Suppose a market is described by the following demand and supply equations: QD=180−3PQS=2PQD=180−3PQS=2P A

We are given:

• QD=180−3PQD=180−3P

• QS=2PQS=2P

Question (A)

To obtain the equilibrium price and equilibrium quantity, equate the demand and supply equations as given below:

QD=QS180−3P=2P5P=180P∗=$36Q∗=2P=2(36)Q∗=72unitsQD=QS180−3P=2P5P=180P∗=$36Q∗=2P=2(36)Q∗=72units

The equilibrium price is $36, and the equilibrium quantity is 72 units.

Question (B)

The social cost function can be obtained by including the negative externality of $15 per unit in the supply equation. This is calculated as:

QS=2PP=0.5QSP=0.5QS+15QS=2PP=0.5QSP=0.5QS+15

To obtain the socially-optimal price and quantity, equate the new supply equation inclusive of negative externality with the demand equation:

0.5Q+15=180−Q31.5Q+45=180−Q2.5Q=135Q=54unitsP=0.5(54)+15P=$420.5Q+15=180−Q31.5Q+45=180−Q2.5Q=135Q=54unitsP=0.5(54)+15P=$42

The socially-optimal price is $42, and the socially-optimal quantity is 54 units.

Question (C)

The deadweight loss resulting from the negative production externality is:

DWL=0.5×(PS−PC)×(Q∗−Q)=0.5×(42−542)×(72−54)=135DWL=0.5×(PS−PC)×(Q∗−Q)=0.5×(42−542)×(72−54)=135

So, the deadweight loss generated due to the negative externality of $15 per unit is $135.