91影视

By Fisher鈥檚 equation of quantity theory of money, the product of the economy鈥檚 money supply and its velocity of circulation equals the nation鈥檚 GDP.

MV = PQ, where M is the money supply, V is the velocity of money, P is the price level, and Q is the number of domestic products. PQ is the nominal GDP.

When M is $400 billion, and V is 4, the nominal GDP in year 1 is:

GDP = $400 x 4

= $1600

Since the annual growth rate of nominal GDP is 3%, the nominal GDP in year 2 is:

Nominal GDP₂= Compound Growth Rate x GDP₁

Nominal GDP₂= 1.03 x $1600

= $1648

By Fisher鈥檚 equation:

$$\begin{gathered} M=\frac{PQ}{V} \\ M=\frac{1648}{4} \\ M=412 \end{gathered}$$

The money supply has to be increased by $12 billion (= 412 鈥� 400) in year 2. The Fed will buy the U.S. securities equal to the ratio of money created to the money multiplier to increase the money supply.

As given, the required reserve ratio is 10% (or 0.1), the money multiplier is:

$$\begin{gathered} m=\frac{1}{r} \\ =\frac{1}{0.1} \\ =10 \end{gathered}$$

The amount of U.S. securities purchased by the Fed is:

$$\begin{gathered} USSecurities=\frac{Moneycreated}{Moneymultiplier} \\ =\frac{12}{10}=1.2 \end{gathered}$$

Hence, the Fed will buy U.S. securities worth $1.2 billion.