9781118041581

The study of managerial economics emphasizes that decisions are taken to max-

imize certain objectives. Although the precise objective may vary, the key point

is that the manager should be able to quantify his or her ultimate goals. For

instance, if the manager’s objective is to maximize profit, he or she must be

able to estimate and measure the profit consequences of alternative courses of

action (such as charging different prices). This appendix introduces and

reviews the use of calculus in optimization problems. These techniques will be

applied throughout the book. Let’s begin with an example.

MAXIMIZING PROFIT A manager who is in charge of a single product line is

trying to determine the quantity of output to produce and sell to maximize

the product’s profit. Based on marketing and production studies, she has esti-

mated the product’s profit function to be

[2A.1]

where is profit (thousands of dollars) and Q is quantity of output (thousands

of units). Here the level of output, Q, is identified as the manager’s decision

variable,the item the decision maker controls. The profit function shows the

relationship between the manager’s decision variable and her objective. (For

this reason, it often is referred to as the objective function.)

2Q.1Q^2 3.6

62

APPENDIX TO CHAPTER 2

Calculus

and Optimization

Techniques

c02OptimalDecisionsUsingMarginalAnalysis.qxd 8/17/11 5:17 PM Page 62