1 This is an Open-Book and Take-Home quiz. Please answer all five questions.
2 Please submit your answer to NTULearn by November 28, 12pm(noon)
Consider the following savings problem. A decision maker has income x0 in period 0 and income varying randomly between x1−ε and x1+ ε in period 1 (ε>0); the outcomes are equally likely. Now, the individual can save an amount s in period 0 returning (non‐randomly) rs, with r > 0, 0 ≤ s ≤ x0, in period 1. The individual has expected utility preferences exhibiting risk aversion; preferences are time additive.
(a) Analyze how s depends on x0 and x1 (i.e. derive comparative‐statics results and interpret
them in terms of properties of the utility function).
(b) Note that ε measures the riskiness of future income. Show that for a prudent decision
maker (whose utility has positive third-order derivative) the saving is a increasing
function of ε.
(c) Briefly discuss how would the analysis in (a) change if the decision maker were instead
a risk lover?