Assume fringe supply curve is Q=-1+0.2P and demand is given by Q = 11 - P. Calculate the profit maximizing output and price of the dominant firm whose marginal cost is constant at $6?
The fringe supply is given by the curve Q = -1 + 0.2*P. The total demand is given by Q = 11 - P. The residual demand of the dominant firm is Q = 11 - P - (-1 + 0.2*P) = 12 - 1.2*P
In terms of Q, P = (12 - Q)/1.2
The revenue of the dominant firm is P*Q = 10Q - Q^2/1.2. The marginal revenue is the first derivative of the total revenue with respect to the demand and is given by 10 - 2Q/1.2
The marginal cost is $6. To maximize profit, the marginal cost should be equal to the marginal revenue. This gives 6 = 10 - 2*Q/1.2 or 2*Q/1.2 = 4 or Q = 2.4. For Q = 2.4, P = 8.
To maximize revenue the dominant firm should sell 2.4 products and the price of each should be $8.