Two monopolies in different markets have identical, constant marginal cost funct

Question

Two monopolies in different markets have identical, constant marginal cost functions. (a) Suppose each faces a linear demand and the two demands are parallel. Which monopolist will have a higher Lerner index: the one whose demand is closer to the origin or the one whose demand curve is farther from the origin? EXPLAIN your answer. (b) Suppose their linear demands have identical vertical intercepts but different slopes. Which monopolist will have a higher Lerner index: the one with the flatter demand or the one with the steeper demand? EXPLAIN your answer. (c) Suppose their linear demands have identical horizontal intercepts but different slopes. Which monopolist will have a higher Lerner index: the one with the flatter demand or the one with the steeper demand? EXPLAIN your answer.

Explanation / Answer

(a) Lerner Index = (Price - MC) / MC

A monopolist equates his MC with Marginal Revenue, MR. The farther from origin the demand curve is, the farther from origin the MR curve also is & MC intersects MR at a higher output & higher price.

So, Lerner Index is higher (Since price is higher) for demand curve that lies farther from the origin.

(b)

A steeper demand curve will have a steeper MR as well, and MC intersects the flatter MR curve at a higher output and higher price.

So, Lerner index is higher (Since price is higher) for a flatter demand curve.

(c)

If two demand curves have same horizontal intercept but different slope, the flatter demand curve will lie below the steeper demand curve. In this case, MC will intersect the steeper MR curve at a higher output & higher price.

So Lerner Index will be higher (Since price will be higher) for the steeper demand curve.

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