Answer Happy

9. Consider a household choosing a plan for current consumption C, and future consumption C, according to the Fisher model with two time periods. Both our rent and future consumption are assumed to be normal goods. The household receives current income Y, and expects to receive future income Ys. You may ig nore taxes and transfers in this question. Household saving is S-Y₁ the real interest rate received on any saving is r. Assume here that the house- C₁, and hold has already accumulated assets of positive value A at the beginning of the current period. (a) [3 marks] Noting that the budget constraint on future consumption C, is G=Y₂ + (1+r)(A + S), show how the following present-value budget constraint is derived: (b) [3 marks) Illustrate the present-value budget constraint and the household's indifference curves in a diagram and explain how the optimal consumption plan is found. (c) [3 marks] Suppose that owing to better macroeconomic policies, income Y, increases and that income is expected to be permanently higher, so Y, rises by the same as Y₁. Following this, explain whether current consumption C rising by the same amount as income Y, is inconsistent with the model. (d) [3 mark] If the value of the household's initial assets A increases, does the model predict that current consumption C, rises by: (1) more than A, (ii) less than A, or (iii) the same as A? Explain your answer. In what follows, consider a household that was initially planning to dis-save, that is, spend more than income in the current period (C₁ > Y₁). (e) [4 marks] If the real interest rate r rises, does the model predict that the household will unambiguously consume less in the current time period? (Hint: observe that the budget constraint always passes through the point with coordinates (A + Y₁, Y₂).] Assume the household is unable to borrow. Mathematically, this requires that S2-1. Suppose the household faces a temporary negative income shock, for example, a period of unemployment. This reduces Y, but leaves Y₂ unchanged. (1) [4 mark] Illustrate the effect of the borrowing constraint on the set of fea- sible consumption plans. How might households with low A or high A re- spond differently to the income shock?