Question #70551

Suppose that price of a pair of shoes rises from $160 to $180. As a result, there are now 5,800 pairs of shoes demanded versus 7,000 as before.
Calculate price elasticity of demand for these shoes. USE MIDPOINT FORMULA.

Expert's answer

by definition,

midpoint elasticity = [ (Q2 - Q1)/((Q1 + Q2)/2)] / [ (P2 - P1)/((P1 + P2)/2)]

where Q - quantity demanded and P - price of a pair of shoes.

Using the formula above and the given values we get:

midpoint elasticity = [(5800 - 7000)/((7000 + 5800)/2)] / [($180 - $160)/(($160 + $180)/2)] = -0.1875 / 0.1176 = -1.59

midpoint elasticity = [ (Q2 - Q1)/((Q1 + Q2)/2)] / [ (P2 - P1)/((P1 + P2)/2)]

where Q - quantity demanded and P - price of a pair of shoes.

Using the formula above and the given values we get:

midpoint elasticity = [(5800 - 7000)/((7000 + 5800)/2)] / [($180 - $160)/(($160 + $180)/2)] = -0.1875 / 0.1176 = -1.59

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