Question

Consider a market consisting of several small pulp & paper mills operating in the South-east. These firms discharge chlorine and other waste products into nearby rivers and streams. The rivers and streams are not privately owned, and the mills’ discharges are currently unregulated by the EPA or by the states’ environmental agencies. The demand for paper produced by the mills in this market is P = 800 - 0.5Q. The marginal cost of producing paper in this market is MC = 20 + 0.3Q, where P and MC are expressed in dollars, and Q is expressed in tons of pulp and paper.

a. Determine this market’s equilibrium price and quantity, total revenue, marginal cost, consumer and producer surplus.

b. University researchers estimate that chlorine emissions from the industry's production impose costs, unaccounted for the industry or the market in which it operates, equal to P = 0.05Q. Determine the market’s efficient equilibrium price and quantity when all costs are accounted for.

c. The researchers then suggest that a tax, equal to the unaccounted for costs, be imposed on the production of pulp & paper in this market. What is the dollar amount of the tax? How much in revenue would the government collect? Would the market be inefficient with the tax? Explain (briefly and concisely) your answer.

Answer 1

(a) Equilibrium is set up at crossing point of interest and supply (MC) bends.

800 - 0.5Q = 20 + 0.3Q

0.8Q = 780

Q = 975

P = 20 + (0.3 x 975) = 20 + 292.5 = 312.5

Complete income (TR) = P x Q = 312.5 x 975 = 304,607.5

MC = P = 312.5

From interest bend, when Q = 0, P = 800 [Reservation price]

Purchaser excess (CS) = Area between request bend and cost = (1/2) x (800 - 312.5) x 975 = (1/2) x 487.5 x 975

= 237,656.25

Maker overflow (PS) = Area between supply bend and cost = (1/2) x 312.5 x 975 = 152,343.75

(b) Social minor expense (SMC) = MC + MEC = 20 + 0.3Q + 0.05Q = 20 + 0.35Q

In social result, request rises to SMC.

800 - 0.5Q = 20 + 0.35Q

0.85Q = 760

Q = 894

P = 800 - (0.5 x 894) = 800 - 447 = 353

(c) When Q = 894, MC = 20 + (0.3 x 894) = 20 + 268.2 = 288.2 and SMC = 20 + (0.35 x 894) = 20 + 312.9 = 332.9

Unit charge = SMC - PC = 332.9 - 288.2 = 44.7

Assessment income = 44.7 x 894 = 39,961.8

The market will become effective due to the duty. At the point when the expense was not forced, the nearness of negative externality brought about an amount higher than and a value lower than the socially proficient amount and value, which brought about social wastefulness misfortune (deadweight misfortune). Inconvenience of the duty brings amount and raises value down to the socially proficient level, consequently eliminitating the deadweight misfortune. Thusly the externality charge isn't wasteful.

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