We arc now ready to find the maximum-profit equiIihriun of the monopolist. IT a monopolist faces a given demand curve and wishes to maximize total profit (TP). what should it do? B definition. total profit equals total revenue minus total costs; in symbols. TP= TR- TC= (PX q) – TC To maximize its profits. the firm mus.t find the equilibrium price and quantity that give the largest profit, or the largest difference between TR and TC The major finding is that maximum Profit will occur iohen output is at that level where the firm s marginal revmile is equal to its marginal cost; One way to determine this maximum-profit condition
is by using a table of costs and revenues. such as Table 9-5. To find the profit-maximizing quantity and price, compute total profit in column (5). This column tells us that the monopolist’s best quantity, which is 4 units, requires a price of $120 per unit.
This produces a total revenue of$480. and, after subtracting total costs of $250. we calculate total profit to be $230. A glance shows that no other price-output combination has as high a level of total profit.
A second and equivalent way of arriving at the same answer is to compare marginal revenue, column (6), and marginal cost, column (7). A’I long as each additional unit of output provides more revenue than it costs-that is to say, as long as MR is greater than MC-the firm’s profit will increase. So the firm should continue to increase its output as long as MR is greater than Me.. By contrast. suppose that at a given level of output MR is less than Me.. This means that increasing output would lead to a lower level of profit a, 10 the profit-maximizing firm should at that point cut back on output. Clearly, the best-profit point comes at the point where marginal revenue exactly equals marginal cost, as is shown by the data in Table 9-5. The rule for finding maximum profit is therefore: .The maximum-profit price (P*) and quantity (q”) of a monopolist come where the firm’s marginal rev ( equals its marginal cost: MU = MC at the maximum-profit P* and q* These examples show the logic of the Me = MR rule for maximizing profits, but we always want to understand the intuition behind the rules. Look for a moment at Table 9-5 and suppose that the monopolist is producing q = 2. At-that point, its MR for producing 1 full additional unit is +$100, while its MCis $20. Thus, if it produced 1’additional unit, the firm would make additional profits of MRMC= $100 – $20 = $80. Indeed, column (5) of Table 9-5 shows that the extra profit gained by moving from 2 to 3 units is exactly $80. Thus, when MR exceeds Me. additional profits can be made by increasing output; when MCexceeds MR, additional profits can be made by decreasing q. Only when MR= MCcan the firm maximize profits. because there are no additional profits to be made by changing its output level.
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