Consider a household choosing a plan for current consumption C, and future consumption C, according to the Fisher model

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Consider A Household Choosing A Plan For Current Consumption C And Future Consumption C According To The Fisher Model 1 (104.67 KiB) Viewed 25 times

Consider a household choosing a plan for current consumption C, and future consumption C, 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 ig- 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) Noting that the budget constraint on future consumption C, is C₂ Y₂ + (1+r)(A + S), show how the following present-value budget constraint is derived: CA G₁+1+r =A+Y₁+ Y₂ 1+r (b) 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) Suppose that owing to better macroeconomic policies, income Y₁ increases and that income is expected to be permanently higher, so Y₂ 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)f the value of the household's initial assets A increases, does the model predict that current consumption C, rises by: (i) more than A, (ii) less than A, or (iii) the same as A? Explain your answer. W 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) T 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 Y, but leaves Y₂ unchanged. (f) 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?