Low-Cost Price Leader Model Assignment Help

Price Leadership - Low-Cost Price Leader Model

Low-Cost Price Leader Model:

Let us consider a duopoly (firms A and B) selling a homogeneous product at different costs. Let us also assume that firm A is the price leader. The firms may have equal market as shown in Figure (shown by a common market demand curve) or unequal market as shown in Figure (represented  by two different market demand curves). We would consider the case when the firms have unequal costs.  

In Figure, the different cost structures are represented by the two marginal cost curves MCA and MCB with MCA < MCB. Both the firms face the same market demand curve d so the aggregate demand curve D is given by the horizontal summation of each duopolist's. Firm A being the leader equates MRA with MCA and arrives at the price OPA  . Firm B would accept the price even though it is not the profit-maximising price for her. The profit-maximising price for B is OPB. With this kind of an arrangement, firm B does make some profit. Firm A's profit is given by the shaded area. Finally, we see that the two firms produce the same level of output.

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In Figure the only difference is  that the firms face different market demand curves dA and dB and the output levels are different for the two firms but the price charged is the same. The  profit earned by the leader is higher than that of the follower. The firm with the lowest cost will charge a price PA  and this price will be followed by the high cost firm B, although at PA  it does not maximise profit.

In fact the follower could earn a higher profit by charging PB and producing XB. However, it prefers to follow the leader in order to avoid any price war. Otherwise, if a price war ensues, then price may fall so much as not to cover the average cost.
Even though the follower has an incentive to comply with the leader in terms of price, the firms must also enter a share-of-the-market agreement. Otherwise, the follower may not produce the stipulated amount of output required to maintain the price in the market and the leader may be pushed away from the profit maximising position.

Mathematical Representation of Low-Cost Price Leader Model

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