Incorporating a "public good factor" into the pricing of large-value payment systems

We study optimal pricing rules for a public large-value payment system (LVPS) that produces a public good (like prevention of systemic risk) but faces competition by a private LVPS for the private provision of large value payments. We show that the marginal cost of the public LVPS has to be corrected by a "public good factor"that can be interpreted alternatively as the decrease in the cost of providing the public good when the private activity of the public system increases, or as the subsidy needed for private banks to internalize the cost of systemic risk. In either interpretation, the public good factor is easy to measure: it corresponds to the subsidy needed for private banks to allocate their payments in the way that is desired by banking authorities.