5. Consider a household choosing a plan for current consumption C1 and future consumption C2 according to the Fisher model with two time periods. Both current and future consumption are assumed to be normal goods. The household receives current income Y1 and expects to receive future income Y2. Taxes and transfers may be ignored in this question. The household's net saving in the current period is S=Y1C1, and the real interest rate on any saving or borrowing between the current and future time periods is r. Assume the household already has incurred debts D (including interest) that are due for repayment in the current time period. Given saving S, the net debt of the household at the end of the current period is DS. The budget constraint on consumption in the future time period is C2=Y2(1+r)(DS). (a) [2 marks] Using the budget constraint on C2 and the definition of S, derive the present-value budget constraint of the household in terms of C1 and C2. (b) [3 marks] Illustrate the budget constraint in a diagram with C and C2 on the axes. What is its gradient? What point does it pass through for every possible interest rate r ? (c) [2 marks] Illustrate the household's indifference curves and the optimal choice of consumption plan in a diagram for the case where the choice of saving S is positive, but less than existing debt D. Suppose there is an increase in the interest rate r. In what follows, assume that the household is initially choosing saving S with 0