# improper integrals question (consumer surplus)

• Aug 3rd 2009, 10:54 PM
lionell84
improper integrals question (consumer surplus)
http://www.fileden.com/files/2008/6/...6/Untitled.jpg

This is from my economics class lecture. Can someone explain how the last part (in yellow box) is done? How was the answer obtained?

Since one of the limits of the integration is infinite, this is an improper integral. So, i thought that since [P^(e+1)]/(e+1) approaches infinity when P approaches infinity, the integral diverges and is meaningless.
• Aug 4th 2009, 12:32 AM
BobP
If \$\displaystyle e < -1 \$, (I'm assuming that \$\displaystyle e \$ is not 2.718... ), the result would be correct, but otherwise I'm with you.
Also, if \$\displaystyle P_0 \$ is positive, \$\displaystyle e < -1 \$ would be needed to make \$\displaystyle CS \$ positive. Should it be ?
• Aug 4th 2009, 07:30 PM
lionell84
Quote:

Originally Posted by BobP
If \$\displaystyle e < -1 \$, (I'm assuming that \$\displaystyle e \$ is not 2.718... ), the result would be correct, but otherwise I'm with you.
Also, if \$\displaystyle P_0 \$ is positive, \$\displaystyle e < -1 \$ would be needed to make \$\displaystyle CS \$ positive. Should it be ?

Thanks! I finally got it. Sorry for omitting important information. I got the screen shot straight from my lecture slides.

The above is an example in a monopoly market. Thus, e<-1 because a monopoly will choose to operate only in regions in which the market demand curve is elastic.

http://www.fileden.com/files/2008/6/...6/solution.jpg