9. Consider the two-period problem with income risk and quadratic preferences we studied in class. Assume...

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9. Consider the two-period problem with income risk and quadratic preferences we studied in class. Assume that there're more than two states of the world, s = 0, 1,...,S, S > 2; assume also that 3(1+r) = 1 and Ao = 0. We have shown in class that consumption at time 0 will equal 1+r 2+r Yo + E[₁] 1+r) where E[₁] = 7(0)y₁ (0)+7(1)y₁ (1) +...+(S)y₁ (S). (a) Argue that consumption at time 1 will equal consumption at time 0 only in those states of the world in which y₁ (s) = E[₁]); in other words, consumption at time 1 will equal consumption at time 0 only if expectations are fulfilled. (Hint: use the relation c₁ (s) = y₁(s) + so(1+r) for any state s = 1,..., S, and evaluate the formula for optimal saving for a state where y₁(s) = E[₁].) (b) Argue that consumption at time 1 will never equal consumption at time 0 if there're only two states of the world (S = 2) with distinct realizations of income, that is, y₁ (0) ₁ (1). 9. Consider the two-period problem with income risk and quadratic preferences we studied in class. Assume that there're more than two states of the world, s = 0, 1,...,S, S > 2; assume also that 3(1+r) = 1 and Ao = 0. We have shown in class that consumption at time 0 will equal 1+r 2+r Yo + E[₁] 1+r) where E[₁] = 7(0)y₁ (0)+7(1)y₁ (1) +...+(S)y₁ (S). (a) Argue that consumption at time 1 will equal consumption at time 0 only in those states of the world in which y₁ (s) = E[₁]); in other words, consumption at time 1 will equal consumption at time 0 only if expectations are fulfilled. (Hint: use the relation c₁ (s) = y₁(s) + so(1+r) for any state s = 1,..., S, and evaluate the formula for optimal saving for a state where y₁(s) = E[₁].) (b) Argue that consumption at time 1 will never equal consumption at time 0 if there're only two states of the world (S = 2) with distinct realizations of income, that is, y₁ (0) ₁ (1).

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Lets take a look at the two parts of the question youve provided a Argue that consumption at time 1 will equal consumption at time 0 only in those sta... View the full answer