Question

Consider the case of a positive consumption externality. Suppose demand and supply are given by: Demand: Xd=(A-P)/α Supply: Xs=(B+P)/β where P is the price of the good, Xd is the quantity of good demanded, Xs is the quantity of good supplied, and A, B, α, and β are parameters. Answer the following questions. Note that graphs will be helpful in your analysis. However, make sure to provide mathematical derivations of the solutions. Derive the competitive equilibrium price and output level. Suppose that the marginal positive external benefit is k per unit of output. Derive the function for the social marginal benefit (SMB) curve. What is the socially optimal output level? Is it higher or lower than the competitive equilibrium output? What is the Pigouvian subsidy for question (b)? Derive its impact on prices paid by consumers and prices received by producers, and illustrate that it achieves the socially optimal outcome. Next, suppose that the total external social benefit is given by 〖(δX)〗^2. Derive both competitive market outcome and the socially optimal outcome. Derive the Pigouvian subsidy under scenario (d), and illustrate that it achieves the social optimum.

Answer 1

Since consumers are the only group deriving benefit, then the demand curve is the marginal social benefit curve.

SMB function- Xd= +k

sosocially optimal quantity is higher than competitive quantity

pigouvian subsidy is a subsidy that is used to encourage behaviour that have positive effects on others who are not involved or society at large. Behaviors or actions that are a benefit to others who are not involved in the transaction are called positive externalities.