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

MATH104 December 2011

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Question 05 (c)
Use elasticity to estimate the percentage change in price from $2 required to result in a 5% increase in demand.

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
One way to estimate elasticity is to calculate the fraction of percentage change in demand over the percentage change in price.

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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. The elasticity approximates the percentage change in demand over the percentage increase in price. If $x$ denotes the percent change in price, at p=2$, for a 5% increase in demand then we need to find $x$ so that $\epsilon =5/x$. Thus, using the elasticity calculated in the previous question, ${\begin{array}{ccl}x&=&5/\epsilon \\&=&5/(-1/3)\\&=&5(-3)\\&=&-15\%\end{array}}$. This is a negative number, as we'd expect (to increase demand, the price must decrease). The price should be decreased by about 15% to yield a 5% increase in demand.

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