# Cournot oligopoly

Now consider the Cournot model of oligopoly. Suppose that there are *n* identical firms, all of whom have the same marginal production costs of *c >*0. The demand curve is still P(Q) = *u'(Q*).

## Strict liability

Consider firm i. Suppose that it produces *q _{i}* units of the good. Under a rule of strict liability, the firm's profits are:

For any *q _{i}* and any choice of care and quantity by the other firms, firm

*i*can minimise its costs by choosing the efficient level of care, so

*x*x*. Therefore, its profits are:

_{i}=The first-order condition is:

Adding up across all *n* firms yields:
or:

where, again, *?* is the elasticity of demand.

Let *Z = w _{i}x* +H*(x*) be the per unit costs of care and harm at the optimal level of care. Then:

Suppose that Z increases by a small amount. The change in the oligopoly price is:

where once again, *E* is the elasticity of the elasticity of demand with respect to price. Again, there will be forward cost shifting under a rule of strict liability if the elasticity of demand is not too sensitive to price - but here the extent of cost shifting is also constrained by the number of firms in the market. The above equation shows that as *n* increases, *P'(Z*) gets smaller, and as *n* we approach the competitive outcome in which

P( Z) = 1.