquid bonds

“…Equation (24) means that an active consumer does not consume the optimal amount of goods in the goods market, because the constraint on the producer's money holdings is binding in the secondary bond market (25). As in the type-I equilibrium, the meaning of (26) is that the constraint on the consumer's bond holdings is non-binding in the secondary bond market.…”

“…From Lemma 8 it follows that for u (q) = q 1−α /(1 − α), we need α ∈ (0, 1) and η ≤ 2 −α to have an overlapping region supporting the type-II and the type-III equilibrium for all γ > γ 12 . 24 The following parameters need to be identified: (i) preference parameters: (β, A, α); (ii) technology parameters: (ξ, n); (iii) market frictions: (δ, η); (iv) and policy parameters (B, γ).…”

“…30 Sinceq = φ(mc + dm) = φ(mc + mp) and q = φmp, ∂q/∂mc = ∂q/∂mp = ∂q/∂mc = φ. Since dm = mp is binding, equation (24) holds. Thus, if a buyer has a little more (or less) mc, agents will still trade dm = mp.…”