Question

Region A’s inverse demand equation for a medical treatment is P = 1200 -.5Q, while the inverse demand equation representing the true value of the medical treatment is P = 1000 -.5Q. Suppose the marginal cost of the treatment is constant at $200.

I. What is the efficient quantity?

II. Does Region A consume the efficient quantity? If not, what is the welfare loss for this region due to inefficiency? Show your calculations and illustrate graphically.

Answer 1

We have the following information

Marginal social benefit (MSB): P = 1200 – 0.5Q

Marginal private benefit (MPB): P = 1000 – 0.5Q

In the above P is price of medical treatment and Q is quantity of medical treatment

Marginal cost: MC = 200

Private Optimum

MPB = MC

1000 – 0.5Q = 200

0.5Q = 800

Private optimum quantity = 1600

P = 1000 – 0.5Q

P = 1000 – 800

Private optimum price = 200

Social Optimum

MSB = MC

1200 – 0.5Q = 200

0.5Q = 1000

Social optimum quantity = 2000

P = 1200 – 0.5Q

P = 1200 – 1000

Social optimum price = 200

For Q = 1600; P = 1200 – 0.5Q = 1200 – 800 = 400

Deadweight loss due to inefficiency = Area of the triangle ABC

Deadweight loss = ½ × Base × Height

Base = 400 – 200 = 200

Height = 2000 – 1600 = 400

Deadweight loss = ½ × 200 × 400

Deadweight loss = 40,000