Chapter Review

Solution

a.Substituting the given information into the demand function yields

b.The price elasticity of demand is given by the expression

This result indicates that a 1% reduction in the price of Sergeant Garcia’s

Revenge results in a 0.04% increase in quantity demanded.Since |ep|< 1,the demand for this product is price inelastic.It suggests,perhaps,that

Sergeant Garcia’s Revenge has no close substitutes. c.The income elasticity of demand is given as

This result suggests that a 1% increase in consumer income results in a 0.16% increase in the demand for this product.Since eI > 0,this good is characterized as a “normal”good.Moreover,since 0 <eI < 1, this product is also characterized as a “necessity.”This suggests that people just cannot get along without Sergeant Garcia’s Revenge hot sauce. d.The advertising elasticity of demand is given as

This result suggests that a 1% increase in Rubicon & Styx’s advertising budget would result in a 0.54% increase in sales.

Q P I A = - + +62 2 02 25 . = - () + ( ) + () = - + + = 62 24 02150 254 62 8 30 100 184 .

ep = Ê Ë ∂Q ∂P ˆ ¯Ê Ë P Q ˆ ¯ 2=- Ê Ë 4 184 ˆ ¯ = -8 184 =-004 .

eI = Ê Ë ∂Q ∂I ˆ ¯Ê Ë I Q ˆ ¯ = 02Ê Ë 150 184 ˆ ¯ = =

30 184

016. .

eA = Ê Ë Q∂ ∂A ˆ ¯Ê Ë A Q ˆ ¯ = Ê Ë25

4 184 ˆ ¯ = = 100 184 054 .

CHAPTER REVIEW

Elasticity is a general concept that relates the sensitivity of a dependent variable to changes in the value of some explanatory (independent) variable.Suppose,for example,that the value of variable y depends in some systematic way on the value of variable x.This relationship can be read “y is a function of x.”Elasticity measures the percentage change in the value of y given a percentage change in the value of x.There are several elasticity concepts associated with the demand curve including priceelasticityof demand, incomeelasticity, cross (or cross-price) elasticity, advertisingelasticity,and interestelasticity.

There are two measures of elasticity:the arc-price and the point-price elasticitiesofdemand.The elasticity measure calculated will depend on the purpose of the analysis and the type of information available.The pointprice elasticity of demand requires a rudimentary knowledge of differential calculus.

The price elasticity of demand measures the percentage increase (decrease) in the quantity demanded of a good or service given a percentage decrease (increase) in its price.By the law of demand,the price elasticity of demand is always negative.If the price elasticity of demand is between zero and negative unity (<1 in absolute terms),then demand is said to be priceinelastic.If the price elasticity of demand is equal to negative unity,then demand is said to be unitelastic.If the price elasticity of demand is less than negative unity (greater than unity in absolute terms), then demand is said to be priceelastic.

If the demand curve is linear,all price–quantity combinations above the midpoint of the curve are price elastic.All price–quantity combinations below the midpoint are price inelastic.At the midpoint of the demand curve,demand is unit elastic.

There is also an important relationship between the price elasticity of demand and total revenue.If demand is price elastic,a decrease (increase) in price will result in an increase (decrease) in total revenue.If demand is price inelastic,then a decrease (increase) in price will result in a decrease (increase) in total revenue.Finally,total revenue is maximized at the price–quantity combination at which demand is unit elastic.Since marginal revenue is zero when total revenue is maximized,it must also be true that the price elasticity of demand is equal to negative unity when marginal revenue is zero.This further implies that for linear demand curves,total revenue is maximized at the price–quantity combination that corresponds to the midpoint of a linear demand curve.

The income elasticity of demand measures the percentage change in the demand for a good or service given a percentage change in consumers’ income.The income elasticity of demand is used to classify goods and services as normalgoods and inferiorgoods.Normal goods are further classified as luxury (superior) goods and necessities.A good or service is a luxury if the income elasticity of demand is greater than unity.A good or service is a necessity if the income elasticity of demand is less than unity.Finally,a good or service is inferior if the income elasticity of demand is negative.

The cross-price elasticity of demand measures the percentage change in the demand for a good or service given a percentage change in the price of a relatedgoodorservice.Related goods and services may be either substitutes or complements.If two products are substitutes,the cross-elasticity of demand is positive.If two products are complements,the cross-elasticity of demand is negative.