Illustrating the Saving‑Investment Linkage
Roger M. Clites,
Many students are baffled by the idea that when investment exceeds saving, national income will rise; when investment is less than saving, national income will fall, and that only when investment equals saving will national income be in equilibrium. To give them an alternative view of the concept I have tied the equations Y = C + S and Y = C + I together for consecutive time periods.
First I write on the board Y(1) = S + C and point out that when people receive the national income from businesses they save some of it and spend most of it. Then I point out that the C portion spent out of the first of two consecutive time periods becomes part of the monies received by businesses to be paid out as national income during the next time period. I write on the board C + I = Y(2). Then, after pointing out that the C figure is the same in both of the equations I connect them as shown.
Y(1) = S + C
C + I = Y(2)
I then draw a box around the Cs and point out that the relative size of I vs. S determines the relative size of Y(2) to Y(1).
Dynamic Multiplier: A "Pebble In Pond" Analogy
V. C. Kharadia,
Economics instructors must try to get several important points across in lectures on the dynamic multiplier process: (a) how an economy in equilibrium is disturbed by an exogenous force, (b) the timing of the multiplier process with its infinite number of multiplier rounds and linkages, where most of the multiplier effects are realized in the earlier rounds, and (c) how the multiplier process gradually peters out. Most freshmen find these concepts difficult, and tend to be unimpressed by mathematical equations!
To make it easier for my students to mentally visualize and more fully comprehend with a lasting impression the dynamic working of the multiplier process, I use an analogy of throwing a pebble (an exogenous force like autonomous investment) into a tranquil pond (an economy in equilibrium). Then, the students can imagine how the ripples (the multiplier rounds and the linkage effects) form, multiply into an infinite number, but gradually peter out. Like the ripples in a pond, the multiplier process creates a pervasive, but gradually diminishing economic impact. When the force of the pebble striking the water equals the shock absorbed by the pond in the form of ripples generated, the pond's tranquility is restored. Likewise, when investment injections equal the shock‑absorbing saving leakages from the economic ripples of spending and income creation, the economy absorbs the exogenous shock and achieves a new equilibrium.
Explaining the Investment Multiplier
Kishore Kulkarni, Metropolitan
In explaining the investment multiplier idea of Keynesian economics, I always initially define real investment as an expenditure on buying machinery, tool and equipment, or construction activities, or increase in the stock of inventories. By taking an example of construction activity in a city, I emphasize the income generated for a group of individuals responsible for the construction, and call it X. Group X therefore consists of plumbers, electricians, landscapers, etc. When these people receive income, National Income (or GDP) also increases by the value of the building, say $100 million. Depending upon the value of marginal propensity to consume, the recipients of this income would consume a part of it on their favorite activity. Let us say group X has a favorite activity of drinking beer. Then their consumption becomes income of the bar owners, and the National Income (or GDP) in the second round goes up further. If we assume marginal propensity to consume to be .5, then group X would consume $50 million and save the rest.
The process of further income generation continues as the bar owners consume a part of $50 million. We are concentrating on equilibrium GDP changes, at the end of the process, GDP has to increase by several amounts like 100 + 50 + 25 + 12.5 + . . . etc. The ultimate change in equilibrium GDP is thus a multiple of the original change in investment.
David Priddy,
The concept of the earnings multiplier is especially well suited to analogy, particularly since students are immediately suspicious of any claim that the market can turn "one dollar into ten."
Begin by producing a large one dollar bill; usually a sheet of paper with large numerals and the picture of a local personality on it (or xerox Figure 10‑1, or use a blow‑up of a real bill). In order to keep track of the various transactions put column headings on the board: "Change in Income," "Change in Savings," and "Change in Spending" and establish a marginal propensity to save.
Figure 10‑1 Money to Illustrate the Multiplier Process
Now, give the dollar to a student as new income. This student will "save" according to the MPS by tearing off a portion of the dollar and then spend the remainder by passing it on to the next student. This continues, with each series of transactions being recorded on the board, until it becomes apparent that the process will continue ad infinitum. The instructor can then total each column as if it had continued, and then lead the students to all the appropriate conclusions.
A similar example can be used to demonstrate the banking multiplier since the underlying process is essentially the same. Because they have already learned one concept, the similarity of example makes it much easier to understand the other.
Barbara A. Vatter,
This is the house that Jack built
This is the carpenter paid by Jack when the house was built
This is the grocer paid by the carpenter
who was paid by Jack when the house was built
This is the wholesaler paid by the grocer who was
paid by the carpenter who was paid by Jack
when the house was built
This is the warehouse person paid by the wholesaler
who was paid by the grocer who was paid by the carpenter
who was paid by Jack when the house was built
Now the carpenter, the grocer, the wholesaler
and the warehouse person consumed and saved,
saved and consumed, consumed and saved and
saved and consumed
With such intensity
They produced a propensity,
while the economist produced what was marginal, but
Together the sum became quite large in all
Although MPC + MPS = only 1,
1/MPS = the multiplier, x the house that Jack built!
Charles W. Brown,
The multiplier is a difficult concept for students to comprehend. One of the best ways to teach this principle is to let the students actually experience it in action. This can be done by using pennies rather than dollars or billions of dollars.
The equipment needed for this demonstration of the multiplier are three jars and 100 pennies. Ten students are needed to participate in the exercise and one student with a calculator is utilized to provide quick calculations. The instructor or another student can serve as recorder to keep tract of the transactions on the board.
The demonstration then proceeds as follows:
1. Certain assumptions are explained to the class such as
MPC = 3/4 MPS = 1/4 therefore K = 4
2. Three jars are set on a table or desk
a. One jar to serve as the GDP jar (now empty)
b. One jar to serve as the spending jar (contains 100 pennies)
c. One jar to serve as the savings jar (now empty)
3. Each of the ten students participating is asked to drop $1.00 in the GDP jar. This represents all of the spending for that year, thus the GDP is $10.
4. The instructor, representing a Japanese investor or some other new spender, then injects the spending jar into the economy. This jar contains 100 pennies and is passed to the first student to represent a new purchase.
5. The first student, upon receiving the 100 pennies, will remove 25 pennies and place them into the saving jar. The remaining 75 pennies are then spent by passing them to the second student.
6. The second student will remove 25 percent of the pennies and place them into the saving jar and will spend the rest by passing them on to the next student. The person with the calculator is determining 25 percent and 75 percent each time for precision and in order to save time. The recorder is placing the information on the board in three columns (change in income, change in spending, and change in saving) as each transaction occurs.
7. This same procedure is followed until the money has passed to each student and then it starts over again. Eventually the spending jar will be almost empty (we usually stop at 2 pennies left) and the saving jar will contain most of the pennies. The records on the board will show that almost $4.00 of new income has been created because of the fact that 100 pennies came into the economy as new spending. These are prolific pennies indeed!
Multiplier Leakages: A "Poking a Pipeline" Analogy
V.C. Kharadia,
It is difficult to effectively explain the declining numerical value of the multipliers in the three‑sector, four‑sector and money economies as additional leakages of marginal tax rate, net import rate and interest rate effect are introduced. Mathematical models are the methods that are generally used to explain the falling value of the multipliers. But freshmen in particular find it difficult to mathematically comprehend the universe of the multiplier leakages.
To explain the impact of additional leakages on the multiplier process, I use an analogy of a water pipeline (spending stream). For a two‑sector economy in equilibrium, a given MPS (a leakage from the spending stream) implies some multiplier and total income or spending level, given the autonomous expenditures (water tank, the exogenous force in the water system). Spending, income creation and the multiplier effect depend on the number and magnitude of the leakages from the spending stream. Water pressure in the pipeline and water received by the customers can depend on the number and size of holes (leakages) in the pipeline. Each multiplier leakage can be compared with a hole in the pipeline. With the increased number and size of leakages from the spending stream, the numerical value of the multipliers and income creation decline. Similarly, the increased number and size of holes in the pipeline (spending stream) would reduce water pressure (spending pressure) and water received by the customers (spending and income creation). Just as the water pressure (and water flow) would be a reciprocal of the sum of the holes in the pipeline, the multipliers (and income flow) are likewise a reciprocal of the sum of the leakages form the spending stream. While mathematical presentations on the multiplier tend to silence a class, the "poking a pipeline" analogy seems to create a spark, probably with a more lasting and clearer impression of the multiplier universe.
Spending Multipliers: A Physical Demonstration
M. Dudley Stewart, Jr.,
After I have shown my students how to calculate the investment spending multiplier and how to apply it, I ask them to assume that I have received $1.00 in new income, and I write $1.00 on the blackboard. I then ask them to further assume that I and each of them have a marginal propensity to consume (MPC) of 0.50. Finally, I ask them what I will do with the $1.00. They naturally reply that I will spend half and save half, so I write $0.50 under the $1.00 on the board and tell them that I spend the $0.50 with the female student sitting in row one column one and ask them what she will do with it. They again respond that she will spend half and save half, so I write $0.25 on the board and tell them to assume that she spends it with the male student to her right and ask them what he will do with it. Again, they respond that he will spend half and save half, so I write $0.125 on the board and remark that $1.875 is new income has thus far been generated. I write three descending dots and $2.00 on the board under the other numbers. I then tell them to note that the numbers become smaller and smaller and that we would never reach an end using such a method, but that by using the formula for the investment spending multiplier we can calculate $2.00 as a limit, because it is based upon a convergent infinite geometric series.
I then give them a physical demonstration of the multiplier and a convergent infinite geometric series. I back up to the right wall of the classroom, as close to it as I possibly can, and tell the students that I am going to calculate the left wall as a limit of two (2), continuing to assume an MPC of 0.50. I then take half of the distance to the left wall and half of the remaining distance and half again until my nose is almost touching the wall. I have to really suck in my stomach for this part. I then tell them that I will never ever reach the wall, because I am taking half of the distance to it each time, but by using the formula for the multiplier, the wall as a limit of two (2) can be calculated. During the physical demonstration, the students smile, chuckle, and otherwise seem to enjoy it.
I have used this method for many years and have achieved great success with it. When I ask the students if they now understand better the concepts of the investment spending multiplier and a convergent infinite geometric series, they respond enthusiastically and positively. A few students have come to me at the end of class and told me they never understood the latter concept in their math classes. (See The Concept of the Simple Deposit Multiplier.)
Explaining the Spending Multiplier
Tantatape Brahmasrene,
Another fun way to explain the spending multiplier process is to use fake money from a “Monopoly” game. I capture students' attention by bringing a stack of Monopoly money to class. Let's assume that MPC = 0.5. Then I purchase a fictitious commodity from a student for $ 800. Quarters and pennies may be provided depending upon how far you want to play in the spending process. The process continues as the initial student purchases another commodity from another student. This exchange progresses for five rounds. This is usually sufficient to make the point clear. Students do have fun counting money while understanding how the multiplier works. The instructor or an assigned student can record the transaction on the board. as shown below.
Round Increase in Income Increase in Consumption
1 $800 $400
2 400 200
3 200 100
4 100 50
5 50 25
All other rounds 50 25
Total 1,600 800
A $ 800 of initial spending led to a $1,600 increase in income.
Xeno's Paradox: Why the Multiplier Ends
When students are first introduced to the idea of a multiplier, they are generally told that people can do two things with income: save it or consume it. In general they will consume only a fraction of their income and save the remaining fraction. Thus, individuals have a marginal propensity to consume (MPC) and a marginal propensity to save (MPS), respectively. If MPC is 0.9, a person receiving a $1 will save $0.10. Someone else will obtain $0.90 and will save $0.09, and so forth. Adding $1 + $.90 + $.81 + . . . = $10. Since the multiplier is 10 (= 1/MPS), income will increase to $10. One student noted that the process for multiplying by 0.9 could continue indefinitely, so how do you reconcile the two methods. I noted that the question is nontrivial, but that a trivial analogy may help to clarify it. The numbers get so small that at some point you can ignore them. I added that if someone pointed a gun at you and fired, theoretically, and by his reasoning, the bullet should never hit him since he could infinitely divide the distance between the gunman and himself (or the distance traveled by the bullet). But he would still be dead. He got the message.
Using Transactions with Students to Illustrate Multipliers
Ralph T. Byrns
Provide
intuition for the autonomous spending multiplier by assuming a constant MPC of,
say 0.80. Suggest that, in spite of an absence of change in your own income,
you have decided to have a home custom‑built for $100,000. Award the
contract to a student sitting in the front row, who represents all workers on
this house. The $100,000 increase in this student's income causes purchases of
$80,000 worth of merchandise from the person behind him or her. Keep a running
tally of these transactions on your blackboard. Emphasize "receipts of
income" and subsequent "spending" with each transaction round.
The $80,000 in income stimulates $64,000 in purchases from a person in the
third row. And so on. Ask when the process will stop. If no one knows the
answer, kid your students by alleging that you have solved a concept from calculus
called a
The derivation of this multiplier is in the Optional Material following Chapter 10. Many mathephobic students may think that this algebra is incomprehensible. Show your students the following summary equations after stressing that MPS = 1‑MPC:
a. DY = DA (1/mps), and b. DY = DA (1/1-mpc).
Take a few minutes in class in which you offer various fractions for the values of the MPC (9/10, 4/5, 3/4, 2/3, 1/2) and have them provide the resulting multipliers. When they see that all that is required is inverting a reciprocal, they will be much more comfortable with these numbers. Do the same for fractions representing the MPS (1/10, 1/5, 1/4, 1/3, 2/5, and 1/2). Now use the blackboard to provide a series of values for A (any form of autonomous spending), DA, MPC, and MPS, and have students calculate equilibrium (Y) or the change therein (DY). Then provide the Y or DY and the MPC or MPS, and ask them to calculate the autonomous spending required to achieve equilibrium. This prepares students for calculations of recessionary, inflationary, and GDP gaps in the next chapter. Spending about half of a lecture on these exercises may bore mathematically adept students, but it is very worthwhile for the rest.
Explaining Keynesian Equilibrium with an Innertube
William Foeller,
One of the basic conditions in elementary Keynesian economics is that a system is in equilibrium when leakages from the system equal injections into the system.
After a discussion of the concepts of circular flow, consumption (C), saving (S), investment (I), taxes (T), governmental spending (G), exports (X), and imports (M), a simple innertube analogy can be used to show the equilibrium
I + G + X = S + T + M
Beginning with the concept of a simple closed tube with no leakages or injections, the volume of air can be assumed to indicate the volume (value) of dollar flow in the system from households to firms to households, etc.
Figure 10-2
But if households don't spend all their income, i.e., they save (leakage), and if there are other leakages and other spenders (injections), the tube will have a series of "valves" (leakage outlets) and "pumps" (injection inlets).
Figure 10-3
One can imagine taking a measurement of the economy in equilibrium by using a caliper to measure the tube's diameter (flow volume is a function of tube size).
In a given time period, if any or all of the valves are depressed, but the pumps are not working, the tube will deflate (economic contraction). Only if the valves and pumps are working, allowing total leakages to be matched by total injections, does the tube remain stable: I + G + X = S + T + M.
The analogy can be pushed a bit farther (but not too far) by asking for the effects of various combinations of operating pumps and valves. For example, "If G, X, T, and M are not active, what maintains constant volume?" Answer: The I pump injecting air equivalent to the air released by the S valve. (I = S).
Another example might be: "If X is not pumping, and T is not active, but the I and G pumps are pumping faster than the S and M valves are releasing air, what is happening to the tube (economy)?" Answer: I + G > S + M ==> tube is "expanding".
The students can envision a group of people standing around the tube, measuring the diameter, pumping and depressing chosen valves in a given time period, then measuring the change in the diameter of the tube.
A larger tube indicates that the combinations of injections were greater than the combination of leakages, implying "expansion" in the economy. A smaller tube indicates that leakages were greater than injections, causing a "contraction". Using the analogy, the nature of Keynesian equilibrium, expansion, and contraction can thus be introduced in an elementary way.
The
By Mark Pernecky,
The circular flow of income often seems like a maze of plumbing to many students. I depict the relationships between GDP, factor costs, national income, and aggregate demand (expenditures) in what I call the "magic circle". (I abstract from depreciation, indirect business taxes, and undistributed corporate profits, though these items could be included.)
Starting from the top of the circle, as GDP is produced an equal amount of factor costs must be paid to produce that GDP. (I show this equality by example elsewhere.) Factor costs to one group (firms) are national income to the factors of production (households). Some income is spent by these factors (represented by AD, aggregate demand) for consumption (C). Investment (I), government spending (G) and net exports (X) may be assumed to be autonomous. The circle is completed.
Figure 10-4
I depict and describe the idea behind the "magic circle" quite often during the semester - almost like a mantra: "As-GDP-is-produced-it-becomes-an-equal-amount-of-factor-costs-which-becomes-an-equal-amount-of- income-which-is-spent-on-the-GDP." Several concepts which can be depicted by the magic circle include the relation between injections and leakages, Say's Law, the Keynesian spending gap, the savings-investment link for growth, and the multiplier.
The relation between leakages (savings (S), taxes (T), imports (M)) and injections (I, G, X) can be depicted as follows.
Figure 10-5
Say's Law can easily be contrasted with the Keynesian view of leakages and injections. The circular flow holds for the latter; GDP is bought back. The supply of GDP has generated its own demand. For Keynes, the demand gap created by a leakage from savings can be seen. If investment is not forthcoming, government spending is required.
The savings/investment link for economic growth can also be seen on the circle.
Finally, the multiplier can be demonstrated on the magic circle. The initial spending boost from an autonomous expenditure increase can be shown to generate income in the first round, via GDP. Some of the income leaks out before the consumption expenditures in the second round. The higher the marginal propensity to save, the lower the multiplier, and the greater the leakage in each round.
Illustrating the Accelerator Principle
Ray M. Johns,
Accelerator theory is a difficult concept for students because it lacks empirical results and practical application. But a simple illustration will drive home the importance of this concept to students. Pick out a capital equipment manufacturer in the surrounding region. Ask the students if they know anything of the employment history of that factory. Usually some students will have friends or family working there. And, typically, the factory will be working overtime and all three shifts at one time and then abruptly lay everyone off at another time, only to hire them back again later. This illustration of the accelerated impact of the business cycle on the capital goods industry is a valuable lesson in understanding both acceleration theory and the instability of employment in certain industries or even in regions dominated by capital goods producers.
Investment, Profits, and Your Waistline
By Gregg Davis,
When thinking about the role of business spending, or investment, and its role with profit and the state of the economy, it may help to personalize these concepts to your "Battle of the Bulge," or the fight of the expanding waistline. The waistline contracts, expands or remains the same depending upon your caloric intake each day with respect to the body's needs to replace the calories used up during our day to day activities (ignoring for now the role of exercise). When we speak of investment, part of that investment goes towards replacing what has become worn out or obsolete. This type of investment is comparable to the intake of calories to replace those calories burned off in the human body. If investment, or caloric intake, just offsets the loss of capital, or calories, then what we call net investment is zero. Under this scenario, our waistline remains the same, as does the state of the national economy. Neither growth nor contraction occurs.
Now, in the case where we consume more calories than the body needs to replace, or where business spends above what is needed to replace the capital worn out, the "waistline" expands. Net investment is now positive, and the economy is growing. Investment raises the net worth of firms, and hence profits increase. A declining economy, or one that is dangerously contracting, represents the reduction of the waistline. Here net investment is negative, the economy's caloric intake is less than what is needed to replace the calories burned off, and hence the waistline contracts. Business is not even spending enough to replace what is being worn out, and as a result, profits fall, which causes investment to fall still more. Just as too much weight loss is dangerous for the body, too little net investment is dangerous for the economy.
To summarize, our rule for the economy follows that of our waistline. When forced to loosen the belt, net investment is positive, and the economy is expanding, profits are on the rise. Bring the belt in a few notches and the economy is contracting, profits are falling, and net investment is negative.
Business Investment and the Great Depression
Dick Kennedy,
Explain to the class that any business contraction is likely to be quite severe if businessmen decide to shelve or postpone their long range investment plans in plant and equipment, and any subsequent business recovery is likely to be quite weak unless those investment plans are revived.
CASE STUDY: The 1929‑33 business contraction was quite long and severe, and business did shelve long range investment plans due to the magnitude of the contraction. The business recovery that began in March, 1933, and ended in May, 1937, was quite weak, and GDP did not return to the level of the 1920s expansion. The economy fell back into the depression in May, 1937, and the 1937‑38 contraction reached a lower point than the 1929‑33 contraction. The weakness of the 1933‑37 expansion and the severity of the 1937‑38 contraction can be attributed, in no small part, to the lack of long term business investment.
Although
the 1937‑38 contraction was more severe than the 1929‑ 33
contraction, the 1937‑38 decline was relatively short because business
began to revive their long range investment plans by June, 1938. By that date
the
Long term business investment in plant and equipment plays a key role in the business cycle because the multiplier principle primarily operates on business investment. Small changes in business investment cause national income or GDP to increase by some multiple of the investment. The multiplier principle can and should be explained in relation to the business cycle.
This case study should be illustrated by duplicating Figure 10‑6 on the blackboard.
Figure 10‑6
Note that GDP did not return to the $104 billion level until 1941. Insufficient long term investment caused the 1933‑37 expansion to be quite weak and the 1937‑38 contraction to be quite severe.
Quantity Versus Price Adjustments
Ralph T. Byrns
Few students immediately recognize the importance of why Keynes emphasized quantity adjustments, and was skeptical of the efficacy of Classical wage and price flexibility. Here is one approach to facilitate student understanding of this skepticism. When you introduce the Keynesian system, review simple demand and supply curves. Illustrate a market in which the current price is below equilibrium, and allow your students to identify this as a shortage. Indicate that Classical and Keynesian analyses concur that when there is excess demand (XD), the price rises rapidly to clear the market, and that this idea holds for resource markets (e.g., labor) as well as markets for goods.
The next step is to graph a goods market for which the current price exceeds the market clearing price, and allow your students to identify this as a situation of surplus. Then draw a market for the labor that produces this good, and suggest that the surplus in the goods market is paralleled by a surplus of labor. Assert that both markets began at points "a" in the Figure 10‑7, and that the market disequilibria are caused by a decline in the demand for goods. Ask students if the price of the good will fall to equilibrium very quickly if wages are "sticky" downwards; firms do face pressures to cut their production costs. After a little discussion, your students should perceive that it may be easier for firms to do this by laying off workers than by trying to get workers to take wage cuts.
Ask why labor is reluctant to accept wage reductions, i.e., why does the process by which the prices of surplus goods are "bid down" appear to work only slowly and erratically in labor markets? If classical price mechanisms operate smoothly in a labor market, anyone threatened by a layoff could retain his or her job by agreeing to a wage cut. Suggest the following possible reasons for wage stickiness:
Figure 10‑7
a. Few labor contracts are for the sale of only a single resource unit (e.g., one hour of work). Rather, they cover sales of many labor hours over long periods because recontracting is costly. Thus, wage agreements are not lightly renegotiated. (In contrast, sales of, e.g., a can of soup or a lawnmower involve only single transactions.)
b. Workers sometimes react violently toward anyone threatened by layoff who accepts a wage cut because this threatens the jobs of those not laid off. (Cite violence against "scabs" during labor disputes as examples. Most students find these examples persuasive and interesting.)
c. Union contracts and minimum wage laws infectiously tend to make all wages sticky downwards.
d. Point
to the
e. Suggest that workers may quit or accept layoffs in preference to wage cuts if they perceive that their alternative employments have remained stable (or if unemployment compensation is sufficiently generous). Thus, if workers fail to perceive an economy‑wide collapse of demand, they may be less willing to accept wage cuts.
All of these are reasons why wages (and consequently, prices) may be sticky or even rigid, and help to explain the Keynesian focus on quantity rather than price adjustments to deficient demand.
Keynesian Inventory Adjustments
Ralph T. Byrns
To illustrate that in a Keynesian model of a closed, private economy (C + I = C + S), unexpected inventory changes reconcile conflicts between planned saving and investment, graph a simple Keynesian cross and select an income level where Aggregate Spending is below national output (the 45‑degree reference line is mathematically C + S.) Ask whether inventories will unexpectedly shrink or grow. (ANSWER: Grow). Point out why undesired growth of inventories causes reductions of employment in the Keynesian model (prices and wages do not decline). Then select an income level where AE exceeds National Output. Inventories will shrink, stimulating expanded output and employment. Numerical examples are very helpful in clarifying this discussion.
Parallel this analysis with discussions of the Keynesian diagram for planned saving and investment. If S > I, inventories unexpectedly grow, causing declined in employment. If I > S, inventories unexpectedly fall, stimulating employment.