Calculus Marginal Revenue to Total Revenue
[Pages:1]Calculus
Marginal Revenue to Total Revenue
Aim To demonstrate an application of integration. Learning Outcomes At the end of this section you will be able to:
? Identify a practical application of integration, ? Calculate the total revenue(TR) function from the marginal revenue(MR) func-
tion.
Marginal revenue is an important concept in basic microeconomics. Marginal rev-
enue(MR) is the extra revenue that an additional unit of product will bring a firm. It
can also be described as the change in total revenue/change in number of units sold.
Therefore,
MR
=
d dQ
(T
R).
From
this
we
can
conclude
that
M R dQ = T R The very same relationship exists between the marginal cost(MC) and the total cost(TC) functions for the product, M C dQ = T C.
Example If a marginal revenue function is given as M R = 10Q2 + 6Q - 3, find an expression
for the total revenue function(TR).
We know therefore
M R dQ = T R
(10Q2
+ 6Q
-
3)dQ
=
10
Q3 3
+
6
Q2 2
- 3Q
=
10 3
Q3
+ 3Q2
-
3Q
+
C
Related Reading
Jacques, I. 1999. Mathematics for Economics and Business. 3rd Edition. Prentice Hall.
1
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