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Conventionally both demand and supply for goods and services are both more elastic in the long run than in the short run.

My Question

Is there ever an instance where demand and/or supply for a given good be more elastic in the short run than in the long run?

That being said if there is never such an instance, does there exist a general proof refuting such an instance?

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It is possible. We normally think demand and supply are more elastic in the long run because consumers/firms have more options in the long run. For example if gas becomes more expensive consumers can buy more more fuel efficient cars.

So what if consumers or firms are more constrained in the long run? This could be the case when goods are storable.

Suppose I need to drink coffee every day or I get a headache. At home I have a canister of coffee that I use every day. If coffee doubles in price I can hold off buying and hope the price comes down, so I am fairly elastic. In the longer term though I'll run out of coffee and I'll need to buy more regardless of the price.

Of course in the even longer term maybe I can stop my caffeine addiction so I become more elastic again.

This maybe isn't the best example, but the key thing to think about is how constrained the agent is at each point in time. When people are more constrained in their options they are less elastic.

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    $\begingroup$ Actually I think it is a great example! $\endgroup$ – ssn Feb 25 '18 at 6:05
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In practice, there are many variables to it. I know such theories have extended lists of ceteris paribus (with everything else held equal). Hold enough things equal and elasticity can always be higher in the long run. I'd like to add a few examples to the ones dsmithecon provided.

When people's buying power drops in the short term due to some crisis. One can switch from driving a car to a bicycle during tough times and then go back to driving the car when income goes back up.

New substitutes can become available in the short term. Same example, a bicycle would never be considered by some if they could afford a car. Historically this happened even to staples such as bread during famines when people would start eating stuff they never ate before. It was especially acute before central banks figured out to ease monetary policy during crises or there were no central banks at all. Or gold or strictly limited commodity or currency of another country was used as a currency, or still is in some places. Or there are constraining regulations in place. Or a command economy entirely.

I could probably extend this list even more, but the point is as far as I know there isn't an economic theory that exists without assumptions and can have a general proof or be completely refuted. If something is challenged, it is often added as an assumption and the theory may look sound again. It doesn't imply economic theories are wrong or even flawed. Economics, as all social sciences, deal with so many variables there is just no way to control them all and come up with something general, proven, and irrefutable.

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I think of a case of transport selection. Say there are two islands connected only with a congested bridge in the past, and now a newly built tunnel having the same function emerges. Both roads charge toll fees.

In the short term, people are not informed about the congestion level of the two roads, but they can observe the differences of the toll fees. In other words, the full cost of traveling between the two islands is composited mainly by the toll fee.

In the longer term, after trials and errors, people realize the full cost to be the money value of average time of travel plus the toll fee. So even if the “cheaper” but congested road reduce further the toll fee, some people care about time cost are unlikely to switch.

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