Question

PLEASE HELP! Suppose that a particular commodity has demand function p=D(q) given by
D(q)=25e−0.07q
Find the consumers' surplus when demand is q0=2.

Answer 1

When q0=2, we have p0=D(2)=25e-0.07(2)=25e-0.14
The consumer surplus is given by \[\int\limits\limits\limits_{0}^{q _{0}}D(q)dq-q _{0} p _{0}\] \[\int\limits_{0}^{2}(25e-0.07q)dq-(2)(25e-0.14)\]

Answer 2

So should I plug in 2 & 0 into q because I got a negative number?

Answer 3

I got positive 0.14

Answer 4

It says that's incorrect. any idea why?

Answer 5

Before, I just put the equation that I saw into the formula. Now that I look more closely at it I realize that it is a very strange function that you posted. Is it possible that the -.007q is up in the exponent and the original function looks like...\[D(q)=25e ^{-0.07q}\]That would be a far more typical demand curve. I will assume that it is. In that case...\[D(2)=25e ^{-0.07(2)}=25e ^{-0.14}\]\[C.S.=\int\limits_{0}^{2}25e ^{-0.07q}dq-(2)(25e ^{-0.14})\]\[\frac{25}{-0.07}[e ^{-0.07q}]_{0}^{2}-50e ^{-0.14}\]\[\frac{25}{-0.07}(e ^{-0.14}-1)-50e ^{-0.14}\approx3.1899\]Be sure to round appropriately for you program, if my assumption about your original function was correct.

Answer 6

Thank you so much!!!