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If the price of a haircut is $12, the number of haircuts provided is 100
If the price of a haircut is $12, the number of haircuts provided is 100. If the price rises to $18 per haircut, barbers will work much longer hours, and the supply of haircuts will increase to 300. What is the price elasticity of supply?
Expert Solution
The price elasticity of supply (PED) is mathematically defined as the percentage change in quantity supplied per percentage change in price. We will calculate the numerator and denominator separately and then combine them.
The percent change in quantity supplied is the (Q2 - Q1) / Q1 where the numbers are the time period. In this instance Q1 =100 and Q2 = 300, implying that the percent change in quantity supplied is (300 - 100) / 100 = 2.
The percent change in price is calculated with a similar formula: (P2 - P1)/P1, where P1 is the first period price and P2 is the second period price. Therefore, the percent change in price is (18 - 12) / 12 = 1/2.
We can now construct the PED as the ratio of the two calculated percent changes. PED = %change in quantity supplied / %change in price = 2 / 0.5 = 4. Since this is greater than 1, the good is price elastic.
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