III. Consider a monopolist firm that faces a market demand for a good given by:

Question

III. Consider a monopolist firm that faces a market demand for a good given by: Q = 1 – P, where P is the price and Q is the quantity sold. The total cost (C) function of the firm is C= ½Q2.

(iv) Find the total profit of the firm when it is maximizing it profit. How much consumer surplus are consumers then enjoying? (10 marks)
(v) Find the elasticity of demand at the optimal price and quantity. (See note below.) Find the marginal cost at the optimal quantity and show how we can use the rule of thumb we saw in class at the optimum to infer the optimal price from the marginal cost and elasticity. (10 marks)

Explanation / Answer

d) Total profit= TR- TC
= Q- Q2 - 1/2Q2 = 1/3 - 1/9 - 1/18= 1/6

e) Elasticity = % change in quantity/ % change in price

= 2

MC= Q= 1/3

We know MR= P( 1- 1/Elasticity)

AT Optimal condition MC= MR

MC= P( 1- 1/Elasticity)

So, 1/3= P(1-1/2)

P= 2/3

:)

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