0. Class Slides for EC 204
To Accompany Chapter 18

1. Chapter objectives Money supply Theories of money demand
how the banking system “creates” money
three ways the Fed can control the money supply
why the Fed can’t control it precisely
Theories of money demand
a portfolio theory
a transactions theory: the Baumol-Tobin model

2. 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.

3. A few preliminaries
Reserves (R ): the portion of deposits that banks have not lent.
To a bank, liabilities include deposits, and
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.
You might explain why deposits are liabilities and why reserves and loans are assets.

4. 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’s $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.

5. SCENARIO 2: 100 Percent Reserve Banking
Initially C = $1000, D = $0, M = $1000.
Now suppose households deposit the $1000 at “Firstbank.”
After the deposit, C = $0, D = $1000, M = $1000.
100% Reserve Banking has no impact on size of money supply.
FIRSTBANK’S balance sheet
Assets
Liabilities
reserves $1000
deposits $1000

6. 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 $1800:
The depositor still has $1000 in demand deposits,
but now the borrower holds $800 in currency.
FIRSTBANK’S balance sheet
Assets
Liabilities
reserves $1000
deposits $1000
reserves $200
loans $800

7. SCENARIO 3: Fractional-Reserve Banking
Thus, in a fractional-reserve banking system, banks create money.
The money supply now equals $1800:
The depositor still has $1000 in demand deposits,
but now the borrower holds $800 in currency.
FIRSTBANK’S balance sheet
Assets
Liabilities
deposits $1000
reserves $200
loans $800

8. SCENARIO 3: Fractional-Reserve Banking
Suppose the borrower deposits the $800 in Secondbank.
Initially, Secondbank’s balance sheet is:
But then Secondbank will loan 80% of this deposit
and its balance sheet will look like this.
SECONDBANK’S balance sheet
Assets
Liabilities
deposits $800
reserves $160
loans $640
reserves $800
loans $0
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.

9. 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
deposits $640
reserves $640
loans $0
reserves $128
loans $512
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.

10. 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 )  $ where rr = ratio of reserves to deposits
In our example, rr = 0.2, so M = $5000

11. 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.

12. A model of the money supply
exogenous variables
the monetary base, B = C + R
controlled by the central bank
the reserve-deposit ratio, rr = R/D
depends on regulations & bank policies
the currency-deposit ratio, cr = C/D
depends on households’ preferences

13. Solving for the money supply:
M = C + D and B = C + R
Divide M by B:
M/B = [C+D] / [C+R]
M/B = [C/D + D/D] / [C/D + R/D]
M/B = [cr + 1] / [cr + rr]
M = {[cr + 1] / [cr + rr]}B
The point of all this algebra is to express the money supply in terms of the 3 exogenous variables described on the preceding slide.

14. The money multiplier M = {[cr + 1] / [cr + rr]}B = m x B
If rr < 1, then m > 1
If monetary base changes by B, then M = m  B
m is called the money multiplier.

15. Exercise Determine impact on money supply.
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.
Solution:
1. An increase in cr causes the money multiplier and therefore M itself to fall. 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 find (dm/dcr) < 0.
2. 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.
The following slide shows the solution.

16. 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 too.
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.

17. Three instruments of monetary policy
Open market operations
Reserve requirements
The discount rate

18. 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, the Fed---can buy or sell in this market.

19. Reserve requirements
Definition: Fed regulations that require banks to hold a minimum reserve-deposit ratio.
How it Works: Reserve requirements affect rr and thus m: If Fed reduces reserve requirements, then banks can make more loans and “create” more money from each deposit.

20. 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.

21. 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.

22. Why the Fed can’t precisely control M
M = {[cr + 1] / [cr + rr]}B = m x B
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.

23. CASE STUDY: Bank failures in the 1930s
From 1929 to 1933,
Over 9000 banks closed.
Money supply fell 28%.
This drop in the money supply may have caused the Great Depression.
It certainly contributed to the Depression’s severity.

24. Table 18-1: The Money Supply and its Determinants: 1929 and 1933
Source: Adapted from Milton Friedman and Anna Schwartz, A Monetary History of the United States, (Princeton, NJ: Princeton University Press, 1963), Appendix A.
cr rose due to loss of confidence in banks

25. Table 18-1: The Money Supply and its Determinants: 1929 and 1933
rr rose because banks became more cautious, increased excess reserves

26. Table 18-1: The Money Supply and its Determinants: 1929 and 1933
The rise in cr and rr reduced the money multiplier.

27. Should We Blame the Fed?
Monetary base increased by 18 percent from 1929 to
Money multiplier fell by 38 percent.
Critics of Fed argue that Fed could have acted as a “lender of last resort,” helping maintain confidence in the banking system
Critics also argue that the Fed could have always increased the monetary base by more than they did.

28. Could this happen again?
Many policies have been implemented since the 1930s to prevent such widespread bank failures.
Example: Federal Deposit Insurance, to prevent bank runs and large swings in the currency-deposit ratio.

29. 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.

30. A Simple Portfolio Theory
(M/P)d = L(rs, rb, pe, W)
where:
rs is the return on stocks
rb is the return on bonds
pe is the expected inflation rate
W is 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.

31. The Underground Economy
Amount of currency per capita for United States is $2000.
Half is in form of $100 bills.
Some of this currency is used in the underground economy.
With few other investment options, these people hold currency for portfolio reasons.
Money is not a dominated asset for them.
Inflation may be desirable as a tax on these holdings.

32. 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 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.

33. Money holdings over the year
Time 1
N = 1
Average = Y/ 2
Figure 18-1 on p.493.
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.

34. Money holdings over the year
Time 1
1/2
N = 2 Y
Y/ 2
Average = Y/ 4
Figure 18-1 on p.493.
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.

35. 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.493.

36. The Cost of Holding Money
In general, average money holdings = Y/2N
Foregone interest = i  (Y/2N )
Cost of N trips to bank = F x N
Thus,
Total Cost = i  (Y/2N ) + F  N
Given Y, i, and F, consumer chooses N to minimize total cost

37. Finding the cost-minimizing N
Figure 18-2 on p.495.
(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 equals zero at N*.

38. Finding the cost-minimizing N
Total Cost = i  (Y/2N ) + F  N
Take the derivative of total cost with respect to N, then set it equal to zero:
dTotal Cost/dN = -iYN-2/2 + F = 0
This slide uses calculus to derive N*.
Solve for the cost-minimizing N*
N* = [iY/2F]0.5

39. The Money Demand Function
The cost-minimizing value of N :
N* = [iY/2F]0.5
To obtain the money demand function, plug N* into the expression for average money holdings:
Average Money Holdings = Y/2N*
= [YF/2i]0.5
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 .

40. The Money Demand Function
The Baumol-Tobin money demand function:
(M/P)d = [YF/2i]0.5
How the B-T money demand function differs from the money demand function from previous chapters:
B-T shows how F affects money demand
B-T implies that the: income elasticity of money demand = 0.5, interest rate elasticity of money demand = 0.5
Page 495 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

41. Integer Constraints
Because trips to the bank must be integers, the problem is a bit more complicated.
When the solution is in between two integers, people will choose either the higher or lower number of trips depending on the total cost at those points.
Small changes in interest rates and income will not affect the number of trips to the bank for these people.
Thus, money demand will not respond to small changes in interest rates and will respond proportionately to changes in income.

42. Integer Constraints
For these people, the income elasticity of money demand is one and the interest elasticity is zero.
If some people face these integer constraints and others behave exactly according to the model, this has the effect changing the overall elasticity of demand predictions:
Income elasticity of money demand = 0.5 to 1.0
Interest rate elasticity of money demand = 0.5 to 0.0
This is what we find empirically for these elasticities when we estimate money demand functions.

43. 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.

44. 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.

45. 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 officially switched from targeting monetary aggregates to targeting the Federal Funds rate.
In mid-1980s had effectively shifted away from emphasizing monetary aggregates.
This change may help explain why the U.S. economy was so stable during the rest of the 1990s.

46. 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

47. 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
is an example of the transactions theories 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