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. 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. f) Compute the price consumers should pay and the price producers should receive. Compute the government’s revenue for the tax. Show them area on the 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.

Price paid by Consumers = $14

Price received by Producers = $12.5

Total Government Revenue from Tax = 1.5 × 3 = 4.5