1. [14 marks] Kal and Jo are two farmers who live beside each other. Both of their properties flood in the springtime. However, by spending time digging ditches they can alleviate the damage caused by floods. Let q and q; be the hours each farmers spends digging. Their costs of digging in dollars are Ck - 2(qk) and C, - 2(q;)2. The total benefits in dollars (same for both) are: BK - B, = 120(qk + q; ) + qkq; a. [6 marks] For each person, find the marginal benefits and marginal costs of digging time (given the choice of the other farmer). Use these to find and draw each person's best-response functions. b. [4 marks] Find the equilibrium number of hours each farmer spends digging, and each person's net benefit in equilibrium. Show your work. c. [4 marks] Given your answer in (b), show that if each person doubled the amount of time they spent digging, both people would be better off. Why is this not a Nash equilibrium? Explain briefly