   Chapter 8, Problem 19RE

Chapter
Section
Textbook Problem

The demand function for a commodity is given by p = 2000 − 0.1 x − 0.01 x 2 Find the consumer surplus when the sales level is 100.

To determine

To calculate: The consumer surplus when the sales level of 100.

Explanation

Given information:

The demand function is p(x)=2,0000.1x0.01x2 .

The sales level is x=100 .

Calculation:

Show the demand function p(x) as follows:

p(x)=2,0000.1x0.01x2 (1)

Find the value of price (P):

Substitute 100 for x in Equation (1).

P=2,0000.1(100)0.01(100)2=1,890

The expression to find the consumer surplus is shown below.

Consumersurplus=0x(p(x)P)dx (2)

Here, the sales level is x.

Substitute 100 for x, (2,0000.1x0.01x2) for p(x) , and 1,890 for P in Equation (2).

Consumersurplus=0100(2,0000

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