Coase Conjecture
Encyclopedia
The Coase conjecture, developed first by Ronald Coase
, is an argument in monopoly theory
. The conjecture sets up a situation in which a monopolist sells a durable good
to a market
where resale is impossible and faces consumer
s who all have different valuations. The conjecture proposes that a monopolist that does not know individuals' valuations will have to sell its product at a low price
if the monopolist 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 monopolist will have to offer a competitive price in the first period which will be low. The monopolist could avoid this problem by committing to a stable linear pricing strategy or adopting other business strategies .
and 
with valuations
of good
with
and 
respectively. The valuations are such as 
. 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 so that once a consumer buys it, he or she will still have it in all subsequent periods. This means that after the monopolist has sold to all consumers, there can be no further sales. Also assume that production is such that average cost and marginal cost
are both equal to zero.
The monopolist could try to charge at a
in the first period and then in the second period 
, hence price discriminating
. This will not result in consumer
buying in the first period because, by waiting, she could get price equal to 
. To make consumer 
indifferent
between buying in the first period or the second period, the monopolist will have to charge a price of
where 
is a discount factor between 0 and 1. This price is such as 
.
Hence by waiting,
forces the monopolist to compete on price with its future self.
consumers with valuations ranging from 
to a valuation just above zero. The monopoly will want to sell to the consumer with the lowest valuation. 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
where 
is the number of consumers. If the discount factor is high enough this price will be close to zero. Hence the conjecture is proved.
Ronald Coase
Ronald Harry Coase is a British-born, American-based economist and the Clifton R. Musser Professor Emeritus of Economics at the University of Chicago Law School. After studying with the University of London External Programme in 1927–29, Coase entered the London School of Economics, where he took...
, is an argument in monopoly theory
Monopoly
A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity...
. The conjecture sets up a situation in which a monopolist sells a durable good
Durable good
In economics, a durable good or a hard good is a good that does not quickly wear out, or more specifically, one that yields utility over time rather than being completely consumed in one use. Items like bricks or jewellery could be considered perfectly durable goods, because they should...
to a market
Market
A market is one of many varieties of systems, institutions, procedures, social relations and infrastructures whereby parties engage in exchange. While parties may exchange goods and services by barter, most markets rely on sellers offering their goods or services in exchange for money from buyers...
where resale is impossible and faces consumer
Consumer
Consumer is a broad label for any individuals or households that use goods generated within the economy. The concept of a consumer occurs in different contexts, so that the usage and significance of the term may vary.-Economics and marketing:...
s who all have different valuations. The conjecture proposes that a monopolist that does not know individuals' valuations will have to sell its product at a low price
Price
-Definition:In ordinary usage, price is the quantity of payment or compensation given by one party to another in return for goods or services.In modern economies, prices are generally expressed in units of some form of currency...
if the monopolist tries to separate consumers by offering different prices in different periods. This is because the monopoly is, in effect, in price competition
Competition
Competition is a contest between individuals, groups, animals, etc. for territory, a niche, or a location of resources. It arises whenever two and only two strive for a goal which cannot be shared. Competition occurs naturally between living organisms which co-exist in the same environment. For...
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 monopolist will have to offer a competitive price in the first period which will be low. The monopolist could avoid this problem by committing to a stable linear pricing strategy or adopting other business strategies .
Simple two-consumer model
Imagine there are consumers, called and with valuationsValue (economics)
An economic value is the worth of a good or service as determined by the market.The economic value of a good or service has puzzled economists since the beginning of the discipline. First, economists tried to estimate the value of a good to an individual alone, and extend that definition to goods...
of good
Good (economics and accounting)
In economics, a good is something that is intended to satisfy some wants or needs of a consumer and thus has economic utility. It is normally used in the plural form—goods—to denote tangible commodities such as products and materials....
with
and respectively. The valuations are such as . 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 so that once a consumer buys it, he or she will still have it in all subsequent periods. This means that after the monopolist has sold to all consumers, there can be no further sales. Also assume that production is such that average cost and marginal costMarginal cost
In economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. That is, it is the cost of producing one more unit of a good...
are both equal to zero.
The monopolist could try to charge at a
in the first period and then in the second period , hence price discriminatingPrice discrimination
Price discrimination or price differentiation exists when sales of identical goods or services are transacted at different prices from the same provider...
. This will not result in consumer
buying in the first period because, by waiting, she could get price equal to . To make consumer indifferentIndifference curve
In microeconomic theory, an indifference curve is a graph showing different bundles of goods between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another. One can equivalently refer to each point on the indifference curve...
between buying in the first period or the second period, the monopolist will have to charge a price of
where is a discount factor between 0 and 1. This price is such as .Hence by waiting,
forces the monopolist to compete on price with its future self.n consumers
Imagine there are consumers with valuations ranging from to a valuation just above zero. The monopoly will want to sell to the consumer with the lowest valuation. This is because production is costless and by charging a price just above zero it still makes a profitProfit (economics)
In economics, the term profit has two related but distinct meanings. Normal profit represents the total opportunity costs of a venture to an entrepreneur or investor, whilst economic profit In economics, the term profit has two related but distinct meanings. Normal profit represents the total...
. Hence to separate the consumers, the monopoly will charge first consumer
where is the number of consumers. If the discount factor is high enough this price will be close to zero. Hence the conjecture is proved.Further reading
- Coase, Ronald. "Durability and Monopoly" in Journal of Law and Economics, vol. 15(1), pp. 143–49, 1972.
- Orbach, Barak. "The Durapolist Puzzle: Monopoly Power in Durable-Goods Market" in Yale Journal on Regulation, vol. 21(1), pp. 67–118, 2004.