Chapter 6.7, Problem 9E

To determine

To Estimate: The sales level and the consumer surplus using a graph for a given demand function and selling price.

Answer to Problem 9E

The sales level is approximately $3727$ and the consumer surplus is approximately $\$37850$ .

Explanation of Solution

Given Information: The demand function is modelled as $p(x)=\frac{800,000e^{\left(\frac{-x}{5000}\right)}}{x+2000}$ and the selling price is $\$16$ .

Concept Used:

• The sales level is at the intersection of the demand curve and the price line.
• The consumer surplus is the area enclosed by the demand curve and the price line.

Graph: In the graph below, the intersection of the price line and the demand curve is approximately at $X=3727$ and the area enclosed by the price line and the demand curve (blue area) is approximately 37830.

  

Therefore, the sales level is $3727$ and the consumer surplus is $\$37830$ .