Table 27-1

Matt's Utility Function

Wealth

(Dollars)

Utility

50,000 7,000
51,000 7,250
52,000 7,499
53,000 7,746

Refer to Table 27-1. If Matt's current wealth is $51,000, then

Question

Table 27-1

Matt's Utility Function

Wealth

(Dollars)

Utility

50,000	7,000
51,000	7,250
52,000	7,499
53,000	7,746

​

Refer to Table 27-1. If Matt's current wealth is $51,000, then

BlackTom AI · Accepted Answer

Diminishing marginal utility: compute the change in utility from a $1,000 gain and a $1,000 loss around $51,000.

1) Relevant knowledge points and concepts
- Utility measures satisfaction from wealth. 
- Marginal utility of wealth is the change in utility from an incremental change in wealth.
- Diminishing marginal utility means each additional dollar yields less extra utility than the previous dollar.
- Risk aversion is indicated when the loss in utility from losing a given amount exceeds the gain in utility from gaining the same amount (concave utility).

2) Step-by-step reasoning
- We compare utility at three wealth levels: $50,000, $51,000, $52,000 (data given).
- Compute the utility gain from increasing wealth from $51,000 to $52,000.
- Compute the utility loss from decreasing wealth from $51,000 to $50,000.
- Compare these two numbers to determine whether Matt is risk averse, risk neutral, or risk loving.

3) Calculations (all intermediate steps)
- Utility at $52,000 = 7,499
- Utility at $51,000 = 7,250
- Gain in utility from +$1,000 = 7,499 − 7,250 = 249
- Utility at $50,000 = 7,000
- Loss in utility from −$1,000 = 7,250 − 7,000 = 250

4) Why the correct answer is correct
- The loss in utility (250) is slightly larger than the gain in utility (249) for equal $1,000 changes. This asymmetric response (loss > gain) indicates diminishing marginal utility and a concave utility function, which is the hallmark of risk aversion: Matt dislikes losses more than he likes equivalent gains.

5) Why other possible options would be incorrect
- Risk neutral would require gain = loss (249 would have to equal 250), which is false.
- Risk loving would require gain > loss, but here 249 < 250, so that is false.
- Any claim that gain exceeds loss or that Matt is risk-neutral/ risk-loving is therefore incorrect.

6) Conclusion
- The loss in utility from losing $1,000 exceeds the gain from gaining $1,000; Matt is risk averse. This matches the provided answer exactly.

Table 27-1 Matt's Utility Function Wealth (Dollars) Utility 50,000 7,000 51,000 7,250 52,000 7,499 53,000 7,746 Refer to Table 27-1. If Matt's current wealth is $51,000, then单项选择题

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Table 27-1 Matt's Utility Function Wealth (Dollars) Utility 50,000 7,000 51,000 7,250 52,000 7,499 53,000 7,746 ​ Refer to Table 27-1. If Matt's current wealth is $51,000, then单项选择题