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

d) Compute the optimal social quantity to be produced. Graph.

Answer 1

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

From social point of view, the equilibrium will occur at the point where social marginal cost = price.

So, equating these two to get the equilibrium quantity and price,

Price = Social marginal cost

20 - 2X = 5 + 3X

20 - 5 = 3X + 2X

5X = 15

X = 3 is the answer.

Price = 20 - 2X

= 20 - 2(3)

= 20 - 6 = 14 is the answer.

The equilibrium occurs where the price and social marginal cost intersect each other. Price is constant at 14 while the marginal cost curve is upward sloping and increases at a constant rate.