Question

Consider a market for electricity with aggregate inverse demand curve: p = 10 where p is the price of electricity in dollars per unit. The market demand curve is thus horizontal at a price of 10 Let e denote consumption of electricity. A single firm has variable production costs of: c(e) = 2 Fixed costs are zero. Assume that each unit of production generates a units of damages de): d(e) = ae Assume that a = 2 (1) Assume there's a social planner who maximizes social welfare. What are the equilibrium price and consumption? Calculate social welfare. (2) Instead of a social planner, suppose the market is perfectly competitive. What are the equilibrium price and quantity? Calculate social welfare. (3) Draw the marginal private cost curve and the marginal social cost curve on a graph, along with the aggregate demand curve. Show the two equilibria on the graph, from parts (1) and (2). (4) Suppose the social planner imposes an emission tax (t) on the production. What's the efficient tax that maximizes social welfare?

Answer 1

де P=10 cce) = 2 d(e) = xe, x=2 i for social planner, P = SMC SM C= PMC+ MED (Marginal extemal damage) PMC= aC =20, MED = ad = x=2 80. SMC= 2e + 2 at Eqm, P=2e+2 = 10=2eta e*=4 ,P* = 10. 2. In perfect compt, P= PMC. 10 = aC, el=5, P=10 3.) Graph. 4.) émission tax t =MED = $2 efficient tax, value of MED at socially efficient eam.

Graph

-15 (4, 10) (5, 10) Agg demand curve SMC PMC

•1) social welfare = Total Revenue- total cost = (1084) - (4) 2 - 4x2 = 40-16 - 8 = $. 16 2) Bivate Eqm, sowal welferne = 15810) - (5)² - 5x2 = 50-25-10 = $15 Ang