(25 points) The tiny neighboring countries of Homewood and Peabody have strict isolationist policies that prohibit international trade. In each country, the main food staple is carrots. The demand curve for carrots in each country is Q = (12 - P). Each country is served by its own carrot monopolist. Each of these monopolists has a cost function of C(q) = q. (a) Find the profit-maximizing price and quantity in each country. i. What are the monopoly profits (total across the two countries)? ii. What is the consumer surplus (total across the two countries)? iii. What is the dead-weight loss (total across the two countries)? (b) A new treaty is signed that opens up trade between the two nations. Now both firms can sell in both countries. i. What is the market demand curve for the new, integrated two-country market? ii. What is the Cournot equilibrium quantity for each firm now? What is the market price? iii. What are the profits of each firm now? What is the Consumer surplus? What is the Deadweight loss? iv. Who did the policy help? Who did it harm? What happened to the total economic value created in the carrot market(s) as a result of the policy? Explain.