Question

The demand for cigarettes is given by P = 500 – 2Q. Cigarettes are manufactured at a constant marginal cost of 50 and sold in a competitive market.

a. What is the quantity of cigarettes sold in equilibrium?

b. If cigarettes generate a marginal external cost of MEC = 0.1Q, what is the socially optimal level of cigarettes?

c. Draw a diagram illustrating the private and social MC curves and the demand curve. Point out the private market quantity, the socially optimally quantity and the social welfare cost.

Answer 1

Answer 2

a. Competitive Market Equilibrium Quantity

• Demand: $P=500-2Q$

• Marginal Cost (MC): $50$

• Equilibrium condition (P = MC):

  $$500-2Q=50$$$$2Q=450⟹Q^{\ast }=225$$

  Answer: 225 units

b. Socially Optimal Quantity (with External Cost)

• Marginal External Cost (MEC): $0.1Q$

• Social Marginal Cost (SMC) = MC + MEC:

  $$SMC=50+0.1Q$$

• Social optimum condition (P = SMC):

  $$500-2Q=50+0.1Q$$$$450=2.1Q⟹Q_{\text{social}}=\frac{450}{2.1}\approx 214.29$$

  Answer: ~214.3 units

c. Diagram Summary

• Private Equilibrium (Q = 225): Where P = MC (50) meets demand.

• Social Optimum (Q ≈ 214.3): Where P = SMC (50 + 0.1Q) meets demand.

• Welfare Cost: Deadweight loss triangle between Q = 214.3 and Q = 225 under the SMC curve.