In the following work the Levin model of monetary integration is going to be derived and then used to show that the union monetary expansion reduces income divergence between the countries in the union and that fiscal expansion in one of the countries increases income divergence. Also it is going to be shown that under the assumption of a constant total output of the two countries neither positive nor negative change in income divergence is a Paretto improvement.
The Levin model looks at the case of two countries creating a monetary union in the form of a common currency area. Let's assume that these two countries are European Union (EU) and United Kingdom (UK) and the rest of the world is just the one economy denoted W. Framework of the Levin model corresponds to the Mundell-Fleming model of an open economy with a freely floating exchange rate.
[...] Effect of the monetary expansion on the vertical intercept of the locus: So changes in the monetary policy do not affect the set of combination of the exchange rate and level of income divergence that correspond to the dynamic equilibrium in commodity market ( locus). Effect of the monetary expansion on the vertical intercept of the locus: Therefore increase in money supply shifts the locus upwards. This shift is shown on the Graph 2. Increase in money supply shifts locus from the position ( into ( so in the long run system gravitates to the new equilibrium point 3. [...]
[...] Level of the exchange rate in the long run is unchanged by the fiscal policy. Conclusion It is assumed that total output of two countries is constant over time ( is in the matrix of exogenous variables, so it doesn't change within the model) , therefore change in the income divergence is never a Peretto improvement: Positive change in Y implies increase in income divergence, which under an assumption of constant total output of two countries means that the country which was better off for a start gets richer, while a country that was poorer becomes even worse off. [...]
[...] Using a concept of the eigen value of the matrix, it is possible to determine that this model gravitates to it's stable equilibrium point following the saddle path. It follows from the fact that determinant of the matrix of coefficients A is less than zero. Slope of the saddle path is given by the formula: Saddle path is horizontal. Dynamic equilibrium in the money market corresponds to the constant level of the exchange rate over time i.e Different combination of the exchange rate and level of income divergence that correspond to the equilibrium in money market are determined by the locus. [...]
[...] At the new equilibrium exchange rate is greater than it used to be so expansionary monetary policy results is depreciation of the domestic currency and therefore increases competitiveness of the domestic goods on the international market. Fiscal expansion in UE. It was assumed that therefore increase in government spending in UE while UK level of government spending is constant will result in increase in the government spending differential. Changes in G results in permanent changes in commodity market this affects the simultaneous long run equilibrium in money and commodity markets and monetary union ends up with the new long run equilibrium values s and Y. [...]
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