7.4: Profit Maximization for a Monopolist or Monopolistically Competitive Firm
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The profit maximizing condition can be used to solve the monopolist’s problem. Suppose, as in Demonstration \(\PageIndex{1}\) below, that the inverse demand curve facing the monopolist is \(P = 100 - 3Q\). Since this inverse demand curve is linear, the marginal revenue curve has the same intercept and a slope that is twice as steep. Thus, \(MR = 100 - 6Q\). Suppose further that marginal cost is equal to $4Q. Set \(MR = MC\) or \(100 -6Q = 4Q\)and solve for \(Q\). You get \(Q\) = 10 units. This is the profit maximizing quantity.
Next, use the inverse demand curve to find the profit maximizing price. Although the monopolist equates marginal revenue with marginal cost, it uses the inverse demand curve (not the marginal revenue curve) to set the price. Substituting the profit maximizing quantity into the inverse demand curve, you get a price of \(100-3(10) = $70\).
Notice in the demonstration that the area of the blue rectangle represents profits. Use Demonstration 1 to verify that profits go down if the monopolist does no set the quantity so that \(MR = MC\).
Demonstration \(\PageIndex{1}\). Profit Maximization Problem for a Monopolist
Marginal Cost (MC) = $40.00
Average Total Cost (AC) = $30.00
Profit = (P - AC)Q =$400.00
The steps involved in finding the solution to the firm’s problem under monopolistic competition are exactly the same as the monopolist’s problem above. The primary difference between monopoly and monopolistic competition is that entry is possible in monopolistic competition. If profits are positive, new firms will enter the market and/or existing firms will mimic the successful practices of competitors. When economic profits are zero, there is no additional entry, and the market is at an equilibrium. In a no-entry equilibrium under monopolistic competition, the rectangular area that represents profits will be just equal to the sunk costs that would need to be incurred if the market were to be entered by a new firm. New firms would see entry into the market as unattractive since the profits to be gained would be consumed by the sunk costs of entry.