Coase Conjecture

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Coase Conjecture is the idea developed first by Ronald Coase. The conjecture says that if a normal monopoly which sells a durable good to a market where resale is impossible and faces consumers which all have different valuations without the monopoly knowing individual's valuations, the monopoly will have to sell at a very low price if the monopoly tries to separate consumers by offering different prices in different periods. This is because the monopoly is in effect in price competition with itself over several periods and the consumer with the highest valuation, if he is patient enough, can simply wait for the lowest price. Thus the monopoly will have to offer a competitive price in the first period which will be very low. The monopoly could avoid this problem by committing to a stable linear pricing strategy or adopting other business strategies [1].

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[edit] Simple two consumers model

Imagine there are consumers, called X and Y with valuations of good with x and y respectively. The valuations are such as x < y and 2x < y. The monopoly cannot directly identify individual consumers but it knows that there are 2 different valuations of a good. The good being sold is durable which means ones a consumer buys it it will still have it in the all subsequent periods. This means after the monopoly has sold to all consumers there are no more sales. Also assume that production is costless such as average cost and marginal cost is zero.

The monopoly could charge at a price = y in the first period and then in the second period price = x hence price discriminating. This will not result in consumer Y buying in the first period because by waiting it could get price equal to x. To make consumer Y indifferent between buying in first period and second period monopoly will have to charge a price of price = dx + (1 − d)y where d is the discount factor between 0 and 1. This price is such as dx + (1 − d)y < y.

Hence by waiting Y forces the monopoly to compete on price with it future self.

[edit] n consumers

Imagine there are n consumers with valuations ranging from y to a valuation just below zero. The monopoly will want to sell to the consumer with the lowest valuation consumer. This is because production is costless and by charging a price just above zero it still makes a profit. Hence to separate the consumers the monopoly will charge first consumer (1 − dn)y where n is the number of consumers. If the discount factor is high enough this price will be close to zero. Hence the conjecture is proved.

[edit] References

  1. ^ http://papers.ssrn.com/sol3/papers.cfm?abstract_id=496175 [Orbach (2004)

[edit] Further reading

  1. Coase, Ronald. "Durability and Monopoly" in Journal of Law and Economics, vol. 15(1), pp. 143-49, 1972.
  2. Orbach, Barak. "The Durapolist Puzzle: Monopoly Power in Durable-Goods Market" in Yale Journal on Regulation, vol. 21(1), pp. 67-118, 2004.