Science:Math Exam Resources/Courses/MATH104/December 2011/Question 05 (a)

MATH104 December 2011

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Question 05 (a)
In the following figure, the curved graph is a demand curve where q is the demand and p is the price in dollars. The straight line is the tangent line to this demand curve at the point (p,q) = (2,6). Recall that the price elasticity of demand is given by $\epsilon (p)={\frac {p}{q}}{\frac {dq}{dp}}$ (a) Comput $\epsilon (2)$, the elasticity at price $2.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Remember that the derivative $dq/dp$ at $p=2$ is the same as the slope of the tangent line at $p=2$.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. We can calculate the slope of the line by using two points on the line, say $(0,8)$ and $(8,0)$. These two points give us a slope of $-1$. Because the line is tangent to the graph at $(p=2,q=6)$ and its slope is $-1$, we know that ${\frac {dq}{dp}}=-1$ at $(2,6)$. Thus, by using the elasticity formula above, we get $\epsilon ={\frac {p}{q}}{\frac {dp}{dq}}={\frac {2}{6}}(-1)=-1/3$.

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