Alphonse, A, and Brigitte, B, are food farmers. Each can produce 2 units of food for every hour that they work, denoted by ly with J E {A, B}. They also have access to an oven to turn food into ready meals. This requires 2 units of raw food for each ready meal produced. Alphonse and Brigitte have preferences r +2/Tj - (1,) where rj is raw food consumption and yj is consumption of ready meals. (a) Set the price of raw food to one and let p be the price of ready meals. How much food will Alphonse and Brigitte produce and consume? (b) Show that the equilibrium price of ready meals is 2. How much trade takes place at the equilib- rium prices? (c) Suppose that Brigitte invents a new method of farming at a cost of 2 and can now produce 4 units of food for every hour of work. How much does she gain from the new technology and will she choose to pay the cost of the new technology? (d) Suppose that Alphonse can copy Brigitte's new technology if she invests without having to pay the cost of 2. Explain why this makes the new technology a public good. Who gains/loses from this? (e) Now suppose that both Brigitte and Alphonse could choose to invest in the new technology where, if one invests, it is available to both. Write down the payoff matrix representing their decisions and compute the Nash equilibrium. What is the probability that the new technology is used? What is the probability that they both invest in the technology? Is the Nash equilibrium Pareto efficient? Explain. (f) Is there a case for government intervention to invest in the new technology and what form should it take? In answering, feel free to draw on the course reading.