Consider the case of a positive consumption externality.
A. Suppose throughout this exercise that demand and supply curves are linear, that demand curves are equal to marginal willingness to pay curves and that the additional social benefit from each consumption unit is k and is constant as consumption increases.
(a) Draw two graphs with the same demand curve but one that has a fairly inelastic and one that has a fairly elastic supply curve. In which case is the market output closer to the optimal output?
(b) Does the Pigouvian subsidy that would achieve the optimal output level differ across your two graphs in part (a)?
(c) Draw two graphs with the same supply curve but one that has a fairly inelastic demand curve and one that has a fairly elastic demand curve. In which case is the market output closer to the optimal output?
(d) Does the Pigouvian subsidy that would achieve the optimal output level differ across your two graphs in part (c)?
(e) True or False: While the size of the Pigouvian subsidy does not vary as the slopes of demand and supply curves change, the level of under-production increases as these curves become more elastic.
(f) In each of your graphs, indicate who benefits more from the Pigouvian subsidy — producers or consumers.
B. Suppose demand is given by xd = (A−p)/α and supply is given by xs = (B +p)/β.
(a) Derive the competitive equilibrium price and output level.
(b) Suppose that the marginal positive externality benefit is k per unit of output. What is the function for the social marginal benefit SMB curve?
(c) What is the optimal output level?
(d)What is the Pigouvian subsidy? Show the impact it has on prices paid by consumers and prices received by producers—and illustrates that it achieves the optimal outcome.
(e) Next, suppose that the total externality social benefit is given by SB = (δx)2. Does the market outcome change? What about the optimal outcome?
(f) Derive the Pigouvian subsidy now—and illustrate again that it achieves the social optimum.