Final answer:
The long-run industry supply curve in a regulated tobacco industry considering the different cost functions of firms is not perfectly elastic; it will only include the supply from profitable firms at each price level. Furthermore, when accounting for negative externalities like second-hand smoke, the socially optimal price and quantity (Pe and Qe) are typically higher and lower, respectively, compared to the private equilibrium (Pm and Qm), resulting in a deadweight loss.
Step-by-step explanation:
The student's question pertains to the construction of the long-run industry supply curve in a regulated tobacco industry with firms facing two distinct types of cost functions. To summarize a long-run industry supply curve, consider that in the long run, firms will participate in the market only if they can cover their costs of production. In this scenario, we have two types of firms with different cost structures: 30 firms with cost function c(q)= ½q²+2 and 40 firms with cost function c(q)=q². Market participation depends on the price level: only firms that can at least break even at a given price will produce.
To calculate the aggregate supply, we will need to add up the individual supplies from all firms that are profitable at each price level. If the industry were a constant cost industry, where the entry of firms does not affect the input costs, the long-run supply curve would be perfectly elastic. However, since there are fixed numbers of firms due to entry barriers, the industry does not exhibit constant returns to scale, and the long-run industry supply curve will not be perfectly elastic.
Beyond this theoretical explanation, to graphically show the market equilibrium and consider the externality caused by second-hand smoke, the student should draw a standard supply and demand diagram. The equilibrium without considering externalities is where the market supply and demand curves intersect (Pm and Qm). Externalities like second-hand smoke require us to adjust the demand curve to reflect true social costs, resulting in a new social demand curve. The new equilibrium (Pe and Qe), which accounts for externalities, typically shows a lower quantity and a higher price than the private equilibrium. The area between the market quantity and socially optimal quantity represents the deadweight loss due to the externality.