Question

The demand Curve facing a firm operating under monopoly is given by P = 85 - 2.5Q; The cost function is given by TC = 20 + 25Q + 2,5Q^2.

1) What is the Maximum profit?

2) What is the Profit Maximizing Price Elasticity of demand?

3)What is the Revenue Maximizing Price elasticity of demand?

Answer 1

1)The profit maximization condition of the monopoly is MC = MR.

In order to maximize monopoly profits, it is necessary to produce such a volume of production that marginal revenue is equal to marginal cost

MC = TC ’(Q) = 25 + 5Q;

MR = TR '(Q) = (P ∙ Q)' = ((85 - 2.5Q) Q) '= (85Q - 2.5Q²)' = 85 - 5Q.

Then:

25+ 5Q = 85-5Q, hence maximizing monopoly profits sales Q = 6 units.; P = 85 - 2.5 ∙ 6 = 70 den. units

2)Profit-maximizing monopoly always chooses a price in the elastic demand segment, i.e. at

eD> 1.

3)The condition for maximizing the monopoly revenue: MR = 0. Then: 85 - 5Q = 0; Q = 17 units P = 42.5 units

$πmax = TR - TC = 6 \times70- (20 + 25\times6 + 2.5\times 6^2) = 420-260=160 den.units$