10. a. With a required reserve ratio of 10 percent and no excess reserves, the money multiplier is 1/.10 = 10. If the Fed sells $1 million of bonds, reserves will decline by $1 million and the money supply will contract by 10 x $1 million = $10 million.

b. Banks might wish to hold excess reserves if they need to hold the reserves for their day-to-day operations, such as paying other banks for customers' transactions, making change, cashing paychecks, and so on. If banks increase excess reserves such that there's no overall change in the total reserve ratio, then the money multiplier doesn't change and there's no effect on the money stock.

11. a. With banks holding only required reserves of 10 percent, the money multiplier is 1/.10 = 10. Since reserves are $100 billion, the money stock is 10 x $100 billion = $1,000 billion.

b. If the required reserve ratio is raised to 20 percent, the money multiplier declines to 1/.20 = 5. With reserves of $100 billion, the money stock would decline to $500 billion, a decline of $500 billion. Reserves would be unchanged, since all available currency would be held by banks as reserves.

1. In this problem, all amounts are shown in billions.

a. Nominal GDP = P x Y = $10,000 and Y = real GDP = $5,000, so P = (P x Y)/Y = $10,000/$5,000 = 2.

Since M x V = P x Y, then V = (P x Y)/M = $10,000/$500 = 20.

b. If M and V are unchanged and Y rises by 5 percent, then since M x V = P x Y, P must fall by 5 percent. As a result, nominal GDP is unchanged.

c. To keep the price level stable, the Fed must increase the money supply 5 percent, matching the increase in real GDP. Then, since velocity is unchanged, the price level will be stable.

d. If the Fed wants inflation to be 10 percent, it will need to increase the money supply 15 percent. Thus M x V will rise 15 percent, causing P x Y to rise 15 percent, with a 10 percent increase in prices and a 5 percent rise in real GDP.

2. a. If people need to hold less cash, the demand for money shifts to the left, since there will be less money demanded at any price level.

b. If the Fed doesn’t respond to this event, the shift to the left of the demand for money combined with no change in the supply of money leads to a decline in the value of money (1/P), which means the price level rises, as shown in Figure 28-1.

 

 

 

Figure 28-1

c. If the Fed wants to keep the price level stable, it should reduce the money supply from S₁ to S₂ in Figure 28-2. This would cause the supply of money to shift to the left by the same amount that the demand for money shifted, resulting in no change in the value of money and the price level.

Figure 28-2

3. With constant velocity, reducing the inflation rate to zero would require the money growth rate to equal the growth rate of output, not zero, according to the quantity theory of money (M x V = P x Y).

10. The functions of money are to serve as a medium of exchange, a unit of account, and a store of value. Inflation mainly affects the ability of money to serve as a store of value, since inflation erodes money's purchasing power, making it less attractive as a store of value. Money also isn’t as useful as a unit of account when there’s inflation, because stores have to change prices more often and because people are confused and inconvenienced by the changes in the value of money. In some countries with hyperinflation, stores post prices in terms of a more stable currency, such as the U.S. dollar, even when the local currency is still used as the medium of exchange. And sometimes countries even stop using their local currency altogether, using a foreign currency as the medium of exchange as well.