Price Competition

Bertrand Model

Assumptions Homogenous good both firms: C1 = C2 = $0 Consumers are willing to pay $10. The total number of consumers is N.

Price Competition

How will consumers respond to a price differential?

Price Competition.

The Nash equilibrium:

P1 = P2 = $0

0

There are N consumers, and each of them is willing to pay $10 for the product.

If the two firms can cooperative, P=$10, Profit1=Profit2= $10*N/2

But how can they achieve it? Price collusion – but it is usually

illegal & difficult to maintain.

How to change the game? How to achieve the collusive

outcome more easily?

1. Upstream Joint Company

F1 & F2 form a joint company U, providing a key input to both firms.

Without the key input, F1 & F2 cannot produce.

After F1 & F2 buy the key inputs from the joint company, they continue to engage in the price competition.

When the joint firm sells the key input at X, their unit production costs become X, respectively.

The price competition brings the final price X. Each firm does not make any profit from the final sales.

However, the joint company makes X*n profits by selling the key input to the two firms.

F1 & F2 have ½ shares of the joint firm.

Thus, the final profit by each firm is ½ X*n.

What is the optimal X? That’s is $10. The profit level for the joint firm is 10n.

The two firms split the profit equally, and each firm’s profits = 10*n/2.

2. Cross Licensing Firms 1 and 2 have similar

technologies. They make licensing contracts

each other. Licensing fee is r. Production cost is increased by r.

A cross-license is simply an agreement between two companies that grants each the right to practice the other’s patents.

Rather than blocking each other and going to court or ceasing production, the two enter into

a cross-license.

The patent system, while surely a spur to innovation overall, is in danger of imposing an unnecessary drag on innovation by enabling multiple rights owners to “tax” new products, processes and even business methods.

The vast number of patents currently being issued creates a very real danger that a single product or service will infringe on many patents.

The essence of science is cumulative investigation combined with hypothesis testing. The notion of “cumulative innovation,” each discovery building on many previous findings, is central to the scientific method.

Government Concerns Anti competitive effects Pro competitive effects

Double mark-up problem If the two technologies are

complementary with each other, there is a double-mark up problem.

Connection Fee

1) AT&T and competitorsIn the past, AT&T declined a

connection between AT&T and other local firms. However, by law, it must allow the connection.

Connection Fee

2) Cellular Phone and Fixed LineWhen someone makes a call from a

cellular phone to a fixed line, he pays service fees to the cellular service provider. However, as the call is connected to the fixed line phone, the cellular service provider must pay some amount of fees to the fixed line company.

Connection Fee

3) Long Distance Call or International CallWhen we make a phone call to New York,

we pay service fees to HK phone companies. However, as the phone call is connected to New York, using the phone networks of New York, HK phone companies need to pay some amount of fees to US companies.

Connection Fee

Questions: What is the strategy use of connection

fees? Under deregulation, can we allow

telephone firms to choose the fees?

Telecommunication Two telephone service sectors: A and B The cost of providing each service is c. There are multiple firms in each sector. Suppose that consumers are in

sector A, and (1-) are in sector B.

We assume a balanced calling pattern.

That is, the traffic inside sector A is .

The out-going traffic from sector A to sector B is (1- ).

The out-going traffic from sector B to sector A is (1- ).

Telecommunication The connection fee is denoted by

a. The cost of serving each customer

in sector A: *c+(1-)*(c+a) = c+(1-)*a

Note that the cost increases with a.

When several firms compete each other to get customers in each sector, the price will go down to the cost, c+(1-)*a.

Profits in sector A= [p- c+(1-)a ]+ (1-)a = (1-)a.

Profit comes from only the access fee sector, not from your own customers.

Telecommunication From your own customers, the net

profit is zero, because the price is the same as the cost.

However, there is a transfer from firms in the other sector. Actually, you make money from customers on the other Telephone Company.