Problem 2. A group of scientists discover a new carbohydrate-free strand of rice. They have a patent, but rms are freely able to license the patent. Together, with the licensing fee, the cost of producing this rice is the same for every potential rm that may enter, and it is C,(q,-) = 5000 +40q, for 2' = {1, 2, . . . ,N}. Total demand for a ton of carb-free rice in the United States is described by P = 400 Q, where Q is the total quantity (in tons per week) produced by all rms in the market. Any rms that enter this new market will compete in simultaneous Cournot competition. 1. Write the prot of a given rm 2' as a function of the other amount of carb-free rice that is producted, Q_,-. 2. What is the best response function of this rm 73, as a function of Q_,-? 3. Let's suppose that N new rms decide to enter this market. How much rice will each of the N rms produce? 4. What is the equilibrium price now that these N rms are all offering the prod- uct? And what is each rm's prot? 5. If an additional rm were to enter the market, would the prots of the existing rms increase or decrease? 6. (Not graded) There are many many producers of the existing (carb-full) kinds of rice in the US, and they all have access to this technology. In a long run equilibrium, how many rms should we expect to be offering this new strain of carbfree rice? 7. (Not graded) In Mexico, there are twice as many rice consumers as there are in the United States. Write the inverse demand function for Mexico. (Hint: It may be easier to work with Q(P) than P(Q)) 8. (Not graded) How many rms should we expect to offer this product in Mexico? Without solving it all out, can you provide an upper bound