David K.H. Begg, Gianluigi Vernasca-Economics-McGraw Hill Higher Education (2011)

CHAPTER 2 Tools of economic analysis
After some practice, most people can work with two-dimensional diagrams such as Figure 2.3. A few
gifted souls can even draw diagrams in three dimensions. Fortunately, computers can work in 10 or 20
dimensions at once, even though we cannot imagine what this looks like.
This solves the problem of trying to hold other things constant. The computer measures the tube fare on
one axis, the bus fare on another, petrol prices on a third, passenger incomes on a fourth and tube revenue
on a fifth, plots all these variables at the same time, and fits the average relation between tube revenue and
each influence when they are simultaneously considered. Conceptually, it is simply an extension of fitting
lines through scatter diagrams.
Econometrics uses
mathematical statistics to
measure relationships in
economic data.
Q
400
300
200
0
Figure 2.4
Reading diagrams
By disentangling separate influences from data where many different things move
simultaneously, econometricians conduct empirical research even though
economics is not an experimental science like physics. Although later chapters
report the results of econometric research, in the text we never use anything more
complicated than two-dimensional diagrams.
You need to be able to read a diagram and understand what it says. Figure 2.4 shows a hypothetical relationship
between two variables: P for price and Q for quantity. The diagram plots Q = f (P). This notation
means that the variable Q is related to the variable P through the function f If we know the function f,
knowing the value of P tells us the corresponding value of Q. We need to know values of P to make statements
about Q. In Figure 2.4, Q is a positive function of P. Higher values of Pimply higher values of Q.
When, as in Figure 2.4, the function is a straight line, only two pieces of information are needed to draw
in the entire relationship between Q and P. We need the intercept and the slope. The intercept is the height
of the line when the variable on the horizontal axis is zero. In Figure 2.4, the intercept is 100, the value of
Qwhen P=O.
Lots of different lines could pass through the point at which Q = 100 and P = 0. The other characteristic is
the slope of the line, measuring its steepness. The slope tells us how much Q (the variable on the vertical
axis) changes each time we increase P (the variable on the horizontal axis) by one unit. In Figure 2.4, the
slope is 100. By definition, a straight line has a constant
slope. Q rises by 100 whether we move from a price of
1 to 2, or from 2 to 3, or from 3 to 4. The equation of
Q f(P) the straight line plotted in Figure 2.4 is
=
Slope
I
+
I
I
Intercept.
100
t
2 3
A positive linear relationship
p
Q = 100 + lOOP
Therefore in this case we have: f(P) = 100 + 1 OOP.
Figure 2.4 shows a positive relation between Q and P.
Since higher P values are associated with higher Q
values, the line slopes up as we increase P and moves
to the right. The line has a positive slope. Figure 2.5
shows a case where Q depends negatively on P. Higher
P values now imply smaller Q values. The line has a
negative slope.
The equation of the straight line plotted in Figure 2.5 is
Q=300 - 100P
Economic relationships need not be straight lines or
linear relationships. Figure 2.6 shows a non-linear
relationship between two variables, Y and X. The slope
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