The people in Stars Hallow live for 2 periods. In period 0, they are younger. work. and earn a labour income of $1,000. In period 1. they are older and do not earn any labour income. They can save ( S) some part of their labour income in when younger to consume when they are older. They earn an interest of r on their savings. Everyone in Stars Hallow maximize the following (intertemporal)utility function: In Co + B In C1 where C is the consumption and B is the discount rate, e.g., the rate at which individuals discount utility at period 2. (a) (2 points) Without any pension program, what is the optimum ratio of consumption in period 2 to consumption in period 17 Explain the intuition behind this ratio in no more than 3 sentences. (b) (2 points) Suppose that the interest rate is 3%. If the people in Stars Hallow are patient (e.g.. B = 1), what is their optimum amount of savings? (c) (2 points) Assume the interest rate is 3%. If the people in Stars Hallow are myopic (e.g.. 8 =0), what is their optimum amount of savings? Now, suppose that the government of Stars Hallow implements a tax of T = 500 to fund a public pension system. The government taxes everyone in period 1. and pays the tax plus the interest back in period 2. (d) (1 point) How much does patient individuals save? Does the public pension plan make them better-off? (e) (1 point) How much does myopic individuals save? Does the public pension plan make them better-off? (f) (1 point) Considering your findings, do you recommend the government of Stars Hallow to implement this public pension program? Explain your rea- soning using at most 3 sentences