Problem
Consider a hypothetical economy with a nominal GDP of $1.2 trillion, real GDP of $600 billion, and money supply of $60 billion. Suppose commercial banks are required to maintain a reserve requirement of 10% of deposits. Assume that banks do not hold excess reserves.
1. Calculate the money multiplier for this economy. If the central bank buys $1 billion of government bonds, what is the effect on money supply? Show your work.
2. Using the quantity theory of money, calculate the price level and the velocity of money for this economy prior to central bank action. Show your work.
3. Assume that velocity is constant and real GDP increases by 2% each year. What will happen to nominal GDP and the price level next year if money supply does not change? Show your work.
4. In (3), what money supply should the central bank set next year to keep the price level unchanged? Show your work.
5. In (3), what money supply should the central bank set next year if it wants inflation of 5%? Show your work.