Two firms compete in a Bertrand-Hotelling fashion in the sale of Soma. 1000 customers are uniformly distributed on the line between 0 and 1. Seller 1 is at the left endpoint, i. e. at 0 and the seller 2 at the right endpoint, i. e. at 1. Travel costs for consumers are $1 a unit per mile. Each firm has a constant marginal cost of 0.2 a unit. Hence, if firm i produces qi units it incurs a production cost of 0.2qi. You have an invention that will lower the costs of producing Soma. With your technology the cost of producing q units of Soma will be 0.1q.

Suppose firm 1 only adopts your technology and pays you a share r of their revenue. Firm 2 does not adopt your technology. What will equilibrium profits for each firm be? The answer will be a function of r.

Suppose both firms 1 and 2 adopt your technology and each gives you a share r of their revenue. What will equilibrium profits for each firm be? The answer will be a function of r.

Suppose you offer the technology to both firms simultaneously for a share r of their revenue. What value of r should you set to maximize your gain? To help your thinking, fill in the table below with the profits that each firm will earn depending on whether they accept or reject your offer.

Firm 2 Accepts Firm 2 Rejects
Firm 1 Accepts
Firm 1 Rejects