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.
we also have the same problem...
To explain further, when calculating price elasticity of demand, we typically use the arc elasticity formula:
E = (ΔQ/Q) / (ΔP/P)
where ΔQ is the change in quantity demanded, Q is the initial quantity demanded, ΔP is the change in price, and P is the initial price.
However, in this case, you are asked to find the price elasticity of demand at a specific price, P=50. This means we need to find the elasticity at a single point rather than calculating a change.
In this situation, the point elasticity of demand is calculated using the derivative of the demand curve:
E = -(dQ/dP) * (P/Q)
where dQ/dP is the derivative of the quantity demanded with respect to price.
Let's calculate the point elasticity at P=50:
Given the demand equation Q = 350 - 7P,
we first find the derivative dQ/dP:
dQ/dP = -7
Now, substitute the values into the point elasticity formula:
E = -(dQ/dP) * (P/Q)
= -( -7) * (50 / (350 - 7(50)))
= 7 * (50 / 0)
= ∞ (infinity)
This means that at a price of P=50, the price elasticity of demand is undefined or infinite. It indicates an extreme and discontinuous change in quantity demanded when there is a small change in price.
So, yes, in this case, the price elasticity of demand at P=50 does not exist or is considered infinite because the denominator becomes zero. This indicates a unique situation where the demand curve intersects the price axis in a way that the percentage change in quantity demanded becomes infinitely large for an infinitesimally small change in price.