Question

the sss co has a patient on a particular medication. the medication sells for $1 per daily dose and marginal cost is estimated to be a constant at 20. assuming linear demand and marginal cost curves, use this information to estimate the deadweight loss from monopoly pricing if the firm currently sells 1000 doses per day. can this loss be justified?

Answer 1

We have

P = 100 cents

MC = 20 cents

Q(current) = 1000

Now we know that at profit maximizing level 1/ed = (P – MC)/P

1/ed = (100 – 20)/100

This gives ed = 1.25 or -1.25

Now demand is Q = A – BP

1000 = A – B*100

And ed = slope of demand * P/Q which gives -1.25 = -B * 100/1000

This results in B = 12.5 and A = 2250

Demand function is Q = 2250 – 12.5P

DWL = 0.5*(monopoly price – competitive price)*(competitive quantity – monopoly quantity)

Here monopoly price is 100 cents, competitive price is 20 cents, monopoly quantity is 1000 and competitive quantity is 2250 – 12.5*20 = 2000

DWL = 0.5*(100 – 20)*(2000 – 1000)

= 40000 cents

= $400.

As far as the justification is concerned, note that the firm has patent which means it has invested huge amount initially in research and development. Patents do generate deadweight loss due to the creation of monopoly but they are necessary for encouraging firms to take up investment and continue innovate new drugs. In this manner, this deadweight loss is justified.