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

2. 7 Diagrams, lines and equations
Q
300
Q
B',
,'A'
,,
'
'
200
100
Q =
f(P)
0
2 3
p
0
x
Figure 2.5
A negative linear relationship
Figure 2.6 A non-linear relationship
keeps changing. Each time we raise X by one unit we get a different rise (or fall) in Y. Consider the relationship
between the income tax rate X and income tax revenue Y. When the tax rate is zero, no revenue is raised.
When the tax rate is I 00 per cent, nobody bothers to work and revenue is again zero. Beginning from a
zero tax rate, rises in tax rates initially raise total tax revenue. Beyond some tax rate, further rises in tax
rates then reduce tax revenue, which becomes zero by the time the tax rate is 100 per cent. Diagrams
display the essence of real-life problems.
An equation that can give rise to the graph in Figure 2.6 is given by
Q= 100x-x 2
The equation above is non-linear since, on the right-hand side, there is a variable with an exponent different
from 1.
Landing the big iob
•
Two students, David and Samantha, have to decide how hard to work for the final exam.
They need a mark of 70 to get the job with Greenpeace that they want. Their tutor has promised
them that the exam will be just as hard (or easy) as previous exams. David and Samantha have all the marks
from their previous exams, and also know how hard they worked (minimum effort is I, maximum effort is 5,
and neither student worked all that hard in the exams leading up to their finals). From past experience, they
know there is a linear relationship between effort and exam results.
Effort level
Exam marks 1 2 3
David 20 40 60
Samantha 30 60 90
0
35