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.

MONETARY UNION: Equilibrium with Local Currency Constraints 2

Determination of Equilibrium Inflation Rates

Using the equilibrium from Proposition 2, let V{<!,&*) and V*(a*,<r) be the lifetime expected welfare of ал agent in the home and foreign islands respectively. Formally,
Again, there are analogous expressions for the foreign consumption levels. Note that the rate of money creation in foreign countries does effect the utility level of home agents through their equilibrium consumption levels of foreign goods. Further, in equilibrium, domestic money creation has three apparent influences: directly on the level of employment, through the transfer (the numerator of c*) and through the rate of price inflation (the denominator of ch).

MONETARY UNION: Equilibrium with Local Currency Constraints

Given the conditions for optimization by the representative agent in each country and the market clearing conditions, the goal is to characterize the steady state equilibrium with valued fiat money in both economies given the two exogenous rates of money growth, о and <r*.8 We then turn to the determination of the equilibrium rates of inflation Source

Steady States Given Rates of Money Creation

To characterize the equilibrium, we conjecture that agents on the home (foreign) island hold a fraction ф (ф*) of their local currency earnings in youth in domestic currency and the remainder is used to purchase foreign currency. Thus,

MONETARY UNION: World Economy with Local Currencies 2

The first constraint implies that the agent takes the money earned in youth and allocates it to the holdings of domestic currency (m£) and foreign currency (m(). Here et is the period t exchange rate: the amount of domestic currency per unit of foreign currency add comment.

The second and third constraints imply that old agents take their money holdings and spend them on home and foreign goods. These constraints reflect two important aspects of our environment. First, within a period, exchange markets open after goods markets. Hence old agents cannot adjust their portfolio holdings before going to goods markets: this is a basic friction in our model.7 Second, agents are required to make purchases using local currency. This is an assumption of our model at this point, though in Section IV we show that this type of constraint will arise endogenously in the game between governments. Given these constraints, old agents have no choice: they will optimally spend all of their money holdings.

MONETARY UNION: World Economy with Local Currencies

In this way, the paper also contributes to the theoretical international macroeconomics literature by providing ал explanation for local currency cash-in-advance constraints.
In fact, the game between governments is one of a prisoners dilemma with the monetary union outcome arising from the ” cooperation” of both countries. From this perspective, monetary union is viewed as a cooperative outcome requiring joint action for its construction and its stability.

World Economy with Local Currencies

We consider an overlapping generations structure in which all agents live for two periods.6 The horizon is infinite with time indexed by t = 1, 2,…..

Further, there are two islands, ” home” and ” foreign”, which axe identical. There is trade across these islands (explained in detail below) but labor is immobile. Each island’s government issues its local currency and imposes that local good is traded through the use of this currency. This corresponds to the imposition by each government of a local currency cash-in-advance constraint.

MONETARY UNION: Introduction 2

While distortionary, inflation is desired as it taxes the money holdings of foreign agents and thus benefits home citizens.4 In contrast, a central bank under a monetary union will internalize the interdependence between countries and optimally choose a lower inflation rate.

While this argument is cast here through an abstract seignorage game between governments, there is a very general and powerful point underlying the analysis: the gains to centralization arise from the internalization of the external effects of national policies. This theme appears often in the literatures on fiscal federalism and trade policies as well.5 With reference to monetary policy, the European Commission report (Emerson et al. [1992, pg. 114]) notes, the adoption of a common monetary policy handled by EuroFed will remove the possibility of beggar-thy-neighbour monetary and exchange rate policies.”