# Help with Area under a curve surplus

• April 26th 2009, 12:43 AM
v3ndetta
Help with Area under a curve surplus
The demand function http://www.webassign.net/www24/symIm...d7ef59fa2f.gif
where p = price in dollars and x = sales level in hundreds, is pictured below.
http://www.webassign.net/userimages/33311?db=v4net

The area of the grey rectangle in the picture has area = sales level times price = revenue generated by sales.
The area of the shaded portion under the curve above the rectangle represents the consumers' surplus.

First find the price, then revenue from sales, then the consumers' surplus for a sales level of 900.

Note: The consumers' surplus formula involves p(x) and hence x values must be in hundreds. The output of the consumers' surplus integral is in hundreds of dollars though, so be careful with your units!

Find Price, Revenue from sales and consumer surplus!

Help this for me please. I have no idea how to start can anyone give me an idea
• April 26th 2009, 07:43 AM
skeeter
Quote:

Originally Posted by v3ndetta
The demand function http://www.webassign.net/www24/symIm...d7ef59fa2f.gif
where p = price in dollars and x = sales level in hundreds, is pictured below.
http://www.webassign.net/userimages/33311?db=v4net

The area of the grey rectangle in the picture has area = sales level times price = revenue generated by sales.
The area of the shaded portion under the curve above the rectangle represents the consumers' surplus.

for a sales level of 900 ...

First find the price ... evaluate p(900)

then revenue from sales ... 900[p(900)]

consumers' surplus ... $\textcolor{red}{\int_0^{900} p(x) \, dx}$ - 900[p(900)]

Note: The consumers' surplus formula involves p(x) and hence x values must be in hundreds. The output of the consumers' surplus integral is in hundreds of dollars though, so be careful with your units!

.