Answer Happy

9. Consider a household choosing a plan for current consumption C, and future consumption C₂ according to the Fisher model with two time periods. Both cur- rent and future consumption are assumed to be normal goods. The household receives current income Y, and expects to receive future income Y₂. You may lg- nore taxes and transfers in this question. Household saving is S - Y₁ - C₁, and the real interest rate received on any saving is r. Assume here that the house- 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 C₂ is C₂ = Y₂ + (1 + r) (A+S), show how the following present-value budget constraint is derived: C₁+ =A+Y₁+ Y₁₂ 1+r 1+r (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 Y₁ increases and that income is expected to be permanently higher, so Y₂2 rises by the same as Y₁. Following this, explain whether current consumption C₁ rising by the same amount as income Y₁ 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 C₁ rises by: (i) 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-A. Suppose the household faces a temporary negative income shock, for example, a period of unemployment. This reduces Y₁ but leaves Y₂ unchanged. (f) [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?