## PROBLEMS AND APPLICATIONS

1. The U.S. money supply fell during the years 1929 to 1933 because both the currency–deposit ratio and the reserve–deposit ratio increased. Use the model of the money supply and the data in Table 19-1 to answer the following hypothetical questions about this episode.

1. What would have happened to the money supply if the currency–deposit ratio had risen but the reserve–deposit ratio had remained the same?

2. What would have happened to the money supply if the reserve–deposit ratio had risen but the currency–deposit ratio had remained the same?

3. Which of the two changes was more responsible for the fall in the money supply?

2. To increase tax revenue, the U.S. government in 1932 imposed a 2-cent tax on cheques written on deposits in bank accounts. (In today’s dollars, this tax was about 25 cents per cheque.)

1. How do you think the cheque tax affected the currency–deposit ratio? Explain.

2. Use the model of the money supply under fractional-reserve banking to discuss how this tax affected the money supply.

3. Now use the IS–LM model to discuss the impact of this tax on the economy. Was the cheque tax a good policy to implement in the middle of the Great Depression?

3. Give an example of a bank balance sheet with a leverage ratio of 10. If the value of the bank’s assets rises by 5 percent, what happens to the value of the owners’ equity in this bank? How large a decline in the value of bank assets would it take to reduce this bank’s capital to zero?

4. Suppose that an epidemic of street crime sweeps the country, making it more likely that your wallet will be stolen. Using the Baumol–Tobin model, explain (in words, not equations) how this crime wave will affect the optimal frequency of trips to the bank and the demand for money.

5. Let’s see what the Baumol–Tobin model says about how often you should go to the bank to withdraw cash.

1. How much do you buy per year with currency (as opposed to cheques or credit cards)? This is your value of Y.

2. How long does it take you to go to the bank? What is your hourly wage? Use these two figures to compute your value of F.

3. What interest rate do you earn on the money you leave in your bank account? This is your value of i. (Be sure to write i in decimal form—that is, 6 percent should be expressed 0.06.)

4. According to the Baumol–Tobin model, how many times should you go to the bank each year, and how much should you withdraw each time?

5. In practice, how often do you go to the bank, and how much do you withdraw?

6. Compare the predictions of the Baumol–Tobin model to your behaviour. Does the model describe how you actually behave? If not, why not? How would you change the model to make it a better description of your behaviour?

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6. In Chapter 4, we defined the velocity of money as the ratio of nominal expenditure to the quantity of money. Let’s now use the Baumol–Tobin model to examine what determines velocity.

1. Recalling that average money holdings equal Y/(2N), write velocity as a function of the number of trips to the bank N. Explain your result.

2. Use the formula for the optimal number of trips to express velocity as a function of expenditure Y, the interest rate i, and the cost of a trip to the bank F.

3. What happens to velocity when the interest rate rises? Explain.

4. What happens to velocity when the price level rises? Explain.

5. As the economy grows, what should happen to the velocity of money? (Hint: Think about how economic growth will influence Y and F.)

6. Suppose now that the number of trips to the bank is fixed rather than discretionary. What does this assumption imply about velocity?