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I need help answering if this is demand elastic of inelastic.

A policy adviser suggests that in order to improve its balance of trade with china, Canada should lower the price of some heavy machinery equipment. Suppose the demand function is: $$ Q=\frac{5000}{(3P+1)^2} $$ Where $Q$ is quantity per year and $p$ is price (measured in hundreds of thousands of dollars).

Find an expression for the price elasticity of demand for this equipment. Suppose the current $p$ is equal to $3$; at this price is the demand elastic or inelastic?

I can't determine how to get the expression, any help would be great!

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  • $\begingroup$ What are the formulas, definitions, or equations of interest for this type of problem? $\endgroup$ – dustin Nov 17 '14 at 2:51
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By definition,

$$\begin{align}PED &= \frac{dQ}{dP}\cdot\frac{P}{Q}\\ &=\frac{P}{Q}\cdot\frac{d}{dP}\left(\frac{5000}{(3p+1)^2}\right)\\ &=\frac{P(3P+1)^2}{5000}\cdot\frac{-30000}{(3P+1)^3}\\ &=\frac{-6P}{3P+1}\end{align}$$

At $P = 3$, $PED = -1.8$. Since $|PED| = 1.8 > 1$, then by the definition of "elastic", the demand is price elastic at $P=3$ since a change in $P$ yields a more than proportionate change in $Q$.

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  • $\begingroup$ Thank you, just for clarification why do you take |PED|instead of the -1.8 answer? $\endgroup$ – Amber Nov 17 '14 at 3:09
  • $\begingroup$ @Amber The law of demand tells us that the demand curve slopes downward (the exception being Giffen/Veblen goods). It is therefore generally expected that the PED will be negative and the minus sign can be omitted without causing confusion in most cases. $\endgroup$ – Ubiquitous Nov 18 '14 at 16:01

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