microeconomics

Ok, if anyone is able to help me within the next 12 hours or so, that would be wonderful! I think I am going about this problem correctly -- I am not looking for someone to solve this problem for me, but for someone to tell me if I am doing it right...

You can see this chapter, and the question, by going to google and typing in "consider a linear demand curve, Q" (with the quotations), then choosing the last result (the PDF).

That is a .pdf version of the chapter. I am working on question 2.9, part C (this is the second to last page of the .pdf)

The question says "Consider a linear demand curve, Q = 350 - 7P. What is the price elasticity of demand at P = 50?

Using an equation in that chapter, (-b)(P/Q), I end up with the equation:

-7 ( 50 / (350 - 7(50)) )

But the problem is that 350 - 7(50) is 0! That means that the division can't be done, because the denominator is 0! So does this mean that the price elasticity of demand at P = 50 does not exist? How is this possible?

Thanks in advance! Dave


It's been some time since I had micro-econ, so I'm quite reluctant to speak like an expert on the subject. The math involved doesn't look exceptionally difficult, but I don't recall what the terms and symbols stand for.
I can comment on your observation/question, "...the denominator is 0! So does this mean that the price elasticity of demand at P = 50 does not exist? How is this possible? " though.
If you're calculations are correct, then the change in x is 0. This means you have a vertical asymptote at that point. I'm unsure how that should be interpreted though. You might want to study how the curve behaves in a very small neighborhood of the point P=50 to see how the curve is behaving there.
Does that help?


The short answer: the POINT elasticity at P=50 is infinite.

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