of the linear demand curve. Show that moving to higher levels of output along the demand curve increases elasticity.

Transcription

1 ORDINARY MONOPOLY 18. Monopoly - Overview Monopoly - A firm that sells a good where no other firm sells any good that is a close substitute for it. Unlike a competitive firm, a monopolist has some control over the price. 19. Monopoly - Revenue Functions Total Revenue (TR) - just like it sounds. If the monopolist is selling all of its output at the same price (an 'ordinary monopolist'), total revenue is price times quantity. Marginal Revenue (MR) - the rate of change of total revenue as output changes. TR MR =. Roughly, the additional revenue generated by an additional unit of output. y Graph a linear demand curve and marginal revenue together. (Price on the vertical axis and output on the horizontal.) Lined up below it graph total revenue. (Revenue on the vertical axis and output on the horizontal.) Where MR is positive, TR slopes up and demand is elastic; where MR is negative, TR slopes down and demand is inelastic; where MR is zero, TR is at a maximum and the elasticity of demand is -1. y P Determine own price elasticity of demand ε = at the endpoints and the midpoint P y of the linear demand curve. Show that moving to higher levels of output along the demand curve increases elasticity. 20. Monopoly - Profit-maximization π ( y) = TR ( y) TC ( y) Where, by definition, total cost is minimized for any given level of output and total revenue is maximized for any given level of output. Assuming the profit function is wellbehaved we have a necessary condition for a level of output to be profit-maximizing: π TR TC = = 0 y y y which becomes: MR = MC e.g. What is a monopolist's profit-maximizing level of output, the price it charges, and the profits it earns when: QD = 100 P TC = 5y + y 4

2 21. Monopoly - Efficiency Issues A monopoly market structure results in a different outcome (P>MR=MC) from the competitive market structure (P=MC). If the independence assumption holds (e.g. no pollution) then the competitive market outcome is optimal/efficient and the monopoly outcome involves too little output. e.g. What is the deadweight loss arising from the monopoly market structure when: QD = 100 P TC = 5y + y Sources of Monopoly Government Franchise - By law no one else can compete in the monopolist's market. Patent - Includes both copyright and patents. Resource-Based - Arises when only one company owns all the natural resources necessary for the production of some good. Natural - Costs are such that only one firm can profitably expect to operate in the market. Good Management - A market where the monopolist does not set MR=MC because that would allow for entry but instead chooses some other (higher) level of output that deters entry but still allows for positive profits. Note that since the output is higher under monopoly by good management than under other types of monopoly, the welfare costs are, other things equal, lower. Natural Monopoly In order to assess whether a potential entrant to a monopolist's market could expect to profitably enter the market we need a theory about what that entrant would expect upon entry. Sylos Postulate: A potential entrant assumes that the existing monopolist continues to sell the same quantity as before at the same price. Under the Sylos postulate, the entrant expects to be able to work with a residual demand curve arising from the consumers who do not buy from the existing monopolist. e.g. If potential entrant's expectations are consistent with the Sylos postulate, Q D =100-P and TC=12y+FC, for what values of FC is this a natural monopoly?

3 23. Regulation of Monopoly The inefficiency of monopoly creates a potential rationale for government intervention in the market. We'll focus on responses to natural monopolies. Average Cost Pricing: a regulatory agency requires that the monopolist produces at the point where average cost crosses the demand curve. Depending on costs and demand, this could result in too little or too much output. Rate-of-Return Regulation: a regulatory agency sets an upper limit on the monopolist's rate of return on its investment. Plush Carpet Theorem: the notion that these sorts of regulations create incentives for the firm to be deceitful about its costs of production, typically expected to be manifested in the form of perks for management.

4 Monopoly with Alternative Pricing Options When constrained to sell every unit of output at the same price and when this per-unit price is the sole source of the monopolist's revenue, deadweight loss results. If the monopolist has some sort of option(s) involving the ability to charge different prices it may (and generally will) be able to capture some of this deadweight loss as producer's surplus/profit. Similarly for the generation of additional revenue source(s). Price Discrimination 3 types: perfect price discrimination (a.k.a. 1st degree price discrimination), ordinary price discrimination (3rd degree price discrimination), and block pricing (2nd degree price discrimination or non-linear pricing or multipart pricing). Perfect Price Discrimination The monopolist knows each individual consumer's maximum willingness to pay. The monopolist can distinguish between different individual consumers. There are no resale options between consumers. Result: The monopolist charges individual consumers their maximum willingness to pay. The marginal revenue curve coincides with the demand curve. Profit maximization at MR=MC gives the competitive level of output. The outcome is efficient (assuming independence of preferences and costs). Total surplus is maximized. Producer's surplus is equal to total surplus; consumers' surplus is zero. It doesn't get any better from the monopolist's point of view. Ordinary Price Discrimination The consumers can be divided into two or more market segments where: The monopolist knows the demand curves arising out of each market segment considered separately. The monopolist can identify which market segment any individual consumer belongs in. The resale options between consumers (or at least between any two consumers in different market segments) are costly. A standard example of market segments would be children, students, adults, seniors. Independence of preferences suggests that revenue arising out of a market segment can be expressed as a function of output sold in that segment (independent of sales in other segments). If we assume that the cost of providing output in the different segments is the same, then costs of production depend upon the sum of output in all the market segments.

5 Two-segment case: π = TR1( y1) + TR2( TC( y1+ Profit-maximization where π π = 0, = 0 y1 y2 π TR1 TC ( y1+ y1 y1 ( y1+ y1 = + 0 = 0 MR1( y1) = MC( y1+ Similarly: π TR2 TC ( y1+ = + 0 = 0 y2 y2 ( y1+ y2 MR2( = MC( y1+ So we have: MR1( y1) = MR2( = MC( y1+ Graph what this generally looks like. An example: A monopolist sells its patented miracle drug. The market can be usefully divided into two segments: Seniors that, together, have demand for the miracle drug given by: Q DS =100-P and other consumers that, together, have demand for the miracle drug given by Q DA =50-2P. If the monopolist's marginal cost is MC=(1/6)y what price does it charge and how much does it sell in each of the two markets? Note that seniors here have greater demand and end up paying a higher price. There's a relationship here between the price in a market segment and the elasticity of demand: y P 1 P y ε = P y ε = y P P MR = y y + P P P MR = y + P P y MR = P + P P y y P P y ( y P 1) MR = P + 1 ( 1) MR = P + ε Now set the MR's in each market segment equal and see what happens if the price is higher in one market segment:

6 MR P = MR 1 1 ( ε + 1) = P ( ) 1 ε > P ( ε + 1) < ( ε + 1) P < 1 1 ε1 ε2 ε2 ε > 1 1 ε2 < ε1 ε > ε 2 1 So market segment one will have a higher price if and only if demand in less elastic in that market segment (at the relevant points anyway). Does the monopolist increase profits by practicing price discrimination? One way of determining this would be to figure out what the monopolist's profits would have been if it couldn't price discriminate. This tends to be a lot of work. The straightforward linear demand cases will typically produce a kink in the un-segmented demand curve which results in a discontinuity in both the MR and profit functions at that level of output and the possibility that there are two local maximums that need to be considered. This is the textbook's approach (and they mistakenly believe you can aggregate the separate MR curves) and, apart from being a lot of pointless, tedious work, only makes the point for the specific example under consideration. Generally, the argument can be made as follows: If setting the derivatives of profits to zero results in a unique result, this result involves higher profits than any other option the monopolist had. One of those options was to effectively not practice price discrimination by setting the two (or more) prices equal. So it must be better off being able to charge different prices than being forced to charge the same price. Examples of price discrimination (arguably) include: Different rates for seniors, students, children, etc.; predictable sale events; the use of coupons (both the standard clip-and-save ones and the ones you 'win' by rolling up the rim); hard-cover vs. soft-cover books; different rates for flights depending on things like whether there is a weekend spent at the destination; declining prices for new gadgets or fashions; books (academic journals according to Varian) with geographic segmentation; phone and utilities for businesses vs residences and/or different times. Block Pricing The monopolist is able to keep track of how much output each consumer has purchased. The resale options between consumers are costly. The monopolist has the option of charging a given consumer a price that depends upon how much the consumer has purchased. Typical examples of this sort of market include utilities and phone service.

7 Profits here will be higher than the ordinary monopolist facing the same demand and costs of production. A simple example: Consider a monopolist choosing two prices: P 1 applying to the first x units a consumer purchases (x also being chosen by the monopolist) and P 2 applying to the rest of the purchases. MC is constant and each consumer has the same individual demand. If the monopolist chooses P 1 to be the ordinary monopoly price and x to be the ordinary monopoly purchases per consumer then any P 2 less than P 1 (but higher than MC) will capture (as profits) some of what would be DWL under an ordinary monopoly. More generally: one option available to a monopolist practicing block pricing is to choose some P 1 equal to the ordinary monopoly price and other price(s) to sell the ordinary monopoly level of output. If it chooses to do otherwise, we can conclude that this other choice involves more (or at least as much) profit. Two-Part Tariffs This involves a monopolist able to charge both a per-unit price (P) as well as some sort of membership fee (T) necessary for the consumer to pay prior to any purchases. e.g. golf courses, fitness clubs, video rentals?, amusement parks Simple case: Each consumer has the same demand and MC is constant. Result: For any particular P, the profit-maximizing T is the resulting (individual) consumer's surplus. Profit will be the revenue from the membership fees minus any fixed costs (since the revenue generated by per-unit sales will equal variable cost). So the profit maximizing choice of P will be the one that makes the resulting consumers'- surplus-turned-into-membership-fee as large as possible: P=MC. The outcome is efficient since all possible surplus is realized. It shows up entirely as producer's surplus. Be careful extending this to multiple types of consumers: e.g. A market consists of 200 consumers: 100 of which have inverse demand P=10-y and 100 of which have demand P=5-y. If MC=1, what is the profit-maximizing choice of P and T?