ECO101— PRINCIPLES OF MICROECONOMICS—Notes
Tools of Economic Analysis
Overview
In this chapter we will briefly examine the various tools, which economists use to analyse real life
phenomena. These are models, graphs, diagrams, and data collection, data calculations and data
interpretation techniques.
Models and Theories
Economists observe real life economic phenomena over a period of time and develop a theory or model to
grasp or understand the essence of the issue / problem at hand. In order to test the predictive validity of the
theory / model, economists collect economic data and use various statistical and other techniques to derive
conclusions. In practice or reality, researchers never confirm a theory: they simply attempt to reject it by
subjecting it to real-world evidence. If the data do not substantiate the model / hypothesis, then it is
rejected. If the data “fit”, and economists are very confident about the predictive validity of the model /
hypothesis over time (after continuous testing and re-testing) then this model may be called a ‘law’.
Using Graphs to Illustrate Relationships
Economic relationships (as any other relationship) may be expressed in a number of ways: in words, as a
mathematical expression (i.e., an equation), in a table (or schedule), or as a graph. In the table below, we
represent one such relationship (revenues as determined by sales, Q):
E x p r e s s in g E c o n o m ic R e la t io n s h ip s
E q u a t io n :
Q d = 1 0 0 – 0 .5 P
T a b le :
G ra p h :
10
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“A picture is worth a thousand words …” Graphs are like a picture. Certainly economics is not all about
graphs. They are simply a very useful tool to help us illustrate the various economic relationships. It is
generally easier to communicate an idea using a picture (or a graph) than describe it in words.
A graph is a visual representation of the relationship between two or more variables—these are
things/quantities that can change. There are two types of variables in a relationship: independent
variable(s), which can change in value freely due to a number of reasons, and a dependent variable,
which changes in value depending on the changes in the value of the independent variable(s).
From a Schedule (or Table) to a Graph
Before we go further into the different forms of graphs, how we construct them, and how we use them, let’s
examine how the “thousand words”—i.e., the data, the information—can be represented and then see how
they can be converted into a graph.
Let’s return to the law of demand that we examined in Chapter 1, and use the price of CDs as an
illustration. How many CDs would the students in this class buy if they were priced at £15? Perhaps 10.
What would be the outcome if prices dropped to £10? Let’s say, 15 might be bought. What if the price
dropped further – say to £5? Then perhaps 20 students in the class would decide to buy a CD.
This information can be represented into a table (or a schedule as may also be called), showing the
relationship between the price of CD’s and the quantity demanded at each price as follows:
Price
Quantity
£15.0
10
10.0
15
5.0
20
We can construct a graph to show the relationship between price and quantity demanded of CDs, with a
scale of 0 – 30 on the quantity axis (in lots of 5). Likewise a price axis can be constructed in £1 units (up to
£20). Using the combinations of price and quantities of CDs referred to above, we can plot the demand
curve (line) for the CD’s demand schedule. We can use the graph we derived to find out how many CDs
would be bought at a price of, say, £12. Work out the price at which no one would buy CDs.
Price
£20
A
Demand Curve
£15
B
£10
C
£5
10
15
20
Quantity
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Of course, not all relationships lead to graphs that are straight lines, and not all are downward sloping. If we
were to graph the relationship between average weight and average height, the graph will be upwardsloping indicating a positive relationship between the two variables. In economics, such positive relationship
(upward-sloping curve) exists between price and quantity supplied.
Additionally, some relationships may not be linear, in which case the “curve” will indeed exhibit a
“curvature”. In economics, we will see when we study the economics of the firm that such graphic behavior
is present for Average and Marginal Costs. At other times, the curves may be complex, exhibiting both
positive and negative relationship between the variables (such may be the behavior of total cost curves).
Negative linear relationship
Positive linear relationship
Complex non-linear relationship
Holding All Other Things Constant (Ceteris Paribus)
In the simple relationships we described above and represented in a graph, we were forced to have one
dependent variable and one independent variable, since a graph is two-dimensional. In reality, however, we
know, for instance, that the quantity demanded of a normal good (say CD’s) may influenced by other
variables and factors other than price alone. These may be income, tastes, prices of competing goods, etc.
We also know that their influence on quantity may be concurrent. However, we cannot represent the
concurrent influences in a two-dimensional graph. This is the reason economists represent relationships
(such as demand and supply) between two variables (such as price and quantity), holding all other things
constant, (or ceteris paribus), in order to isolate the influence of one independent variable (such as price) on
the dependent variable (such as quantity).
The Slope of a Linear Curve
The slope of a line (or a curve) is a very important property with many applications in economics. Consider
the demand schedule and the graph of CD’s as discussed above. The graph is reproduced below. They
show the quantities of CD’s that students are willing to buy at different prices.
The slope of a line is defined as the change in the value of the y variable shown on the vertical axis (in this
case price) divided by the corresponding change in the value of the x variable represented on the horizontal
axis (in this case quantity demanded).
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S lo p e o f a L in e
S lo p e b e tw e e n A & B
∆ P / ∆ Q = -5 / + 5 = - 1
In the graph above, let’s measure the slope of the demand curve (line) as we move from point A to point B.
The change in the y variable (the price) is - £5 (minus five pounds, from £15 to £10), whereas the change in
the x variable (quantity in this case) is + 5 units, the number of CD’s that students are willing to buy at that
reduced price. Applying the formula of the slope—defined above as the change in the y variable divided by
the change in the x variable—we get:
-5/5 =-1
A useful way to apply and compute the slope of a line is to think of the change in the y variable as the “rise”
–movement in the vertical direction—over the “run”—movement along the horizontal axis. Conceptually, this
can be shown in the exhibit below, where the slope is measured as the value of the “rise” divided by the
value of the “run”. When both the rise and the run are positive, the slope is positive. When the rise and the
run have opposite signs—that is, one is positive and the other is negative—then the slope is always
negative.
(-)
Slope = ------- = Negative
(+)
(- ) Rise
(+) Run
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S lo p e o f N o n -L in e a r R e la tio n s h ip s
S lo p e o f T R a t A is p o s it iv e :
T o ta l R e ve n u e
Î
S lo p e o f t a n g e n c y a t p t . A
S lo p e o f T R a t B is n e g a t iv e
Î
S lo p e o f t a n g e n c y a t p t. B
B
A
TR
Q u a n t it y
Real and Nominal Variables
Many economic variables are measured in money terms: our monthly salary, the value of savings
we have in the bank, the prices we observe on shoes and clothes and other items in shops, as well
as many macroeconomic variables, such as the money supply, the value of goods and services
produced in one year (GDP), the revenues from tourism in one year, the profits reported by
companies every year, the daily value of transactions on the Cyprus Stock Exchange, etc.
However, in many cases it is useful to know the real values of things. The real value is the
variable’s value after we adjust for changes in prices compared to a base year (sometimes referred
by economists as ”constant prices”). Below, we present an example using hypothetical values for
house prices and the overall Retail Price Index (as proxy for the movement of the general price
level.
R e a l & N o m in a l V a lu e s --E x a m p le
1960
1980
2000
£ 2 ,5 0 0
£ 2 7 ,0 0 0
£ 1 2 5 ,0 0 0
7 .4
3 9 .3
1 0 0 .0
R e a l H o u s e P r ic e ( in
2 0 0 0 p r ic e s )
£ 3 3 ,7 8 3
£ 6 8 ,7 0 2
£ 1 2 5 ,0 0 0
R e a l H o u s e P r ic e ( in
1 9 6 0 p r ic e s )
£ 2 ,5 0 0
£ 5 ,0 8 4
£ 9 ,2 5 0
H o u s e P r ic e
P r ic e I n d e x (2 0 0 0 = 1 0 0 )
(2 ,5 0 0 * 1 0 0 ) / 7 .4 = 3 3 ,7 8 3
(1 2 5 ,0 0 0 * 7 .4 ) / 1 0 0 = 9 ,2 5 0
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Scatter Diagrams
Up to now, we talked about the various ways of expressing relationships and explained in some detail the
way we plot relationships between two variables, in an attempt to visualize how an independent variable
impacts on (influences) another variable (the dependent variable). The examples given above—as we will
do many times during the course—are hypothetical.
The real-world data that economists collect to test their theories (hypotheses) typically produce graphs and
diagrams that are “scattered all over the place,” rather than the neat ones we plotted above. It is from these
“scatter diagrams” that they try to derive (infer) trends. In the diagram below, we present a set of data for
price and quantity demanded collected over a period of time (called time-series data). When plotted on a
graph these data are represented by the X’s. Though the relationship is not perfect since the points are
scattered, when viewed closely these points exhibit a downward trend, validating the inverse relationship
that we expect to have between price and quantity demanded, as taught by economic theory.
There are some statistical techniques that economists use to “fit” a curve to these scatter points which will
come close to resembling the neat demand curve we derive from our hypothetical values of price and
quantity.
D a ta & S c a tte r D ia g ra m s
P ric e
Y ear
P r ic e
Q u a n tity
1
6 .0
100
2
5 .5
105
3
6 .0
90
7 .0
X (7 .0 , 8 0 )
X
4
6 .5
85
5
6 .0
87
6
7 .0
80
7
6 .5
88
X
X
6 .0
X
X (6 .0 , 1 0 0 )
X
80
100
Q u a n tity
Index Numbers
An Index number expresses data relative to a given base value. They are useful in that they enable us to
compare numbers without express reference to the unit of account / measurement. The table below shows
how index numbers are calculated for a set of values of silver prices at different time periods.
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In d e x
S ilv e r
N u m b e rs
1 9 7 0
1 9 9 0
2 0 0 0
1 7 7
4 8 2
5 0 0
3 7
1 0 0
1 0 4
P r ic e
S ilv e r I n d e x
( 1 9 9 0 =
1 0 0 )
1 7 7
/ 4 8 2
=
0 .3 6 7
=
3 7
5 0 0
/ 4 8 2
=
1 .0 3 7
=
1 0 4
2
Index Averages
We frequently come across a number of index averages: the Retail Price Index RPI), the stock market
Index, the metals index, the purchasing managers’ index, etc are only a few examples of many index
averages. If we think of the stock market index, we know that prices of different stocks change differently.
For instance, the price of Bank of Cyprus may be moving upwards over a given time period, while the price
of Cyprus Cement may be moving down. To derive a single measure of how all the stock prices on the
stock exchange move we average different stock prices.
To see how index averages are calculated lets use the prices of different metals over the same time period
as in the table above to construct the metals index. The calculations are shown in the following graph:
I n d e x
S ilv e r
( 1 9 9 0
=
=
( 1 9 9 0
=
1 9 9 0
2 0 0 0
3 7
1 0 0
1 0 4
5 3
1 0 0
6 8
1 0 0 )
I n d e x
1 0 0 )
S ilv e r I n d e x
C o p p e r I n d e x
M e t a ls
1 9 7 0
I n d e x
C o p p e r
( 1 9 9 0
A v e r a g e s
W e ig h t
W e ig h t
5 0
I n d e x
1 0 0 )
(3 7 * 0 .2 ) +
( 5 3 * 0 .8 ) =
4 9 .8
=
=
2 0 %
8 0 %
1 0 0
(1 0 7 * 0 .2 ) +
7 5
(6 8 * 0 .8 ) =
7 5 .2
3
Total, Averages and Marginal Values
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Students may associate more with their course grades in order to understand better the meaning of
averages and marginal values. Let’s assume that during the semester, a student attending ECO101—
Principles of Microeconomics at Cyprus College has the following grades: 80, 85, 90, and 75 (assume all
grades have equal weighting). The total value (in this case it has no meaning!) is 330.
Average Value: The average value (average grade in this case) is the addition of all four grades—which
happens to be the total value of 330—divided by the number of observations (the number of tests in this
case) which happens to be 4. Thus, the average grade is:
( 75 + 86 + 93 + 84 ) / 4 = 330 / 4 = 84.5
Notice that we can find the average grade after the first two exams [(75 + 86) /2] = 80.5, or after the first
three exams [( 75 + 86 + 93) / 3] = 84.7, and so on.
Marginal Value : Let’s now calculate a slightly more difficult concept for students to understand, that of the
marginal value and perhaps one of the most important concepts in economics. In mathematics, a marginal
change is a very, very small (infinitesimal!) change in the total value (the total value of your grade) as a
result of a change in the quantity of another variable (the number of exams). In the examples we will be
using in economics, the size of the change will be one unit.
Again sticking with the example of the grades, let’s ask the question: How can you improve (that is,
increase) your average grade? The answer is of course easy: Get a higher grade than your average in your
next exam! After the first two exams, we found that the average was 80.5 – a total of 161 divided by two
exams. The grade on the third exam was 93, which is substantially higher than the average of 80.5.
Therefore, we should expect the average to improve! Let’s see this in numbers: [( 75 + 86 + 93) / 3] = 254 /
3 = 84.7. Indeed the average has improved from 80.5 to 84.7. So what is the marginal value of the third
grade?
We defined the marginal value as the “change in the total value as a result of a unit change in the quantity
of another variable”. Therefore, from two exams we go to three exams. The total value of grades goes from
161 (after two exams) to 254 (after three exams). Therefore, the total value changes by 93. In the fourth
exam, however, the student scored 84 which a lower grade than the average, and therefore the average fell
from 84.7 to 84.5.
In the table below we present a similar example of the relationship between total, average and marginal
values using an economic example, that of costs.-
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T o ta l, A v e r a g e , & M a r g in a l C o s t
A C = T C /Q
M C = ∆ T C /∆ Q
Q
0
1
2
3
4
5
TC
20
140
160
180
240
480
AC
140
80
60
60
96
M C
120
20
20
60
240
General Relationship Between Average and Marginal Measures
We can now generalize the relationship between averages and marginals by stating a mathematical and
always true relationship:
1. When MARGINAL > AVERAGE Î AVERAGE rises . If the average grade is 80 and the next
grade is higher than the average (say 90) then the average grade will rise.
2. When MARGINAL < AVERAGE Î AVERAGE falls. If the average grade is again 80 and the next
grade is now lower than the average (say 70) then the average grade will fall.
3. When MARGINAL = AVERAGE Î AVERAGE remains the same. If now the next grade is
exactly the same as the average (that is, it is 80) then the average grade will remain the same.
References for further reading:
Bade, R. and Parkin, (2007). Foundations of Economics 3rd edition (Pearson Education).
Begg, D., Fischer, S. and Dornbusch, R. (2005). Economics 8th edition (McGraw-Hill).
Mankiew N. Gregory (2007). Principles of Economics 4th edition (Thomson, South-Western).
McConnel C. and S. Brue (2005). Economics 16th edition (McGraw-Hill).
Miller, R.L (2006). Economics Today 13th edition (Pearson Addison Wesley).
Sloman John (2006). Economics 6th edition (Prentice Hall).
Dr. Savvas C Savvides--School of Business, EUROPEAN UNIVERSITY CYPRUS
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