Question
Monopoly manager has the demand and cost functiones as P=200-2Q and C(q)=2000+3Q2
1- calculate the maximum profits?
2- what price-quantity combination maximizes the profits?
3- at the profit-maximizing price-quantity combination, what is the demand elasticity?
4- what price-quantity combination maximizes revenue?
5-calculate the maximum revenues?
6- at the revenue-maximizing price-quantity combination, what is the demand elasticity is it elastic, inelastic or unit elastic?
Explanation / Answer
Managerial Economics & Business Strategy Chapter 8 Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets Overview I. Perfect Competition n Characteristics and profit outlook. n Effect of new entrants. II. Monopolies n Sources of monopoly power. n Maximizing monopoly profits. n Pros and cons. III. Monopolistic Competition n Profit maximization. n Long run equilibrium. Four Market Types Perfect Competition Environment • Many buyers and sellers. None of the firm has a market power in the industry. • Homogeneous (identical) product. No product differentiation. (Unleaded Gas) • Perfect information on both sides of market. No hidden information. Everybody knows everything. • No transaction costs. • Free entry and exit. Any firm can enter or exit. Key Implications • Firms are “price takers” (P = MR). Price is determined within the industry. All firms take it as given. • In the short-run, firms may earn profits or losses. But in order to be in the market they have to cover at least the variable cost. • Long-run profits are zero. Why? If there is profit, new firms enter into the market and price declines. If there is loss, then some firms exit because of loss and price increases. Unrealistic? Why Learn? • Many small businesses are “price-takers,” and decision rules for such firms are similar to those of perfectly competitive firms. • It is a useful benchmark. • Explains why governments oppose monopolies. • Illuminates the “danger” to managers of competitive environments. n Importance of product differentiation. n Sustainable advantage. Managing a Perfectly Competitive Firm (or Price-Taking Business) Setting Price Firm Qf $ Df Market QM $ D S P e Profit-Maximizing Output Decision • MR = MC. • Since all firms are price takers, MR = P, • Set P = MC to maximize profits. Graphically: Representative Firm’s Output Decision $ Qf ATC AVC MC P e = Df = MR Qf* ATC P e Profit = (P e - ATC) × Qf* A Numerical Example • Given n P=$10 n C(Q) = 5 + Q2 • Optimal Price? n P=$10 • Optimal Output? n MR = P = $10 and MC = 2Q n 10 = 2Q n Q = 5 units • Maximum Profits? n PQ - C(Q) = (10)(5) - (5 + 25) = $20 Example: Perfectly Competitive Firm A firm sells its product in a perfectly competitive market where other firms charge a price of $80 per unit. The firm’s total costs are C(Q)=40+8Q+2Q2. • How much output should the firm produce in the short run? • What price should the firm charge in the short run • What are the firm`s short run profits? • What adjustments should be anticipated in the long run? $ Qf ATC AVC MC P e = Df = MR Qf* ATC P e Profit = (P e - ATC) × Qf* < 0 Should this Firm Sustain Short Run Losses or Shut Down? Loss Shutdown Decision Rule • A profit-maximizing firm should continue to operate (sustain short-run losses) if its operating loss is less than its fixed costs. Operating results in a smaller loss than ceasing operations. • Decision rule in the short run: A firm should shutdown when P MC Too little output, at too high a price. • Deadweight loss of monopoly. $ Q ATC MC D Q MR M P M MC Deadweight Loss of Monopoly Deadweight Loss of Monopoly Arguments for Monopoly • The beneficial effects of economies of scale, economies of scope, and cost complementarities on price and output may outweigh the negative effects of market power. • Encourages innovation. Remember the pharmaceutical companies. • It is meaningless to have two different firm to supply electricity to the same area. Too much competition, very big fixed cost. Waste of resources. Monopoly Multi-Plant Decisions • Consider a monopoly that produces identical output at two production facilities (think of a firm that generates and distributes electricity from two facilities). Let C1 (Q2 ) be the production cost at facility 1. Let C2 (Q2 ) be the production cost at facility 2. • Decision Rule: Produce output where MR(Q) = MC1 (Q1 ) and MR(Q) = MC2 (Q2 ) Set price equal to P(Q), where Q = Q1 + Q2 . Comparison • Perfectly competitive market Most important lesson is that it is extremely difficult to make money. Must be as cost efficient as possible. It might pay for a firm to move into a market before others start to enter. • Monopoly market Most important lesson is not to be complacent or arrogant and assume their ability to earn economic profit can never be diminished. Changes in economics of a business eventually break down a dominating company’s monopolistic power. Monopolistic Competition: Environment and Implications • Numerous buyers and sellers • Differentiated products Implication: Since products are differentiated, each firm faces a downward sloping demand curve. • Consumers view differentiated products as close substitutes: there exists some willingness to substitute. • Free entry and exit Implication: Firms will earn zero profits in the long run. Managing a Monopolistically Competitive Firm • Like a monopoly, monopolistically competitive firms have market power that permits pricing above marginal cost. level of sales depends on the price it sets. • But … The presence of other brands in the market makes the demand for your brand more elastic than if you were a monopolist. Free entry and exit impacts profitability. • Therefore, monopolistically competitive firms have limited market power. Marginal Revenue Like a Monopolist Q Q P TR 100 0 10 20 30 40 50 0 10 20 30 40 50 800 60 1200 40 20 Inelastic Elastic Elastic Inelastic Unit elastic Unit elastic MR Monopolistic Competition: Profit Maximization • Maximize profits like a monopolist Produce output where MR = MC. Charge the price on the demand curve that corresponds to that quantity. Short-Run Monopolistic Competition $ ATC MC D Q MR M PM Profit ATC Quantity of Brand X Long Run Adjustments? • If the industry is truly monopolistically competitive, there is free entry. In this case other “greedy capitalists” enter, and their new brands steal market share. This reduces the demand for your product until profits are ultimately zero. $ AC MC D MR Q* P* Quantity of Brand MR X 1 D1 Entry P 1 Q1 Long Run Equilibrium (P = AC, so zero profits) Long-Run Monopolistic Competition Monopolistic Competition The Good (To Consumers) Product Variety The Bad (To Society) P > MC Excess capacity • Unexploited economies of scale The Ugly (To Managers) P = ATC > minimum of average costs. • Zero Profits (in the long run)! Optimal Advertising Decisions • Advertising is one way for firms with market power to differentiate their products. • But, how much should a firm spend on advertising? Advertise to the point where the additional revenue generated from advertising equals the additional cost of advertising. Equivalently, the profit-maximizing level of advertising occurs where the advertising-to-sales ratio equals the ratio of the advertising elasticity of demand to the own-price elasticity of demand. Q P Q A E E R A , , - = Maximizing Profits: A Synthesizing Example • C(Q) = 125 + 4Q2 • Determine the profit-maximizing output and price, and discuss its implications, if You are a price taker and other firms charge $40 per unit; You are a monopolist and the inverse demand for your product is P = 100 - Q; You are a monopolistically competitive firm and the inverse demand for your brand is P = 100 – Q. Marginal Cost • C(Q) = 125 + 4Q2 , • So MC = 8Q. • This is independent of market structure. Price Taker • MR = P = $40. • Set MR = MC. • 40 = 8Q. • Q = 5 units. • Cost of producing 5 units. • C(Q) = 125 + 4Q2 = 125 + 100 = $225. • Revenues: • PQ = (40)(5) = $200. • Maximum profits of -$25. • Implications: Expect exit in the long-run. Monopoly/Monopolistic Competition • MR = 100 - 2Q (since P = 100 - Q). • Set MR = MC, or 100 - 2Q = 8Q. Optimal output: Q = 10. Optimal price: P = 100 - (10) = $90. Maximal profits: • PQ - C(Q) = (90)(10) -(125 + 4(100)) = $375. • Implications Monopolist will not face entry (unless patent or other entry barriers are eliminated). Monopolistically competitive firm should expect other firms to clone, so profits will decline over time. Conclusion • Firms operating in a perfectly competitive market take the market price as given. Produce output where P = MC. Firms may earn profits or losses in the short run. … but, in the long run, entry or exit forces profits to zero. • A monopoly firm, in contrast, can earn persistent profits provided that source of monopoly power is not eliminated. • A monopolistically competitive firm can earn profits in the short run, but entry by competing brands will