ECON 21 Principles of Microeconomics (Summer 216) Monopoly Relevant readings from the textbook: Mankiw, Ch. 15 Monopoly Suggested problems from the textbook: Chapter 15 Questions for Review (Page 323): 1, 3, 4, 5, and 6 Chapter 15 Quick Check Multiple Choice (Page 324): 2, 3, 4, and 5 Chapter 15 Problems and Applications (Pages 324-327): 1, 5, 6, 8, 9, and 1 Definitions and Concepts: Monopoly a market structure in which there is one single seller of a unique good (with no close substitutes ) and in which there are barriers to entry which prevent rival firms from entering the market curve that a monopolist faces is the market demand curve for the good. Downward sloping nature of demand curve implies i. a monopolist can increase price without demanded dropping to zero ii. a monopolist must decrease price in order to increase demanded Market Power a firm has market power if: (i) it can increase the price of its product without losing all customers, or equivalently (ii) it must decrease the price of its product in order to sell additional units. Market Power control over price Firms in perfectly competitive markets have no market power [ horizontal demand curve ] Firms in imperfectly competitive markets (i.e., all other market structures) have at least some market power [ downward sloping demand curve ] P( Q) ( P) Q P From MR P Q, we see why Q Q 1. For a firm with market power, MR P (since P in order to bring about Q ) [Marginal Revenue is less than Price] 2. For a firm in a perfectly competitive market, MR P (since Q possible even with P ) Inverse Elasticity Pricing Rule to maximize profit, a firm must be operating where the markup of price above marginal costs as a percentage of price is equal to minus the inverse of price elasticity of demand.
Barriers to Entry factors which make it either impossible or very costly for new firms to enter a market and compete with existing firms Common Barriers to Entry: 1. Exclusive Ownership of an essential input. If a firm has exclusive ownership or access to an input which is needed to produce a good, then as a result they will be the only producer of the good. In practice, monopolies rarely arise because of exclusive ownership of an essential input 2. Cost Structure as a barrier to entry. If there are economies of scale, then average costs decrease as of output is increased. Thus, total production costs are lowest when all production takes place within one firm. It may be that one single firm is able to produce a good and earn substantial positive profits, but a second firm could not profitably enter the market (since, with two firms in the market, average total costs for each firm would be substantially higher) Natural Monopoly a monopoly which arises because one single firm can produce a good at lower total cost than could two or more firms 3. Government Created Monopolies. Governments may (for various reasons) erect legal barriers to entry, thereby establishing a particular seller as a monopolist in a market Government may have exclusive ownership of an essential input and must decide who has access to the input. To encourage research and development and creative activity, government awards/grants patents and copyrights. o Patent legal protection which grants the patent holder the exclusive right to create a particular product or use a particular production technique o A patent establishes a successful innovator as a monopolist for a specified period of time. Allows innovator to earn a monopoly profit for a fixed period of time, in order to encourage innovation (i.e., as a reward for successful innovation ) Realize cost savings for society resulting from economies of scale o If an industry is characterized by significant economies of scale, then the Government might establish one particular supplier as a monopolist (in order to avoid wasteful duplication of costs ) and then closely regulate the behavior of the monopolist (in order to minimize the resulting Deadweight Loss) Price Discrimination the practice of charging a different price for different units sold of an essentially identical good (with the difference in price not being a result of differences in cost of production)
First Degree Price Discrimination or Perfect Price Discrimination a practice in which a firm charges every consumer an amount exactly equal to buyer s reservation price for every unit sold Requires firm to know the exact value of reservation price of every consumer for every unit => assumptions are so extreme that it can never be used in practice Second Degree Price Discrimination or Menu Pricing a practice in which a firm presents all consumers with different pricing menus and allows each consumer to choose the menu which they prefer Firm simply needs to know that there are fundamental differences across consumers, but need not be able to identify the particular type of any specific consumer Examples: cell phone pricing packages, first class versus coach air travel, premium cable versus basic cable. Third Degree Price Discrimination or Segmented Pricing a practice under which a firm separates consumers into different market segments, and then charges each different segment of consumers a different constant per unit price for each unit purchased Must be able to easily separate the consumers into different markets (and effectively prevent resale across segments), and have reason to suspect that the optimal constant per unit price differs across the two market segments Examples: student discounts, senior discounts, different prices for DVDs and pharmaceuticals across different countries
Marginal Revenue for a linear demand function: Consider a market in which demand is characterized by the linear inverse demand function P D ( Q) a bq. Our general expression for Marginal Revenue is P MR Q P (" slope" ) Q P Q For P D ( Q) a bq, " slope" b Thus, MR ( b) Q PD ( Q) bq a bq a 2bQ Comparing P D ( Q) a bq and MR a 2bQ, the latter function has the same vertical intercept but is twice as steep a Marginal Revenue (1/2)a (1/2)(a/b) (a/b)
Profit Maximization for firm with Market Power: To maximize profit, the firm should: 1. Produce every unit of output for which MR>MC 2. Don t produce any units for which MR<MC Q* Set price equal to the amount which will make consumers exactly willing and able to purchase Q* => rely upon the vertical interpretation of demand in order to determine the profit maximizing price P* Q*
Profit of firm with market power: P* ATC(q) ATC(Q*) Q* (Profit) = (Total Revenues) (Total Costs) = [P*][Q*] [Q*][ATC(Q*)] = [Q*][P* ATC(Q*)] = ( light green area above ) So, this monopolist is able to earn a positive profit, and will therefore not want to shut down. But, is this always be the case? Shutting down only ever makes sense if it is never possible for the firm to cover their variable costs of production. That is, produce a positive so long as for some the firm has: (Total Revenue) > (Variable Costs) (P)(Q) > [Q][AVC(Q)] P > AVC (Q) But, (P) is simply the height of the demand curve So, the firm will produce a positive in the short run so long as AVC(Q) dips below the demand curve at some level of Q Similarly, the firm is able to earn a positive profit so long as they are able to generate revenues which cover total costs at some level of output. This is true so long as: (Total Revenue) > (Total Costs) (P)(Q) > [Q][ATC(Q)] P > ATC (Q) But, (P) is simply the height of the demand curve So, the firm will be able to earn a positive profit so long as ATC(Q) dips below the demand curve at some level of Q
Alternative Interpretation of Profit Max Condition At this point we have noted that the firm will maximize profit by choosing the for which: MR=MC However, we previously specified MR in terms of price elasticity as: 1 MR P1 p Thus, the condition for profit maximization becomes: 1 1 P1 MC P P MC p p 1 P MC P MC P 1 p P p In this final form, this rule for profit maximization is called the Inverse Elasticity Pricing Rule (IEPR) Inverse Elasticity Pricing Rule to maximize profit, a firm must be operating where the markup of price above marginal costs as a percentage of price is equal to minus the inverse of price elasticity of demand. Surplus and Efficiency (when firm with market power maximizes profit): Efficiency: One any one particular unit (buyer s reservation price) = (height of demand) (seller s reservation price) = (height of MC) For efficiency, we should trade all units for which () > (MC) => (DWL) > at Q* => Firm with market power produces less than the efficient P* CS PS DWL Q* Q E
First Degree or Perfect Price Discrimination: Again, the knowledge required by the seller to actually engage in such behavior can almost never be known => no good real world examples of 1 st Degree P.D. However, it is still insightful to figure out what a firm would do if they were able to engage in such pricing If (at each along the demand curve) the firm charges each consumer an amount exactly equal to reservation price, then Marginal Revenue is simply equal to height of demand = MR Q FDPD Firm would sell (Q FDPD ) units => extract the entire area below the demand curve, up to the sold as Revenue => (Revenue)=( blue + yellow ) ( yellow ) = (Variable Costs) => (PS) = ( blue ) Note that (CS) = () => Consumers are worse off (compared to traditional monopoly ) (DWL) = () => Social Surplus is larger (compared to traditional monopoly ) So, P.D. can clearly increase both PS and Social Welfare
Example of Segmented Pricing leading to increase in CS : Segment A has demand given by the linear inverse function P A D ( q) 1 q Segment B has demand given by the linear inverse function P B D ( q) 2 q Firm has constant marginal costs of MC 4 If these two segments were treated as one single market (i.e., if a common price was set across the two markets), then 52 2-2 -6 Profit maximized by setting price of 52, selling 48 units in Segment A and completely ignoring Segment B Segment A : (CS) and (PS) both positive Segment B : (CS) and (PS) both zero If the firm is allowed to engage in Segmented Pricing : set price of 52 in Segment A => sell 48 units in Segment A set price of 12 in Segment B => sell 8 units in Segment B Outcome in Segment A is identical to what is was before But now, in Segment B : (CS) and (PS) are both positive instead of zero Thus, when the firm is able to practice Segment Pricing (as opposed to restricting the firm to charging a common price across both segments) in this example: Producer s Surplus is larger Total Consumers Surplus is larger Therefore, Total Social Surplus is larger (DWL is smaller) Nobody is worse off and some people are strictly better off
Problem: 1. Consider a firm operating in a market in which, Marginal Costs, and Average Variable Costs are as illustrated below. Note that demand is a linear function. Also illustrated is the resulting Marginal Cost curve, if the firm was to charge all consumers the same per unit price for every unit of output purchased. 1 6. 4.5 3.6 3 1A. If this firm charged a common price for every unit of output sold, how many units would they choose to sell and what price would they charge? 1B. If this firm was able to practice Perfect Price Discrimination, how many units would they sell? How much Total Revenue would they generate? For what values of Fixed Costs would they be able to earn a positive profit? Multiple Choice Questions: 1,6 2, 2,5 2,2 AVC(q) 4, 1. Edna sells bathing suits. She offers customers a 15% discount if they show her a valid student I.D. at the time of purchase. This behavior by Edna is an example of A. a monopolist erecting a substantial entry barrier. B. First Degree Price Discrimination (or Perfect Price Discrimination). C. Third Degree Price Discrimination (or Segmented Pricing). D. a firm choosing to produce a positive of output in the short run, even though they are unable to earn a positive profit. 2. is a market structure in which there is one single seller of a unique good (with no close substitutes ) and in which there are barriers to entry which prevent rival firms from entering the market A. Perfect Competition B. Monopoly C. Oligopoly D. Monopolistic Competition
3. Carl sells turnips in a small, rural town in South Dakota. Since he is the only turnip seller in town, he has some market power. He is currently charging 1.25 for each five pound bag of turnips, a price at which he sells 4 bags per month. If he were to increase his sold to 5 bags per month A. he would be able to increase the price he charges. B. he would not have to change is price whatsoever. C. he would have to decrease the price he charges. D. he would have to be able to avoid all Fixed Costs of production. 4. According to the Inverse Elasticity Pricing Rule, when maximizing profit a firm must be operating in a way such that 1 is equal to p A. P. B. P MC. C. P. MC D. P MC. P 5. is a legal protection which grants the holder the exclusive right to create a particular product or use a particular production technique. A. A Natural Monopoly B. A Menu Price C. A Patent D. An Inverse Elasticity Pricing Rule 6. In general, a monopolist will A. set the price of their product equal to the value of the highest reservation price that any buyer has for their product. B. produce/sell every unit of output for which Marginal Costs are positive. C. produce/sell the level of output which makes Average Fixed Costs as small as possible. D. produce/sell the level of output which equates Marginal Revenue to Marginal Costs. 7. For a firm with market power, while for a firm in a perfectly competitive market. A. Marginal Revenue is less than Price; Marginal Revenue is greater than Price. B. Marginal Revenue is less than Price; Marginal Revenue is equal to Price. C. Marginal Revenue is equal to Price; Marginal Revenue is less than Price. D. Marginal Revenue is less than Price; Marginal Revenue is also less than Price.
For questions 8 through 11, consider a monopolist operating in the market illustrated below. Suppose throughout that the monopolist is restricted to charging a common price for every unit of output sold. 7. 6. 1 AVC(q) 4. 2. 4 6 1, 1,2 8. In order to maximize profit this monopolist should A. sell 1, units of output. B. charge a price of 1 per unit. C. charge a price of 6 per unit. D. None of the above answers are correct. 9. The efficient level of trade in this market is A. units. B. 4 units. C. 6 units. D. 1,2 units. 1. Assuming that the per unit price received by the monopolist is equal to the height of demand at the of output traded, Producer s Surplus would be negative if this monopolist were to produce A. 4 units of output. B. any level of output between 4 units and 6 units. C. exactly 1,2 units of output. D. more than 1,2 units of output. 11. The maximum profit of this monopolist would be exactly equal to if Fixed Costs were A. exactly equal to zero B. less than 1,6 C. exactly equal to 2, D. greater than 2,8
Answer to Problem: 1A. The firm would maximize profit by producing the at which is equal to. From inspection of the graph, this occurs at 1,6 units of output. The corresponding price which they would want to charge is obtained by determining the height of the demand curve at this desired. In section of the graph shows that this optimal price is 6. per unit. 1B. If the firm is able to practice Perfect Price Discrimination, then Marginal Revenue is in essence the Curve. The firm would therefore want to produce the at which intersects. From inspection of the graph, this is 2,2 units. The given curves reveal that AVC of producing 2,2 are 3.6. Thus, Variable Costs at this are 7,92. Since demand is a linear function, Total Revenue (which is the entire area below the demand curve in this situation) is: (4.5)(2,2)+(1/2)(5.5)(2,2) = (9,9)+(6,5) = 15,95. Thus, Producer s Surplus is 8,3. It follows that the firm could earn a positive profit if and only if Fixed Costs are less than 8,3. Answers to Multiple Choice Questions: 1. C 2. B 3. C 4. D 5. C 6. D 7. B 8. D 9. C 1. D 11. C