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Paul G. Coldagelli,
A good way to illustrate the velocity of money is to hypothesize that each student owes some other student a dollar and is owed a dollar by someone else. Each could pay off his debts by taking a dollar out of his pocket and giving it to his creditor. In this way, all debts are settled with $n dollars. (n = the number of students.) Or, each could wait until he received the dollar owed him, and use it to pay his creditor. In this way, the same number of transactions ($n) is supported with only $1. Velocity has increased n‑fold.
The exercise also points up the need for precautionary balances as students come to realize that their debt obligations can be resolved only if they themselves receive the payment they expect. This illustrates the debt pyramid and the rationale behind reserve requirements.
Students can calculate their personal checking account (or saving account) velocity. They find this an interesting exercise. Have them look at their most recent bank statement and figure out their (weighted) average daily balance (M). Then have them look at the total value of checks written that month (PQ). They can then calculate their monthly velocity: PQ/M. Suggest that students with very low velocity should be keeping some of their wealth in interest bearing form, rather than "idle" in their checking accounts.
Gary Galles,
The game of hot potato provides a helpful analogy for students who are struggling with the concepts of velocity and money demand.
a. The velocity with which you pass the potato to the next person is a function of its holding cost, i.e., the hotter the potato, the faster you pass it on and the more round trips it per period. Similarly, the velocity with which you pass money (exchanging money for the next person's goods) is related to the opportunity cost of holding money (the forgone interest rate); i.e., higher interest rates yield higher velocity so that more transactions and nominal national income can be generated with a given amount of money.
b. The game is over when the temperature of the potato falls enough that someone is willing to hold it. Similarly, equilibrium is reached in the money market when people are willing to hold the amount of money in existence, because they consider the marginal benefits of holding it to be equal to the opportunity costs.
c. If people were allowed to wear thin gloves to shield them from some of the heat, the velocity with which the potato was passed around would fall. Similarly, introducing interest earning forms of money shields its holders against some opportunity costs of holding money and tends to reduce velocity, other things equal.
Illustrating the Velocity of Money
Roger M. Clites,
I simply hold up one finger and say, "Irving Fisher could have said, 'One dollar spent and re-spent a total of five times has just as much impact on the economy as (hold up all digits on one hand) a five dollar bill spent one time.'" He pointed out that it was not only the size of the money supply that impacted on the economy. How rapidly it passed from hand to hand also affects, prices, wages, the employment level output, etc.
The Concept of the Income Velocity of Circulation of Money
M. Dudley Stewart, Jr.,
Students often suffer from reversed logic when trying to relate changes in velocity (V) to the demand for money (Md)when studying the equation of exchange: MV = PQ. After having given them ways of viewing V and having shown them on the blackboard how it is calculated using actual data, I give them a physical example. I have the value for V already on the board, say (6). I then tell my students to assume that we have been observing V for a period of a calendar year and that it has risen to 100 from 6. I ask them how individuals have changed their economic behavior and they tell me that they are spending money much more rapidly. So, I begin to put my hand in and out of my pocket very, very rapidly as if I were making payments and tell them to visualize a film that has been sped up substantially in which the actors are moving about very jerkily and overly rapidly.
I then tell my students to assume that V has decreased to (1) from (6) and ask them how individuals are behaving now with respect to spending money. They reply that they are not spending it as rapidly, that they are holding on to it longer. I again begin to put my hand in and out of my pocket very, very slowly as if I were making purchases and tell them to visualize a film in which the actors are moving about in slow motion.
In the first instance, I ask the students what might be the cause of such a rapid and large increase in V and they say a high rate of inflation must exist. I tell them that, other things being equal, that is correct and then ask them what that means with respect to the demand for money. Their response is varied; some say it has increased and some say it has decreased. I then go through the physical exhibition again, and again ask the question. They all then say that it has increased because the individuals are trying to protect themselves against the declining purchase power of the monetary unit. In the second instance, I ask the students what might cause a large decline in V, and they tell me that the economy is in the midst of a deep recession or a depression. I ask them what that means with respect to the demand for money, and they say that it has increased because people are being very cautious and are trying to hold on to their money balances longer by not spending as much as previously.
This method adds levity to the classroom, and I have had excellent success with it for many years.
Judy Butler,
I illustrate the concept of income velocity by passing around a given stock of money at different rates to simulate different income levels. I use monopoly money with all the bills being of one easy‑to‑multiply denomination. Three or four students to participate by passing bills with me in a circle with each student counting his or her income while I speak to the class about the various payments being made. I have another student keep time and stop us after one minute. I show the effect of velocity on income by passing the bills slowly the first time, and more rapidly the second time. The effect of a changed money supply on income can also be shown. To conclude the illustration I usually ask one or two students to hoard money, thus showing how increased money demand affects income.
What is the Reciprocal of the Velocity of Money?
Mark E. Schaefer,
In discussing the equation of exchange and the quantity theory, we often are forced into an embarrassed remark that the reciprocal of velocity, or the Cambridge K, is a mysterious parameter related to the demand for money. But 1/ V is not really obscure, only misrepresented. It has a natural interpretation as the average holding period of money by the seller, or borrower or portfolio manager. You can help students gain insight into this phenomenon by making this analogous to the management of inventory in retail sales. The financial press routinely reports the ratio of inventory to sales which gives the coverage or the number of days until current inventory will run out. For example, auto dealers have a 90‑day backlog on their lots. Ask the students what this means. Someone will eventually say that it would take 90 days to sell the cars they currently have on hand if the current rate of sales continued; similarly, cash‑holdings. This length of time is the reciprocal of the velocity which implies a length of time after which they would run out if they did not rebuild their holdings. This length of time is the reciprocal of the velocity and is the holding period of the last dollar of cash acquired under a last‑in‑first‑out rule. Since the buyer's cash losses are the seller's cash gains, cash holdings are being rebuilt for the system as a whole. Thus, the last dollar acquired is also the typical dollar, and the time it is held is the average holding period.
The actually observed holding period may be contrasted with the desired holding period, which is inversely related to 1) the interest rate foregone on alternative assets, and 2) the expected stability of revenue and spending streams, but directly related to 3) the risk of alternative assets and 4) the brokerage costs of switching between cash and other assets. One may then give an intuitively appealing scenario of a pulse increase of the money supply. First the actual holding period increases, exceeding the desired holding period, and sales increase. If capacity to produce is not being fully utilized, then output can expand. If the economy is already at full employment, then the extra cash chases a fixed flow of goods causing prices to be bid upward.
Gautam Mukerjee,
To explain the velocity concept I resort to a little experiment. I ask my students how long each of them keeps a dollar before spending it. The answers are usually in days or hours. The holding times are then converted into the same unit, that is, in days or hours, and the average is found. A standard length of time such as a week or month is then divided by the average for the class. The result is the velocity of turnover during the specified period of time. I then show how during periods of uncertainty the average holding time of a dollar is likely to be higher, since one is unlikely to go shopping immediately after being laid off, thus leading to a lower velocity. Similarly, times of prosperity and growth are likely to witness a higher velocity of turnover.
William B. Nelson,
Suppose two students decide to sell cans from a case of beer at a rock concert for 50 cents each. However, they have to walk several blocks to the stadium. Student A has 50 cents and student B is broke. Since it is a hot day, student A gets thirsty and desires to drink a beer, student B agrees but demands student A's 50 cents. A few blocks later student B gets thirsty, drinks a beer and gives student A back the 50 cents. Shortly, student A gets thirsty and drinks another beer giving student B the 50 cents. Of course the process accelerates as the beer takes its effect, and before they reach the stadium the beer is gone. Notice what has happened. Twelve dollars worth of economic activity has been supported by a mere 50 cents. You might have the students calculate the velocity. Also ask what the velocity would have been had they not touched the beer but sold it at the stadium.
This analogy has been modified from D. H. Robertson's, Money.
Quantity Theory and Money Multipliers
V. C. Kharadia,
Monetarists contend that changes in nominal income (Y) track movements in the money supply (M) and argue, therefore, that macroeconomic stability requires the FED to follow a steady course of monetary growth. This argument raises two issues:
a. To what extent can the FED control M?
b. How does a given change in M affect Y?
The first issue involves the money supply determination process, which can be discussed in terms of the money multiplier: M = KB, where K = money multiplier and B = monetary base. The factors that affect K would affect the transition from a policy induced change in B to the resulting change in M. The second issue involves the monetary transmission process from a given change in M to the resulting change in Y. This can be discussed in terms of the equation of exchange: MV = Y, where V = income velocity of money. The quantity theory of money per se sheds no light on how the money supply is determined. And the money multiplier says nothing about how a given change in the money supply would affect the economy. The effects of a given change in M on Y depend upon the behavior of V. These two issues, however, are interrelated in the discussion of the economic effects of monetary policy:
monetary D D D
policy ‑‑‑‑‑‑>> K ‑‑‑‑‑‑>> V‑‑‑‑‑>> Y
To present an integrated picture of the money supply determination‑cum‑transmission process, I substitute the money multiplier equation into the equation of exchange and get (KB)V = Y. In its differential form, this can be written as b + k + v = y, where b, k, v and y are the time rates of change in B, K, V, and Y, respectively. This equation allows us to focus on how offsetting or reinforcing movements in K and/or V can mitigate or augment the impact of a policy‑induced change in B on Y. This enables my students to see more clearly two of the major problems the Fed confronts: first, its control of the money supply and, second, the unintended effects of given changes in the money supply.
By William Gissy,
Hand each student ten $5.00 monopoly bills. The students are told that three items will
be available for "purchase" (i.e., Air
Peter V. Mini,
The hero strides into the saloon and asks for 20 minutes of companionship. Upon being told that it'll cost him 20 oz. of gold dust, he is incensed, "Last month it took only 1/4 oz., a mere pinch!" He understands, however, when he is told that during his absence they struck huge gold deposits. The unusual character is this example should illustrate the rarity of pure price inflation.
Dr. Walter P. Scott,
We all demand money, but the reasons are varied. In economics, the concept of the demand for money can be taught by explaining the differences in two opposing theories.
In the first view, the monetarists suggest that money is used mainly to acquire goods and services. As the market rate of interest falls, for example, spending tends to increase for transaction purposes.
The Keynesian perspective suggests that an alternative motive for the demand for money is related to speculative spending. This type of spending is driven by expectations of profits. Remind students that the amount of money individuals and firms demand for speculative reasons vary with their expectations of future price movements. If speculators feel prices of securities are about to fall, they will demand a great deal of money for future investments. As interest rates start to rise, prices of securities will fall, and speculators will reason that by holding money, they can obtain stocks and bonds at lower prices than at present prices. This adds credibility to the old adage to "buy low and sell high".
To illustrate this process, divide a number of students into two groups. One group demands money for transactions. Another group demands money for speculative spending. The participants who demand money for transactions are asked to explain how interest rates generate greater spending. They should respond, "lower rates make purchases less costly". Those who demand money for speculative reasons are asked to explain what they "gave up," and it becomes clear that the group understands that what is given up is current consumption for future "profits" gained.
The two opposing views of the demand for money can be illustrated by a moving see-saw shown below. As interest rates fall, monetary theory suggests consumption spending will increase. However, individuals who are motivated by speculative spending realize as a result of cyclical swings in interest rates, prices of securities will fall as interest rates rise.
The important lesson that students learn is that money not only serves as a store-of-value, but the discussion asks students to examine their values from an economic perspective. The question is: should firms and individuals spend for current consumption, or save in order to build equity? This lesson also gives a practical illustration of "opportunity costs".
Figure 14-1
The Welfare Cost of Inflation and the Inflation Tax
T. Windsor Fields,
Students often have trouble understanding the welfare cost of anticipated inflation and the welfare tax. The following analogy seems to help. Suppose that at current gasoline prices the average car is driven 15,000 miles per year. The government then imposes a tax on gasoline which consumers partially evade by reducing their driving, say to 12,000 miles per car per year. This results in a loss of transportation services amounting to 3,000 miles per car per year. No one gains from this, so it is a net loss (or cost) to society. At the same time, car owners pay tax on the now smaller amount of gasoline purchased to drive the 12,000 miles per car per year. But since these taxes are received by the government, there is no loss to society as a whole.
In the same way, inflation imposes a tax on money holders which they partially evade by reducing their holdings of real money balances. This results in a decline in the aggregate value of the services provided by money which we call the welfare cost of inflation. Since no one gains, the loss of these services is a net loss to society. This is analogous to the transportation services lost when car owners try to evade part of the gasoline tax. The inflation tax arises because inflation requires money holders to continuously increase their nominal money holdings in order to keep their real money holdings constant at the now lower level. This is a loss to them but not to society. Why? Because the government and the banking system appropriate this revenue by creating new money, which fuels the inflation, at virtually no cost. Thus, the tax on money holders is a gain to money producers. This is a transfer, not a social cost, and it is wholly analogous to the revenue that the government derives from gasoline taxes.
Bond Prices and Interest Rates
Steven T. Call,
Many students are mystified by the inverse relationship between the selling price of bonds and the interest rate on that bond. In order to reinforce the relationship, I construct a bond right in class and sell it. The bond is a perpetuity and looks like this:
I, Steven T. Call, promise to pay bearer of this
note 10 cents each December 31st, forever.
Signed,
___________________
(8‑1/2 x 11 sheet of note paper)
Someone can invariably be cajoled into buying the bond. If the bond sells for $1.00, I have a dollar and the purchaser has an I.O.U. at a calculated annual interest rate of 10 percent. The holder now offers the bond for sale again. Usually, another student will only offer 50 cents or less for the bond, particularly if I make noises about defaulting. If the bond price sags to 50 cents, the calculated interest rate jumps to 20 percent, due to the fixed interest payment. I usually put the $1.00 I received for the original bond sale in my pocket and attempt to leave class. Students invariably wish to reverse all transactions, so I `retire' the bond.
The exercise is particularly useful to help students make the jump from series E bonds to the theoretical perpetuity. Capital gains and losses are also easy to identify. Students also quickly see the reason for the inverse relationship between bond prices and interest rates: the interest is fixed in dollar terms.
The Functions of Money and the Motives for Holding It
Ralph T. Byrns
The functions of money can be useful in explaining the motives for holding money. Transactions demands and precautionary demands are held to meet respectively meet expected or unexpected expenditures; therefore, the most important function of money associated with these motives is medium of exchange. The asset demand for money emphasizes money as a store of value. The difference between the Classical and Keynesian views on the cost of holding money (100/CPI and i, respectively) can now be easily explained also by this method.
The Tennis Racquet -- Explaining Liquidity
Philip J. McLewin,
Decision making under conditions of uncertainty means that hoarding is rational at times. By not spending businessmen withhold a commitment to invest in one project over another. They remain liquid, but are prepared to move when conditions are more certain.
To illustrate this process ask a student‑tennis player to come before the class. Give him/her a tennis racquet, you step back, and prepare "to serve" the ball, which is no more than a crumpled up sheet of paper. If the student is good (and serious) he/she will be a crouched position, racquet in front, moving fluidly between both feet. This stance shows liquidity, where the student is not willing to commit to any one direction. The student is uncertain where I will serve the ball of paper. Once it is thrown, the student shifts to (invests in) a proper stance, and smacks the ball.
If the student is not cooperative, or cannot play tennis, the point can still be made because it is easy to throw the serve past the unprepared (and illiquid) player.
Forecasting 13‑Week Treasury Bills Auctions
Elia Kacapyr,
Students must submit evidence (usually a Wall Street Journal article) about how the supply and demand for 13‑week treasury bills (primary market) will change. This evidence must be correctly analyzed and then a forecast is made. They can check their forecast in Tuesday's WSJ. Forecasts with bad evidence or faulty analysis are rejected. At the end of the semester, the students who forecast best are rewarded with bonus points on their final. Make sure to have the forecast due before Monday's auction each week. (I've had students call the FED to get the results just after the auction.)
Monetary and Fiscal College Bowl
Peter M. Schwarz,
To solidify student's understanding of a topic, such as the differences between the Monetarist and Keynesian points of view, I assign a medium‑length (10‑15 pages) interview with an economist on material that has been covered in the text and in class. I divide the class up into teams (4 to 7 students per team), with a maximum of 4 teams. Those students who are not adequately prepared act as scorekeepers and referees, and play the role of the audience.
From here, I test the student's knowledge in a class formatted like the old TV‑game show College Bowl. I toss out a question, and the first hand raised (or buzzer rung on TV) represents the team. Without consultation with team members, a correct response earns the team 10 points. At the end of the response, I tell whether the answer was correct or incorrect; if correct, I might paraphrase the answer to get the key point across. If incorrect, I state this and then recognize the next hand, with this team getting 10 points for a correct answer. If the answer is not correct, any remaining teams have a chance.
In some cases, there is a bonus question worth 5 points. Answering the initial question correctly entitles that team only a chance at the bonus. Usually, this is a slightly more difficult question. The team is allowed to confer on the bonus for 30 seconds, and one member must then give an answer. If the answer is correct, I go on to the next question. If incorrect, I ask for volunteer responses from the other teams or audience, but there are no points for a correct response.
There must be some reward for participation, and an additional reward to the winning team. (I often get rid of left‑over Halloween candy or give out inexpensive business or economics books). The technique is a useful change of pace that gets students excited.
By: Kay Johnson,
While it is extremely easy to criticize our government officials for the state of the economy, it is extremely difficult to develop an alternative fiscal and monetary policy that will solve all of our country's economic woes. To help students understand the enormity of the task and also to develop a greater interest in fiscal and monetary policies, I have implemented the following project as a large portion of the final exam in Introductory Macroeconomics courses. This project is assigned about mid-point in the semester to enable the students ample time to develop their ideas and also to allow them time to review their preliminary outlines with me. I do, however, require that the students actually write their final papers in class during the final exam period as a guarantee that they are doing their own work.
The project
consists of three parts. First, the
students must define what they feel the primary economic goal of the
By assigning this project early in the semester, the students will take an increased interest in the class and also in related news events and articles. I have been told that this assignment creates a lot of "dining room" conversations and debates on campus as well as at home with their families.
Controlling Inflation and Unemployment
Richard J. Pullen,
First, I split the class in half and give one half the right to "raise" various elements and the other half the right to "lower" the same elements. I then list the elements on the blackboard:
1. Federal Reserve's Discount Rate
2. Bank Reserve Requirements
3. Government Spending
4. Federal Taxes
5. Government Short Term Funds
To control inflation, I explain how each of the five elements must be "raised" except government spending which must be lowered. To control unemployment, I explain how each of the five elements must be lowered except government spending which is raised. The class participates in the following days by responding to my inquiry "How does the government control the money supply to fight inflation?" The half of the class assigned "raise", verbally list off the elements 1, 2, 4, & 5. The other half of the class assigned "lower", verbally respond by lowering government spending, element 3. A week of repetition reinforces the desired correct responses.
Notes: