Bertrand-Cournot Model

Bertrand model implies that the firms do not pre-determined in any way in the market meaning that each firm is absolutely free to pick up the right level of price and quantities leaving them as variables. As the firm determines no factor, the supply correspondence will be “flat”. If the firm is not able to pre-determine any factor it has a weak strategy in the market stage.

As all the firms are not pre-determining, prospective capital stocks are reduced to zero. The industry supply function will look like this:

S(p,0,0) = nΞ>nF(0).

The resultant price will be equal to 0, and hence the firm’s profit will be equal to zero too. It is a typical Bertrand model outcome. Production itself can be expected to become efficient as labor and capital investment is selected simultaneously (Dixon, 1984). Bertrand outcome is obtained whenever the firms are absolutely uncommitted and the equilibrium looks like:

Θ-a/Θ=0.

No firm gains anything from pre-commitment, the production is very efficieent since the reduction in the output of one firm is at once reflected in the rise of the outputs of other uncommitted firms. No firm is able to prevent zero profit resulting from Bertrand model.

The perfect competitiveness of the outcome can be reached even with merely one Cournot firm in the market when there is a potential competitor that follows Bertrand model. Sufficient discipline is provided – the threat hidden in the presence of Bertrand competitor guarantees perfect competitive outcome proving that even a potential competitor is able to influence on the market power.