3. Rodrigo is taking a year between high school and college to work and save up. His utility from consumption each year is U(ct) = _,, and he discounts future utility by B. Rodrigo is going to make $1 this year of working, and whatever he doesn't consume from that income will go into a savings account which will earn return r.a. What is Rodrigo's intertemporal budget constraint? b. Set up his intertemporal utility maximization problem and take first order conditions. c. For simplicity, assume Rodrigo discounts the future by B = 1 Itr ' Solve for optimal ci and c2 as a function of Income I and return r. d. The Fed has been increasing interest rates and now Rodrigo is getting higher savings rate offers from banks. How does this affect his optimal consumption this year and next year? e. If Rodrigo gets a scholarship for $E for each of his four years of college, what is the present discounted value of the scholarship