Question
Consider a household in the two-period consumption-savings model. The household has well-behaved preferences over period-1 and -2 consumption given by u(c1,c2), is are con- strained
- Consider a household in the two-period consumption-savings model. The household has well-behaved preferences over period-1 and -2 consumption given by u(c1,c2), is are con- strained by their period budget constraints, At = (1 + i)At1 + Yt Ptct for t = 1, 2.
(a)Use the Fisher Equation to transform the period budget constraints into real terms. (HINT: You may convert one period budget constraint directly, say for t = 1, and generalize to the other.)
(b)Use your answers from part (a) to derive the Lifetime Budget Constraint (LBC) in real terms. Assume the initial and terminal conditions a2 = a0 = 0.
(c)Use indifference curve analysis to graphically locate the optimal choice (c1, c2). Label slopes and intercepts on your graph.
(d)Locate on the budget constraint for your graph in part (c) a potential point for the combination real income (y1,y2) that implies the household is a saver in period 1.
(e)For each of the following assumptions, use indifference curve analysis to illustrate how a decrease in the real interest rate affects optimal choices of consumption (c1,c2)
and period-1 savings, spriv, starting from a situation as drawn in your graph for part 1
(d). Conclude whether the household is better or worse off from the shock.
To keep things from getting too messy, you should use a different diagram as drawn in part (d) for each shock, but omit the slope and intercept labels. Keeping the location for (c1, c2) and (y1, y2) will be helpful.
- i. The income effect dominates the substitution effect
- ii. The substitution effect dominates the income effect
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