Question

Q2) What would a monopoly's marginal revenue be if it chose a point on the demand curve where the price elasticity of demand equals -1? Why would it never be optimal to choose such a point, given positive marginal costs? Would the monopoly rather produce less or more?

Answer 1

The point where price elasticity of demand is -1, is the mid-point of the demand curve, and is the revenue-maximizing point. At this level, marginal revenue (MR) curve intersects horizontal axis and MR is zero**.

If marginal cost is positive, producing at this output level will mean that MC > 0 but MR = 0, therefore monopolist will incur a marginal loss, and therefore will never produce at this point. The monopolist will rather produce less.

**Mathematical derivation:

MR = P x [1 + (1 / Ed)] where P: price, Ed: Price elasticity of demand

When Ed = -1, MR = P x [1 + (1 / -1)] = P x (1 - 1) = P x 0 = 0