Question

A recycling program costs and benefits are modeled as follows : MSC = 70+0.5Q and MPB=350-.9Q and the externality MEB= 56 - .2Q a. Determine the private market solution. b. Determine The Marginal social benefit: The sum of private and external benefit. c. Determine the Socially optimal Q where MSB=MSC d. Is the socially optimal solution more costly? By how much? is the higher cost necessary? Is it a good idea? Explain.

Answer 1

(a) In private market equilibrium, MPB= MSC

350 - 0.9Q = 70 + 0.5Q

1.4Q = 280

Q = 200

P = 70 + (0.5 x 200)= 70 + 100 = 170

(b) Marginal social benefit (MSB) = MPB + MEB = 350 - 0.9Q + 56 - 0.2Q

MSB = 406 - 1.1Q

(c) In social optimal, equating MSB with MSC,

406 - 1.1Q = 70 + 0.5Q

1.6Q = 336

Q = 210

P = 70 + (0.5 x 210) = 70 + 105 = 175

(d) Reduction in Deadweight loss due to socially optimal outcome = (1/2) x Difference in Q x Difference in P

= (1/2) x (210 - 200) x (175 - 170) = (1/2) x 10 x 5 = 25

This is the cost to achieve social optimum from private market equilibrium level. Instead of this, government can provide an equivalent Pigouvian subsidy to internalize the positive externality which will not increase cost.