Appendix to ‘Pairwise Trade and Coexistence of Money and Higher-Return Assets’

This is the appendix to Zhu and Wallace [4]. In it, we prove the claims in section 3 of that paper that are made about the model with a non degenerate wealth distribution. We begin by formally setting out the definition of an equilibrium for that model. Let Y = {y = (y1, y2) ∈ Z × Z : y1 + y2 ≤ Z}. An element of Y is an individual portfolio after bond purchases (y1 is the amount of money and y2 is the amount of bonds measured at maturity value) that satisfies the restriction that total nominal wealth not exceed Z. For y ∈ Y, we again let yz = y1 + y2 denote the total nominal wealth implied by y. Given π0 (an initial distribution of money holdings over the set Z), an equilibrium is a sequence {wt, ht, θt, πt+1}t=0 that satisfies the conditions described below. The functions wt and πt pertain to the start of date t, prior to bond purchases: wt : Z→R, where wt(z) is the expected discounted value of having wealth z, and πt : Z→ [0, 1], where πt(z) is the fraction of each specialization type with wealth z. The functions ht and θt pertain to the situation after bond purchases and before meetings: ht : Y → R, where ht(y) is the expected discounted value of having the portfolio y, and θt : Y → [0, 1], where θt(y) is the fraction of each specialization type with portfolio y. We start with bond buying. We let a person with wealth z buy any lottery over portfolios in Y whose expected cost does not exceed z. Let Γ(z, p), a ∗Department of Economics, Cornell University †Department of Economics, The Pennsylvania State University An alternative would have lotteries only over portfolios whose cost does not exceed z. All our results also hold for that version.