12. 13. 14. What is the marginal rate of substitution of current consumption for future con- sumption MRS\": given this utility function? How does it change with c and c\"? Solve the household's optimization problem with the lifetime budget constraint. That is, find the household's optimal current consumption 0 and future consump- tion 0' in terms of (y, y', t, t', r, ,8). You can solve the household's problem with El- THER of the two methods below. (You DO NOT need to do both.) (a) Solve the system of two equations in two unknowns ( c and c') defined by the two optimality conditions in Question 9. (b) Solve the household's problem with the method of Lagrange multipliers. From your answer to the last question, what is the household's savings 5 in the current period? Your answer should be in terms of (y, y', t, t', r, [3)