Question

A new antibiotic has just gained approval from the Food and Drug Administrationso it is now legal to sell. Demand for the drug is: P = 1000 –Q and supply of the drug is: P = 50 + Q.

a.What is the producer surplus and consumer surplus gained from legalization? Assume zero total surplusexisted before legalization.

b.Policymakers realize there is a negative consumption externality from the drug: as people use the new antibiotic, bacteria become slightly more resistant to the old types of antibiotics. (Note: Just assume this is plausible and true!). In fact, for each unit of drug sold, there is $450 marginal cost to society. What is the magnitude (in $) of the negative externality from the free (unregulated) market solution? [Hint: Only calculate the size of the negative externality, not the deadweight loss.]

c.Propose a policy that would bring the market into efficiency. (Note that this is a short answer question. Be specific enough to show how the policy would bring the market into efficiency. You may use a graph if it would be helpful.)

d.How much would society as a whole be better off (in $) due to your policy from part c, relative to a free (unregulated) market?(This is a quantitative problem.)

Answer 1

Part - (a). After legal approval the demand for Drug is shown by P = 1000 - Q , and supply of Drug is P = 50 + Q.

Equilibrium price and quantity will be determined demand = Supply.

1000 - Q = 50 + Q

Or, 2Q = 950

Or, Q = 475.

Therefore, P = 1000 - 475 = $525.

Equilibrium price P = $525, Equilibrium Quantity Q = 475

Now consumer surplus at P = $525, Q = 475 is -

C.S = 1/2*(base)*(height)

C.S = 0.5*475*(1000 - 525)

C.S = 0.5*475*$475 = $112,812.5 . (Ans)

P.S at P = $525 and Q = 475 is -

P.S = 1/2*(base)*(height)

P.S = 0.5*475*(525 - 50)

P.S = 0.5*475*$475 = $112,812.5.  

Part - (b). If each unit of Drug sold in the market create negative externality of $450 /unit.

Now under unregulated market solution the magnitude of negative externality is $450*Quantity sold = $450*475 = $213,750. (Answer).

Part - (c). Market will be if supplier incorporate the negative externality into their supply. It means if we internalize the external cost of the drug sold per unit. We can do that by imposing per unit tax equal to external cost per unit. We will have new supply function which will show supply (S + tax ) and We can show it by below figure -

Part - (d).

Now under no regulations at free market equilibrium total surplus was C.S + P.S and there was external cost.

Total surplus to society under unregulated condition is

Total surplus = C.S ($112,812.5) + P.S ($112,812.5)

Total surplus = $225,625.

Total loss of society in terms of external cost is = $213,750 at unregulated market solution.

So, Net Gain to society = $225,625 - $213,750 = $11,875.

Now if the external cost is internalised then we will have the new supply function is

P = 50 + Q + tax

Or, P = 50 + Q + 450 , where per unit tax = $450

Or, P = 500 + Q -------- New supply function

Now, we can set the equilibrium Demand = Supply

Demand is P = 1000 - Q , and new supply is P = 500 + Q

1000 - Q = 500 + Q

Or, 2Q = 1000 - 500

Or, Q = 500/2 = 250.

P = 1000 - 250 = $750.

Therefore, new equilibrium price and quantity is P = $750. Q = 250 units.

Now under new equilibrium price = $750 and Q = 250, C.S and P.S are -

C.S = 1/2*(base)*(height)

C.S = 0.5*250*(1000 - 750)

C.S = 0.5*250*250 = $31,250.

P.S at P = $750 and Q = 250 is -

P.S = 1/2*(base)*(height)

P.S = 0.5*250*(750 - 500)

P.S = 0.5*250*$250

P.S = $31,250

Total surplus to society = C.S + P.S

Total Surplus = $31,250 + $31,250 = $62,500.

Tax revenue = Quantity sold multiplied by tax

Tax Revenue = 250*$450 = $112,500

DWL to society due to tax = 1/2*(base)*(height)

DWL to society due to tax = 0.5*(500)*(475 - 250)

DWL to society due to tax = 0.5*500*225 = $56,250.

Total Gain to society = $62,500 + $112,500 - $56,250

Net total gain to society with tax = $118,750.

If we take only C.S + P.S net gain to society is $62,500.