It is the start of the mobile phone era. The Australian government is selling "mobile phone spectrum": A mobile phone company that wants its customers to be able to send and receive mobile phone signals in Sydney must buy the right to send/receive signals on spectrum in the Sydney area. The government is selling only 1 license for Sydney and 1 for Melbourne, and no other licenses will ever be sold. The government incurs no costs in providing a license, so its WTS is 0.

Imagine that there are only two populated locations in Australia, Sydney and Melbourne, and two mobile phone companies.

• Telstra will have 2 million customers if it has coverage in Sydney and in Melbourne, because customers will get a lot of utility from being able to use their mobile phones in both cities. (For instance, Sydney residents enjoy being able to use their mobile phones in Melbourne when they travel to Melbourne for work or for holidays.) But Telstra will have 1 million customers if it has coverage in Sydney only, and 500,000 if it has coverage in Melbourne only.
• Optus will have 1.5 million customers if it has coverage in Sydney and Melbourne, because customers will get a lot of utility from being able to use their mobile phones in both cities. Optus will have 300,000 customers if it has coverage in Sydney only, and 700,000 customers if it has coverage in Melbourne onlymost of the interest in Optus is from Melbourne residents.

Each company earns $70 per customer, in present value.

It is 1994, and currently no mobile phone towers have been built.

a. The government sits down with Telstra and Optus, and the three of them negotiate over these licenses. Who gets the Melbourne license? Who gets the Sydney license? (Both licenses can go to the same firm, or the licenses can go to different firms.) Show your calculations.

b. What is the range of possible payments to the government from these negotiations?