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The Price Leadership or Dominant Firm Model

I think this model is easiest to learn diagrammatically, and then mathematically. Here is the graph and then an explanation of what is happening:
Notice first the total market demand curve for the industry as a whole. Then notice the marginal cost curve for the competitive fringe of firms. This is a model in which there is one firm which is dominant and then a fringe of small firms who are so small that they behave like perfectly competitive firms – they take the price that is give by the dominant firm (and then set P = MC to profit maximize).

The basic story in this model is that the dominant firm leaves room for the competitive fringe (and therefore profit maximizes according to the “residual” demand curve. Since the fringe of firms behaves like perfect competitors, the sum of their marginal cost curves is essentially their supply curve. It represents the amount that these firms together will want to supply at any possible price.

Therefore, the residual demand curve is total demand minus this supply by the competitive fringe. This is exactly what the curve labeled DDF represents.

Our story is that the dominant firm profit maximizes using this residual demand curve. That means setting MR = MC for this demand curve. This is exactly where Q*DF comes from (it is the quantity at which MR is just equal to MC for the dominant firm. The dominant firm will charge the profit-maximizing price, which is P*.

Once P* is established by the dominant firm, the competitive fringe (who are price takers) will just take this price and set P* = MC. This gives us the profit-maximizing quantity Q*CF for the competitive fringe.

We can take an algebraic example. Assume that the overall industry demand curve is P = 100 – Q and that the sum of the marginal costs of the competitive fringe is P = 10 + 4Q. The marginal cost of the dominant firm is constant at MC = 18.

The price at which the total demand and the

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