You have a utility function for consumption in each period U (C) = 1-1/2C^-2 , rate of time preference of 0.3 (approximately 0.96 per year), and will live for two periods (each period is approximately 30 years in length). At the beginning of the first periods you receive a wage of one million dollars. You must decide how much to consume now and how much to save for next period (retirement) to maximize the present value of utility (the sum of utility in the first period and utility in the second period discounted by the rate of time preference). Assume that the interest rate between time periods is 80%.

a) What is your utility maximization problem in terms of Ct and Ct+1?

b) How are income and consumption in period one related to consumption in period two?

c) What is the optimal level of consumption in the first period and what is the optimal fraction of income to save for retirement?

d) How does this fraction change if the rate of time preference between time periods is 0.2 (approximately 0:95 per year)?

e) If this model is a reasonable approximation of the real world, do you think most people are saving enough for retirement? Why or why not?

[Hint: Discuss mandatory savings programs