This problem gives you a preview of something you might see in a microeconomics class. Suppose there’s an appliance store that sells dishwashers. It could set its price high and sell very few dishwashers, or it could set its price low and sell many more dishwashers. The following table shows some possible choices this store could make:

Question

Price

Quantity

Total Revenue (P x Q)
(Dollars per dishwasher)

(Dishwashers per year)

(Dollars per year)
A 400 0 0
B 300 100 30,000
C 200 200 40,000
D 100 300 30,000
E 0 400 0

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.

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.)

The total revenue curve reaches its maximum at a quantity of blank (100, 400, 200, 300) dishwashers per year. At this point, the slope of the total revenue curve is blank (at its maximum, at its minimum, postitive, equal to zero, negative).

Answer 1

To analyze the total revenue curve presented in the problem, we begin by examining the data for price, quantity, and total revenue:

• Price A: 400 | Quantity 0 | Total Revenue 0
• Price B: 300 | Quantity 100 | Total Revenue 30,000
• Price C: 200 | Quantity 200 | Total Revenue 40,000
• Price D: 100 | Quantity 300 | Total Revenue 30,000
• Price E: 0 | Quantity 400 | Total Revenue 0

The total revenue curve, which peaks at C (200 dishwashers, $40,000), illustrates the relationship between the quantity sold and total revenue generated. At point C, the total revenue is maximized.

Now, let's consider the slopes of the tangent lines at points B and D. In economics, the slope of the total revenue curve is defined as the change in total revenue divided by the change in quantity sold.

1. At Point B (Price 300, Quantity 100, Total Revenue 30,000):

   • Increase in quantity from 100 to 200 (moving towards C):
     • Total Revenue increases from 30,000 to 40,000 (from B to C).
     • Slope of the tangent line is positive since total revenue is increasing as quantity increases.

2. At Point D (Price 100, Quantity 300, Total Revenue 30,000):

   • Increase in quantity from 200 to 300 (moving towards E):
     • Total Revenue decreases from 40,000 to 30,000 (from C to D).
     • Slope of the tangent line is negative since total revenue decreases as quantity increases.

From this analysis, we can conclude:

• The total revenue curve reaches its maximum at a quantity of 200 dishwashers per year (this is point C).
• At that point, the slope of the total revenue curve is equal to zero (since it is the peak).

Summary:

• The total revenue curve reaches its maximum at a quantity of 200 dishwashers per year.
• At this point, the slope of the total revenue curve is equal to zero.