1. Money Supply and Money Demand18
Money Supply and Money Demand
This chapter is particularly good for students with interests in money and banking and finance.
The first half of this chapter covers money supply, including money creation in the banking system, and how the central bank controls the money supply. Much of this material is review for most students who took a macro principles course. However, this chapter presents a model of the money multiplier that is more realistic than the models found in most principles texts.
The second half of the chapter presents several theories of money demand.

2. In this chapter, you will learn…
how the banking system “creates” money
three ways the Fed can control the money supply, and why the Fed can’t control it precisely
Theories of money demand
a portfolio theory
a transactions theory: the Baumol-Tobin model
CHAPTER 18 Money Supply and Money Demand

3. Banks’ role in the money supply
The money supply equals currency plus demand (checking account) deposits:
M = C + D
Since the money supply includes demand deposits, the banking system plays an important role.
CHAPTER 18 Money Supply and Money Demand

4. A few preliminaries
Reserves (R ): the portion of deposits that banks have not lent.
A bank’s liabilities include deposits,
assets include reserves and outstanding loans.
100-percent-reserve banking: a system in which banks hold all deposits as reserves.
Fractional-reserve banking: a system in which banks hold a fraction of their deposits as reserves.
It might be worthwhile at this point to explain why deposits are liabilities and why reserves and loans are assets.
CHAPTER 18 Money Supply and Money Demand

5. With no banks, D = 0 and M = C = $1000.
SCENARIO 1: No banks
With no banks, D = 0 and M = C = $1000.
In this and the following examples, we assume there is $1000 in currency circulating in the economy.
We then compare the size of the money supply in different scenarios about the banking system: no banks, 100% reserve banking, and fractional reserve banking.
CHAPTER 18 Money Supply and Money Demand

6. SCENARIO 2: 100-percent reserve banking
Initially C = $1000, D = $0, M = $1,000.
Now suppose households deposit the $1,000 at “Firstbank.”
After the deposit, C = $0, D = $1,000, M = $1,000.
100%-reserve banking has no impact on size of money supply.
FIRSTBANK’S balance sheet
Assets
Liabilities
reserves $1,000
deposits $1,000
CHAPTER 18 Money Supply and Money Demand

7. SCENARIO 3: Fractional-reserve banking
Suppose banks hold 20% of deposits in reserve, making loans with the rest.
Firstbank will make $800 in loans.
The money supply now equals $1,800:
Depositor has $1,000 in demand deposits.
Borrower holds $800 in currency.
FIRSTBANK’S balance sheet
Assets
Liabilities
reserves $1,000
deposits $1,000
reserves $200
loans $800
CHAPTER 18 Money Supply and Money Demand

8. SCENARIO 3: Fractional-reserve banking
Thus, in a fractional-reserve banking system, banks create money.
The money supply now equals $1,800:
Depositor has $1,000 in demand deposits.
Borrower holds $800 in currency.
FIRSTBANK’S balance sheet
Assets
Liabilities
deposits $1,000
reserves $200
loans $800
CHAPTER 18 Money Supply and Money Demand

9. SCENARIO 3: Fractional-reserve banking
Suppose the borrower deposits the $800 in Secondbank.
Initially, Secondbank’s balance sheet is:
SECONDBANK’S balance sheet
Assets
Liabilities
Secondbank will loan 80% of this deposit.
Maybe the borrower deposits the $800 in the bank. Or maybe the borrower uses the money to buy something from someone else, who then deposits it in the bank. In either case, the $800 finds its way back into the banking system.
reserves $800
loans $0
reserves $160
loans $640
deposits $800
CHAPTER 18 Money Supply and Money Demand

10. SCENARIO 3: Fractional-reserve banking
If this $640 is eventually deposited in Thirdbank,
then Thirdbank will keep 20% of it in reserve, and loan the rest out:
THIRDBANK’S balance sheet
Assets
Liabilities
Again, the person who borrowed the $640 will either deposit it in his own checking account, or will use it to buy something from somebody who, in turn, deposits it in her checking account. In either case, the $640 winds up in a bank somewhere, and that bank can then use it to make new loans.
reserves $128
loans $512
reserves $640
loans $0
deposits $640
CHAPTER 18 Money Supply and Money Demand

11. Finding the total amount of money:
Original deposit = $1000
+ Firstbank lending = $ 800
+ Secondbank lending = $ 640
+ Thirdbank lending = $ 512
+ other lending…
Total money supply = (1/rr )  $1, where rr = ratio of reserves to deposits
In our example, rr = 0.2, so M = $5,000
CHAPTER 18 Money Supply and Money Demand

12. Money creation in the banking system
A fractional reserve banking system creates money, but it doesn’t create wealth:
Bank loans give borrowers some new money
and an equal amount of new debt.
CHAPTER 18 Money Supply and Money Demand

13. A model of the money supply
exogenous variables
Monetary base, B = C + R
controlled by the central bank
Reserve-deposit ratio, rr = R/D
depends on regulations & bank policies
Currency-deposit ratio, cr = C/D
depends on households’ preferences
CHAPTER 18 Money Supply and Money Demand

14. Solving for the money supply:
where
The point of all this algebra is to express the money supply in terms of the three exogenous variables described on the preceding slide.
CHAPTER 18 Money Supply and Money Demand

15. The money multiplier where If rr < 1, then m > 1
If monetary base changes by B, then M = m  B
m is the money multiplier, the increase in the money supply resulting from a one-dollar increase in the monetary base.
CHAPTER 18 Money Supply and Money Demand

16. Exercise
where
Suppose households decide to hold more of their money as currency and less in the form of demand deposits.
Determine impact on money supply.
Explain the intuition for your result.
CHAPTER 18 Money Supply and Money Demand

17. Solution to exercise
Impact of an increase in the currency-deposit ratio cr > 0.
An increase in cr increases the denominator of m proportionally more than the numerator. So m falls, causing M to fall.
If households deposit less of their money, then banks can’t make as many loans, so the banking system won’t be able to “create” as much money.
Note:
An increase in cr raises both the numerator and denominator of the expression for m. But since rr < 1, the denominator is smaller than the numerator, so a given increase in cr will increase the denominator proportionally more than the numerator, causing a decrease in m.
If your students know calculus, they can use the quotient rule to see that (dm/dcr) < 0.
CHAPTER 18 Money Supply and Money Demand

18. Three instruments of monetary policy
1. Open-market operations
2. Reserve requirements
3. The discount rate
CHAPTER 18 Money Supply and Money Demand

19. Open-market operations
definition: The purchase or sale of government bonds by the Federal Reserve.
how it works: If Fed buys bonds from the public, it pays with new dollars, increasing B and therefore M.
Why it’s called “open market operations”:
The “operations” are the buying and selling. The market in which U.S. Treasury bonds are traded is “open” in the sense that anyone---you, me, your Aunt Zelda, the Fed---can buy or sell in this market.
CHAPTER 18 Money Supply and Money Demand

20. Reserve requirements
definition: Fed regulations that require banks to hold a minimum reserve-deposit ratio.
how it works: Reserve requirements affect rr and m: If Fed reduces reserve requirements, then banks can make more loans and “create” more money from each deposit.
CHAPTER 18 Money Supply and Money Demand

21. The discount rate
definition: The interest rate that the Fed charges on loans it makes to banks.
how it works: When banks borrow from the Fed, their reserves increase, allowing them to make more loans and “create” more money.
The Fed can increase B by lowering the discount rate to induce banks to borrow more reserves from the Fed.
CHAPTER 18 Money Supply and Money Demand

22. Which instrument is used most often?
Open-market operations: most frequently used.
Changes in reserve requirements: least frequently used.
Changes in the discount rate: largely symbolic. The Fed is a “lender of last resort,” does not usually make loans to banks on demand.
Why not reserve requirements? Making them too low creates a risk of bank runs. Making them too high makes banking unprofitable.
In addition, banking would be difficult if the Fed changed reserve requirements frequently.
CHAPTER 18 Money Supply and Money Demand

23. Why the Fed can’t precisely control M
where
Households can change cr, causing m and M to change.
Banks often hold excess reserves (reserves above the reserve requirement).
If banks change their excess reserves, then rr, m, and M change.
CHAPTER 18 Money Supply and Money Demand

24. CASE STUDY: Bank failures in the 1930s
From 1929 to 1933,
Over 9,000 banks closed.
Money supply fell 28%.
This drop in the money supply may have caused the Great Depression.
It certainly contributed to the severity of the Depression.
CHAPTER 18 Money Supply and Money Demand

25. CASE STUDY: Bank failures in the 1930s
where
Loss of confidence in banks  cr  m
Banks became more cautious  rr  m
CHAPTER 18 Money Supply and Money Demand

26. CASE STUDY: Bank failures in the 1930s
August 1929
March 1933
% change
13.5
5.5
19.0
–40.3
41.0
–28.3%
22.6 D
3.9 C
26.5 M
2.9
5.5
8.4
–9.4
41.0
18.3
3.2 R
3.9 C
7.1 B
Table 18-1, p.517. Source: Adapted from Milton Friedman and Anna Schwartz, A Monetary History of the United States, (Princeton, NJ: Princeton University Press, 1963), Appendix A.
To the table, I have added an extra column with the percent changes.
I have animated the table so that the rows appear in three groups.
First group: M, C, and D, because M = C + D
Second group: B, C, and R, because B = C + R
Third group: m and its components, rr and cr
The base rises, yet the money multiplier falls so much that the money supply falls.
0.41
0.21
2.3
141.2
50.0
–37.8
0.17 cr
0.14 rr
3.7 m
CHAPTER 18 Money Supply and Money Demand

27. Could this happen again?
Many policies have been implemented since the 1930s to prevent such widespread bank failures.
E.g., Federal Deposit Insurance, to prevent bank runs and large swings in the currency-deposit ratio.
CHAPTER 18 Money Supply and Money Demand

28. Money Demand Two types of theories Portfolio theories
emphasize “store of value” function
relevant for M2, M3
not relevant for M1. (As a store of value, M1 is dominated by other assets.)
Transactions theories
emphasize “medium of exchange” function
also relevant for M1
Why portfolio theories are not relevant for M1:
As a store of value, M1 is dominated by other assets: other assets serve the store of value function as well as M1, but offer a better risk/return profile, so there is no reason why anybody would hold M1 for a store of value.
CHAPTER 18 Money Supply and Money Demand

29. A simple portfolio theory
where
rs = expected real return on stocks
rb = expected real return on bonds
 e = expected inflation rate
W = real wealth
Intuition for the signs:
Stocks and bonds are alternatives to money. An increase in their expected returns makes money less attractive, and thus reduces desired money holdings.
The real return to holding money is -e. An increase in e is a decrease in the real return to holding money, which would cause a decrease in desired money balances.
And finally, an increase in wealth causes an increase in the demand for all assets.
CHAPTER 18 Money Supply and Money Demand

30. The Baumol-Tobin Model
a transactions theory of money demand
notation:
Y = total spending, done gradually over the year
i = interest rate on savings account
N = number of trips consumer makes to the bank to withdraw money from savings account
F = cost of a trip to the bank (e.g., if a trip takes 15 minutes and consumer’s wage = $12/hour, then F = $3)
In the Baumol-Tobin model, we assume for simplicity that the consumer’s wealth is divided between cash on hand and savings account deposits. The savings account pays interest rate i, while cash pays no nominal interest.
Alternatively, we can think of “money” in the Baumol-Tobin model as representing all monetary assets, including some that pay interest. Then, i in the model would be the interest rate on non-monetary assets (e.g. stocks & bonds) minus the interest rate on monetary assets (interest-bearing checking & money market deposit accounts). F would be the cost of converting non-monetary assets into monetary ones, such as a brokerage fee. The decision about how often to pay the brokerage fee is analogous to the decision about how often to make a trip to the bank.
CHAPTER 18 Money Supply and Money Demand

31. Money holdings over the year
Time 1
N = 1
Average = Y/ 2
Figure 18-1 on p.521.
Our first step: compute average money holdings as a function of N. (Then, we will find the optimal value of N.)
If N=1, then the consumer withdraws $Y from her savings account at the beginning of the year. As she spends it gradually throughout the year, her money holdings fall.
CHAPTER 18 Money Supply and Money Demand

32. Money holdings over the year
Time 1
1/2
N = 2 Y
Y/ 2
Average = Y/ 4
Figure 18-1 on p.521.
If N = 2, consumer makes one trip at the beginning of the year, withdraws half of the money she will spend throughout the year. She spends it gradually over the first half of the year until it runs out. Then she makes another trip, withdrawing enough money to last her the second half of the year, and spends it down gradually.
CHAPTER 18 Money Supply and Money Demand

33. Money holdings over the year
1/3
2/3
Money holdings
Time 1
N = 3 Y
Average = Y/ 6
Y/ 3
Figure 18-1 on p.521.
CHAPTER 18 Money Supply and Money Demand

34. The cost of holding money
In general, average money holdings = Y/2N
Foregone interest = i (Y/2N )
Cost of N trips to bank = F N
Thus,
Given Y, i, and F, consumer chooses N to minimize total cost
CHAPTER 18 Money Supply and Money Demand

35. Finding the cost-minimizing N
Figure 18-2 on p.523.
(For any value of N, the height of the red line equals the height of the blue line plus the height of the green line at that N.)
This slide shows the graphical derivation of N*.
The following slide uses basic calculus to derive an expression for N*. It is “hidden” and can be omitted without loss of continuity. If you display it, then before leaving this slide you might point out that the slope of the cost function (red line) equals zero at N*.
CHAPTER 18 Money Supply and Money Demand

36. The money demand function
The cost-minimizing value of N :
To obtain the money demand function, plug N* into the expression for average money holdings:
If you did not show your students the slide with the calculus derivation of the expression for N*, then you can just say
“it turns out that N* is equal to this expression….”
Money demand depends positively on Y and F, and negatively on i.
CHAPTER 18 Money Supply and Money Demand

37. The money demand function
The Baumol-Tobin money demand function:
How this money demand function differs from previous chapters:
B-T shows how F affects money demand.
B-T implies: income elasticity of money demand = 0.5, interest rate elasticity of money demand = 0.5
Page 523 of the text contains a very nice paragraph discussing things that alter F, and hence money demand:
automatic teller machines
internet banking
wages (higher wages increase the opportunity cost of time spent visiting the bank)
bank or brokerage fees
CHAPTER 18 Money Supply and Money Demand

38. EXERCISE: The impact of ATMs on money demand
During the 1980s, automatic teller machines became widely available.
How do you think this affected N* and money demand? Explain.
Answer:
(From p.523)
“The spread of automatic teller machines reduces F by reducing the time it takes to withdraw money.”
Lower F increases N* and decreases money demand - you can see this from the expressions N* and money demand.
A decrease in the cost of withdrawing money allows consumers to hold lower real money balances relative to their spending, so they can keep more of their money in interest-bearing bank accounts. Of course, they will need to make more trips to the bank now, but doing so is less costly.
CHAPTER 18 Money Supply and Money Demand

39. Examples of financial innovation:
Financial Innovation, Near Money, and the Demise of the Monetary Aggregates
Examples of financial innovation:
many checking accounts now pay interest
very easy to buy and sell assets
mutual funds are baskets of stocks that are easy to redeem - just write a check
Non-monetary assets having some of the liquidity of money are called near money.
Money & near money are close substitutes, and switching from one to the other is easy.
CHAPTER 18 Money Supply and Money Demand

40. Financial Innovation, Near Money, and the Demise of the Monetary Aggregates
The rise of near money makes money demand less stable and complicates monetary policy.
1993: the Fed switched from targeting monetary aggregates to targeting the Federal Funds rate.
This change may help explain why the U.S. economy was so stable during the rest of the 1990s.
CHAPTER 18 Money Supply and Money Demand

41. Chapter Summary
1. Fractional reserve banking creates money because each dollar of reserves generates many dollars of demand deposits.
2. The money supply depends on the
monetary base
currency-deposit ratio
reserve ratio
3. The Fed can control the money supply with
open market operations
the reserve requirement
the discount rate
CHAPTER 18 Money Supply and Money Demand
slide 41

42. Chapter Summary 4. Portfolio theories of money demand
stress the store of value function
posit that money demand depends on risk/return of money & alternative assets
5. The Baumol-Tobin model
a transactions theory of money demand, stresses “medium of exchange” function
money demand depends positively on spending, negatively on the interest rate, and positively on the cost of converting non-monetary assets to money
CHAPTER 18 Money Supply and Money Demand
slide 42