Q5

Question 5 Two rms 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 rm has a constant marginal cost of 0.2 a unit. Hence, if rm 3' produces (15 units it incurs a production cost of 0.29:. You have an invention that will lower the costs of producing Soma. With your technology the cost of producing q units of Some will be 0.1g. 1. Suppose rm 1 only adopts your technology and pays you a share 1' of their revenue. Firm 2 does not adopt your technology. What will equilibrium prots for each rm be? The answer will be a function of r. 2. Suppose both rms 1 and 2 adopt your technology and each gives you a share 1' of their revenue. What will equilibrium prots for each rm be? The answer will be a function of r. 3. Suppose you offer the technology to both rms simultaneously for a share 1" of their revenue. 'What value of 1' should you set to maximize your gain? To help your thinking, ll in the table below with the prots that each rm will earn depending on whether they accept or reject your offer. Firm 2 Accepts Firm 2 Rejects Firm 1 ejects