Question

Suppose we are in a two-period environment where the representative consumer has a utilit;y function of the form: Let the discount factor, β , represent the idea that the consumer values consumption at the future with some weight less than 1. Let initial assets, a 0 and the households income in the two periods be given as y,-5, y,-10. The real interest rate in this economy, r is equal to .1 (ie 10% return on any wealth saved). 1. Intuitively, why do we only need to consider the savings choice in period if this consumer lives for two periods? (Financial markets don't disappear when one is old, right?) 2. Solve for the consumer's allocations, (ie, ci, c2, a1). Is our consumer a saver or a borrower, and does this make sense intuitively? 3. Suppose now consumers are no longer allowed to be in debt following period 1 (ie a1 2 0 must hold). You may think of this either as banks imposing a strict limit on lending or government regulations prevent households from being leveraged. What are the new allocations? Explain 4. Is this borrowing limit welfare reducing, enhancing, or neutral? Explain intuitively, then compare utility levels in both environments.