# 8 : Hope maximum of a wwire

This problem gives you a preview of something you might see in a microeconomics class. Suppose there’s an appliance store that sells refrigerators. It

could set its price high and sell very few refrigerators, or it could set its price low and sell many more refrigerators. The following table shows some

possible choices this store could make:

Price

Quantity

Total Revenue (P x Q)

(Dollars per refrigerator)

(Refrigerators per year)

(Dollars per year)

400

0

300

200

60,000

200

400

80,000

100

600

60,000

800

The graph below plots the firm’s total revenue curve: that is, the relationship between quantity and total revenue given by the two right columns in

the table above. The five choices are also labeled. Finally, two black lines are shown; these lines are tangent to the green curve at points B and D.

100-

( ( 400, 30 )

Total Revenue

( thousands of $) per year )

80-

B ( 200, 60 )

(500, 80)

(300 80 )

D ( 600, 60)

gt; Tangent lin

oh boy

(700, 40)

30

20-

B (0 , 800 )

100 200 300 400 500 600 700300

Ouantity ( refrigerators per year )

Using the information on the slope of the lines tangent to the curve at points B and D, plot the slope of the total revenue curve on the graph below.

(As it turns out, it’s a straight line, so the two points you plot will determine a line.)

?

O-

REVENUE (Dollars per refrigerator)

Slope of TR

8 8 .

-250

100

200 300 400 500 600

QUANTITY (Refrigerators per year)

700

The total revenue curve reaches its maximum at a quantity of

refrigerators per year. At this point, the slope of the total revenue curve isTrigonometry