As you know, the European Monetary Union (EMU) has recently adopted a common currency a single central bank (the ECB). Assume the cen- tral bank has direct control over the rate of inflation and has a standard loss function defined over output and inflation. Further suppose that all economies in the EMU follow the same underlying model, and that the ECB cannot commit to a particular policy.
(a) Suppose a country has a different target level of output than the ECB. Further assume that a country which decides to leave the EMU pays some annual cost C in units of the loss function (this may be lost trade, fines, lost prestige, etc.) Work out the conditions under which a country will choose to leave the EMU. Provide an intuitive explanation for your answer.
(b) Now suppose that a country has a different weight on inflation in its loss function. Assuming the same cost C as in part (a), work out the conditions under which a country will choose to leave the EMU. Provide an intuitive explanation for your answer. Provide an intuitive explanation for your answer.
(c) Now suppose that a country has the same loss function as the ECB, but has a different slope to its short-run aggregate supply curve. Assuming the same cost C as in part (a), work out the conditions under which a country will choose to leave the EMU. Provide an intuitive explanation for your answer.