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 qi units of the good. Under a rule of strict liability, the firm's profits are:

For any qi 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 xi = x*. Therefore, its profits are:

The first-order condition is:

Adding up across all n firms yields: or:

where, again, ? is the elasticity of demand.

Let Z = wix* +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.

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