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CHAPTER 22 MONEY DEMAND. THEORY OF MONEY DEMAND. Money demand is proportional to nominal income: M d = kPY where k is assumed stable at equilibrium conditions. Fisher on the Quantity Theory of Money: MV = PY where V = 1/k is also assumed stable.

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Chapter 22 money demand

CHAPTER 22MONEY DEMAND

THEORY OF MONEY DEMAND


Classical money demand function

  • Money demand is proportional to nominal income: Md = kPY

  • where k is assumed stable at equilibrium conditions.

  • Fisher on the Quantity Theory of Money: MV = PY

  • where V = 1/k is also assumed stable.

  • Classical demand function focuses on the transaction feature of money as the medium of exchange.

Classical Money Demand Function


Classical determinants of money demand

  • Money supply (M) equals money demand at equilibrium.

  • M = Md Md = kPY M = kPY

  • Since k is stable/fixed, then changes in nominal income (PY) depends on M.

  • When M changes, then PY will change by 1/k:

  • PY = 1/k M Δ PY = Δ 1/k M

  • Only fiscal policies that affect money supply will influence income.

  • Changes in M  shifts LM (vertical)  changes level of income. Changes in IS curve does not change level of income.

Classical Determinants

of Money Demand


Keynesian money vs bonds

  • Money as a store of value + medium of exchange

  • Keynes divides an individual’s portfolio into 2 categories:

  • Wealth  Money + Bonds

  • Interest rate on bonds determines the distribution of wealth.

  • Keynes’s theory of the speculative demand for money:

    • High r, prefer bonds because:

      • opportunity cost of holding money is high

      • low demand for money at a store of value

      • future r will fall, capital gain on bonds

Keynesian Money vs Bonds


Keynesian money demand motives

Level of income positively influence:

Transactions Demand holding money for use in transactions

Precautionary Demand

holding money for unexpected expenditure

Keynesian Money Demand Motives

Higher income will increase money demand for both transactions and precautionary purposes.


Keynesian money demand function

Md = L (Y, r)

  • Money demand depends on income and interest rate.

  • Money does not depend only on Ms as in the classical functions.

  • Income is not proportional to money supply. Other fiscal policies or changes in investment demand may lead to changes in income.

  • LM curve upward-sloping. Shifts in IS also changes the level of income.

  • Monetarists: LM curve is very steep, supports classical, M mostly determines income.

Keynesian Money Demand Function


The inventory theoretic approach

“money as an inventory of the medium of exchange held along the lines of a firm’s holding of an inventory of goods”

by William Baumol (1952) & James Tobin (1956)

Assumption = An individual’s decision to hold money is based on his uniform spending throughout the period:

- earns $Y at the beginning of month, t=0

- spend uniformly throughout the month, finish all by t=1

- average inventory of money = Y/2 = money held at mid- point, middle-of-month, t=1/2

i.e. earns $1,200 early April, holds $600 by 16th, has $0 by 30th.

The Inventory-Theoretic Approach


Money holdings

Money holdings along the lines of a firm’s holding of an inventory of goods”

Money holdings

Y/2

Y/2

Money Holdings

1/2

1/2

1

1

Time

Time

  • earns Y, hold all as money

  • spends uniformly

  • has Y/2 on average, Y=0 at t=1

  • earns Y, hold half money half bond

  • spends uniformly, sell bond at t=1/2

  • has Y/4 on average, t, Y=0 at t=1/2, 1


Brokerage fee

  • The inventory-theoretic approach: level of inventory holding for money depends on

    • the carrying cost of the inventory (interest gain from bonds forgone when decide to hold money)

    • the transfer cost from money to bond (brokerage fee)

  • Pr (n=2) = r Y/4 – 2b number of transactions, n = 2 (buy then sell)

  • interest rate form bond, r

  • fixed brokerage fee, b

  • net profit, Pr

Brokerage Fee


Net profit

Pr = r Y/4 – 2b for money depends on

Net profit

for 2 transactions

Interest earning on average bond holding

Brokerage fee x number of transactions

Net Profit

If choose to buy 2/3Y value of bonds: then

at t = 0 hold 1/3Y in cash, 2/3Y in bonds

at t = 1/3 hold 1/3Y more in cash by selling some bonds, maintaining balance of 1/3Y in bonds

at t = 2/3 sell off remaining bonds, hold 1/3Y cash to spend

Net profit for n=3 Pr (n) = r (n-1)Y/2n – nbPr = r Y/3 – 3b


Average money vs bond holding

Average money holding: for money depends on

M = 1/2n Y if n=2, then M = Y/4 if n=3, then M = Y/6

Average bond holding:

B = (n-1)/2n Y if n =2, then B = Y/4 if n=3, then B = Y/3

Pr (n) = r (n-1)Y/2n – nb

Average Money vs Bond Holding

Net profit

for n transactions

Brokerage fee x number of transactions


Optimal number of n

Pr (n) = r (n-1)Y/2n – nb for money depends on

n* is determined by MC (constant) and MR (declining):

MCMR

MCMR

Optimal Number of n

MC(b1)

MC(b0)

MC

MR(r0)

MR(r1)

MR

n

n

n*1

n*0

n*1

n*0

An increase in r will shift MR to the right, increase n*.

A decrease in b will shift MC to the left, decrease in n*.


Conclusion

  • Keynes’ transaction demand for money depends on income, interest rate and brokerage fee, Md = L (Y, r, b).

  • Money does not depend only on Ms as in the classical functions.

  • Income is not proportional to money supply. Other fiscal policies or changes in investment demand may lead to changes in income. LM curve is upward-sloping.

  • The Inventory-Theoretic Approach states money as an inventory of the medium of exchange held along the lines of a firm’s holding of an inventory of goods assuming an individual’s decision to hold money is based on his uniform spending throughout the period.

  • Net profit of holding money and bonds: Pr (n) = r (n-1)Y/2n – nb and optimal n is determined by MR(r) and MC(b).

Conclusion


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