.'2. Consider a censumer with a lifetime utility function We, 6') = \"(6} + WE") that satises all the standard assumptions listed in the book. The period 1 and 2 budget constraints are (a) What is the optimal value of s"? Impose this optimal value and derive the lifetime budget constraint. {b} Derive the Euler equation. Explain the economic intuition of the equation. (c) Graphically depict the optimality condition. Carefully label the intercepts of the budget constraint. What is the slope of the indifference curve at the optimal pointJ {c*, cl\")? {d} Graphically depict the effects of an increase in 3.". Carefully label the intercepts of the budget constraint. Is the slope of the indifference curve at the optimal pointJ {c*, cl") dierent from before