The multiplier effect: a classroom exercise.

Mago, Shakun D.

I. Introduction

The word fiscal comes from the root fisc, which refers to the "treasury" of a government. Accordingly, fiscal policy refers to the government's spending and taxing behavior. Most students are aware that in response to the 2008 recession, the American Recovery and Reinvestment Act was passed in February 2009. However, they are usually unclear about how precisely the policy initiative was supposed to stimulate the economy. The $831 billion package comprised both federal tax incentives, and direct spending on infrastructure, education, health, and energy. In light of the large and ever-increasing national debt problem, a crucial part of the current economic discussion is which fiscal policy mechanism is more effective increased government spending or lower tax rates. There is a general perception that government spending and tax cuts are equivalent in their impact and therefore are interchangeable, i.e. a dollar increase in government expenditure increases GDP by the same amount as a dollar decrease in taxes. Students often believe that the appropriate policy prescription for fiscal stimulus and economic growth depends solely on one's political ideology, with the liberal activists recommending increased government spending and the conservatives arguing for higher tax cuts. The media sources and the political discussions tend to be highly partisan, and the classroom presentation of formulae does not make the process any less perplexing. The primary objective of this exercise is to demonstrate a) how change in the fiscal policy parameters leads to a change in GDP and b) which fiscal stimulus spending is more effective (i.e. the difference between the expenditure multiplier and the tax multiplier).

In this exercise, students alternatively take on the roles of business owners, owners of capital and labor, and consumers. Through the "bottoms-up" participatory approach they experience firsthand the economic incentives and forces governing the multiplier process. Going through a sequence of financial decisions of how much to save and spend, students learn how the initial shock sets off a chain reaction, leading to successive rounds of changes in spending and income. We believe that this exercise creates a concrete mental image of the multiplier process such that students are able to easily decipher how their propensity to save/spend not only affects the income of other sellers and the overall output production in the economy, but also their income in the future. This simple framework can then be used to evaluate the effect of relaxing standard assumptions, and to demonstrate the impact of automatic stabilizers (which reduce the size of the multiplier) such as taxes and transfer payments. Finally, this exercise can be used to initiate a discussion on how the theoretical predictions differ from the actual real-world results due to credit liquidity restrictions, unemployment benefits, inflation, and governmental inefficiency.

Our demonstration is ideal for smaller Principles of Macroeconomics classes, and the benefits will be diminished in classes larger than 50 students. The initial exercise takes about 1525 minutes of class time, and depending on the learning objectives, 25-50 minutes can be reserved for discussion.

II. Step-By-Step Procedure For The Instructor

1. Some preparation needs to done before the start of the class. Each student should receive a copy of the instructions and the record sheets provided in the appendix. They must also have a pen or pencil and a simple calculator. Before class, the instructor will need to prepare classroom dollars in different denominations. It is easiest to use play dollar bills, which are very inexpensive and available at most retail stores. With regard to the breakdown of denominations, we recommend that the instructor brings to class at least six $20 bills, ten $10 bills, eighteen $5 bills and thirty five $1 bills. (1) The instructor must also bring placards identifying various businesses and a financial lender or a resident bank. The businesses range from large corporations employing a number of workers such as American Car and American Steel & Ore, to small self-employed businesses such as Rickety Rentals, Trader's Food and Shimmery Shirts.

2. Recruit six volunteers: Five to serve as the business owners and one to serve as the financial lender. (2) Hand all of them their business placards, and ask them to face the class. The instructor acts as the government with a fiscal stimulus plan. The remaining students serve as the pool of potential workers and/or consumers. Not all students can participate in this exercise, but in my experience, the prospect of future participation is usually very effective in keeping the entire class engaged.

3. Read the instructions aloud to the students. Reiterate that GDP may be calculated using the expenditure approach (measure of all goods and service produced) or using the factor payments approach (measure of income earned by all factors of production). (3) Emphasize the following assumptions:

a. Marginal Propensity of Consumption is 0.8.

b. This is a closed economy.

c. There are no taxes and transfer payments.

d. Firms have no inventories.

None of these assumptions are crucial in terms of the qualitative aspects of the results. In fact, the later part of the exercise will focus on the effects of relaxing these simplifying assumptions.

II.1 Expenditure Multiplier

4. We begin with the demonstration of the expenditure multiplier. Announce that as the federal government, you would like stimulate the economy by building and improving the national highway system. To accomplish this you would need to buy road rollers and other construction equipment (hereafter, simply referred to as "cars") worth $100 from American Car. (4) Give $100 to American Car (preferably broken into small denomination bills of two $20, two $10, five $5 and fifteen $1; I usually ask the banker to assist me in these transactions). Upon receiving the $100 from the Federal government, American Car must make the production decision. A couple of leading questions will guide the class through the production decision: Does American Car have any inventory in its warehouse? (No, by assumption.) By what amount should American Car increase its production? ($100.)

5. Next, note that when American Car produces $100 worth of cars it must also pay its workers wages for their labor services, the lender an interest on the borrowed loans, and its supplier (American Steel & Ore) for the raw materials. In turn, American Steel & Ore must also pay its workers and the financial lender. (5) In my experience, it is never a problem to find students who are willing to work for American Car and American Steel & Ore, and you can assign the first 4 students who volunteer as workers--2 for each business. Instruct the students acting as business owners to make the factor payments. Suppose, American Car pays its workers $20 each, buys $40 worth of raw material from American Steel & Ore, and pays an interest of $10 on loans secured from the lender, leaving it with a profit of $10. Next, American Steel & Ore pays its workers a total wage of $30 and spends $2 in interest payments, making a net profit of $8. (6)

6. Instruct all the students to record the appropriate allocations in the record sheet (Table 1), and then ask what has been the initial change in income or GDP in the economy. It should be fairly obvious that the total income has increased by $100 (in our example, $70 as wages, $18 as profit and $12 as interest). The answer would be the same if, instead of the factor payments approach, students use the expenditure approach to calculate the increase in GDP - cars worth $100 were produced. Reiterate the point that, "each time a dollar in output is produced, a dollar in income is created."

7. Given the increase in income, student participants will be able to consume more. Since taxes are assumed to be zero, a $100 increase in income is also a $100 increase in disposable income. For the sake of simplicity, we will restrict consumption to basic necessities like food, clothing and housing. A series of leading questions will guide the class through the consumption decisions. Do you have to pay any taxes? (No, by assumption) How much of the additional income is available for consumption? (All of it) What percentage of your income would you consume? (MPC = 0.8). What do you do with your savings? (Save/ put it in the bank). (7) In our example, workers will spend $56 (0.8 of the wages of $70), American Car and American Steel & Ore will spend $14.4 (0.8 of the profit of $18) and the lender/banker will spend $9.6 (0.8 of the interest income of $12) on Trader's Food, Shimmery Shirts and Rickety Rentals.

Thus, the total increase in spending will be $80 (=0.8*$100). Instruct the business owners, the financial lender and the workers to make their consumption decisions and ask the students to record the total change in their record sheets. Suppose, in response to these consumption decisions, Trader's Food and Shimmery Shirts produce food and clothing worth $20 each, and Rickety Rentals produces housing services worth $40. (8)

8. Before proceeding further, ask the class what is the change in income as a result of this second round increase in consumption spending on food, clothing and housing ($80). Employing the expenditure approach, students will note that $100 worth of car and $80 worth of food, clothing and housing services were produced. Employing the factor payments approach, it is easy to compute that the wages for workers, the interest income for the lender, and the profit for all 5 businesses totals $180. The instructor should record this second round increase in GDP on the board, and point out that although the government increased its spending by $100, the total change in GDP is $ 180. Thus, when consumers spend an additional $80 on consumption, firms that produce those goods and services will earn an additional $80 in sales revenue, which in turn, will become income for the households that supply those resources to these firms.

9. It is not necessary to repeat this procedure for many rounds, but the instructor may wish to do at least one more round of consumption spending to demonstrate the change in income. In the interest of time, this may be done amongst the four business owners (with the exclusion of American Steel & Ore). For instance, suppose Rickety Rentals, who earns income of $40 and spends 80 percent of it, has the following expenditure breakdown $20 on American Car, $6 each on Shimmery Shirts and Trader's Food. Similar transactions can be made by the other two businesses, Shimmery Shirts and Trader's Food who earned an income of $20 each. The instructor should ask the class what is the change in income as a result of this second round of consumption spending (0.8*$80 = $64), and should also record this third round increase in GDP on the board while students make appropriate entries on their record sheets.

10. By this point in the exercise, it should be obvious to the students that the initial increase in government spending leads to much greater increase in GDP. They also grasp that the increase in GDP is smaller at each stage (each successive round of additional spending is 80 percent of the previous round income), and the process must eventually end. At this point, the standard discussion of MPC and the expenditure multiplier can be used to show that the initial spending of $100, with a MPC of 0.8, will lead to a total increase in GDP by $500.9

Before proceeding further, it would be useful to summarize the change in GDP for each round, and the aggregate change in GDP in the summary section of the record sheet. The students can use this to contrast the expenditure multiplier with the tax multiplier, described later.

11.2 Relaxing the Standard Assumptions

1. MPC: Ask the students what will be the increase in GDP if MPC was 0.6, instead of 0.8. (or the instructor could use whatever MPC amount is used in the assigned text). It is not necessary to go through the entire calculation in class, and we recommend that the instructor use the summary sheet instead. It is instructive to show that although the first round increase in GDP remains at $100, in the second round GDP increases by $60 and in the third round by $36. Ask the class to calculate the total change in GDP ($250 = 1/1-0.6 * 100). Next, ask them to re-do the calculations of each of the three rounds and for the total change in GDP when MPC is 0.9 ($1000). These numerical examples should amply display that the value of expenditure multiplier (and therefore, the impact of spending on GDP) is positively related to the MPC. Detailed calculations with varying MPC levels (Table 2) can be assigned as a homework problem. Emerson (2011) is a nice supplementary reading on the history of MPC in the U.S., and can also be assigned as an optional homework assignment after the in-class exercise.

2. Imports: In the U.S. for every additional dollar of spending, 15 cents goes to imports. Even goods made domestically have many imported components. If the additional spending is on goods and services imported from abroad, then these spending changes do not stimulate additional domestic production that can power the next round of the multiplier, causing a much smaller change in GDP in subsequent rounds. To demonstrate this, assume that Shimmery Shirts is not based in the U.S. but in Mexico. Redo the calculations. The first round increase in income and spending remains at $100 but in the second round, goods and services produced in U.S. amount to $60 (instead of $80). This in turn, affects the consumption spending in the third round and so on. Table 3 contains the corresponding record sheet. After a brief in-class discussion this can be assigned as a homework problem.

3. Taxes and Transfer Payments: So far, we have assumed that there are no taxes and transfer payments. Thus, when government spending increased by $100, both income and disposable income rose by $100 and in the next round of multiplier process both households and businesses spend 80 percent of their disposable income, or $80. But in the real world, as income rises some taxes such as payroll and income taxes automatically rise and some transfer payments such as unemployment benefits automatically fall. As a result, the increase in (disposable) income is smaller in each round, resulting in an even smaller rise in consumption in the subsequent rounds. To demonstrate this, relate the following scenario: Suppose American Car, which has 2 workers, hired one of its workers only when it received the government stimulus of $100. Suppose this worker who receives a wage of $20 had previously received an unemployment benefit of $10. Thus, the increase in his disposable income is not by $20 but only by $10. Further suppose that as income rises by $100, the government collects a total of $15 in taxes from all entities. Combining the two, net taxes (= taxes - transfer payments) increase by $25. As a result, when the income increases by $100 in round 1, the disposable income increases only by $75. In the next round of the multiplier process, consumption spending (and income) increase only 0.8*75 = $60. We believe that by this point in the demonstration it is not necessary to redo the entire calculations, but asking students a series of leading questions would yield a fruitful discussion on how taxes and transfer payments reduce the impact of fiscal spending. Be certain to point out that such factors that reduce the size of the multiplier are called automatic stabilizers.

4. Inventories: This assumption can be relaxed by discussing the simplest case - one where American Car has $100 worth of inventory in its warehouse. This means that an increase in the purchases by the U.S. government does not automatically lead to any increase in the production by American Car, and the multiplier process fails to commence. This is usually suffice to drive home the argument that spending changes that fail to stimulate additional domestic production have no lasting impact on the GDP.

In our experience, it is important to spend sufficient time explaining each step of the initial simulation. Recruiting volunteers, reading instructions (staged at the beginning of each individual round), answering queries and then the exercise itself usually takes about 15-25 minutes. We recommend that any questions that do not directly pertain to the initial exercise be postponed for the expost discussion. (10) The second part of the exercise comprising the relaxing of standard assumptions is more amendable to the time constraint. For instance, as mentioned earlier, varying levels of MPC (Table 2) and imports (Table 3) serve as useful homework problems after only a brief discussion. However, we recommend that the instructor spends some time discussing the net taxes. The latter is a good segue to the tax multiplier, described below.

11.3 Tax Multiplier

To demonstrate the tax multiplier, we recreate the scenario of the 2008 Bush tax cuts where tax cuts were given to all households below a certain income limit. (11) Reiterate that all students in the class are households. Some may be employed, some may be unemployed, and yet others may be Social Security recipients. Suppose government passes a stimulus bill of $100, but instead of increased spending, a $100 tax cut is proposed. Distribute $100 among some students and ask them what they will do with their additional income. The answers may range from buying new clothes, books, televisions etc., to going on an exotic vacation, to paying off credit card debt, to putting all the money in the bank. A series of leading questions will guide the class through the consumption decisions - (a) As an economy, how much of the additional income is available for consumption, i.e. what is the increase in disposable income? ($ 100) (b) As an economy, what percentage of your income would you consume? (MPC =

0.8, by assumption), (c) As a result of economywide increased consumption spending, what is the first round increase in GDP ($80 = $100*0.8) (d) How does this initial increase in the GDP compare when the stimulus spending is in the form of governmental purchase from American Car vs. tax cuts for all households? Students should readily see that government spending leads to a dollar-for-dollar increase in aggregate spending; but in case of tax cuts, the impact on spending comes indirectly through an effect on household's disposable income. This means that if households' after tax income (disposable income) rises by $ 100, they will increase their consumption not by full $100, but only by a fraction of it.

What happens after the initial rise in GDP by $80? When households spend an additional $80, firms that produce consumption goods and services will earn an additional $80 in sales revenue, which in turn, will become income for the households that supply resources to these firms, and the cycle of multiplier process proceeds as before. Thus, the series of the subsequent increase are the same, except that for tax cut, the first $100 is missing. This difference between the expenditure and the tax multiplier becomes very evident in the summary section of the record sheet. Since $100 increase in government spending increases GDP by $500, a $100 cut in taxes must raise GDP by $400 (= $500 - $100). At this point, the standard discussion of the MPC and the tax multiplier can be used to show that tax cuts of $100, with a MPC of 0.8, will lead to a total increase in GDP by $400 (= -0.8/1 -0.8 x -100).

III. Discussion

After the initial simulation, students should be encouraged to ask questions, although some answers may be postponed until after the entire demonstration is over. Below we list some common concerns and suggest plausible responses. (12)

1. Real world evidence on the multipliers: There is a vast empirical literature studying the fiscal multiplier, and the summary of this literature is that the multiplier is somewhere in the range of 0.7 to 1.0 (see Hall, 2009 for a discussion of the empirical findings). All economists acknowledge that the size of the multiplier varies according to the economic conditions and various other factors (discussed below). But since there is no general consensus on the precise impact, the debate of spending vs. tax multiplier rages on (Auerbach and Gale, 2009). For instance, economists in the Obama administration, who assumed that the federal interest rate will stay constant for a four-year period, estimated a multiplier of 1.6 for government spending and 1.0 for tax cuts. (13) Other economists, such as Barro (2010) estimate the spending multiplier to be between 0.4-0.6 and the tax multiplier to be equal to 1.1.

2. MPC: Students frequently find it suspicious that the MPC for all entities--individual workers, small or large businesses--is assumed to be homogenous. Since both the expenditure and the tax multiplier rely on the value of MPC, it casts a shadow on the credibility of the demonstration. However, by the end of the exercise when students have a vivid picture of the multiplier process, they will be able to decipher fairly easily that this is only a simplifying assumption. Indeed, all consumption is not homogeneous, and some consumption may be seen as more beneficial to the economy than others. The ex-post discussion can focus on situations with varying MPC. Some examples are:

-- Government spending on 'shovel ready' infrastructural projects has a bigger multiplier effect than a tax cut especially if consumers save a portion of their tax windfall. Historic examples include the New Deal and the Hoover Dam project.

-- An individual with above average income and/or wealth will have a lower marginal propensity to consume compared to a worker with minimum wage income. Thus, a tax cut targeted at poorer sections of the society may have a bigger impact on spending than one meant for the more affluent members. Other individuals with a higher MPC include the unemployed, students, families with young children, social security recipients, consumers close to their borrowing limit etc. (14)

-- Consumers may be forward looking and therefore, the overall size of the fiscal multiplier depends on how people react to the higher cash inflow. In case of tax rebates and payroll tax cuts, if consumers realize that the extra cash flow is temporary then their consumption spending is less sensitive to the changes in current income, producing a smaller multiplier effect. For instance, only about one-fifth of respondents in the Reuters/University of Michigan survey report that the 2008 tax rebates led them to mostly increase spending, while over half said it would lead them to mostly pay off their existing debt (Sahm, Shapiro and Slemrod, 2009). Additionally, it is important to recognize the importance of the time horizon--while the decision to pay off the personal debt may reduce the multiplier effect in the short run, in the long run the potential for increased leverage can stimulate both consumption and investment. The precise impact of such intertemporal substitution mechanism on the expansionary effects of fiscal stimuli is not clear and has aroused considerable interest in the political and academic arena, especially in the last two years. (15)

Fiscal multipliers can also to be used to demonstrate the "Paradox of Thrift." When households and firms cut their spending in anticipation of tough economic times, the slump in spending causes a fall in equilibrium GDP that is several times larger than the original decrease in spending. Thus seemingly virtuous behavior--cautious saving for hard times--ends up harming everyone while seemingly reckless behavior makes everyone better off.

3. Other economic variables that affect the fiscal multiplier:

--Current state of the economy: Consistent with the classical view, in the long run as the economy approaches the full employment level of output the fiscal multiplier should be close to zero. "Since there are no spare resources, any increase in government demand would just replace spending elsewhere. But in a recession, (in accordance to the Keynesian view) when workers and factories lie idle, a fiscal boost can increase overall demand. And if the initial stimulus triggers a cascade of expenditure among consumers and businesses, the multiplier can be well above one." (Economist 2009).

--War versus Peace: Some economists argue that fiscal multiplier differs in war and peace times fiscal stimulus is welfare improving for a wartime event when most of the spending is defense related but is likely to be welfare reducing for a recessionary event (Andolfatto 2010).

--Forward looking behavior: If government's actions bolster confidence in the markets and revive the animal spirits, then consumption and private investment gets "crowded in" and the multiplier effect increases. But if households anticipate higher taxes in the future to finance increased governmental spending, or if interest rates climb in response to government borrowing then consumption and private investment could get "crowded out" reducing the impact of the fiscal multiplier. This may be a good starting point to introduce a debate on the impact of austerity measures followed by Europe versus the discretionary spending done by the U.S. in response to the 2008 global recession.

4. Impact of Fiscal Policy versus Monetary Policy: Even those who do not ascribe to the policy of laissez-faire when it comes to government intervention, acknowledge that fiscal policy can be too ham-fisted in practice. One practical problem that limits the effectiveness of discretionary fiscal policy is timing. Given the visceral disagreements within the political establishment on how the benefits of increased spending or tax cuts should be distributed among the general populace, it can take too long to design and pass the necessary fiscal legislation. Second, problems persist both with increased spending and tax cuts. As noted above, most of the money generated by tax cuts is saved, not spent. The task of finding appropriate 'shovel ready' spending projects is also clumsy at best, and only 3 percent of the last stimulus was spent on infrastructure. Furthermore, spending increased only at the federal level, and money given to the state governments was spent on reducing the states' reliance on borrowing and on other "non-purchase" items, such as subsidies, and interest payments. Finally, to be effective, discretionary fiscal policy must be reversible, but reversing changes in government spending or tax cuts have become increasingly difficult. This is evident in the recent debate over extending the tax cuts implemented by the Bush administration in 2001 and 2003. Similarly, spending programs that create new departments, or expand existing departments become difficult to eliminate. As a consequence of these fiscal policy pitfalls, the Federal Reserve has taken over the main role in reacting to and smoothing out economic fluctuations over the past five decades. In most cases, it can act more rapidly and with greater flexibility. One exception is the recent 2008 recession. With unemployment hovering around 10 percent and with interest rates close to zero, a large fiscal stimulus package was needed to supplement both the conventional and non-conventional monetary policy tools employed by the Fed.

Appendix

Instructions

This exercise demonstrates how federal government can stimulate the economy through increased spending and tax cuts. There will be an opportunity for many of you to play a role in this exercise. There will be 2 large businesses: American Car and American Steel & Ore. There will be 3 small businesses: Rickety Rentals, Trader's Food and Shimmery Shirts. In addition, there will be a financial lender. Others in the class will have the opportunity to play the role of workers and/ consumers. I will act as the government with a fiscal stimulus plan.

In the beginning of the exercise, we will make some simplifying assumptions. These are not restrictive and we shall relax them later in the exercise. These assumptions are:

a. Marginal Propensity of Consumption is 0.8. For example, if you receive an additional income of $10, you will consume $8 (=0.8*10) and save the remaining $2.

b. This is a closed economy, so there are no exports or imports.

c. There are no taxes and transfer payments.

d. Firms have no inventory.

Instructions for Round 1: As the federal government, I will introduce a fiscal stimulus bill aimed at improving the National Highway System. To accomplish this, I need to buy road rollers and other construction equipment (hereafter, simply referred to as "cars") worth $100 from American Car. Since the firm has no inventory (by assumption), an increase in purchases automatically leads to the same amount of increase in production for American Car. American Car will have to pay its factors of production--(a) American Steel & Ore for raw materials, (b) wages to its 2 workers, and (c) interest payment to the financial lender. It can keep the remaining amount as its profit. Next, American Steel & Ore has to pay wages to its 2 workers and interest payments to the financial lender. It can keep the remaining amount as its profit. After the two businesses decide on their allocation decisions:

-- Please make the necessary entries in your record sheet.

-- Calculate the total increase in income or GDP using both expenditure and factor payments method (Column 2).

-- Calculate the increase in consumption spending as a result of increased income (Column 3).

Instructions for Round 2: Because of increased income, workers and businesses will be able to consume more. For the sake of simplicity we restrict consumption to basic necessities like food, clothing and housing. At this point, all participants with increased income should decide on their consumption allocation for Rickety Rentals, Trader's Food and Shimmery Shirts. After the two businesses and the 4 workers decide on their allocation decisions:

-- Please make the necessary entries in your record sheet.

-- Calculate the total increase in income or GDP using both expenditure and factor payments method (Column 2).

-- Calculate the increase in consumption spending as a result of the increased income (Column 3).

Instructions for Round 3: Suppose consumption decisions are restricted to the 3 small businesses. That is, Rickety Rentals can spend its increased income on Shimmery Shirts, Trader's Food and/or American Car. Similarly, for the other 2 small businesses. After the three small businesses decide on their allocation decisions:

-- Please make the necessary entries in your record sheet.

-- Calculate the total increase in income or GDP using both the expenditure and factor payments method (Column 2).

-- Calculate the increase in consumption spending as a result of the increased income (Column 3).

Record Sheets (Accompanying the Instructions)

TABLE 1.
Increase in Government Spending by $100 when MPC = 0.8

Round #                Expenditure Approach   Factor Payments Approach

Round 1                                       Income
American Car           Car =                  Wages =
                                              Profit =
                                              Interest =
                                              Cost of Raw Material =
American Steel & Ore                          Wages =
                                              Interest =
                                              Profit =
                       Change in GDP =

Round 2                                       Income
Trader's Food          Food =                 Wages & Profit =
Shimmery Shirts        Shirts =               Wages & Profit =
Rickety Rentals        Housing =              Wages & Profit =
                       Change in GDP =

Round 3                                       Income
Trader's Food          Food =                 Wages & Profit =
Shimmery Shirts        Shirts =               Wages & Profit =
Rickety Rentals        Housing =              Wages & Profit =
American Car           Car =                  Wages & Profit =
                       Change in GDP =

Round #                MPC = 0.8

Round 1                Spending
American Car           Consumption/ Business Spending
                       = MPC* Change in Income
                       =

American Steel & Ore

                       Change in Spending =

Round 2                Spending
Trader's Food          Consumption/ Business Spending
Shimmery Shirts        = MPC* Change in Income
Rickety Rentals        =
                       Change in Spending =

Round 3                Spending
Trader's Food          Consumption/ Business Spending
Shimmery Shirts        = MPC* Change in Income
Rickety Rentals        =
American Car
                       Change in Spending =

Change in GDP = First Round + Second Round + Third Round

Total Change in GDP == 1 / 1 - MPC * [DELTA] Spending

Summary Result: Change in GDP is higher/ lower/ the same
as the initial change in spending, (i.e. value of the
Expenditure Multiplier is greater than one)

TABLE 2.
Relaxing Standard Assumptions #1: MPC Suppose MPC - 0.6 instead of 0.8

Round #                Expenditure Approach   Factor Payments Approach

Round 1                                       Income
American Car           Car =                  Wages =
                                              Profit =
                                              Interest =
                                              Cost of Raw Material =
American Steel & Ore                          Wages =
                                              Interest =
                                              Profit =
                       Change in GDP =

Round 2                                       Income
Trader's Food          Food =                 Wages & Profit =
Shimmery Shirts        Shirts =               Wages & Profit =
Rickety Rentals        Housing =              Wages & Profit =
                       Change in GDP =

Round 3                                       Income
Trader's Food          Food =                 Wages & Profit =
Shimmery Shirts        Shirts =               Wages & Profit =
Rickety Rentals        Housing =              Wages & Profit =
American Car           Car =                  Wages & Profit =
                       Change in GDP =

Round #                MPC = 0.6

Round 1                Spending
American Car           Consumption/ Business Spending
                       = MPC* Change in Income
                       =

American Steel & Ore

                       Change in Spending =

Round 2                Spending
Trader's Food          Consumption/ Business Spending
Shimmery Shirts        = MPC* Change in Income
Rickety Rentals        =
                       Change in Spending =

Round 3                Spending
Trader's Food          Consumption/ Business Spending
Shimmery Shirts        = MPC* Change in Income
Rickety Rentals        =
American Car
                       Change in Spending =

Change in GDP = First Round + Second Round + Third Round

Total Change in GDP == 1 / 1 - MPC * [DELTA]Spending

Summary Result: Change in GDP (i.e. value of the
Expenditure Multiplier) is higher/ lower/ the same
when the MPC is lower.

TABLE 3.
Relaxing Standard Assumptions #2: Imports (i.e. Open Economy)

Suppose Shimmery Shirts is not a U.S.firm, hut instead it is
based in Mexico. Consumers and businesses spend some of their
income on Shimmery Shirts in Round 2, but this Round 2 spending
is transferred out of U.S. and no longer affects future income or
spending.

Round #           Expenditure Approach        Factor Payments Approach

Round 1                                       Income
American Car      Car =                       Wages =
                                              Profit =
                                              Interest =
                                              Cost of Raw Material =
American Steel                                Wages =
  & Ore                                       Interest =
                                              Profit =
                  Change in GDP =

Round 2                                       Income
Trader's Food     Food =                      Wages & Profit =
Shimmery Shirts   Shirts =                    Wages & Profit =
Rickety Rentals   Housing = Change in GDP =   Wages & Profit =

Round 3                                       Income
Trader's Food     Food =                      Wages & Profit =
Shimmery Shirts   Shirts =                    Wages & Profit =
Rickety Rentals   Housing =                   Wages & Profit =
American Car      Car =                       Wages & Profit =
                  Change in GDP =

Round #           MPC = 0.8

Round 1           Spending
American Car      Consumption/Business Spending
                  = MPC* Change in Income =

American Steel
  & Ore

                  Change in Spending =

Round 2           Spending
Trader's Food     Consumption/Business Spending
Shimmery Shirts   = MPC* Change in Income =
Rickety Rentals   Change in Spending =

Round 3           Spending
Trader's Food     Consumption/Business Spending
Shimmery Shirts   = MPC* Change in Income =
Rickety Rentals
American Car
                  Change in Spending =

Change in GDP = First Round + Second Round + Third Roilnd
Total Change in GDP = 1 / 1 - MPC * [DELTA]Spending

Summary Result: Change in GDP (i.e. value of the Expenditure Multiplier) is higher/ lower/ the same when additional spending is on goods and services imported from abroad.

Summary Sheet

A.1 Increase in Government Spending by $100 when MPC = 0.8 (Table 1)

Change in GDP __/First Round + __/Second Round + __/Third Round

Total Change in GDP = 1/1-MPC

* [DELTA] Government Spending

A. 2 Increase in Government Spending by $100 when MPC = 0.6 (Table 2)

Change in GDP __/First Round + __/Second Round + __/Third Round

Total Change in GDP = 1/1- MPC * [DELTA] Government Spending

Summary Result: Change in GDP (i.e. value of the Expenditure Multiplier) is higher/ lower/ the same when the MPC is lower.

B. Tax Cuts of $100 when MPC = 0.8

Change in GDP __/First Round + __/Second Round + __/Third Round

Total Change in GDP = - MPC/1 - MPC * [DELTA] Tax

=

Summary Result: Change in GDP is higher/ lower/ the same when the fiscal stimulus is in the form of increased government spending rather than lower taxes.

References

Andolfatto, D. 2010. "Fiscal Multipliers in War and in Peace." Federal Reserx'e Bank of St. Louis Review 92(2): 121-27.

Auerbach, A. J. and Gale, W. G. 2009. "Activist Fiscal Policy to Stabilize Economic Activity." NBER Working Paper 15407, National Bureau of Economic Research (October 2009).

Barro, R. J. 2010. "The Stimulus Evidence One Year On." The Wall Street Journal (February 23, 2010).

Cogan, J. F., Cwik, T., Taylor, J. B. and Wieland, V. 2010. "New Keynesian versus Old Keynesian Government Spending Multipliers." Journal of Economic Dynamics and Control 34(3): 281-295.

Emerson, J. 2011. "Consumption-Saving Investigation: United States." Journal of Economic Educators 11(1): 39-46.

Hall, R. E. 2009. "By How Much Does GDP Rise if the Government Buys More Output?" NBER Working Paper 15496, National Bureau of Economic Research (November 2009).

Laury, S. and Holt, C. 2000. "Classroom Games: Making Money." Journal of Economic Perspectives 14(2): 205-213.

"Much ado about Multipliers." The Economist (September 24, 2009).

Krugman, P. 2012. "The Conscience of a Liberal." The New York Times (October 9, 2012).

Sahm, C. R., Shapiro, M. D. and Slemrod, J. B. 2009. "Household Response to the 2008 Tax Rebates: Survey Evidence and Aggregate Implications." NBER Working Paper 15421, National Bureau of Economic Research (October 2009).

Zandi, M. 2008. "A Second Quick Boost From Government Could Spark Recovery." Edited excerpts from Congressional Testimony (July 24, 2008).

Uhlig, H. 2010. "Some Fiscal Calculus." American Economic Review, P&P 100(2): 30-34.

Notes

(1.) This amounts to $340 which is greater than the total spending in the demonstration ($244). The extra reserve of different denominations allows the instructor and/or the banker to provide smaller denomination bills as needed for the later rounds of the simulation.

(2.) The bank does not play a pivotal role in this fiscal policy demonstration, and the instructor can choose not to employ the "financial lender" without comprising student learning. However, inclusion of the lender reinforces the way in which interest payments factor into the GDP calculations. It also allows for greater student participation, and the instructor can ask the banker to assist in the moneyed transactions e.g. counting the bills, making change for smaller denomination bills etc. Finally, and perhaps most importantly, the banker provides a point of continuity if the instructor wishes to follow-up this fiscal multiplier exercise with the money multiplier exercise. We recommend the "Making Money" classroom game (Laury and Holt, 2000) that focuses on the process of money multiplier through multiple creation of deposits. In fact, this exercise is inspired by the latter demonstration.

(3.) The instructor can chose only one approach without adversely affecting student learning. Record sheets can be easily modified by eliminating the corresponding column.

(4.) For ease of calculation, we keep the stimulus amount small at $100, but during the ex-post discussion, the instructor can reiterate that the fiscal stimulus bill of 2008 was worth $831 billion.

(5.) Since ore is mined from the ground, the cost of raw materials is assumed to be zero.

(6.) These numbers are purely for illustrative purposes. It is imperative to allow firms (students) to make their own allocation decisions. Since the remaining students in the class serve as a pool of potential workers, it is usually very straightforward for the firms to hire workers. However, to avoid several rounds of wage negotiations, which would likely slow down the experiment and detract attention from its main point, instructor can also choose to assign a wage rate per worker. The latter may or may not differ by industry/firm.

(7.) Our focus is solely on the fiscal policy decisions, and we want to abstract from any interaction with the monetary policy. However, some students might question why banks cannot loan out the consumer saving deposits this not only puts more money in the hands of the consumers but the lender also makes additional profit. A succinct response would be that the multiplier effect is further amplified in the presence of banks. However, this query is best answered at a later date.

(8.) We have already demonstrated the relation between a business and its raw material supplier (American Car and American Steel & Ore). Therefore, for the sake of simplicity, we will assume that cost of raw materials for these small, self-employed business owners is zero and they retain their entire income as profit. This assumption can be easily modified to reflect a more plausible scenario (for e.g. Trader's Food may buy its raw materials from Forest Farms etc.) but it makes the demonstration needlessly complicated.

(9.) To derive the multiplier formula, we start with the numerical values in our example.

The change in GDP: AGDP = 100 + 80 + 64 + 51.2 +......

Factoring out $100, we get: [DELTA] GDP = 100* (1 + 0.8 + [0.8.sup.2] + [0.8.sup.3] +.....)

In our example, $100 was the initial increase in government spending and 0.8 was assumed to be the value of MPC. Generalizing for any change in spending or any value of MPC, we get [DELTA[GDP = [DELTA]Spending *(1 + (MPC) + [(MPC).sup.2] + [(MPC).sup.3] +....).

Applying the formula for sum of infinite geometric series, we get [DELTA] GDP - [DELTA] Spending * {1/(1 - MPC)}.

(10.) The instructor can make a note of the queries on the board. In our experience, students are able to answer most of the queries themselves by the end of the exercise.

(11.) Most taxpayers below the threshold income limit received a rebate of at least $300 per person ($600 for married couples filing jointly). For people with an income tax greater than $300 (or $600 in case of married couples), the tax rebate was equal to the payer's net income tax liability, but could not exceed $600 (for a single person) or $1200 (for married couple filing jointly). Those with dependent children received an additional $300 per child.

(12.) An easy to read article from the Economist (2009) can also be assigned as a homework reading after the in-class exercise.

(13.) In the congressional testimony given in July 2008, Mark Zandi, the chief economist for Moody's Economy.com, provided estimates of the one-year multiplier effect for several fiscal policy options. He testified that any form of increased government spending would have more of a multiplier effect than a tax cut of an equivalent amount. For instance, the lowest multiplier for a spending increase (general aid to state governments, 1.36) had a higher multiplier effect than the highest tax multiplier. Among tax cuts, multipliers ranged from 1.29 for a payroll tax holiday down to 0.27 for accelerated depreciation. It bears pointing out that refundable lump-sum tax rebates, the policy used in the Economic Stimulus Act of 2008, had the second-largest multiplier for a tax cut, 1.26.

(14.) This explains why Zandi (2008) estimated that the most effective policy is a temporary increase in food stamps, with an estimated multiplier of 1.73.

(15.) For instance, Krugman's (2012) short run analysis can be contrasted with the long run prognosis discussed by Cogan, et al. (2010) and Uhlig (2010).

Shakun D. Mago

Department of Economics, Robins School of Business, University of Richmond, 1 Gateway Road, Richmond, VA 23173. E-mail: sdatta@richmond.edu; Phone: 804-287-6631, Fax: 804-289-8878

I would like to thank the participants of the National Conference on Teaching Economics 2012 for helpful comments and suggestions.