1. Chapter 15
Money, Inflation and Banking

2. Chapter 15 Topics Alternative forms of money.
Money and the absence of double coincidence of wants.
The causes and effects of long-run inflation.
Financial intermediation and banking.
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3. Alternative Forms of Money
Commodity money (made of precious metal)
Circulating private bank notes (local currency)
Commodity-backed paper currency
(entitled to gold, save cost of carrying goods)
Fiat money (valueless, believe to be accepted in future transaction)
Transactions deposits at banks (purchase by check or debit card)
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4. Role of Money Barter trade: exchange of goods for goods.
Money trade: exchange of goods for money.
Why do people need to use money as medium of exchange (existence of money trade) ?
Barter exchange is difficult in highly-developed, specialized economies.
For example, lack of double coincidence of wants problem happens all the time.
Money trade helps to fix this problem, and therefore, promote transactions and welfare.
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5. Lack of Double-Coincidence of Wants and the Role of Money
An economy with many goods and people are specialize in what they produce and consume.
Ex: Person I produces good 1, but need to consume good 2.
Trade between person I and II without money can be performed if person II produces good 2 and consumes good 1. That is, double-coincidence of wants occurs.
In a economy with many goods, a successful trade is hard to perform due to lack of double-coincidence of wants problem.
To pursue a successful trade, people have to search hard, which is costly. This hurts welfare (transactions are low).
Search costs are reduced dramatically if everyone accepts money.
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6. Figure 15.1 An Absence-of-Double-Coincidence Economy
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7. Figure 15.2 Good 1 as a Commodity Money in the Absence-of-Double-Coincidence Economy
Good 1 is served as
commodity money.
More transactions happen
with commodity money.
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8. Figure 15.3 Fiat Money in the Absence-of-Double-Coincidence Economy
With money as medium
of exchange, successful
transactions increase greatly.
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9. The Effects of Long-Run Inflation
Money may not be neutral in SR (sticky nominal wage models in Ch. 12).
Money is neutral in LR (a change in level of Ms has no long-run effect when prices can adjust freely).
However, a change in growth rate of Ms has LR effect on real variables (not superneutral).
Why: an increase in the money growth rate increases the inflation rate and the nominal interest rate, and reduces employment and output.
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10. Figure 15. 4 Scatter plot of the Inflation Rate vs
Figure Scatter plot of the Inflation Rate vs. the Growth Rate in M0 for the United States, 1960–2006
Conventional Wise:
the sustained inflations are
usually the result of sustained
growth in Ms.
The best fit to the set of
points is the positively sloped
straight line in the figure. So
the two variables are positively
correlated, though not strongly so.
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11. Equation 15.1
Assume that the central bank causes the money supply to grow at a constant rate x.
M’: money supply in future period.
M: money supply in current period.
x: growth rate of money supply from current period to future period.
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12. Equation 15.2
In equilibrium, nominal money supply equals nominal money demand.
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13. Equation 15.3
Nominal money supply also equals nominal money demand in the future period.
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14. Equation 15.4 Combine the previous two equations.
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15. Implication of Equation 15.4
With constant growth rate in Ms, all real variables stay constant, and the growth in Ms is reflected by growth in price level.
Money growth rate = inflation rate
That is, x = i
Q: if x increases, what happens to real variables?
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16. Equation 15.5
The consumer’s intertemporal marginal condition (recall two-period model in Ch.8).
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17. Equation 15.6
Marginal condition reflecting the consumer’s tradeoff between current leisure and future consumption:
Wage income cannot be spent on consumption goods until next period,
The effective real wage is, therefore, P w / P’.
Recall from Ch.4, the MRS l , C = w (real wage)
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18. Equation 15.7
Marginal condition reflecting the consumer’s tradeoff between current leisure and current consumption:
R: nominal interest rate.
The RHS is the relative price of leisure to consumption.
When R increases, leisure becomes cheaper, so consumer trades C for l.
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19. Figure 15.5 The Long-Run Effects of an Increase in the Money Growth Rate
Ns curve shifts as a result of substitution effect.
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20. Conclusion
A change in the growth rate of money supply has real effects in that higher growth in money leads to higher inflation, which changes consumer’s decision on leisure and consumption, which affects equilibrium output and employment.
Moreover, higher inflation increases the nominal interest rate, which is opportunity cost of carrying money. As a result, consumers tend to hold less money balances.
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21. The Friedman Rule
Inflation causes an inefficiency, in that it distorts intertemporal decisions (more leisure, less consumption goods).
The Friedman rule is a prescription for monetary growth that eliminates the inefficiency caused by inflation.
The Friedman rule specifies that the money stock grow at a rate that makes the nominal interest rate zero.
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22. Equation 15.9 Pareto optimality requires that (recall from Ch.5)
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23. Equation 15.10 In a competitive equilibrium (recall from Ch.4),
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24. Equation 15.11 Also, in a competitive equilibrium,
Compared with Equation 15.9, the CE is not PO if R>0.
Inefficiency arises due to the positive nominal interest rate.
Particularly, with R>0, too much leisure is consumed, which leads to
lower labor supply, lower outputs and lower consumption in economy.
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25. How to Restore Efficiency? Optimal Monetary Policy - Friedman Rule
To restore efficiency, one needs to set R = 0.
This implies x = -r < 0. That is, the money supply decreases over time. So the optimal policy to for CB to generate a deflation that continues forever.
By doing so, because of zero opportunity cost of carrying money, all transactions are carried out by money.
Efficiency is restored since consumers do not consumer leisure too much, which increases labor supply, and therefore, output.
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26. Why not Popular in Practice
In practice, no central bank appears to have adopted a Friedman rule to guide monetary policy.
Friedman rule is not followed by CB.
Reason 1: Welfare losses from moderate inflation is quite small.
Reason 2: Liquidity trap: monetary policy does not function any more with zero nominal interest rate.
With R = 0, money and bond are identical assets. So the open market operation would have no real effect in SR.
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27. Properties of Assets
Rate of return: payoff on the asset over some specified period of time divided by the initial investment in the asset, minus one.
Risk: the risk that matters is the one that an asset contributes to the whole portfolio.
Maturity: the time it takes for an asset to pay off.
Liquidity: a measure of how long it takes to sell an asset for its market value and of how high the costs are of selling the asset.
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28. Defining Characteristics of Financial Intermediaries
Borrow from one group of economic agents and lend to another.
Well-diversified with respect to both assets and liabilities.
Transform assets.
Process information.
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29. The Diamond-Dybvig Banking Model
Capture key features of banks.
Explain why bank run (bankruptcy) may happen.
What should government do to prevent bank run.
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30. The Diamond-Dybvig Banking Model
Three periods, T = 0, 1, 2.
N consumers with endowment of one unit of good at T=0.
Production function: convert one unit of good at T=0 to (1+r) unit of good at T=2.
If production is interrupted at T=1, receive one unit of good at T=1. And production stops with nothing produced at T=2.
Two types of consumers: early (consume in period 1) and late (consume in period 2).
Information on type is unknown at T=0, but reveal at T=1. At T=1, with prob. t to be early type and (1-t) to be late type.
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31. Figure 15.6 The Utility Function For a Consumer in the Diamond–Dybvig Model
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32. Equation 15.12
The marginal rate of substitution of early consumption for late consumption is
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33. Figure 15.7 The Preferences of a Diamond–Dybvig Consumer
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34. Optimal Arrangement without Bank
At T=0, the optimal arrangement for consumers is
c1 = 1, c2 = 1 + r.
However, the arrangement with bank is better than this one.
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35. Bank and Deposit Contract
Offer deposit contract (c1, c2) to consumers. That is, early consumers receive c1 at T=1, and late consumer receive c2 at T=2.
Banks behave competitively, so earn zero profits.
Bank cannot tell who is who. That is, if late type come to withdraw at T=1, bank offers them c1.
However, the contract is designed in a way that late type have no incentive to withdraw early.
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36. Equation 15.13
First constraint that a deposit contract must satisfy is
At T=0, all consumers deposit goods at banks (N goods at T=0) and banks
invest all deposits.
At T=1, banks interrupt x fraction of investment to pay C1 to early consumers.
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37. Equation 15.14
Second constraint that a deposit contract must satisfy is
At T=2, banks obtain (1+r)(1-x) N goods from production that is not interrupted
and pay C2 to late consumers.
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38. Equation 15.15 Combine the two constraints to get one:
Lifetime budget constraint for bank, which governs how
the deposit contract (c1, c2) is determined.
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39. Equation 15.16 Re-write the constraint:
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40. Figure 15.8 The Equilibrium Deposit Contract Offered by the Diamond–Dybvig Bank
A: optimal deposit contract.
D: optimal arrangement without bank.
B: arrangements where c1 = c2.
Two features at A:
1. c2 > c1.
2. c1 > 1, c2 < (1 + r)
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41. Bank Run
The fact that bank supplies consumers with insurance against the need for liquidity leaves the bank open to bank run.
Good equilibrium: with optimal deposit contract, early consumers withdraw at T=1, and late consumers withdraw at T=2.
Bad equilibrium: with optimal deposit contract, all consumers withdraw at T=1. Bank run happens because bank cannot satisfy total withdrawal demand at T=1.
(N-1)c1 > N
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42. Deposit Insurance
Remove the incentive of late consumers to withdraw early by assuring them that they will receive c2 given by bank deposit contract.
In the U.S., deposits in depository institutions are insured up to $100,000 by the Federal Deposit Insurance Corporation. So even banks fail, each depositor can receive the value of their deposit up to $100,000.
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