Lecture 4: Monopoly. Daniel Zhiyun LI. September Durham University Business School (DUBS)

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1 Lecture 4: Monopoly Daniel Zhiyun LI Durham University Business School (DUBS) September 2014

2 Plan of the Lecture Introduction The Problem of Monopoly Price Discriminations

3 Introduction the other extreme case is monopoly A monopolist is the only supplier of a certain product in a market It is a price maker, yet subject to the constraint of market demand To set the pro t maximizing price / quantity on the demand curve

4 Introduction Why does monopoly exist? Barriers to entry: not possible for other rms to enter a market. patent; government regulations, restricting market entry; Increasing returns to scale (natural monopoly): the more you produce, the lower the average cost the most e cient way of production is monopoly electricity supply (industries with large xed cost)

5 The Problem of a Monopolist Reminder: the problem of a competitive rm max q p q c (q) where p is the market price, which is xed. The Problem of a Monopolist max q p (q) q c (q) price p no longer xed, determined by the inverse demand curve p (q); p (q) is normally downward sloping) q " implies p #

6 The Problem of a Monopolist (2) The Problem of a Monopolist max q p (q) q c (q) the rst order condition p (q) + p q q = c q MR = MC, exactly the same condition as in competitive case! Marginal Cost: MC = q c Marginal Revenue: MR (q) = p (q) + p q q p (q): unit price p q q: selling one more item will decrease the price at which the rm can sell all it s output

7 The Problem of a Monopolist (3) marginal revenue is lower than demand curve as p/ q < 0; monopoly outcomes (q m, p m ) and competitive outcomes (q e, p e ) q m < q e p m > p e marginal revenue monopoly outcomes

8 The Problem of a Monopolist (4) Welfare Implications: consumer+producer surplus competitive economy: A + B + C + D monopoly economy: A + B + D welfare loss in a monopoly economy

9 The Problem of a Monopolist (5) The optimal price for the monopolist h i p (q) 1 + p q q p = c q if de ne the price elasticity of demand (PED) ε (q) = p (q) [1 1/ε (q)] = MC (q) The optimal monopolistic price is thus q p p q, then p (q) = MC (q) 1 1 ε(q) > MC (q) mark up that a monopolist charges over marginal cost is dependent on ε (q): more elastic demand ) lower mark up.

10 The Problem of a Monopolist (5) Example A linear example: demand p (q) = a pro t function is thus bq and cost c (q) = cq, a > c, the π (q) = p (q) q c (q) = (a bq) q cq the rst order condition π q = a 2bq c = 0 The monopoly price and output are q m = a c 2b p m = a + c 2

11 Price Discrimination: Introduction So far, we restrict to the case where the monopolist can just charge ONE price to all the consumers; However, in the case of monopoly, the monopolist can adopt various kinds of pricing strategies as now price is now his control variable to explore more consumer surplus and achieve greater pro t We here examine some of the most common cases of price discrimination of a monopolist

12 Price Discrimination: Two-Part Tari Example Two-Part Tari consists of two fees: A xed fee for joining the service, i.e. membership fees then an additional fee every time you use the service - i.e. pay-as-you-go mobile phone tarrifs Is this a good idea? Can the monopolist achieve greater surplus? Again, a linear example: demand p (q) = a bq and cost c (q) = cq, a > c. Suppose the monopolist takes the following two-part tari pricing strategy: 1) Fixed Fee: T = 1 (a c) 2 2 b ɛ 2) Additional Unit price: p = c

13 Price Discrimination: Two-Part Tari Example (a c) 2 b ɛ; 2) The following two-part tari pricing strategy: 1) T = 1 2 p = c, extracts nearly all the consumer surplus. The rm is maximizing total surplus, by setting price equal to marginal cost, then extracting the whole surplus with the xed cost it charges the consumer. And the outcome is e cient! Comparison with the uniform monopolistic price: p m = a+c 2.

14 Price Discrimination: 1st Degree Price Discrimination So far, the case of only one consumer, or all consumers are identical; How if consumers are heterogenous, and have di erent willingness to pay for a product? What is the ideal pricing strategy for the monopolist? 1st degree price discrimination: charge each consumer s willingness to pay for di erent unit of the product ) extract all consumer surplus the problem is Z q max π (q) = p (x) dx cq the optimal condition is π 0 (q) = p (q) c = 0 ) q = q e! 0

15 Problems with 1st Degree Price Discrimination It s perfect for the monopolist! What are the problems? perfect information about consumers preferences! strong implementation power of the monopolist (charge di erent prices to di units, di people) no re-sale markets. Figure: 1st degree price discrimination

16 Price Discrimination: 3rd Degree Price Discrimination 3rd degree price discrimination : prices varies by attributes such as location, or by consumer groups monopolist knows the attributes within each attributes or groups, prices are the same e.g. student discount, international edition textbooks

17 Price Discrimination: 2nd Degree Price Discrimination 2nd degree price discrimination means charging di erent unit prices for di erent quantities, e.g. larger quantity at lower unit price (non-liner pricing); price di er across the quantities of the good, but not across people.

18 Price Discrimination: 2nd Degree Price Discrimination Let s consider a less information demanding situation The monopolist knows di erent groups of consumers present in a market It knows di erent groups demand curves, but cannot tell which consumer in which group Second Degree Price Discrimination O ering various (price-quantity) packages to all the consumers and let di erent groups of consumers self-select the package they prefer.

19 Price Discrimination: 2nd Degree Price Discrimination Example Suppose there are two groups of consumers of equal size in the market, and their demand functions are respectively D 1 (q) = a bq D 2 (q) = a dq and b < d. If the monopolist can perfectly tell the two di erent groups, he can provide the following two packages for group 1 and 2 consumers respectively: 1) charges A + B + C + D + E + F on group 1 for the quantity of q 1 2) charges A + D on group 2 for the quantity of q 2 and it extract all the consumer surplus of the two groups

20 Price Discrimination: Second Degree Price Discrimination Example (continued) However, if it cannot tell them apart, what will happen in this case? Group 1 will choose the package designed for Group 2, as their net consumer surplus is now B > 0. So when designing the optimal schemes of 2nd degree price discrimination, the monopolist needs to consider the incentive compatible constraint.

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