The equilibrium in which countries impose cash-in-advance constraints and, as shown in Proposition 3, create positive inflation is inefficient along two dimensions. First, ex post consumption profiles do not sufficiently reflect the taste of individual agents. Ftom the solution of (l)-(2), consumption levels are not state contingent since monetary holdings are determined prior to the taste shock.
Second, there is positive inflation which, as we show in this section, is an undesirable outcome of the interaction between governments each attempting to reap positive gains for its citizens by money creation. While inflation is individually rational, in equilibrium, these policies lead to a welfare loss fully.
The point of this section is to argue that the creation of monetary union in which there is a single currency and a single central bank will lead to a welfare increase for all agents. These welfare gains come from the increased liquidity created by a single currency and by the elimination of the incentive for unilateral inflation.
Basic Model of a Monetary Union
Under a monetary union, there is a single currency and a single price system. Let MtMU represent the stock of common currency in period ty crMU the growth rate of this stock, q£ the period t money price of home goods and q( the period t money price of foreign goods.
Equilibrium and Seignorage with Monetary Union
While there are two distinct goods in this economy, the islands are completely symmetric and agents are ex ante identical. We assume that newly created currency is distributed equally across all agents.10 Thus, we focus on characterizing a symmetric steady state equilibrium. Denote by nMU the steady state level of employment by an agent on either of the islands, qt the period t money price of goods and cMU the steady state level of consumption of either of the two goods.