Figure 27-1

The following figure shows a utility function for Britney.

Refer to Figure 27-1. From the appearance of the utility function, we know that

Question

Figure 27-1

The following figure shows a utility function for Britney.

​

Refer to Figure 27-1. From the appearance of the utility function, we know that

BlackTom AI · Accepted Answer

A concave (increasing at a decreasing rate) utility function indicates diminishing marginal utility of wealth and therefore risk aversion.

Relevant concepts:
- Utility as a function of wealth: u(w) maps dollars to satisfaction; a slope > 0 means more wealth gives higher utility.
- Diminishing marginal utility: the additional utility from each extra dollar falls as wealth increases; graphically this makes u(w) concave (bends downward).
- Risk aversion: a consumer with a concave utility function prefers the certain value of expected wealth to a gamble with the same expected wealth.

Step-by-step reasoning using the figure:
1. The curve in the figure rises as wealth increases but becomes flatter at higher wealth levels — the slope declines as we move right. That is the signature of a concave utility function.
2. The dashed verticals at wealth = 750, 1050, and 1350 map to utilities A, B, and C. The vertical increase in utility from 750 → 1050 (A → B) is larger than the increase from 1050 → 1350 (B → C). This shows marginal utility of wealth falls as wealth rises.
3. Numerical illustration (example consistent with the shape): using u(w) = sqrt(w) as a concave function, u(750) ≈ 27.386, u(1050) ≈ 32.403, u(1350) ≈ 36.742. Increase 750→1050 ≈ 5.017; increase 1050→1350 ≈ 4.339. The first increment is larger, confirming diminishing marginal utility.

Why the correct answer is correct:
- The concave shape (increasing but flattening) is the textbook representation of risk-averse preferences: with diminishing marginal utility, an individual dislikes risk because the utility loss from a downward shock exceeds the utility gain from an equivalent upward shock. Thus “Britney is risk averse” follows directly.

Why the other options are incorrect:
- “Britney gains more satisfaction when her wealth increases by X than she loses when her wealth decreases by X” contradicts the concave shape; for concave u, the loss from −X is larger than the gain from +X.
- “The property of diminishing marginal utility does not apply” is false because the graph explicitly shows diminishing marginal utility (flattening slope).
- “Britney enjoys engaging in risky behavior” describes risk loving (convex utility), which would be an upward–curving slope; the graph is concave, not convex.

Conclusion: The figure shows a concave utility function and thus Britney is risk averse. This matches the provided correct answer: Britney is risk averse.

Figure 27-1 The following figure shows a utility function for Britney. Refer to Figure 27-1. From the appearance of the utility function, we know that单项选择题

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Figure 27-1 The following figure shows a utility function for Britney. ​ ​ ​ Refer to Figure 27-1. From the appearance of the utility function, we know that单项选择题