1. Chapter 22
The Demand for Money

2. Quantity Theory of Money
Velocity
V = (P × Y) / M
Equation of Exchange M  V = P  Y
(an identity)
Quantity Theory of Money
1. Irving Fisher (1911): V is fairly constant in the short run (determined by the institutional and technological features).
2. Nominal income, PY, determined by M
3. Classicals assume Y fairly constant (flexible p and w, and full employment)
4. P determined by M

3. Quantity Theory of Money
Quantity Theory of Money Demand
M = (1/V)  PY
Md = k  PY
Implication: interest rates not important to Md
© 2004 Pearson Addison-Wesley. All rights reserved

4. Change in Velocity from Year to Year: 1915–2002
© 2004 Pearson Addison-Wesley. All rights reserved

5. Cambridge Approach Is velocity constant?
1. Classicals thought V constant because didn’t have good data
2. After Great Depression, economists realized velocity far from constant
© 2004 Pearson Addison-Wesley. All rights reserved

6. Keynes’s Liquidity Preference Theory
3 Motives
Transactions motive—related to Y
- Since money is a medium of exchange it can be used to carry out everyday transactions. Keynes believed that these transactions were proportional to income.
Precautionary motive—related to Y
- People hold money as a cushion against an unexpected need. This motive is determined primarily by the level of transactions that they expect to make in the future and that these transactions are proportional to income.
3. Speculative motive
- Since money is also a store of value, Keynes called this reason for holding money the speculative motive. Keynes divided the assets that can be used to store wealth into two categories: money (that pays no interest rate) and bonds (that pays positive interest rates).
- Money demand is negatively related to i
© 2004 Pearson Addison-Wesley. All rights reserved

7. Keynes’s Liquidity Preference Theory
Liquidity Preference (real money balances) Md
= f(i, Y)
P – +
Keynes’s conclusion that the demand for money is related to
income and interest rates is a major departure from Fisher’s
view of money demand.
© 2004 Pearson Addison-Wesley. All rights reserved

8. Keynes’s Liquidity Preference Theory
Implication: Velocity not constant
P 1 =
Md f(i,Y)
Multiply both sides by Y and substitute in M = Md
PY Y
V = =
M f(i,Y)
1. i , f(i,Y) , V 
2. Change in expectations of future i, change f(i,Y) and V changes
© 2004 Pearson Addison-Wesley. All rights reserved

9. Baumol-Tobin Model of Transactions Demand
Assumptions
1. Income of $1000 each month
2. 2 assets: money and bonds
If keep all income in cash
1. Yearly income = $12,000
2. Average money balances = $1000/2
3. Velocity = $12,000/$500 = 24
Keep only 1/2 payment in cash
2. Average money balances = $500/2 = $250
3. Velocity = $12,000/$250 = 48
Trade-off of keeping less cash
1. Income gain = i $500/2
2. Increased transactions costs
Conclusion: Higher is i and income gain from holding bonds, less likely to hold cash: Therefore i , Md 
© 2004 Pearson Addison-Wesley. All rights reserved

10. Cash Balance in Baumol-Tobin Model
© 2004 Pearson Addison-Wesley. All rights reserved

11. Baumol-Tobin Model
Suppose that the cost of a banking transaction (trip) is b and that the interest rate is i.
Total cost = Forgone interest + cost of trips
© 2004 Pearson Addison-Wesley. All rights reserved

12. Baumol-Tobin Model
The optimal value of n, denoted n* can be calculated as follows:
FOC:
n can be solved as:
© 2004 Pearson Addison-Wesley. All rights reserved

13. Baumol-Tobin Model Therefore, the optimal money demand is:
The model predicts that the demand for money will increase in less than proportion to the volume of transactions (income), that is, there are economies of scale in money holding for the individual. Also, demand for money depends on interest rate.
© 2004 Pearson Addison-Wesley. All rights reserved

14. Baumol-Tobin Model Take logarithm: Income elasticity of money demand:
or, increasing returns to the scale
Note: classical model, ,income elasticity is 1.
© 2004 Pearson Addison-Wesley. All rights reserved

15. Precautionary and Speculative Md
Precautionary Demand
Similar tradeoff to Baumol-Tobin framework
1. Benefits of precautionary balances
2. Opportunity cost of interest foregone
Conclusion: i , opportunity cost , hold less precautionary balances, Md 
Speculative Demand
Problems with Keynes’s framework:
Hold all bonds or all money: no diversification
Tobin Model:
1. People want high Re, but low risk
2. As i , hold more bonds and less M, but still diversify and hold M
Problem with Tobin model: No speculative demand because T-bills have no risk (like money) but have higher return

16. Friedman’s Modern Quantity Theory (1956)
The demand for money must be influenced by the same factors that influence the demand fro any asset.
The demand for money therefore should be a function of the resources available to individuals (their wealth) and the expected returns on other assets relative to the expected return on money.
© 2004 Pearson Addison-Wesley. All rights reserved

17. Friedman’s Modern Quantity Theory
Theory of asset demand: Md function of wealth (YP) and relative Re of other assets Md
= f(YP, rb – rm, re – rm, e – rm)
P + – – –
Differences from Keynesian Theories
1. Other assets besides money and bonds: equities and real goods
2. Real goods as alternative asset to money implies M has direct effects on spending
3. rm not constant: rb , rm , rb – rm unchanged, so Md unchanged: i.e., interest rates have little effect on Md
4. Md is a stable function
Implication of 3:
Md Y
= f(YP)  V =
P f(YP)
Since relationship of Y and YP predictable, 4 implies V is predictable: Get Q-theory view that change in M leads to predictable changes in nominal income, PY

18. Friedman’s Modern Quantity Theory
Even though velocity is no longer assumed to be constant, the money supply continues to be the primary determinant of nominal incomes in the quantity theory of money.
In Keynesian liquidity preference function, i and V are procyclical, while in Friedman’s quantity theory, income (Y) and V are procyclical.
© 2004 Pearson Addison-Wesley. All rights reserved

19. Empirical Evidence on Money Demand
Interest Sensitivity of Money Demand
Is sensitive, but no liquidity trap
Stability of Money Demand
1. M1 demand stable till 1973, unstable after
2. Most likely source of instability is financial innovation
3. Cast doubts on money targets
© 2004 Pearson Addison-Wesley. All rights reserved