Consider a two-period closed economy composed of a continuum of mass 1 of identical consumers. The representative consumer's utility function is U(C, C') = log(C) + log(C') 1 + p where C is current consumption, C' is future consumption, and p is the rate of time preferences, p > 0 The representative consumer receives a stream of income Y in the current period and Y in the future period. Given the real interest rate, r, she decides how much to consume in the current and future period. The model has no capital, only consumption goods. 1. What are the consumer's current and future budget constraints? Comment. 2. What is the consumer's lifetime budget constraint? Comment. 3. Write down the consumer's problem. Comment. 4. Use the Lagrangian method to compute the three first order conditions. 5. Compute the Euler equation. How do r and p affect future consumption? Comment