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Chapter 12: Problem 40

Show the market for cigarettes in equilibrium, assuming that there are no laws banning smoking in public. Label the equilibrium private market price and quantity as \(\mathrm{Pm}\) and \(\mathrm{Qm}\). Add whatever is needed to the model to show the impact of the negative externality from second-hand smoking. (Hint: In this case it is the consumers, not the sellers, who are creating the negative externality.) Label the social optimal output and price as Pe and Qe. On the graph, shade in the deadweight loss at the market output.

Short Answer

Expert verified
To depict the market for cigarettes in equilibrium, draw a graph with price (P) on the y-axis and quantity (Q) on the x-axis. Draw downward sloping demand curve (D) and upward sloping supply curve (S), with equilibrium price \(\mathrm{Pm}\) and quantity \(\mathrm{Qm}\). Include the negative externality of second-hand smoking by drawing a new demand curve (D') above D, representing the marginal social cost. The social optimal output \(\mathrm{Qe}\) and price \(\mathrm{Pe}\) occur at the intersection of D' and S. The deadweight loss is the area between \(\mathrm{Qm}\) and \(\mathrm{Qe}\), enclosed by D and D'.

Step by step solution

01

Draw the initial market diagram

Begin by drawing a graph with the price (P) on the y-axis and the quantity (Q) on the x-axis. Draw a downward sloping demand curve (D) and an upward sloping supply curve (S). The point where these two curves intersect is the market equilibrium, with quantity \(\mathrm{Qm}\) and price \(\mathrm{Pm}\).
02

Add the marginal social cost curve

Since the consumers create the negative externality due to second-hand smoking, the curve representing social cost will be the demand curve shifted upwards by the magnitude of the externality (E). Draw a new demand curve (D') above the original demand curve (D). The distance between D and D' represents the negative externality.
03

Identify the social optimal output and price

The social optimal output and price occur where the new demand curve (D') intersects the supply curve (S). Label the social optimal output as \(\mathrm{Qe}\) and the social optimal price as \(\mathrm{Pe}\). The new equilibrium \(\mathrm{Pe}\) and \(\mathrm{Qe}\) takes into account the negative externality from second-hand smoking and reflects the true cost to society.
04

Calculate the deadweight loss

The deadweight loss is represented by the area between the market equilibrium output (\(\mathrm{Qm}\)) and the social optimal output (\(\mathrm{Qe}\)) enclosed by the original demand curve (D) and the marginal social cost curve (D'). It represents the cost to society associated with the market not operating at the socially optimal level. Shade this area to illustrate the deadweight loss. By following these steps, you will have successfully shown the market for cigarettes in equilibrium, the impact of the negative externality due to second-hand smoking, the social optimal output and price, and the deadweight loss at the market output.

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Most popular questions from this chapter

As the extent of environmental protection expands, would you expect marginal costs of environmental protection to rise or fall? Why or why not?

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