Question

(a) Suppose you know one of the demand curves is for a life-saving cancer drug, and the other is an appetite suppressant drug intended for weight loss. Which demand curve (A or B) is more likely to be the one for the drug? Explain. (b) Demand curve A has equation Q = 200 – 2P, and demand curve B has equation Q = 100 – 0.25P. Which demand curve is more elastic at a price of $80? What about at a price of $40? Show your work. (If you want to calculate elasticities using the midpoint formula we used in class, you can consider $1 price changes. Alternatively, you can use the point elasticity formula discussed in the textbook.) (c) (challenging) At what price is the demand for good B unit elastic? (d) (challenging) Suppose John is the only person in the world who consumes good B. Fur- thermore, John always spends one-tenth of his income on good B, regardless of his income level. What is John's income elasticity of demand for good B?

Answer 1

Answer a. Demand elasticity for life saving drug will be inelastic, while demand elasticity for appetite suppressant drug will be relatively elastic.

Demand curve for life saving drug is demand curve B. As demand curve B is more steeper than demand curve A, demand for good B is more inelastic than demand for good A.

Answer b. When P=$80,

Qa=200-2*80=40

Qb=100-0.25*80= 80

Elasticity of Good A=( ∆Qa/∆P)( P/Q)= -2(80/40)= -4 (Elastic demand)

Elasticity of Good B= -0.25(80/80)= -0.25 (Inelastic demand)

Answer c. When demand for good B is unit elastic, it means it is equal to 1.

When P=0, Qb=100

When Qb=0, P= 400

So Damd is unit elastic when Q=50, P=200. This is the midpoint of the demand curve, where demand is unit elastic.

Elasticity= -0.25(200/50)= -1

So, demand is unit elastic when Price=$200

d. John's income elasticity of demand for good B is 1.

Income elasticity of demand= Percentage change in quantity demanded/Percentage change in income.

John spends on good B equal to income/10.

Since the portion of income spend on good B is always fixed it induces a proportionate change in demand for good B. It means the Percentage change in income and demand will also be equal. So income elasticity is equal to 1.

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