Suppose that inflation rates are initially zero in the euro area and the US, nominal interest rates

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Question:

Suppose that inflation rates are initially zero in the euro area and the US, nominal interest rates in the two economies are initially equal, and the price level is constant in the short run and flexible in the long run. Today, the ECB adopts the digital euro, leading to a permanent decline in the demand for real money balances in the euro area, while the ECB keeps the level of its nominal money supply unchanged. The US Federal Reserve maintains its current monetary and payment system.

Use the complete theory of the FX determination to answer the following questions, treating the euro area as the Home country.

(a). Analyse the short-run and the long-run effects of adopting the digital euro on the nominal interest rate, the price level and real money balances in the euro area, respectively. Explain your findings intuitively.

(b). Analyse how the nominal exchange rate E_€/$ changes in the short run and in the long run, respectively. Does the exchange rate overshooting occur? Explain your findings intuitively. [Hint: Identify the base currency and stick with your choice in the entire analysis]

(c). If the ECB intends to avoid exchange rate movements, how should it change the level of its nominal money supply when adopting the digital euro? Explain your findings intuitively.