The price of a product rises $1.89 to $2.17 per gallon and in response the quantity demanded decreases from 20,000 to 18,000 gallons.  What is the price elasticity of demand for this product?

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To find the elasticity coefficient for this product, we use the midpoints formula.  This is expressed as

Elasticity coefficient = [(Q2 – Q1)/(Q1 + Q2) divided by [(P2 – P1)/(P1 + P2)].

It does not matter which price and quantity we call P1 and Q1, but we have to be careful not to mix up the prices and quantities.

To get the first part of this we calculate (18,000 – 20,000)/(20,000+18000).  That gets us -2,000/38,000 or -.05.  The sign does not matter here, so we essentially have 5% for this part of the equation.

To get the second part, we calculate (2.17-1.89)/(1.89+2.17).  That gets us .28/4.06 or .07.  So we have 7% for this part of the equation.

We now divide 5% by 7% and get .71.

Our elasticity coefficient for this product is .71.  Any product with an elasticity coefficient of less than 1 is said to have demand that is price inelastic.  

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