Q.If the value of price elasticity of demand is infinity (∞), what will be the relationship between price and marginal revenue?

Lerner's Index of monopoly power equals the reciprocal of the absolute value of the price elasticity of demand facing the firm.

Lerner's Index measures the degree of monopoly power as the proportionate gap between price and marginal cost: Lerner's Index = (Price - Marginal Cost)/Price. Using the profit-maximising condition for a monopolist (MR = MC, with MR expressed as Price x (1 - 1/|e|), where |e| is the absolute value of price elasticity of demand), this expression simplifies exactly to (Price - Marginal Cost)/Price = 1/|e|. So …

At a monopolist's profit-maximising equilibrium, the absolute price elasticity of demand must exceed 1, option (b).

A monopolist maximises profit at the output where marginal revenue equals marginal cost (MR = MC), with MC normally positive. Using the standard relation between marginal revenue, price and (absolute) price elasticity of demand, e:

MR = P (1 - 1/e)

For MR to equal a positive MC, we need MR itself to be positive:

P(1 - 1/e) > 0

Since P > 0, this requires (1 - 1/e) > 0, i.e. 1/e < 1, i.e. e > 1. …