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c Roberto Barrera, Fall 2015
Math 142 4.5 Elasticity of Demand
Elasticity of Demand
Demand is the populations willingness to buy goods at a certain price.
Elasticity guages the sensitivity of the demand for a product to changes in the price of
the product.
Want to write the demand x as a function of the price p, that is, x = f (p).
Any reasonable demand curve should be decreasing.
x
p
Q: How much does an increase in price affect demand?
Makes sense to work with percentages instead of dollar amounts.
Example: If the price of sofas increased 30% then the number of sofas purchased decreased by 10%. The ratio of percentage decrease in demand to the percentage increase
in price is:
Example: If the price of milk increased 10% then the number of sofas purchased decreased by 1%. The ratio of percentage decrease in demand to the percentage increase
in price is:
Conclusion:
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c Roberto Barrera, Fall 2015
Math 142 Let x = f (p) be a demand equation.
x
p
Elasticity of demand: If the demand equation is x = f (p), then the elasticity of demand
is
• If E > 1 then demand is elastic.
• If E = 1 then demand has unit elasticity.
• If E < 1 then demand is inelastic.
c Roberto Barrera, Fall 2015
Math 142 3
Example: A restaurant owner sells 100 dinner specials for $10 each. After raising
the price to $11, she noticed that only 80 specials were sold. What is the elasticity of
demand?
Example: A small grocery store makers their own candy bars. Their demand equation
is given by p(x) = 2 − x where p is the price of a candy bar and x is the number of
hundreds of candy bars they sell in a week. Find the elasticity of demand when
(a) p = .75, (b) p = 1.5, (c) p = 1.00.
(a)
(b)
(c)
Theorem: If E < 1, increasing price increases revenue. If E > 1, increasing price
decreases revenue. Revenue is optimized when E = 1.
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c Roberto Barrera, Fall 2015
Math 142 Example: The demand equation for sofas is
x(p) = 82 − p2 .
(a) Find a formula for the price elasticity of demand for the sofas.
(b) What is the elasticity of demand if the price is set at $30? Interpret the result.
(c) How much should the sofas be sold for to maximize daily revenue? What will be
maximum revenue be?