Size Effects and Welfare Analysis of Monetary Union

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According to my analysis using a large-country intertemporal open economy macro model, it was shown that the relative price of a monetary union (MU) against the non-MU decreases as the MU's size increases, and the MU's terms of trade deteriorate accordingly. The welfare levels of both MU and non-MU increase, but the former's increase is larger than that of the latter. Examining the actual historical data of MUs and approximating the size by population o width, the size effect due to population was statistically shown on the welfare level proxied by GDP.