Chapter 15, Problem 15.10P

Inverse elasticity rule

Use the first-order condition (Equation 15.2 ) for a Cournot firm to show that the usual inverse elasticity rule from Chapter 11 holds under Cournot competition (where the elasticity is associated with an individual firm's residual demand, the demand left after all rivals sell their output on the market). Manipulate Equation 15.2 in a different way to obtain an equivalent version of the inverse elasticity rule:

$\frac{p-MC}{p}=-\frac{s_i}{e_{Q,p}}$ ,

where $s_i=q_i/Q$ is firm i's market share and $e_{Qp}$ is the elasticity of market demand. Compare this version of the inverse elasticity rule with that for a monopolist from the previous chapter.