Durable goods monopolist

Jeremy I. Bulow

Kishore Kumar Gangwani

Coase conjecture: A monopolist selling good has no monopoly power.

• Although Q1 is optimal output of the monopolist, it faces a residual demand of BC in the future. At that time the optimal quantity is (Q2-Q1) and price is lower, and so on.

• If this is true, then consumers (foreseeing this) will wait for the future low price, rather than buy it at P1 . If the period of waiting is short enough, then monopolist will be reduced to a competitive firm.

Why?

Then what should a monopolist do?

Bulow (1982)

There are many ways out for the monopolist. • Rent rather than sell the good. • Planned Obsolescence • price guarantee • service contract • implicit contract (reputation)

What are durable goods? • Products that yield a flow of services to the owner over a

given period of time. • Also includes products whose current demand depends

upon their previous demand (ticket).

Difference between a renter and a seller

• If a renter produces much, then he suffers the loss from old units. Cost of production is thus internalized.

• If a seller produces much, then the loss of overproduction is born by the purchasers. Thus he is tempted to produce too much in the future.

• Expecting this, current buyers are only willing to buy the good with lower price.

• Sometimes, the monopoly renter is able to make as much profit as a non-durable good monopolist.

Model

• 2 periods, one monopolist.

• Cost of production: 0

• One period rental price: p

• Interest rate:ρ

• Demand for service: p=α-βq

• Quantity produced by the competitive industry at period i:qiC

• Quantity produced by monopolist renter at period i : qiR

• Quantity produced by monopolist seller at period i: qiS

Competitive Case

Maximize q1C(α-βq1C)+ q2C(α-βq2C)

Solution:

q1C =(α/β),

q2C =0

profit =0,

price=MC=0

Monopolist Renter

Solution:

q1R =(α/2β),

q2R =0

price= α/2

Profit= (α/2β)(α/2)=(α2/4β)

Monopolist Seller

• Suppose a quantity of q1S was sold in period 1, then the effective demand in period 2 is

α-β(q1S +q2S)

• To maximize period 2 profit, the monopolist sets

q2S = (α-βq1S)/2β

• Anticipating this, in period 1 the consumer is only to demand the commodity with price P1

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Monopolist Seller…

Now the problem of the monopolist is :

Comparing profits of monopolist seller and renter

Comparing quantities if monopolist’s selling and renting situations:

If we compare profit ‘s of monopolist seller and renter , we can say that:

The profit of monopolist is strictly lower in case when it sells.

If firms can invest in technologies

Let one time sunk cost is F(c)

Marginal cost is c

Then monopolist seller’s profit equation is :

For ρ =0, solution is:

Why Planned Obsolescence?

• Results have shown that monopolist renter can make more money than monopolist seller.

• If a monopolist produces less durable goods , the monopolist seller , becomes more like a monopolist renter.

• As we know that renter provides services for his market one period at a time.

• Hence monopolist seller can make the same profits by producing goods that last for only one period , i.e., less durable.

Model with constrained capacity

• Assumptions:

Capacity can be constructed costlessly, but can not be destroyed.

Infinite time horizon.

• Let demand curve is exponential;

pT=αe-βQT

Where, rental price is p and QT=∫qT

• Firms problem can be written as :

• Profit maximizing solution is :

q= ρ/β

Profit = α/4ρβ

Extensions

1. Price Guarantees

2. Service contracts

3. Implicit contracts: such as reputation (example DeBeers)

Thank You