Assume the following information for a hypothetical economy in year 1: money sup

Question

Assume the following information for a hypothetical economy in year 1: money supply = $400 billion; long-term annual growth of potential GDP = 3 percent; velocity = 4. Assume that the banking system initially has no excess reserves and that the reserve requirement is 10 percent. Also suppose that velocity is constant and that the economy initially is operating at its full-employment real output.

Instructions: In part a, enter your answer as a whole number. In part b, round your answer to 1 decimal place.

a. What is the level of nominal GDP in year 1? $_______ billion.

b. Suppose the Fed adheres to a monetary rule through open-market operations.

What amount of U.S. securities will it have to sell to, or buy from, banks or the public between years 1 and 2 to meet its monetary rule? (Click to select) Sell/ Buy $________ billion.?

Explanation / Answer

a. What is the level of nominal GDP in year 1?

To find nominal GDP for year 1 we use the equation of exchange:

   M (Money Supply) V (Velocity) = P (Price Level) Q (Real GDP)

Note that P (Price Level) Q (Real GDP) = Nominal GDP.

   P (Price Level) Q (Real GDP) = Nominal GDP = MV = $400 billion x 4 = $1600 billion

b. Suppose the Fed adheres to a monetary rule through open-market operations. What amount of U.S. securities will it have to sell to, or buy from, banks or the public between years 1 and 2 to meet its monetary rule?

First, we need to find Nominal GDP for year 2 at a 3% rate of annual growth.

   Nominal GDP = (1.03) x $1600 billion = $1648 billion

Second, we use the equation of exchange to determine the Money Supply necessary to achieve the new level of nominal GDP of $1648 billion (Match the growth in nominal GDP).

   M (Money Supply) = P (Price Level) Q (Real GDP) / V (Velocity) = $1648/4 = $412 billion

This implies that the money supply for the entire banking system must increase by $12 billion ($412 - $400).

Finally, since the Fed needs to increase the money supply by $12 billion it must buy securities from the banks. Since the required reserve ratio is 10%, this implies that the money multiplier is 10 (= 1/required reserve ratio =1/.10 = 10). If the Fed buys $1.2 billion in securities the money supply will expand by $12 billion (= $1.2 (purchase of securities) x 10 (money multiplier)).

In conclusion, the Fed needs to buy $1.2 billion in securities from the bank to meet the 3% rate of growth in nominal GDP (monetary rule is actual growth equals potential growth).

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