Question

An industry producing chemicals shows the following marginal cost function: MgCp = 5+2X Where X is the quantity produced. The demand for X is represented by the following function: P = 20 – 2X. Assume that the market is perfectly competitive and unregulated. In the productive process the firms throw their wastes throw their wastes in a river, the society is facing a cost for the firm’s actions. The social marginal cost is given by the following function MgCs = 5 + 3X

e) If the market is perfectly competitive, the efficient level of output could be achieved by setting a per unit tax order to correct the externality. Compute the amount of the tax needed to correct the externality and show the result in a graph.

Answer 1

We have the following information

Demand equation: P = 20 – 2X, where P is price and X is output of chemicals

When X =0, P = 20

When P =0, X = 10

Private Marginal Cost (MgCp) = 5 + 2X

In a perfectly competitive market equilibrium is the point where the price is equal to the marginal cost.

P = MgCp

20 – 2X = 5 + 2X

15 = 4X

Equilibrium output (X) = 3.75

P = 20 – 2X

P = 20 – (2 × 3.75)

Equilibrium price (P) = $12.5

Now, it is given that social marginal cost (MgCs) = 5 + 3X. Equating it with the price

20 – 2X = 5 + 3X

15 = 5X

Output level when social cost is taken into consideration = 3.

P = 20 – 2X

P = 20 – (2 × 3)

P = 20 – 6

Price when social cost is taken into consideration = $14

So, the per unit tax that is needed to correct the externality is

Price with Social Cost – Price with Private Cost = $14 – $12.5 = $1.5

So, the government should impose a per unit tax of $1.5 to correct the externality.