Q4 . Rachel and Michele are flatmates and they just moved into a flat on Heriot Row. For extra f40 per month, they have the option to access Queen Street gardens. Either one of them can pay the full sum or they can split it evenly. In any case when the access is purchased neither of them can prevent the other one from walking in the park. Michele thinks that if they have access to the park, she will spend less time in various cafes and estimates the benefit to her to be f30 per month. The ability to walk through the park would shorten Rachel's way to work and she would use public transport less often. She thinks the monetary benefit to her is f25 per month. To make the decision Rachel and Michele agreed to simultaneously send text messages to their landlord. If both messages say "agree" they split the costs, if only one of the messages says "agree" the person who sends it pays the full sum, if neither message agrees to pay, they don't get access to the gardens. a) Write down the payoff matrix for the problem. [4 marks] b) Find the Nash equilibrium. Will they purchase the access? [3 marks] c) Is the outcome socially optimal (consider Rachel and Michele to be the whole society)? If not, what is the problem that results in the socially suboptimal outcome? If yes, what is the mechanism that allows them to avoid sub-optimality? [3 marks]