function Consider a consumer with a lifetime utility U u(C)+ Bu(C++1) that satisfies all the standard assumptions listed in the book. The period t and t+1 budget con- straints are Ct + St=Y C++1 + St+1=Y++1 + (1+r)St (a) What is the optimal value of St+1? Impose this optimal value and derive the lifetime bud- get constraint. (b) State the Euler equation. Explain the economic intuition of the equation. (c) Graphically depict the optimality condition. Carefully label the intercepts of the budget constraints. What is the slope of the indifference curve at the optimal consumption baskets, (Ct, C++1)? (d) Graphically depict the effects of an increase in Y+1. Carefully label the intercepts of the budget constraint. Is the slope of the indifference curve at the optimal consumption basket, (C, C+1), different than in part (c)? (e) Suppose Ct Yt, how will the optimal consumption basket, (C, C++1) change? Explain in words, using the graph.