ECN349 Summer exam paper with solutions

A 部分（回答 Q1 和 Q2；回答 Q3 或 Q4） 50 分
Q1。回答问题的以下部分。
a) 简述什么是 Arrow-Pratt 绝对风险系数

b）计算并解释对数的ARA和RRA值

>0.注意x可以理解为与每个可能的结果相关联

a) 绝对风险厌恶的 Arrow-Pratt 系数 (ARA, 2-

ARA系数越大，规避风险越大（或风险越小）

𝐴�𝐴(�) = −�′′
(�)/�′
(�)

��𝐴（�）= −�𝑢′′
(�)
𝑢’（�）

Section A (answer both Q1 and Q2; answer either Q3 or Q4) 50 marks
Q1. Answer the following parts of the question.
a) Briefly explain what Arrow-Pratt coefficients of absolute risk
aversion (ARA) and relative risk aversion (RRA) are. (5 marks)
b) Calculate and interpret the ARA and RRA values for the logarithmic
utility function �(�) = log𝑎 �, where a is a positive parameter and x
>0. Note x can be understood as each possible outcome associated
with a given choice, or the level of wealth given each possible
outcome of a choice. (5 marks)

a) Arrow-Pratt coefficient of absolute risk aversion (ARA, 2-
dimentional) describes local curvature of a utility function. Given a
monotone increasing utility function (indicating non-satiable agents
assumption), negative values of the measure correspond to risk-
seeking behaviour and positive values to risk-avoiding behaviour.
The greater the ARA coefficient, the more risk averse (or less risk
loving) an individual is at the level of x.
𝐴�𝐴(�) = −�′′
(�)/�′
(�)
Arrow-Pratt coefficient of Relative risk aversion (RRA, 2-
dimensional) is another local risk aversion measure that describes
an individual’s attitude toward proportional risks.
Constant/decreasing/increasing RRA with increasing wealth means
the proportion of wealth that an individual is willing to put at risk
remains constant/increases/decreases as wealth increases.
��𝐴(�) = −�𝑢′′
(�)
𝑢′(�)

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