1 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: 2 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. 4 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?