Darryl has a coefficient of risk aversion of 3. This means he is:[Fill in the blank]

Question

BlackTom AI · Accepted Answer

A positive Arrow–Pratt risk-aversion coefficient means the individual is risk-averse; with value 3 Darryl is therefore risk adverse (risk-averse). 1) Relevant concepts: - Arrow–Pratt measures quantify risk aversion from a utility function u(w): absolute risk aversion A(w) = −u''(w)/u'(w) and constant relative risk aversion γ = −w u''(w)/u'(w). - Sign interpretation: A > 0 (or γ > 0) implies risk aversion (concave utility), A = 0 implies risk neutrality (linear utility), A < 0 implies risk seeking (convex utility). 2) Step-by-step reasoning: - The question gives a coefficient of risk aversion = 3. This is a positive number. - By the Arrow–Pratt interpretation, any positive coefficient indicates the person dislikes risk (concave utility), i.e., is risk-averse. 3) Example calculations (intermediate steps): - Exponential utility u(w) = −e−aw has constant absolute risk aversion a. Let a = 3: u(w) = −e−3w u'(w) = −(−3)e−3w = 3 e−3w u''(w) = −9 e−3w A(w) = −u''(w)/u'(w) = −(−9 e−3w)/(3 e−3w) = 9/3 = 3. That demonstrates a coefficient of 3 corresponds to a risk-averse (concave) utility. - For CRRA utility u(w) = w^(1−γ)/(1−γ) with γ = 3, the relative risk aversion is γ = 3 (>0), again indicating risk aversion. 4) Why the correct answer is correct: - The positive value (3) directly signals aversion to risk: the individual requires extra expected return to accept added gamble, and marginal utility is decreasing (concave utility). Thus Darryl is risk-averse. 5) Why other options are incorrect: - b. Risk Seeking: would require a negative coefficient (A < 0), not +3. - c. Risk neutral: would require coefficient = 0. - d. A speculator: descriptive, not a formal measure—does not follow from the coefficient sign. - e. A conservatist: informal term; the precise economic classification is risk-averse, which is option a. Conclusion: Darryl is risk adverse (option a), which matches the provided correct answer.

Darryl has a coefficient of risk aversion of 3. This means he is:[Fill in the blank]单项选择题

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