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Reena Tandon, Lovely Professional University Unit 14: Business Applications of Maxima and Minima

Unit 14: Business Applications of Maxima and Minima Notes

CONTENTS
Objectives
Introduction

14.1 Maximisation of Revenue
14.2 Maximisation of Output
14.3 Minimisation of Cost

14.4 Economic Applications (Continued)
14.4.1 Maximisation of Profits
14.4.2 Profit Maximisation by a Firm under Perfect Competition
14.4.3 Profit Maximisation by a Monopoly Firm
14.5 Summary

14.6 Keywords
14.7 Self Assessment
14.8 Review Questions

14.9 Further Readings
Objectives

After studying this unit, you will be able to:
Discuss economic applications
Explain prectical problems related to business applications of maxima and mininma

Introduction

In last unit you studied about maxima and minima. The terms maxima and minima refer to
extreme values of a function, that is, the maximum and minimum values that the function
attains. Maximum means upper bound or largest possible quantity. The absolute maximum of
a function is the largest number contained in the range of the function. That is, if f(a) is greater
than or equal to f(x), for all x in the domain of the function, then f(a) is the absolute maximum.
In terms of its graph, the absolute maximum of a function is the value of the function that
corresponds to the highest point on the graph. Conversely, minimum means lower bound or
least possible quantity. The absolute minimum of a function is the smallest number in its range
and corresponds to the value of the function at the lowest point of its graph.

14.1 Maximisation of Revenue

We can write total revenue as TR = p.x, where p is price and x is quantity. Total revenue will be
2
d TR d TR
maximum at a level of output where = 0 (or MR = 0) and < 0. The first order
dx dx 2

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