microeconomics question

Question

A pharmaceutical company produces a drug that is effective in reducing blood clots in humans, as well as treating kidney disease in cats. The price elasticity of demand for the drug used by humans is -1.25, and used for animals is -2.6. If the marginal cost of producing each pill is $2, A. for how much would the drug company sell each pill for human consumption? B. for how much would the drug company sell each pill for animal consumption?

Answer 1

MR when given the elasticity coefficient can be written as MR=P(1+(1/elasticity coefficient))

(let Ph be Price for humans, and MRh be MR for humans))

Elasticity for humans = -1.25

MRh = Ph(1+(1/-1.25)) is then set equal to MC=2 (remember profit max decision-making sets MR=MC)

Ph(1+(-.8)) =2 (set MR=MC, and now solve for Ph)

Ph(.2) =2

Ph=2/.2 = $10, so the pharmaceutical company will charge Humans a P=$10.

Doing the same thing for animals:

(let Pa be Price for animals, and MRa be MR for animals)

Elasticity coefficient for animals: -2.6

MRa = Pa(1+(1/-2.6)) is then set = MC=2 (profit max decision-making)

Pa(1+(-.384)) = 2 (set MR=MC, and now solve for Pa)

Pa(.615) =2

Pa= 2/.615 = $3.25, so the pharmaceutical company will charge the P for animals =$3.25.

The group with the higher price elasticity (animals) will pay a lower price, which is what we find in the example above: Pa<Ph. Humans have a lower elasticity, and therefore pay a higher price for the drug.