Question

Suppose that demand for a product is P = MPB= 300-1/4(QD) and supply is P = MPC=
100+1/2(QS)

Furthermore, suppose that the marginal external damage of this product is $10 per unit.
Calculate the deadweight loss associated with this externality

Illustrate graphically the market failure and identify two policies government can use to
correct the externalities

Please remember to attach the graph

Answer 1

Here we will first show quantity demanded equal to quantity supplied.

300-1/4 = 100+1/2

200 = 0.75

Therefore Q = 266.66

The optimal quantity is the quantity for which the marginal social benefit equals the marginal social cost. We will include the external damages in the calculation of marginal social cost. The marginal private cost function is the inverse of the supply function so,

MPC = (1/2)Q +100

The marginal external cost is MEC = 10

The marginal social cost is :

MSC = MPC + MEC

= (1/2)Q + 100+10

= (1/2)Q + 110

Since we have included the externality in the calculation of marginal social cost, marginal social benefit is just equal to marginal private benefit. The marginal private benefit is the inverse of the demand,

MPB = 300 - (1/4)Q

Therefore here, MSB = 300 - (1/4)Q

To find optimal quantity, we set MSB(Q) = MSC(Q)

300 - (1/4)Q = (1/2)Q +110

where Q° = 256

Since Q = 266.67 and Q° = 256, the market provides about 10.67 units more than the social optimum.

The deadweight loss is DWL = (1/2) (266.67-256) (10) = 53.35

c

The government can respond to externalities through command-and-control and market-based policies:

The government use command-and-control policies to regulate behavior directly. Command-and-control regulation can come in the form of government-imposed standards, targets, process requirements, or outright bans. For example, the government may make it illegal for a company to dump certain chemicals in a river.

The government can implement market-based policies such as taxes and subsidies to incentivize private decision makers to change their own behavior.