Question

Pigouvian tax Homework • Unanswered The plastics industry's market demand is x=120-p and market supply is x=p. The amount of externality imposed by producing x units of plastics is 0.5x2. What is the Pigouvian tax? Enter a number (round to two decimal places). Numeric Answer:

Answer 1

Pigouvian tax should be equal to the marginal external cost, so that cost of production at private market equilibrium increases and market moves towards socially optimal equilibrium, thus internalizing the externality.  

Given that, Market demand : x = 120 - p

or, p = 120 - x

Therefore, Marginal private benefit (MPB) = Marginal Social Benefit (MSB) = 120 - x

Marginal private cost (MPC) = x

Marginal social cosst (MSC) = MPC + MEC = x + 0.5x2

MPB = MS B = 120 - X mpe = x mae=mpe + MEC = x+0.5x² At socially optimal equilibrium, MsB=mse = 120-X = x +0.58² => 0-5X?+ 2x - 120 = 0 => x² + 4x - 240 =0 using baythago res formula X= = 4 +/(4)? 4.!.6240). 2.1 - 4 + 16+ 960 - 2 = – 4 + 976 x can't be negative in value. Therefore, &= – 4 +/976 - 13.621 2 N . Amount of pigouvian tax = 0.5x²0.5 (13.621)² =192.76