Why will the optimum monopoly price always lie in the elastic portion of the monopolist's demand...

Why will the optimum monopoly price always lie in the elastic portion of the monopolist's demand curve unless the monopolist has zero marginal costs (what is the elasticity of demand at the price that such a monopolist will set?) or practices price discrimination? Explain with a graph where the monopolist will operate when it has marginal cost and when it has zero marginal cost.

Solutions

Expert Solution

Consider the following fig.

So, here “D” be the downward sloping demand curve and “MR” be the corresponding marginal revenue curve. Now, the monopolist will choose its optimum level of “Q” by the condition “MR=MC”. Now, given the demand curve when “P>P1 and Q<Q1”, => the elastic portion of the demand curve implied “e >1”, when “P<P1 and Q>Q1”, => the inelastic portion of the demand curve implied “e < 1”and at “P=P1 and Q=Q1”, => the unity elastic point of the demand curve implied “e=1”. Now, when “e > 1”, => “MR > 0”, when “e < 1”, => “MR < 0” and “e = 1”, => “MR = 0”.

Now, let’s assume that “MC > 0”. So, at the optimum “MR=MC > 0”, => the optimum output choice will less than “Q1” and the corresponding “P” will be more than “P1”, => it’s the elastic portion of the demand curve. Similarly, let’s assume that “MC = 0”. So, at the optimum “MR=MC = 0”, => the optimum output choice will be exactly equal to “Q1” and the corresponding “P” will be “P1”, => it’s the unity elastic point of the demand curve.

So, here we can see that a monopolist can produce only on elastic portion or unity elastic portion, => a monopolist will not operate on the inelastic portion.

Rahul Sunny answered 1 year ago

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