consumption function final

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TheConsumptionFunction

BrianA.Joubran,LisaHawich,andTinaDinhBusinessCalculus(12pm)

Dr.LeeOctober20th,2008

ConsumptionFunction‐1

TableofContents

1.Introduction........................................................................................................................ 2

2.HistoricalBackground ......................................................................................................... 4

3.TheConsumptionFunction–TheModel ............................................................................. 63.1MarginalPropensitytoConsume(mpc)...................................................................................................................83.2MarginalPropensitytoSave(mps) .........................................................................................................................103.3TheMultiplierModel......................................................................................................................................................104.ConsumptionFunctionandItsAppliedCalculations–CaseStudy ..................................... 144.1GrossDomesticProductandPersonalIncomeIndices...................................................................................154.2GDPandPIfrom2000to2008..................................................................................................................................164.3ChangeinGDPandPIfrom2000to2008 ............................................................................................................174.4MarginalPropensitytoConsume(mpc)from2000to2008 .......................................................................184.5ExpressingtheConsumptionFunctioninTermsofGDPandPI .................................................................19

5.Summary .......................................................................................................................... 22

Sources................................................................................................................................. 24

Bibliography ......................................................................................................................... 25

ListofFigures,Tables,Theorems,Derivations,andImages ................................................... 26


1.IntroductionIn their Complete 2007 Annual Review report for investors, the Coca-Cola Company boasts 1.5

billion servings of their beverages a day. If this many beverages are served around the globe, we

can logically assume that the same amount is consumed. Further, if the current world population

equals approximately 6.7 billion, according to the U.S. Census Bureau, that would mean almost

every human on the planet consumes at least 0.22 beverages owned by the Coca-Cola Company

a day. That is approximately 81 beverages per person a year!

Image 1. From its Complete 2007 Annual Review, Coca-Cola Co. highlights a portfolio boasting more than 1 billion sales a year. Image taken from Coco-Cola Co. 2007 Annual Report.

Why do we consume so much? According to John Maynard Keynes, it is in our nature

(The General Theory, 1936). We begin consuming when we are born and do not stop until the

day we die. Throughout our lives we consume material things (goods) like food, computers, cars,

and gasoline. We even consume intangibles like services and experiences. For example, we pay

an airline to serve us by transporting us from one point of the country to another. We pay a hotel

service to house us in a safe and comfortable place while we vacation in a foreign city. We pay

to watch a film in hopes that it may tap into our emotions and make us laugh or cry. Regardless

of what it is (goods or services) we cannot go throughout the day without consuming.

Keynes, who studied this inevitability in the 1930’s, defined our inclination as a

Marginal Propensity to Consume, and he developed a mathematical relationship between

people’s tendency to consume and to save based on a person’s income level (The General

Theory, 1936). Keynes argued that there is a direct relationship between a person’s income level

and the amount he/she consumes. This report evaluates Keynes’ Consumption Function, and

briefly examines its first introduction in his publication, The General Theory of Employment,

Interest, and Money.

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In addition, this report identifies the function’s main components: Consumption, Savings

and Investment, Income, and the Marginal Propensity to Consume. Once identified, we evaluate

the function’s practicality, and apply it to the current trends of the past eight years (2000-2008).

The report concludes with a brief summary of the facts presented, and offers a simple

analysis on the value of the function to economists and governments that rely on it. To begin, we

evaluate Keynes’ first introduction of the function as well as his motives, or reasoning, behind its

development.


2.HistoricalBackground

At the time Keynes identified his

postulate on consumption, the United States was

in the midst of a great depression. The

unemployment rate reached a maximum of

twenty-five percent (VanGiezen, Schwenk,

2003), which meant that nearly a quarter of

America’s workforce had no jobs and income was

scarce. It was generally assumed that whatever

money people had at the time they put away for

savings. Although saving money may have

seemed like a smart thing to do at the time,

people saved more than they spent, or consumed,

resulting in slow economic growth. In other

words, because no one was spending money, no

one was consuming. This had a strong impact on

the economic situation at the time causing the government to make several policy changes on

how government and businesses run (Case, Fair, 1992).

In The General Theory, Keynes reevaluated several general theories of economics

including what he called the “Postulates of the Classical Economics” (Keynes, 1936), were he

reviewed the classical theory of employment and the demand for employment. He argued that

the classical theory is “misleading and disastrous if we attempt to apply it to the facts of

experience” (Keynes, 1936).

In other words, Keynes believed that traditional thought about employment and the

demand for employment was inaccurate and required reexamination. As a result of his research,

Keynes established a new approach in regards to employment, interest, and money. This new

Keynesian approach had a profound impact on modern economics, as well as political theory,

and governments’ fiscal policies (Case, Fair, 1992).

Image 2. John Maynard Keynes (1883-1946) developed the consumption function and several other theories in economics, known as Keynesian Economics. (Photo taken from the Bretton Woods website.)


Essentially, the Keynesian economics established new means to explaining spending

behavior, whether it is the spending behavior of the government, an individual, or a group of

individuals (households). Keynes’ Consumption Function contributed to determining the amount

of money the government spends and receives, or inputs and outputs (GDP), as well as how

much households spend on consumer goods, and the amount of money companies invest (Case,

Fair, 1992). To better understand this, we define the function, its variables, and its parameters.


3.TheConsumptionFunction–TheModel

Simply stated, the Consumption Function is the relationship between consumption and

income. Economists assume that “The higher someone’s income is, the higher her or his

consumption is likely to be. Thus, people with more income tend to consume more than people

with less income” (Case, Fair, 1992).

Looking at Figure 1 below, we observe the properties of a hypothetical consumption

function, where is the amount of consumption for a given household, and is the amount of

income a given household receives. Therefore, is a function of . Also, is never equal to

zero. In other words, even at an income of zero, consumption is positive. A household must

consume in order to survive regardless if there is no income (Case, Fair, 1992).

One of the key properties of the function is that it yields a positive slope, in other words,

as (an individual’s income) increases, (an individual’s consumption) also increases. Figure

1 illustrates how the change in consumption ( ) over the change in income ( ) equals the

slope of the consumption function. Although this may seem obvious, the slope of the

consumption function is a bit more complex, and will be explained later (see section 3.1

“Marginal Propensity to Consume”) (Case, Fair, 1992).

Figure 1. Graph of a Hypothetical Consumption Function of an Individual Household (Case, Fair, 1992)

C Y

C Y C

Y C

!C !Y

Household Income

Hou

seho

ld C

onsu

mpt

ion

0 Y

C

ΔC

ΔY Slope = ΔCΔY

C(Y )


Now that we have identified the properties of the consumption function in relation to a

given household, we must look at the function in relation to more than one household. To do this

we look at the aggregate consumption, which is defined as “total consumption of all households”

(Case, Fair, 1992). Economists also assume, as with the individual relationship, that the

aggregate yields a positive slope (Case, Fair, 1992).

Knowing all the properties of the function, we can evaluate its expression. The

expression can be easily understood if we express it as a straight line (i.e. y=mx+b) (Case, Fair,

1992). When we do this the expression looks as follows:

Derivation 1. Consumption Function (Case, Fair, 1992)

y = b + mx↓ ↓ ↓C = b + mY

In the above expression, is the consumption in place of the y-axis, and b is the point at

which the function intersects the -axis, is the slope of the line, and is in place of the x-

axis. The graph of this function looks like that illustrated in Figure 2 below.

Figure 2. Relationship of Income and Consumption (Case, Fair, 1992)

C

C m Y

Aggregate Income

Aggr

egat

e C

onsu

mpt

ion

0 Y

C

ΔC

ΔY slope =ΔCΔY

= m

C = b + mY


3.1MarginalPropensitytoConsume(mpc)

One cannot fully grasp the complexity of the consumption function without taking into

consideration the marginal propensity to consume (mpc). The marginal propensity to consume

(mpc) is “the fraction of a change in income that is consumed, or spent” (Case, Fair, 1992). In

other words, the mpc is equal to the slope of the function.

Derivation 2. Slope of the Consumption Function (Case, Fair, 1992)

m = mpc =ΔCΔY

C = b + mY ↓C = b + (mpc)Y

To put the equation into perspective let’s take a hypothetical situation:

If, for example, for Gerald to survive every month, he must spend the bare minimum of a

$1,000 to pay his rent, utilities, and food. However, he spends an additional $375 for his own

enjoyment. His monthly salary is $1,500. As a result of his hard work for the past year, Gerald’s

employer has decided to increase his pay an additional $100 a month. As a result of his raise,

Gerald decides to spend some money on a gym membership. It costs him $25 a month on top of

his current monthly expenses (total of $1400). Gerald saves the rest of his money.

Now that he has gotten a raise and increased his spending, what is Gerald’s average rate

of consumption, or Marginal Propensity to Consume (mpc)?

When we substitute the numbers into the equation we find that based on Gerald’s new

increase in pay of $100 and additional cost of $25 for a gym membership, his total consumption

is $1400 (see Example 1 below), and his marginal propensity to consume is 25%. In other words,

for every $4 his income increases, he spends $1, while saving the rest ($3).


Example 1. Gerald’s Marginal Propensity to Consume

Given, C = b + mpcY ,

Then, Y = 1600, b = 1000, and

mpc =ΔCΔY

=Change in Consumption

Change in Income=

1025 −1000(1500 +100) −1500

=25

100= 0.25

Therefore, C = 1000 + (0.25)1600 = 1000 + 400 = 1400

The graph of Gerald’s example looks like that in Figure 3 below. From this illustration

we observe that Gerald’s consumption, even if he had no income, would be $1,000. At an

income of $1,500 he consumes $1,375. When his income increases by $100, he now consumes

$1,400. In other words, Gerald’s behavior of consuming is proportionately related to his mpc.

We can assume if he were to receive another increase in pay that he would spend 25% of the

increase on consuming goods. We can also deduce from this that he will save the remainder,

which would be 75%.

Figure 3. Gerald’s Propensity to Consume

C = b + mY

Gerald’s Income

0

Y

C

Ger

ald’

s C

onsu

mpt

ion

$1000

$1375

$1400

$1500 $1600

$1600 – $1500 = $100

$1375 – 1400 = $25

mpc =25100

= .25


3.2MarginalPropensitytoSave(mps)

In Gerald’s example above we calculated how much Gerald consumed based on the

increase of his income. Although we calculated Gerald’s behavior in spending his money, we can

also calculate Gerald’s behavior in saving his money. In the above example, Gerald spent $25 of

his increased income of $100. He also saved $75 from that increase. This means that Gerald’s

behavior to save his money is proportionately related to his behavior in consuming his money.

Calculating Gerald’s propensity to save is similar to calculating his propensity to

consume. We use the same formula established earlier, C = b + (mpc)Y , but we substitute

Consumption (C) with Savings ( ). The marginal propensity to save (mps) is equal to the

change in Savings ( ) over the change in Income ( ) (see Theorem 1, below) (Case, Fair,

1992). Therefore, in Gerald’s case, he saved $75 of his $100. This means that his marginal

propensity to save (mps) is 75/100, or 75% of his income.

Theorem 1. Marginal Propensity to Save (Case, Fair, 1992)

Marginal Propensity to Save =Change in SavingsChange in Income

=ΔSΔY

3.3TheMultiplierModel

Essentially, we have applied all the properties of the Consumption Function as explained

in the previous paragraphs to calculate the rate of consumption of a given person such as Gerald;

however, in the real world the function alone does not apply as easily to the complexity of

calculating the rate of consumption for a given nation. To do this, we must consider what

economists call the Multiplier Model. The multiplier model is a more complex model then the

consumption function model. It was originally designed by Alvin Hansen to explain the large

drop in income due to an initial drop in investment during the great depression (Colander, 2006,

p. 616, 621).

The model focuses on Aggregate Expenditures, which is “the total amount of spending on

final goods and services in the economy.” In other words, Aggregate Expenditures (AE) is the

S

!S !Y


sum of Consumption (C) (spending by households), Investment (I) (spending by businesses),

Government Spending (G), and Net Exports (X – M), which is the difference between Exports

(X) and Imports (M) (Colander, 2006, p. 618). Theorem 2 (below) illustrates this model.

Theorem 2. Aggregate Expenditures (Colander, 2006)

AE = C + I +G + (X − M )

Further, the multiplier model distinguishes Autonomous Expenditures from Induced

Expenditures. Autonomous Expenditures are “expenditures that do not systematically vary with

income.” This means that even when the income is zero, there will be some expenditure. Induced

Expenditures are “expenditures that change as income changes.” Usually when someone’s

income rises, his or her expenditures rise due to higher consumption. Figure 4, below, illustrates

the Aggregate Expenditure curve, which shows the relationship between autonomous and

induced expenditures (Colander, 2006, 618-619).

Figure 4. Aggregate Expenditure Curve (Colander, 2006)

AggregateExpendituresCurve


In the example above, Autonomous Expenditures is $3,000 at all times, even when

income is zero, and everything above and beyond $3,000 is Induced Expenditures. The graph

shows that at an income of $6,000, aggregate expenditures is at $6,000. But when income rises

by $1,000 (to a total of $7,000), aggregate expenditures increases by $500 (to a total of $6,500).

The same connection can be seen when income falls by $1,000 (to a total of $5,000), aggregate

expenditures drop by $500 to $5,500. Why is the increase/decrease of aggregate expenditures

smaller than the rise/drop of income? The answer is because only the induced expenditures

change as income changes, autonomous expenditures stay the same (Colander, 2006, p. 618-

619).

The slope of the aggregate expenditure curve is “the ratio of the change in aggregate

expenditures to a change in income”, also known as marginal propensity to expend (mpe). From

here we draw the mathematical relationship as seen in Theorem 3 (Colander, 2006, p. 620).

Theorem 3. The Aggregate Expenditures Function (Colander, 2006)

AE = AE0 + (mpe)Y

The formula above describes the aggregate expenditures as the sum of autonomous

expenditures ( AE 0) and induced expenditures (mpeY ). This formula looks familiar because it is

equivalent to the consumption function, as seen below (Derivation 3).

Derivation 3. Transformation of Aggregate Expenditures Function to Consumption Function

AE = AE0 + (mpe)Y ↓ ↓ ↓ C = b + (mpc)Y


As we can see from the transformation above, Aggregate Expenditures (AE) is equal to

Consumption (C) which makes sense, because the total amount of spending on final goods and

services in the economy is basically the same as the amount of consumption for a given

household. Also, because Autonomous Expenditures (AE0) is that which does not systematically

vary with income, it is equivalent to the y-axis intersect (b) of the consumption function. Lastly,

because expenditures is the same as consumption the marginal propensity to expand (mpe) is

identical to the marginal propensity to consume (mpc) (see Derivation 4 below) (Colander, 2006,

p. 546, 618-619).

Derivation 4. Relationship between Marginal Propensity to Expand (mpe) and Marginal Propensity to Consume (mpc) (Colander, 2006)

Change in ExpendituresChange in Income

= mpe

Change in ConsumptionChange in Income

= mpc

↓ mpe = mpc

Now that we’ve established the complexity of the Consumption Function through the

Multiplier Model, we can now apply this information to real world data and identify some

interesting economic trends. The next section applies the consumption function using the Gross

Domestic Product and Personal Income of a nation to calculate the going rate of consumption for

a given period of time.


4.ConsumptionFunctionandItsAppliedCalculations–CaseStudy

On September 23rd, 2008, Treasury

Secretary Henry Paulson and Federal

Reserve Chairman Ben Bernanke testified

before the House Financial Services

Committee in hopes of persuading congress

to pass a bill that would allocate $700

billion dollars of taxpayer money to

address an aberrant financial crisis.

Financial institutions such as Bear Stearns,

Lehman Brothers, Washington Mutual,

American International Group (AIG),

Fannie Mae and Freddie Mac have all struggled due to toxic securities linked to falling housing

prices and the institution’s inherent lack of capital to maintain those securities (Economist, 338,

17). As a result to the financial institutions’ instability, and the congressional hearing, the Dow

Jones industrial average dropped a record 777 points the following Monday, September 29th, the

largest single-day decline in its history (Paradis). According to Paulson and Bernanke, the $700

billion will be used to purchase the toxic securities freeing the institutions from their assets and

allowing them to recapitalize (Economist, 338, 17), presumably stabilizing the financial market.

How did this financial crisis come to be? No one is exactly sure, but to help paint a

clearer picture we apply Keynes’ Consumption Function to the past eight years preceding the

financial crisis to make some educated guesses as to what may have triggered the economic

trend.

This section of our report will highlight the nation’s consumption variables from 2000 to

2008 in comparison with the nation’s income variables of the same period. Once we identify

these two variables we then determine the Marginal Propensity to Consume (mpc), to determine

the rate of consumption for each year. With these three variables, we will be able to express

Keynes’ Consumption Function for the economic period. With the function expressed we will

look at its graph and observe the behavior of the nation’s consumption and saving trends.

Image3.FederalReserveBoardChairman,BenBernanke(right),andTreasurySecretary,HenryPaulson(left),testifyduringaHouseFinancialServicesCommitteehearingonCapitolHillJuly10,2008inWashingtonDC.(ImagetakenfromZimbio.com.)


We begin with an analysis of the consumption and income variables: Gross Domestic

Product (GDP) and Personal Income (PI).

4.1GrossDomesticProductandPersonalIncomeIndices

The method in which economists use to calculate the nation’s income and consumption

comes from the Gross Domestic Product (GDP) index, and the Personal Income (PI) index.

According to the United States Department of Commerce, the Personal Income (PI) is the gross

personal income of the nation. The GDP is “the total market value of all final goods and services

produced in an economy in a one-year period.” It is defined as the sum of consumption,

investment, government spending and net exports (see Theorem 4) (Colander, 2006, p. 540, 546-

547).

Theorem 4. Gross Domestic Product (GDP)

GDP = C + I +G + (X − M )

Looking at the equation above, we observe that the GDP is equivalent to the definition of

Aggregate Expenditures (AE) as was described in Theorem 1 previously. Accordingly, because

Aggregate Expenditure is equivalent to Consumption (C) (see Derivation 3) we can conclude

that Consumption is also equal to the GDP. So if we substitute these variables into our

Consumption Function model we get the following derivation below.

Derivation 5. Consumption Function in Relation to GDP and PI

C = b + (mpc)Y GDP = b + (mpc)PI


4.2GDPandPIfrom2000to2008

Utilizing the historical database available on the Bureau of Economic Analysis website,

we compiled a list (see Table 1, below) comparing the Gross Domestic Product (GDP) and

Personal Income (PI) of the United States from January 2000 to the end of the third quarter of

2008 (September). The data from 1999 is included only as a reference for later calculations.

Table 1. 2000-2008 Personal Income* (PI) and Gross Domestic Product* (GDP)

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008GDP 9268.4 9817.0 10128.0 10469.6 10960.8 11685.9 12421.9 13178.4 13807.5 14429.2PI 7802.4 8429.7 8724.1 8881.9 9163.6 9727.2 10269.8 10993.9 11663.2 12219.9

*In Billions of Dollars (Source: Bureau of Economic Analysis)

The table above shows the GDP and PI for each year. Using the raw data in the table, we

can graph the GDP and PI to make some interesting observations, see Figure 5 below.

Figure 5. 2000-2008 Graph of GDP and PI

Looking at the graph above we observe that although both GDP and PI increase each

year, PI is always less than the GDP. In other words, the nation consumes more than it makes.

Also, in 2000 the total GDP equaled $9,817B and at 2008 the GDP equaled $14,150.8B. That is

a difference of $4,333.8B. In other words, the GDP increased 44% in eight years!

To see how the consumption and income is distributed in terms of saving and spending

behavior, we apply the same raw data into the graph below (Figure 6).

0

2000

4000

6000

8000

10000

12000

14000

16000

2000 2001 2002 2003 2004 2005 2006 2007 2008

Dollar(inbillions)

Year

GDP(C)

IP(Y)


Figure 6. Consumption and Income Distribution Explanation

From the graph we can see that between 2000 and 2008 the nation consumes more than it

receives in income. We can assume the extra amount of money is borrowed, which may explain

the astronomical debt of the U.S. government, a whopping $10.6 trillion as of November 16th,

2008 (U.S. Dept. of the Treasury, Bureau of the Public Debt).

4.3ChangeinGDPandPIfrom2000to2008

Now that we know the raw data supplied from Table 1 we can calculate the difference in

change of GDP and PI for each year. To calculate this we subtract the succeeding year’s number

from the preceding year’s number. For example, the difference in GDP (ΔGDP) from 2000 to

2001 is calculated by subtracting the GDP for 2001 by the GDP of 2000. In this case, it is

$10,128.0B minus $9,817.0B, which equals $311.0B. Table 2 below lists the change in GDP and

PI from 2000 to 2008.

Table 2. Change in PI* and GDP* from 2000 to 2008

2000 2001 2002 2003 2004 2005 2006 2007 2008ΔGDP 548.6 311.0 241.6 491.2 725.1 736.0 756.5 629.1 621.7ΔPI 627.3 294.4 157.8 281.7 563.6 542.6 724.1 669.3 556.7

*In Billions of Dollars

Spending

Saving

2008

2007

2006

2005

2004

20032002

20012000


Looking at the data we note that the PI is less than GDP in every year except 2000 and

2007. Figure 7 below depicts the relationship of GDP to PI for each year in the form of a bar

chart.

Figure 7. Graph of Change in PI and GDP from 2000 to 2008

Now that we have identified the change in GDP and PI we can calculate the Marginal

Propensity to Consume (mpc).

4.4MarginalPropensitytoConsume(mpc)from2000to2008

Recalling from the previous section (3.1 “Marginal Propensity to Consume”), the

Marginal Propensity to Consume (mpc) is equal to the change of consumption over the change of

income (ΔC/ΔY). We have calculated the mpc for each year and provided the data in Table 3

below.

Table 3. Marginal Propensity to Consume* (mpc) from 2000 to 2008

2000 2001 2002 2003 2004 2005 2006 2007 2008ΔC/ΔY 0.8745 1.056 2.165 1.744 1.287 1.356 1.045 0.940 1.117

% 87.45% 105.6% 216.5% 174.4% 128.7% 135.6% 104.5% 94% 111.7%*In Percentage

We can observe from the table that the rate of consumption exceeds 100% for every year

except in 2000 and 2007, when it was at 87.45% and 94%. This means that the nation consumed

more than 100% of its income, except in 2000 and 2007 where it saved 12.55% and 6% of its

0

100

200

300

400

500

600

700

800

2000 2001 2002 2003 2004 2005 2006 2007 2008

ChangeinGDP(ChangeinConsumptionC)

ChangeinPI(ChangeinIncomeY)


income. Also from the table we see that there was a peak of 216.5% consumption in 2002. This

means that the rate of consumption more than doubled from the previous year—it may be

interesting to note that such a drastic change may have been a result of the preceding 9/11

terrorist attacks.

4.5ExpressingtheConsumptionFunctioninTermsofGDPandPI

With all the variables defined, we can input them in the consumption function model that

we expressed in the first part of this report (see Derivation 2), but because the mpc fluctuates

from year to year, we can only apply the model one year at a time. Table 4 below shows the

consumption function for each year starting from 2000.

Table 4. Consumption Function Models from 2000 to 2001

Year C b mpc

2000 9817 9268.4 0.8745 C = 9268.4 + (0.8745)Y 2001 10128 9817 1.056 C = 9817 + (1.056)Y

2002 10469.6 10128 2.165 C = 10128 + (2.165)Y

2003 10960.8 10469.6 1.744 C = 10469.6 + (1.744)Y

2004 11685.9 10960.8 1.287 C = 10960.8 + (1.287)Y

2005 12421.9 11685.9 1.356 C = 11685.9 + (1.356)Y

2006 13178.4 12421.9 1.045 C = 12421.9 + (1.045)Y

2007 14429.2 13178.4 0.940 C = 13178.4 + (0.940)Y

2008 14429.2 14429.2 1.117 C = 14429.2 + (1.117)Y

To determine b, we assume that the amount of consumption at the beginning of one year

will equal the amount of consumption at the end of its previous year. For example, the amount of

consumption at the beginning of 2001 is equal to the amount of consumption at the end of 2000.

Thus, regardless of how much income the nation made in 2001 it will still need to consume the

same amount that it did at the end of 2000.

Although we could graph each function as it is shown in Table 4, it would be more

interesting to graph the slope, or the mpc, of the function. To focus only on the slope of the

function we set b equal to zero. We can do this, because as we explained in section 3.3 “The

Multiplier Model,” b is equivalent to 5 Expenditures (AE0). In other words, b is only relevant to


identify the y-axis intercept. Table 5 lists the consumption function for each year where b is

equal to zero.

Table 5. Consumption Function Models from 2000 to 2001 – Simplified

Year C = b + (mpc)Y , where b = 0

2000 C = (0.8745)Y

2001 C = (1.056)Y

2002 C = (2.165)Y

2003 C = (1.744)Y

2004 C = (1.287)Y

2005 C = (1.356)Y

2006 C = (1.045)Y

2007 C = (0.940)Y

2008 C = (1.117)Y

With a simpler version of the consumption function, we can now graph the rate of

consumption for each year. Again, for simplicity, we will calculate total consumption where

income (Y) is equal to $1.00. Table 6 lists the values for each year.

Table 6. GDP from 2001 to 2008 for every $1 of Income (Y)

PI(Y)GDP(2000)

GDP(2001)

GDP(2002)

GDP(2003)

GDP(2004)

GDP(2005)

GDP(2006)

GDP(2007)

GDP(2008)

$1.00 $0.87 $1.06 $2.17 $1.74 $1.29 $1.36 $1.05 $0.94 $1.12

The table above lists the value of consumption (GDP) for every $1.00 increase of

personal income. We observe from the table that in 2000 for every $1.00 increase of personal

income, the nation spends $0.87 of that dollar and saves $0.13. In 2001, for each $1.00 increase

in income, the nation spends $1.06 and borrows $0.06, and so on and so forth for the remaining

years. Figure 8 below shows each rate of consumption (mpc) from 2000 to 2008.


Figure 8. Rate of Consumption (mpc) from 2000 to 2008

To exemplify the savings and consumption behavior of the nation from 2000 to 2008, we

can graph the rate of consumption in respect to savings and spending for each year (see Figure 9,

below). When we observe this graph we notice that in the year 2000 and 2007 that for every

increase of $1.00 to the nations income, the nation saved $.013 and $0.06 respectively. Also,

from 2001 to 2006, and 2008, the nation spent so much that it needed to borrow money.

Figure 9. Consumption in Respect to Savings and Spending

‐1.5‐1.25‐1

‐0.75‐0.5‐0.25

00.250.50.75

11.251.51.75

22.252.5

2000 2001 2002 2003 2004 2005 2006 2007 2008

Consumption/Savings

Year

Savings

Consumption

0

0.5

1

1.5

2

2.5

0 1

ChangeinConsumption($)

ChangeinIncome($)

2000

2001

2002

2003

2004

2005

2006

2007

2008


5.Summary

In the first part of our report (section 1 “Introduction) we introduced the concept of

consumption by giving a real world example, such as the number of servings of Coca-Cola

products sold throughout the world in 2007. We have also shown the significance of this concept

by reviewing the history of its development by its creator, John Maynard Keynes (section 2

“History”). We provided the mathematical content as established by economists today,

identifying the functional model, its variables, parameters, and terms (section 3 “The

Consumption Function – The Model”. We showed the derivation of the function from the

equation y = mx + b. We identified the expression and provided a hypothetical scenario (the mpc

of Gerald) as a means to identify the proper application of the function.

In the final part of this report (section 4 “Consumption Function and Its Applied

Calculations – Case Study”), we identified the Gross Domestic Product (GDP) and the Personal

Income (PI) of the nation from 2000 to 2008. We also calculated the change of GDP and PI from

each year. From this information we were able to yield the Marginal Propensity to Consume

(mpc) by dividing the change of consumption by the change of income (ΔC/ΔY). Finally, we

applied the variables to the consumption function for each individual year. To illustrate the rate

of consumption for each year, we simplified the equation to show the value of consumption for

every dollar of personal income and graphed the results.

To conclude, it may not be clearly evident how the consumption function applies to the

real world; however, economists rely on it continuously to help determine the behavior of a

nation. It was the intension of this report to clearly show the application of the function by

breaking down its larger parts and applying it to economic data from 2000 to 2008. The product

from this period yielded some valuable and interesting characteristics of the behavior of a nation.

Surprisingly, the behavior of the United State from this period was one of overspending, so much

to point of borrowing more than it could afford. Likewise, it is at no surprise why the United

States is in the current financial crisis that it is in today. We obviously spend more than we

should, nor do we posses the ability, as a nation, to afford the purchases that we make.

The Consumption Function has proven to be a valuable tool for economists and

governments to make important decisions. It has played a major role in economic decisions and


government fiscal policy. Since its development in 1936, it has helped economists to identify the

rate of consumption of an entire nation, allowing authorities to predict and anticipate economic

trends, such as growth and recessions, ameliorating economic uncertainty. It use will most likely

be applied for many years to come.


Sources

(2008, September 27th). “Leaders: I want your money.” Economist, 338, p17. Paradis, Tim.

(2008, September 29th). “Dow plummets record 777 as financial rescue fails.” Associated Press

(2008, September 27th). “Leaders: I want your money.” Economist, 338, p17.

Case, Karl E., Fair, Ray C. (1992). Principles of Economics. 2nd Ed. Prentice-Hall, Inc.

Englewood Cliffs, New Jersey.

Coca-Cola Co. (2007). Complete 2007 Annual Review. Retrieved October 14th, 2008, from Coca-

Cola website: http://www.thecoca-colacompany.com/investors/annual_review_2007.html

Colander, D. C. (2006). Economics. Boston, Mass: Irwin/McGraw-Hill.

Keynes, John Maynard. (1936). The General Theory of Employment, Interest, and Money.

Harcourt, Brace & World, Inc. 1962.

Robert VanGiezen and Albert E. Schwenk. (2003). Compensation from before World War I

through the Great Depression. Bureau of Labor Statistics. Retrieved October 14, 2008, from

http://www.bls.gov/opub/cwc/cm20030124ar03p1.htm

United States Census Bureau. U.S. and World Population Clocks – POPClocks. Retrieved

October 16, 2008, from http://www.census.gov/main/www/popclock.html

United States Department of the Treasury, Bureau of the Public Debt, Debt to the Penny and

Who Holds It. Retrieved November 16, 2008, from

http://www.treasurydirect.gov/np/bpdlogin?application=np


Bibliography

Bowers, David A., Baird, Robert N. (1971). Elementary Mathematical Macroeconomics.

Prentice-Hall, Inc., Englewood Cliffs, NJ

Ferber, R. (1966). A study of aggregate consumption functions. Ann Arbor: University Microfilms.

Friedman, M. (1957). A theory of the consumption function. Princeton: Princeton University Press.

Hadjimatheou, G. (1987). Consumer economics after Keynes: theory and evidence of the consumption function. New York: St. Martin's Press.

Harcourt, G. C. (2006). The structure of post-Keynesian economics: the core contributions of the pioneers. Cambridge, UK: Cambridge University Press.

Keynes, J. M. (1936). The general theory of employment, interest and money. New York: Harcourt, Brace.

Lavoie, M. (2006). Introduction to post-Keynesian economics. Houndmills, Basingstoke, Hampshire: Palgrave Macmillan.

McKenna, J. P. (1969). Aggregate economic analysis. New York: Holt, Rinehart and Winston.

Speight, A. E. H. (1989). Consumption, Rational Expectations and Liquidity: Theory and Evidence. New York: St. Martin’s Press.

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ListofFigures,Tables,Theorems,Derivations,andImages

Figure 1. Graph of a Hypothetical Consumption Function of an Individual Household (Case, Fair, 1992) Figure 2. Relationship of Income and Consumption (Case, Fair, 1992)

Figure 3. Gerald’s Propensity to Consume Figure 4. Aggregate Expenditure Curve (Colander, 2006)

Figure 5. 2000-2008 Graph of GDP and PI Figure 6. Consumption and Income Distribution Explanation

Figure 7. Graph of Change in PI and GDP from 2000 to 2008 Figure 8. Rate of Consumption (mpc) from 2000 to 2008

Figure 9. Consumption in Respect to Savings and Spending Theorem 1. Marginal Propensity to Save (Case, Fair, 1992)

Theorem 2. Aggregate Expenditures (Colander, 2006) Theorem 3. The Aggregate Expenditures Function (Colander, 2006)

Theorem 4. Gross Domestic Product (GDP) Derivation 1. Consumption Function (Case, Fair, 1992)

Derivation 2. Slope of the Consumption Function (Case, Fair, 1992)

Derivation 3. Transformation of Aggregate Expenditures Function to Consumption Function

Derivation 4. Relationship between Marginal Propensity to Expand (mpe) and Marginal Propensity to Consume (mpc) (Colander, 2006)

Derivation 5. Consumption Function in Relation to GDP and PI

Table 1. 2000-2008 Personal Income* (PI) and Gross Domestic Product* (GDP)

Table 2. Change in PI* and GDP* from 2000 to 2008

Table 3. Marginal Propensity to Consume* (mpc) from 2000 to 2008

Table 4. Consumption Function Models from 2000 to 2001

Table 5. Consumption Function Models from 2000 to 2001 – Simplified

Table 6. GDP from 2001 to 2008 for every $1 of Income (Y)

Example 1. Gerald’s Marginal Propensity to Consume

Image 1. Coca-Cola Product Portfolio

Image 2. John Maynard Keynes


Image 3. Ben Bernanke and Henry Paulson before the House Financial Committee.

consumption function final

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