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This is an economics question, but if I can get the correct answer to this formula I can answer the question. Any help is appreciated, thanks!

If the demand $Q_x^d$ for a product given the price $P_x$ is

$$\ln Q_x^d = 10 – 5 \ln P_x$$

then product $x$ is:

  1. Elastic
  2. Inelastic.
  3. Unitary elastic.
  4. Cannot be determined without more information.
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closed as off-topic by Jonas Meyer, Micah, hardmath, Daniel Rust, voldemort Dec 13 at 18:06

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Since economics uses the term "elastic demand" in a technical sense, you should provide the definition here. Asking at Math.SE about how economists define the term is more than likely off-topic, which is why you need to assume responsibility for it. –  hardmath Dec 13 at 18:02

1 Answer 1

The price elasticity $E$ of a product which has price $P$ given a demand $Q$ is defined as the percentage change in demand for each percentage change in price, i.e.

$$E = \frac{d \ln Q}{d \ln P}\qquad (1)$$

or alternatively

$$E = \frac{P}{Q} \frac{dQ}{dP}\qquad (2)$$

Since in your case you have

$$\ln Q = 10 - 5\ln P$$

You should be able to differentiate $\ln Q$ with respect to $\ln P$ (equation (1)) to get the result you require.

Alternatively, you could express $Q$ in terms of $P$ by exponentiating both sides of the formula, giving

$$Q = e^{10 - 5\ln P} = \frac{e^{10}}{P^5}$$

and apply equation (2) to find $E$, which may be easier if you're not that experienced with differentiation.

Once you have calculated $E$, you can decide whether the good in question is elastic or inelastic by noting that elastic goods have $|E|>1$ and inelastic goods have $|E|<1$.

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... and presumably unitary elastic goods have $|E|=1$. –  Henry Sep 27 '11 at 23:43
(+1)... even though this is quite generous (considering how terrible the OP was, and that the other Chris has done zero to contribute to the solution of his own problem in the past two hours!) –  The Chaz 2.0 Sep 28 '11 at 0:05
I feel like it's better to show first-timers the benefit of the doubt (fix their questions, give them good answers etc) since they don't know the ropes yet, and there are many reasons that someone might not look at a question they've posted for hours or even days after the original posting. –  Chris Taylor Sep 28 '11 at 7:02

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