9781118041581

An equation is the most economical way to express the profit function, but

it is not the only means. Figure 2A.1 presents a table listing the profit conse-

quences of different output choices and graphs the profit function. (The graph

plots profits across a continuum of possible output levels. Remember that out-

put is measured in thousands of units. Thus, Q 6.123 and Q 6.124 are

both legitimate output candidates.) According to convention, the graph plots

the decision variable (also commonly referred to as the independentvariable) on

the horizontal axis and the objective (or dependentvariable) on the vertical axis.

From either the table or the graph, we see that at very low output levels

profit is negative. As the level of output increases, profit rises, becomes positive,

and peaks. For still higher outputs, profit declines and eventually turns nega-

tive. The goal of management is to set production to generate positive prof-

its—in particular, to attain maximum profit.

Marginal Analysis

The marginal value of any variable is the change in that variable per unit

change in a given decision variable. In our example, marginal profit is the

change in profit from an increase in output. A direct way to express marginal

FIGURE 2A.1

The Firm’s Profit

Function

Marginal profit at a

particular output is

determined by the

slope of the line drawn

tangent to the profit

graph.

0

2

4

6

8

–2

–4

2468101214161820515

Profit (Thousands of Dollars)

Quantity

(000s)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

Profit

($000s)

• 3.6
  0
  2.8
  4.8
  6.0
  6.4
  6.0
  4.8
  2.8
  0
  Quantity (Thousands of Units) – 3.6

Appendix to Chapter 2 Calculus and Optimization Techniques 63

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