9781118041581

readers will recognize Equation 2.3 as a quadratic function. Therefore, the

graph in Figure 2.3 is a simple parabola.)

36 Chapter 2 Optimal Decisions Using Marginal Analysis

CHECK

STATION 1

Let the inverse demand function be P  340 .8Q. Find the revenue function.

COST To produce chips, the firm requires a plant, equipment, and labor.

The firm estimates that it costs $380 (in materials, labor. and so on) for each

chip it produces; this is $38,000 per lot. In addition, it incurs fixed costs of

$100,000 per week to run the plant whether or not chips are produced. These

are the only costs. (Remember that we are constructing a highly simplified

example.) The total cost of producing a given quantity of output is given by the

equation

[2.4]

where C is the weekly cost of production (in thousands of dollars) and Q is the

number of lots produced each week. This equation is called the cost function,

because it shows how total cost depends on quantity. By substituting in a given

quantity, we can find the resulting total cost. Thus, the cost of producing Q  2

lots is $176 thousand. Other quantities and costs are listed in Figure 2.4, which

C 100 38Q,

FIGURE 2.4

The Cost of Microchips

The table and graph

show the firm’s total

cost of producing

different quantities of

microchips.

Quantity Cost

(Lots) ($000s)

0.0 100

1.0 138

2.0 176

3.0 214

4.0 252

5.0 290

6.0 328

7.0 366

450

400

350

300

250

200

150

100

50

0246810

Total cost

Quantity (Lots)

Total Cost (Thousands of Dollars)

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