Michael Carlberg

The Basic Model

In this chapter we consider a monetary union of two countries, let us say Germany and France. The exchange rate between the monetary union and the rest of the world is flexible. Take for instance an increase in German government purchases. Then what will be the effect on German income, and what on French income? Alternatively, take an increase in union money supply. Again what will be the effect on German income, and what on French income?

Small Open Economy

The analysis will be conducted within the following framework. Firms produce a single commodity Y by means of capital K and labour N. For ease of exposition, let technology be of the Cobb-Douglas type with constant returns to scale Y = KαNβ, α > 0, β > 0 and α + β = 1. Full employment does always prevail. Domestic output can be devoted to consumption, investment and net exports Y = C + 4 + I + X. Labour grows at the natural rate N = nN with n = const. Here the dot denotes the time derivative N = dN / dt with time t.

International Economic Growth

Brief Survey of the Literature.- I. Small Open Economy.- 1. Solow Model.- 1.1. Foreign Assets.- 1.1.1. Steady State.- 1.1.2. Process of Adjustment.- 1.2. Foreign Debt.- 1.3. Assets.- 1.4. Numerical Example.- 1.5. Delayed Adjustment of Capital Stock.- 1.6. Technical Progress at Home.- 2. Overlapping Generations.- 3. Infinite Horizon.- II. Two Countries.- 1. Different Saving Rates (Overlapping Generations).- 1.1. Steady State.- 1.2. Process of Adjustment.- 2. Different Saving Rates (Solow Model).- 2.1. Steady State.- 2.2. Introducing Capital Mobility.- 3. Technical Progress Abroad (Solow Model).- 3.1. Steady State.- 3.2. Process of Adjustment.- 4. Different Rates of Labour Growth (Overlapping Generations).- 4.1. Steady State.- 4.2. Process of Adjustment.- III. Imperfect Capital Mobility.- 1. Solow Model (Fixed Debt Ratio).- 1.1. Steady State.- 1.2. Process of Adjustment.- 2. Overlapping Generations.- 2.1. Fixed Debt Ratio.- 2.2. Endogenous Interest Rate.- 3. Inifinite Horizon (Fixed Debt Ratio).- IV. Labour Mobility.- 1. Introducing Labour Mobility.- 1.1. Model.- 1.2. Numerical Example.- 2. Different Rates of Labour Growth.- V. Fixed Wage Rate.- 1. Closed Economy.- 2. Perfect Capital Mobility.- 3. Imperfect Capital Mobility.- 4. Land as Immobile Factor.- VI. Endogenous Growth.- 1. Closed Economy.- 2. Small Open Economy.- 3. Two Countries.- 4. Infinite Horizon.- Conclusion.- Result.- Symbols.- References.

Flexible Exchange Rate

The investigation will be carried out within a small open economy characterized by perfect capital mobility. Let us begin with the foreign sector. e denotes the nominal exchange rate. p is the price of domestic goods, expressed in domestic currency. Similarly p* is the price of foreign goods, expressed in foreign currency. So ep*/p is the real exchange rate. F symbolizes foreign assets denominated in domestic currency. Hence F/p are foreign assets expressed in domestic goods.

A leontief model of interregional economic growth

Savings are invested in the region offering the best return, thus increasing its stock of capital. Simultaneously labour grows, moving to the region which pays the highest wages. On which path does this system of regions develop? Theoretical analysis shows that the time path depends on Leontief technology, propensity to save and on the growth of labour. In the case of isolated regions a dynamic equilibrium only exists by chance; in the case of integrated regions, however, a stable equilibrium is likely to exist. There is no need for regional policy in this setting, since the market allocates efficiently and distributes equitably.

Some Numerical Examples

Here are eight distinct cases a demand shock in Germany a supply shock in Germany a mixed shock in Germany another mixed shock in Germany a common demand shock in Europe a common supply shock in Europe a common mixed shock in Europe another common mixed shock in Europe. The targets of policy cooperation are zero inflation and zero unemployment in each of the member countries.

Policy coordination in a monetary union

1. The Basic Model.- 2. Monetary Policy in the Union.- 3. Fiscal Competition between Germany and France.- 4. Fiscal Cooperation between Germany and France.- 5. Competition between the Union Central Bank, the German Government, and the French Government.- 6. Cooperation between the Union Central Bank, the German Government, and the French Government.- 7. Competition between the German Labour Union and the French Labour Union.- 8. Cooperation between the German Labour Union and the French Labour Union.- 9. Competition between the Central Bank, the German Labour Union, and the French Labour Union.- 10. Cooperation between the Central Bank, the German Labour Union, and the French Labour Union.- 11. Inflation in Germany and France.- 1. The Basic Model.- 2. Monetary Competition between Europe and America.- 3. Monetary Cooperation between Europe and America.- 4. Fiscal Competition between Europe and America.- 5. Fiscal Cooperation between Europe and America.- 1. The Basic Model.- 2. Fiscal Competition between Germany and France.- 3. Fiscal Cooperation between Germany and France.- 4. Competition between the European Central Bank, the German Government, and the French Government.- 5. Cooperation between the European Central Bank, the German Government, and the French Government.- 1. The Small Monetary Union of Two Countries.- 2. The World of Two Monetary Regions.- 3. The Large Monetary Union of Two Countries.- Synopsis.- Conclusion.- Result.- Symbols.- A Brief Survey of the Literature.- References.

The Static Model

The world consists of two monetary regions, let us say Europe and America. The exchange rate between Europe and America is flexible. Europe in turn consists of two countries, let us say Germany and France. Germany and France form a monetary union. Take for example an increase in European money supply. Then what will be the effect on German output, on French output, and on American output? Alternatively take an increase in German investment, German nominal wages, or German productivity.

Long-Run Equilibrium

In the steady state, the motion of capital per head and money wages comes to a halt: