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 JE { 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 ry + 2,/y -= (ly)" where cy is raw food consumption and y is consumption of ready meals. 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. [15 marks]