15.9 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 10 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:

P −MC P =−

si eQ, P

, where si = qi /Q is firm i’s market share and eQ, P is the elasticity of market demand. Compare this version of the inverse elasticity rule with that for a monopolist from the previous chapter.