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The biggest factor is substitutability. That may or not be a word, but it means that a good either does or does not have a lot of substitutes. If it has a lot of substitutes (food is this way), then it will be very price elastic. For instance, if corn prices rise, people will just buy carrots. Thus, corn is elastic.

Necessity is another one, although it only applies to certain products. Take insulin for example. Diabetics NEED insulin or else they die. So they will pay whatever the market price of insulin. Thus, insulin is nearly perfectly inelastic. Other examples of this are water and illicit drugs.

Duration is the other big factor. It is how long the price stays high on a good. The longer the duration of the price increase, the higher the elasticity. For instance, if you drive through a McDonald's and find that their Big Mac has risen in price, you will buy it that time, but next time you might go to Burger King or Wendy's.

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Q: What three factors determine the price elasticity of demand?
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