Question

The demand curve for turnip can be represented by the following equation: ? = 2000 − 400? There are only two producers and the marginal cost to produce a turnip is $2 (There is no fixed cost). If the capacity of each firm is 600 output, calculate the price range of turnip under the Bertrand-Edgeworth Model.

Answer 1

Under Bertrand-Edgeworth Model each player sets the price first and then determines the quantity that is to be sold. Hence under this model the firm with low price caters the entire market and firms having same price share the market, each selling to half of the market.

Neither firms set the price below marginal cost (c) as it gives the firm negative profit

Hence let the price of firm 1 be P1 and price of firm 2 be P2.

Where P1>P2>C . However this is not possible as firm 1 will always have a tendency to maintain price below firm 2

Hence P2>P1=C. Note that Bertrand’s model does not lead to the maximization of the industry (joint) profit, due to the fact that firms behave naively, by always assuming that their rival will keep its price fixed and that they never learn from past experience .

Under Bertrand-Edgeworth Model we get same pricing as in the perfect competition. As the price will be equal to MC ( both firm producing identical product).

Here MC=$2

Thus price can be taken as 2$

Q=2000-400p

P=2

Q= 2000-400*2

=1200