Science:Math Exam Resources/Courses/MATH104/December 2012/Question 04 (b)

MATH104 December 2012

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Question 04 (b)
The demand equation for a certain product is $\displaystyle {}q^{2}+p^{3/2}+2p=20$ where q is the number of units per hour the manufacturer can sell at a price of p dollars per unit. If the price is raised slightly from $4 dollars, will the revenue increase or decrease (use the elasticity of demand to do this)?

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
Recall that the formula for the price-elasticity of demand is $\displaystyle \epsilon (p)={\frac {p\cdot q'(p)}{q(p)}}$. Remember to compare this value to -1 to determine if revenue will increase or decrease.

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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. Using the hint and the first part, we have that $\displaystyle \epsilon (p)={\frac {4\cdot q'(4)}{q(4)}}={\frac {4(-5/4)}{2}}={\frac {-5}{2}}<-1$ As the value is less than -1, we see that the revenue will decrease.

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