Question

The market for a particular chemical, called Negext, is described by the following equations:

Demand: Qd=100-5P

Supply:Qs=5P

For each unit of negext produced, 4 units of pollution are emitted, and each unit of pollution imposes a cost on society of $1. Suppose that the government restrict emission to 100 units of pollution. Graph the Negext market under this contraint. find the new equilibrium price and quantity and show them on your graph.compute how this policy affects consumer surplus, producer surplus and the cost of pollution.

Answer 1

SOLUTION:

a) The Equilibrium price and quantity - Consumer surplus - Producer surplus and total surplus in the market equilibrium.

       To find the equilibrium price and equilibrium quantity, we should equal to demand and supply. i.e., Q_D= Q_S.

Therefore,          P* = 10 and Q* = 50. In other words, the equilibrium quantity is 50 and the equilibrium price is $10. The producer surplus is half the area of the rectangle Q* x P*. Producer Surplus = 1/2($10 x 50) = $250

The consumer surplus is half the area of the rectangle defined by Q* = 50, P* = $10. Therefore, Consumer Surplus = $250.

Total surplus is, of course, the sum of the producer and consumer surplus.

That is, Total surplus = PS + CS = $500.

                

The total cost of pollution when the market is at equilibrium:

      In equilibrium, 50 units of Negext are produced, meaning that 4 x 50 = 200 units of pollution are emitted. The cost imposed on society is thus $200. The total surplus from this market after taking into account the cost of pollution is = $500 - $200 = $300.