Question

Decisions are often 'risky' in the sense that their outcomes are not known with certainty. Expected value is the sum of possible outcomes weighted by their probability of occurrence, and a preference between prospects can be judged purely on this basis under the expected value hypothesis, without reference to any personal utility function. Utility functions, and the concepts of concave (risk averse) or convex (risk seeking) curvature, belong to the SEPARATE expected utility hypothesis, not to expected value itself, which is just a plain, objective weighted sum.

Based on the above, look at the decision situation faced by Bablu.

Bablu had four options with probabilities of 0.1, 0.25, 0.5 and 1 respectively. The gains associated with each option are $1000, $400, $200 and $100 respectively. Bablu chose the first option. As per the expected value hypothesis:

• A. Bablu is risk taking.
• B. The expected value function is concave.
• C. The expected value function is convex.
• D. It does not matter which option Bablu should choose.

Hint:

All four options tie at an expected value of $100, and the expected value hypothesis itself has no concept of risk attitude or curvature, so under this hypothesis alone, the four options are equally good.

Answer 1

The Correct Option is D

Step 1: Build a quick table of expected values.
Option 1: $0.1 \times 1000 = 100$. Option 2: $0.25 \times 400 = 100$. Option 3: $0.5 \times 200 = 100$. Option 4: $1 \times 100 = 100$. Every single option lands on exactly $100.

Step 2: Remember what the expected value hypothesis actually is.
Expected value theory just multiplies each outcome by its probability and adds them up, it is a plain arithmetic average, with no personal risk preference or curved utility built into it anywhere. It ranks options ONLY by this number.

Step 3: Rule out the risk-taking and curvature-based options.
Saying 'Bablu is risk taking' requires knowing something about how he personally values outcomes relative to their certainty, that is an expected UTILITY idea, and the expected value hypothesis, by itself, cannot support that conclusion just because he happened to pick the riskiest-looking option. Likewise, 'concave' and 'convex' describe the bend of a utility curve; the expected value calculation is a straight, linear weighted sum with no curve at all, so calling it 'concave' or 'convex' does not make sense. Both of these ideas confuse expected utility language with expected value theory.

Step 4: Settle on the correct reading.
Because all four of Bablu's options tie at exactly $100 in expected value, the expected value hypothesis treats them as interchangeable, there is no basis within this hypothesis to say one tied option is better than another.

Final Answer:
It does not matter which option Bablu should choose. \[ \boxed{\text{Indifferent, all tie at \$100}} \]