# MONETARY UNION: Establishing A Monetary Union 4

Formally, we find:

Proposition 6 A regime in which neither country imposes a CIA is not a subgame perfect Nash equilibrium.

Proof. Consider the configuration in which neither country imposes a CIA requirement and then each chooses their inflation rate. The payoff from this cannot exceed that obtained under monetary union, Vми, since the outcome under monetary union selected the inflation rate that was jointly optimal. Further, from Proposition 5, we know that if neither country imposes a local CIA requirement and each sets the rate of money creation to zero, this is the same outcome as that obtained under monetary union. this

Suppose then that the home country defects from this proposed equilibrium and establishes a CIA. In this case, we consider a steady state equilibrium associated with the (CIA, no CIA) cell of the regime choice game. By following an equilibrium path resulting from the defection of the home government, we axe able to argue that the conjectured equilibrium in which neither country imposes a CIA is not subgame perfect.
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# MONETARY UNION: Establishing A Monetary Union 3

Relationship between Monetary Union and Laissez Faire

We begin our analysis of this game by relating the choice of monetary regime (CIA or no CIA) to a monetary union. Following Kareken and Wallace [1981], we term the regime in which neither country imposes a CIA, a “laissez faire” regime. The following proposition demonstrates that the outcome obtained in a monetary union is a feasible outcome of the game outlined above.

Proposition 5 If neither country imposes a CIA and a = a* = 0, then the resulting allocation is equivalent to that obtained under monetary union.

Proof. See appendix 1

Since there are no local currency constraints, consideration of this economy requires modification of the basic model presented in Section II. Consequently, the characterization of this economy and the proof of this result appear in the appendix. You probably heard about payday loans cash advance options available to the consumer, and you are probably on your way to get one of those. You no longer have to search for a reliable lender though, because we are it. With our help, you can get the money you need in no time. Just apply at cash-loans-for-you.com and it’ll be on its way.
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# MONETARY UNION: Establishing A Monetary Union 2

In the first stage, governments choose their monetary regime, either imposing a local currency cash-in-advance constraint (CIA) or not. If they choose not to impose a CIA, then any currency can be used for malting purchases in that economy. In the second stage, governments simultaneously choose a rate of inflation for their money supply. Finally, we look at the steady state of the world economy given these policy choices.

The interaction between governments can be succinctly represented by the following normal form structure. Here the governments each choose whether to impose a CIA or not. The payoffs in each cell are then determined by the subsequent inflation policies of the government and the consequent steady state equilibrium. The discussion below develops the payoffs for each of these cells.

Note that the structure of our game assumes that governments can commit to a monetary regime. Besides simplifying the analysis, this allows us to distinguish our results from those that rest on internal commitment problems.12 In our economy, if a government could choose the monetary transfer each period after agents chose their labor supply, then each government would have an incentive to inflate the money supply beyond the level calculated in Section II. Alternatively, if the government could commit to a money creation rate prior to the labor supply choice of agents, then it would choose the inflation rate of Z as characterized in Proposition 3. There comes a time when you need money and there seems to be no way out of it. With our speedy cash payday loans online you will not be getting that feeling anymore. Here at speedy-payday-loans.com we give you best rates and APRs for your loans, and the best part is that you can get one within just at few hours!
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# MONETARY UNION: Establishing A Monetary Union

The first goal of this paper was to provide an explicit model of the gains to monetary union. Prom the perspective of price stability, an important implication of Proposition 4 is that the rate of inflation in a monetary union is less than that arising in an equilibrium with multiple currencies. From Proposition 3, the inflation rate in a world economy with multiple currencies will have an inflation rate of Z = ^ which can be quite large in an economy that is reasonably open. For example, if average budget shares for imported goods is .2, then Z = 25%.11

Further, monetary union has the advantage of allowing agents to respond to variations in tastes. To emphasize an important point, having a single currency implies that agents can arrange their consumption bundle after realization of their individual 9.
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# MONETARY UNION: Basic Model 2

Let nMU(aMU) denote the steady state value of employment for both home and, by symmetry, foreign agents. Using this, the steady state level of utility in a monetary union can be expressed as

So, the central bank governing the growth of the money supply will optimally choose zero inflation and the single currency implies that agents can, ex post, optimally respond to their taste shocks. This is not a surprising result given that there are no gains to inflation in the common currency environment.

Measuring the Gains to Monetary Union

Using Proposition 3, let VLC be the expected utility of an agent in the equilibrium of the world economy with local currencies given that both countries inflate at rate Z. This is given by:

where n (0) is the steady state level of employment at zero inflation.
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