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Home Q & A Board Other Fields Homework Help Business Economics
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cloveb cloveb
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Valued Member
Posts: 782
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3 years ago
Suppose the demand for gadgets is given by the following equation where P is the price and Q is the quantity demanded:
P = 50 – Q

a) Suppose the price is originally $10 and increases to $20. Using the regular or standard percentage formula, find the price elasticity of demand for gadgets.

b) Suppose the price is originally $20 and decreases to $10. Using the regular percentage formula, find the price elasticity of demand for gadgets.

c) Now using the arc formula, calculate the price elasticity of demand using the prices from the previous 2 parts. What is the advantage of using the arc formula over the regular percentage formulas?
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wrote...
#1
Staff Member
3 years ago
a) Regular percentage elasticity of demand formula is
e = | (% change Q / % change P) | = | ((new Q – old Q) / old Q) / ((new P – old P) / old P) |
= | ((30 – 40) / 40) / (20 – 10) / 10) | = 1/4

b) Using the formula again we find
e = | ((40 – 30) / 30) / (10 – 20) / 20) | = (1/3) / (1/2) = 2/3

c) The arc formula is

𝑒 = |(𝑄1 − 𝑄2)/(𝑄1 + 𝑄2)/(𝑃1 − 𝑃2)/(𝑃1 + 𝑃2)|

Thus we find
e = (10/70) / (10/30) = 3/7
We can see that the arc elasticity is between the regular elasticities from (a) and (b), and the arc
elasticity measure does not depend on the ordering of the price change.
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