20.3: 预期收益、预期效用和风险厌恶 I

考虑一个假设的示例，其中 John 正在评估一家公司的工作机会。如果公司表现良好，John 将获得 81,000 美元的年收入 ;如果表现不佳，他将获得 49,000 美元。每个结果的可能性相同，概率为 0.5。这两个结果是互斥的，这意味着只能发生一个，并且它们的概率之和为 1。81,000 美元和 49,000 美元的金额代表与每个结果相关的收益。

John 的预期收入是他预期赚取的平均金额，考虑了所有可能的结果及其概率。 

预期收入 = （P₁ × X₁） + （P₂ ×  X₂），

其中 P₁ 和 P₂ 是两种结果的概率，X₁ 和 X₂ 是它们对应的收益。

对于 John 来说，

• 如果公司表现良好，他的收入将是 81,000 美元，概率为 0.5。
• 如果公司表现不佳，他的收入将为 49,000 美元，概率为 0.5。

因此，约翰的预期收入为 （0.5 × 81,000 美元） + （0.5 × 49,000 美元） = 65,000 美元

。这种分析有助于在不确定性下做出决策。但是，应计算预期效用以进行进一步分析，因为仅凭收入并不能反映 John 如何评估不同的收入水平。为此，需要对应于所有可能收入水平的效用值。假设 John 经历的收入边际效用递减，这意味着额外的收入会导致满意度的逐渐变小。下表显示了不同收入水平的效用值:

表:效用-收入关系

考虑一个假设的场景，Neil 在一家公司获得了一份工作。

与工作相关的收入是不确定的。如果他表现良好，他的年薪为 81,000 美元。否则，他的薪水是 49,000 美元。每个结果的概率相等，为 0.5。

预期收入是使用预期值分析计算得出的。 <

要计算预期效用，需要与 Neil 的不同收入水平相对应的效用值，这些值显示在图表上。

像大多数人一样，Neil 的收入边际效用递减。 

该分析提供了对 Neil 的效用如何随收入变化的见解，并为在不确定性下评估他的预期效用奠定了基础。

• Expected Income - The average amount one expects to earn considering all possible outcomes and their probabilities.
• Income Outcome - The potential payoffs associated with different scenarios.
• Probability Factor - The likelihood of a specific outcome occurring.
• Diminishing Marginal Utility of Income- The concept that additional income leads to progressively smaller increases in satisfaction.
• Income Expected Meaning- What a person anticipates earning based on certain variables or factors.

• Define Expected Income - Explain what it represents and how it’s calculated (e.g., expected income formula).
• Contrast Income Outcome & Probability Factor – Explain the difference between potential payoffs vs their probability.
• Explore Examples – Describe scenario like, how John calculates his expected income (e.g., John's job offer).
• Explain Diminishing Marginal Utility of Income - Brief explanation on how additional income leads to smaller satisfaction increases.
• Apply in Context – Short explanation on how this analysis helps in decision-making under uncertainty.

• What is Expected Income and how is it calculated (Including the expected income formula)?
• How do you differentiate between Income Outcome and Probability Factor?
• What is Diminishing Marginal Utility of Income and how does it affect decision-making?

• Students – Understand how understanding 'Expected Income' supports financial learning.
• Educators – Provides a clear framework to teach concepts like Expected Income, Probability, and Utility.
• Researchers – Relevance for scientific research in behavioral economics.
• Finance Enthusiasts – Gain insights into decision-making processes under uncertainty.