Suppose that someone had a simplified version of prospect theory preferences as follows:

They value any gain x from their current reference point simply as x.

They value any loss y from their current reference point as λy where λ≥1 is the person's coefficient of loss aversion.

With these preferences, does the person exhibit diminishing sensitivity?

Question

Suppose that someone had a simplified version of prospect theory preferences as follows:

They value any gain x from their current reference point simply as x.

They value any loss y from their current reference point as λy  where λ≥1  is the person's coefficient of loss aversion.

With these preferences, does the person exhibit diminishing sensitivity?

BlackTom AI · Accepted Answer

In this setup, the value function is defined piecewise with linear forms: gains x are valued as x, and losses y are valued as λy with a constant slope λ ≥ 1.

Option 1: Yes. If the person exhibited diminishing sensitivity, we would expect the incremental value of gains to decrease as the gain increases (a concave shape for the gain domain) and similarly a changing (usually increasing at a decreasing rate) marginal value for losses. However, because both gains and losses are valued linearly (with constant slopes), there is no curvature to produce diminishing sensitivity. The marginal value of an additional unit of gain is always 1, regardless of how large the gain is, and the marginal value of an additional unit of loss is always λ, regardless of how large the loss is. This rules out diminishing sensitivity.

Option 2: No. The defining feature of diminishing sensitivity in prospect theory is the concavity for gains and convexity for losses, leading to decreasing (in absolute value) marginal changes as outcomes move farther from the reference point. Here, the model assigns a constant, linear weight to both gains and losses, so the marginal change does not decline with larger magnitudes. The loss domain scales costs by a fixed factor λ, not by a changing slope, further confirming the absence of diminishing sensitivity.

Additional note: The presence of a kink at the reference point (from gain to loss) does reflect loss aversion (through λ ≥ 1) but does not by itself introduce diminishing sensitivity, since the slopes on both sides are constant rather than varying with the distance from the reference point.

类似问题

Is the following statement true or false? In the products of methylation-hydrolysis, every -OH group corresponds to the position of a glycosidic bond in the starting polysaccharide.

Which of the follwoing structures represents amylopectin?

Which of the following is true about an aldopentose?I. It is a monosaccharide.II. It contains a CHO groupIII. It is a disaccharide.IV. It is an oligosaccharide.

For stock A, we have 𝛽 𝑖 = 0.70. Suppose the expected market risk premium next year is 9% and the risk-free rate is 3%. What is the expected return of this stock based on the CAPM? (Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

The following graph shows the Security Market Line in the current economy. If a stock has a β of 1.2, what is the expected return of this stock based on the CAPM? (Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单