PART 4: EXPLAINING THE BEHAVIOUR OF FINANCIAL ASSET PRICES: MONEY, RISK, AND UNCERTAINTY
CHAPTER 12: The Demand for Money
FOCUS OF THE CHAPTER
This chapter provides a survey of various theories of money demand. The Baumol-Tobin optimal cash management approach and Friedman’s theory of money demand are discussed in particular. A brief overview of empirical estimates of the demand for money functions is also presented.
Learning Objectives:
Explain the important role of money demand in economics
Describe what the demand for money represents
Identify how consumption, income, and nominal interest rates affect the demand for money
Explain the important role of money demand analysis in economics
Identify how we manage cash, in theory
Determine optimal cash holdings in the presence of transactions costs and inflation
Explain some estimates of actual money demand in Canada
Explain how the theory of the demand for money has evolved over time
Describe why the velocity of circulation is an important concept to understanding movements in the demand for money and the evolution of the financial system
SECTION SUMMARIES
The Microfoundations of the Demand for Money: A Sketch
A few principles developed in previous chapters are important for the study of money demand. They are: a) The transactions motive is the foremost reason for holding money; b) the opportunity cost of holding money is the interest foregone; c) the household’s intertemporal consumption decisions influence saving, which may be partly in the form of money; and d) what is important for consumers and savers is the real value of or the purchasing power of consumption and saving.
The demand for money refers to the demand for real balances. The real balance is the nominal stock of money (M) divided by the price level (P). An appropriate price index such as CPI can be used to determine P. Once the household has made the intertemporal consumption decision, it must also decide whether to hold the savings in the form of money, bond, or other assets. Thus the demand for money can be viewed as a result of household utility-maximizing behaviour.
The demand for money function indicates the relationship between the quantity of money demanded and the factors which affect money demand. The demand for money function for a given period (t) can be written as,mdt = f( ct , Rt), where mdt is the real balance demanded, ct is real consumption (i.e., nominal consumption divided by P), andRt is the nominal interest rate. The variables ct and Rt are positively and negatively related to mdt, respectively. Consumption depends on the permanent income, and a measure of actual real income (yt) can be used to represent permanent income. Therefore, the money demand function can be written asmdt = f( yt , Rt). The nominal interest rate (Rt) is the sum of the real interest rate () and the expected rate of inflation (e): Rt= + e. Friedman’s rule shows that the cost of holding money (the nominal rate of interest) can be zero only when there is deflation. (Note that Rt is zero when = -e ). Friedman suggested that a society is better off with low or negligible inflation, but did not advocate deflation. An important feature of the money demand function is that the price elasticity of the money demand should be equal to one [i.e., whenever the price increases (decreases) by some percentage, the quantity of money demanded should also increase (decrease) by the same percentage]. But if the money illusion exists (the belief that nominal and real values are the same), this may not hold true. The stability of the money demand function over time has been an important issue in the literature of money demand.
The Baumol-Tobin Model: Optimal Cash Management
The Baumol-Tobin inventory theory (also called the optimal cash management approach) is a useful way of thinking about the transactions demand for money. This theory recognizes that individuals face income-expenditure gaps and cannot synchronize their income and expenditure streams perfectly. Therefore, they hold both cash and chequing accounts.
Fundamental Concepts: To understand the basic concepts of the optimal cash management approach, consider an individual who receives a paycheque for a monthly income of $2000 at the beginning of each month, and spends at a constant rate so that the total amount is spent by the end of the month (i.e., the cash balance at the end of the month is zero). The average amount of dollars held (Md) in any given month is:
Md = (cash balance at the beginning-cash balance at the end)/2
= ($2000-$0)/2 = $1000
If the person receives $2000 income biweekly in two instalments of $1000, then the average monthly cash holding can be calculated as follows:
Md = ($1000-$0)/2 = $500
Optimal Cash Balance Holding: The level of cash holdings that minimizes the opportunity cost of holding cash is the optimal level of cash holdings. Suppose an individual can hold money either in cash (notes and coins or currency) or in a chequing account. The opportunity cost of holding cash is the interest rate (R) forgone. The cost of holding a chequing account is the transaction cost of transferring cash out of the account. Suppose the transaction cost of each cash withdrawalfrom the account is b. The average cash holding (Md) adjusted for number of transactions (n) is given by the following equation:
Md = Y/2n
where Y is the nominal income level. An increase (decrease) in the number of transactions decreases (increases) the average cash holding, increases (decreases) the total transaction cost (nb), and decreases (increases) the interest cost R(Md), or R(Y/2n). Therefore, the optimal number of transactions is the number of transactions which equates total transaction cost (nb) with the interest cost saved R(Y/2). The optimal n can be found by solving the following equation:
nb = R(Y/2n) ornb = RY/2n
n2 = RY/2b
n = (RY/2b)0.5
The optimal cash holding (demand for money) can be found by the substitution of optimal n in the average cash-holding equation (i.e., Md = Y/2n).
Md= Y/2n
= Y/2 (RY/2b)0.5
The above equation can be simplified as Md = ( b/2)0.5 Y0.5 R-0.5 . The nominal income level (Y) is the product of the real income level ( y ) and the price level (P) (i.e., Y = Py). Therefore, the demand for money equation can also be written as follows:
Md = P ( b/2P)0.5y0.5R-0.5
This equation implies that a one percent increase (decrease) in P or y increases (decreases) cash holdings by 0.05 percent. A one percent increase (decrease) in R decreases (increases) cash holdings by 0.05 percent. Note that, according to this model, the elasticities of money demand with respect to price level, income level, and the interest rate are all less than one. In terms of real balances the demand for money can be expressed as follows:
Md/P = ( b/2P)0.5y0.5R-0.5
The Role of Inflation: According to the Baumol-Tobin optimal cash management approach, the price elasticity of money demand is less than one. A one percent increase (decrease) in p increases (decreases) cash holdings by only 0.05 percent. This implies inflation (increase in the price level) and decreases the demand for real balances (Md /P). Because inflation increases the cost of keeping cash idle and also increases the number of transactions to be made, average cash holdings will fall. Economies with hyperinflation
(monthly inflation rates of 50% or more), such as Hungary after World War II, have experienced a sharp decline in the level of real balances.
A More Complete Model of Money Demand
Another approach to money demand incorporates the quantity of money in circulation (the money supply) and the velocity of circulation. The number of times a given quantity of money turns over to produce a given level of spending is called the velocity of money circulation.
Quantity Theory: In its simplest form, the quantity theory of money is given by the following equation:
Ms V = Py
where Ms= quantity of money in circulation (the money supply)
V = velocity of circulation
P = price level
y = real income level (real GDP or real GNP)
Assuming that the money market is in equilibrium (i.e., Ms= Md ), the equation can be written as follows:
MdV = Py
where Md = quantity demanded of money. By rearranging the terms, an equation for money demand can be derived as follows:
Md = (1/V)Py
Some early theorists believed V to be constant, but others believed it could be influenced by factors such as technological change. Keynes noted that the real interest rate could affect the velocity of circulation.
Friedman’s Monetary Theory: According to Friedman’s version, the money demand function can be expressed as follows:
Md/P = f(RB , RE , ,Wh/Wn , y, u)
where Md = desired demand for money
P = price level
RB = nominal return on bonds
RE = nominal return on equities or stocks
= return on money as measured by the rate of inflation
Wh= human wealth
Wn= non-human wealth
y = real income
u = other factors
The variables RB, RE, and are various measures of the opportunity cost of holding money, and, therefore, they are negatively related to the real balances demanded (Md/P). The ratio Wh/Wn and y are positively related to the real balances demanded. The variables in u (such as tastes and preferences) could be positively or negatively related to the real balances demanded. The variables, included in the above money demand function, influence the permanent income of an individual directly or indirectly. Therefore, Friedman suggested, the above money demand function can be simplified as follows:
Md/P = g(yp), where y p = permanent income.
This equation states that the demand for real balances is simply a function of permanent income. The function does not include an interest rate variable since Friedman believed early empirical findings which showed that the demand for money was insensitive to interest rate changes.
Demand for Money Functions: Empirical Estimates
The results of the empirical estimates of the demand for real balances (using M2 definition) demonstrate that the price level and the real income level are positively related to the demand for real balances. But the relationship between the nominal interest rate and real balances was negative in the pre-World War II period and positive in the post-World War II period. The positive relationship in the post-World War II period was largely due to financial innovations.
Velocity of Circulation
The assumption that the velocity of circulation is constant was not supported by the Canadian data for about a century (1872-1999). The velocity of circulation decreased during the period of monetization (the period when the use of cash and cheques became increasingly common), when the growth of money exceeded the growth of income level. The velocity of circulation has increased during the post-World War II period of financial innovations (the emergence of credit cards, automatic banking machines, etc.), when the growth of income level exceeded the growth of money. Similar changes in the velocity of circulation have been observed in other countries as well.
MULTIPLE-CHOICE QUESTIONS
1. The purchasing power of a given stock of money is called
a) permanent income.
b) real interest rate.
c) real income.
d) real balances.
2. In response to a change in price level, the quantity of real balances demanded does not change
a) when the price elasticity of money demand is unity.
b) when the income elasticity of money demand is unity.
c) when the price elasticity of money demand is greater than one.
d) when the income elasticity of money demand is greater than unity.
3. The money illusion refers to
a) the belief that money can buy everything.
b) the fact that the demand for money function is not stable over time.
c) the belief that nominal values are the same as real values.
d) the fact that an increase in price level decreases the real value of money.
4. In a money demand function, the opportunity cost of money is represented by
a) the rate of inflation.
b) the rate of interest.
c) the growth rate of income level.
d) the velocity of circulation.
5. An individual receives a paycheque for a monthly income of $3000 at the beginning of each month, and spends at a constant rate so that the total amount is spent by the end of the month. According to the Baumol-Tobin optimal cash management approach, the average cash holding in any given month is
a) $3000.
b) $2000.
c) $1500.
d) $1000.
6. According to the Baumol-Tobin cash management model of money demand, a one percent decrease in the price level
a) decreases nominal quantity of money demanded by one percent.
b) decreases nominal quantity of money demanded by 0.5 percent.
c) increases real quantity of money demanded by one percent.
d) increases nominal quantity of money demanded by 0.5 percent.
7. According to the quantity theory of money, the velocity of circulation can
be calculated
a) by dividing the nominal income level by the stock of money.
b) by dividing the real income level by the stock of money.
c) by multiplying the nominal income level by the stock of money.
d) by dividing the nominal income level by the price level.
8. According to the simplified version of Friedman’s demand for money function,
the demand for real balances is a function of
a) the interest rate and current income level.
b) the actual current income level.
c) the permanent income level.
d) the transitory income level.
9. Empirical findings using Canadian data reveal that the real balances and
a) the real GDP are positively related.
b) the price level are negatively related.
c) the real income level are not related.
d) the real income level are negatively related.
10. The velocity of circulation in Canada
a) increased over time during the pre-World War II period.
b) has increased steadily over time since the late 19th century.
c) decreased over time during the pre-World War II period.
d) has been clearly stable over time, during the last century.
PROBLEMS
1. State under what circumstances, according to the quantity theory of money, the rate of inflation might be zero.
2. The Baumol-Tobin model suggests that there are two cost associated with the use of money. What are those two costs? Which of the two costs increases as the quantity of money held increases and which of the two costs decreases as the quantity of money held increases?
3. State the Baumol-Tobin demand for money equation. Calculate the demand for money if the transaction cost (b) is 18, nominal income level is 2500, and the rate of interest is 16%.
4. Explain the effect of each of the following events on the demand for real balances:
a) a decrease in the real GNP
b) an increase in the rate of inflation
c) a decrease in the level of human wealth
5. Explain why there is more risk associated with human wealth than with financial wealth.
6. a) What is the velocity of circulation if the stock of money is 500 million, the real income level is 40 million, and the price level is 125?
b) What is the supply of money in this economy if the price level increases to 150?
7. Reconcile the following: “Inflation means higher prices which require people to hold more money, but it raises the cost of holding money which suggests that people will hold less money.”
ANSWER SECTION
Answers to multiple-choice questions:
- d (see page 221)
- a (see page 222)
- c (see page 222)
- b (see page 222)
- c (see page 223)
- b (see page 226)
- a (see page 228)
- c (see pages 229-230)
- a (see page 231)
- c (see pages 231-232)
Answers to problems:
1.The quantity theory of money is given by the following equation: Ms V = Py
where Ms= quantity of money in circulation (money supply), V = velocity of circulation, P = price level, y = real income level (real GDP or real GNP). In terms of growth rates (GRs), the equation can be written as follows:
GR of Ms + GR of V = GR of P + GR of y
According to this equation, the sum of the growth rates of Ms and V must be equal to the growth rate of y, if the inflation rate were to be zero (i.e., GR of P = 0):
(GR of Ms + GR of V) - (+ GR of y) = GR of P
(GR of Ms + GR of V) - (+ GR of y) = 0
(GR of Ms + GR of V) = (+ GR of y)
2. The two costs of using money are first, a holding cost which increases as the quantity of money used increases and a transactions or brokerage cost which decreases as the quantity of money used increases.
3. The Baumol-Tobin demand for money equation can be stated as:
Md = ( b/2)0.5 Y0.5 R-0.5 or Md = ( b/2)0.5P0.5y0.5R-0.5
Using the data given, the demand for money can be written as:
Md = (18/2)0.5 (2500)0.5 (0.16)-0.5
Md = 3 x 50 x 2.5
Md = 375
4. Using the general version of Friedman’s money demand equation,
[i.e., Md/P = f(RB, RE, ,Wh/Wn , y, u)], the effect of these events can be explained as follows:
a) The real income level (y) is positively related to the quantity of real balances demanded (Md/P). A decrease in y decreases Md/P at each rate of interest (R), causing a decrease in the demand for real balances. The demand curve shifts leftward.
b) The rate of inflation () is negatively related to the quantity of real balances demanded (Md/P). An increase in decreases Md/P at each rate of interest (R), causing a decrease in the demand for real balances. The demand curve shifts leftward.
c) The ratio of human wealth to non-human wealth (Wh/Wn) is positively related to the quantity of real balances demanded (Md/P). This means that the level of human wealth
(Wh ) is positively related to Md/P. An decrease in Wh decreases Md/P at each rate of interest (R), causing a decrease in the demand for real balances. The demand curve shifts leftward.
5. Human wealth represents the discounted present value of lifetime earnings. In order for anyone to maximize their earnings ability they have to specialize in a particular occupation or profession and they cannot readily diversify their skills. Financial wealth is easily diversified through holding portfolios of many financial assets.
6. a) The quantity theory of money is given by the following equation:
Ms V = P y
The velocity of circulation is given by:
V = Py/Ms
V = 125 x 40/500 = 5000/500 = 10
b) MsV = Py
Ms = (1/V)Py
Ms= (1/10) x 150 x 40 = 6000/10 = 600 million
7. The fact that prices rise will shift the demand for money to the right. The fact that inflation causes nominal interest rates to rise causes a movement up the demand for money curve, meaning a decreases in quantity demanded.