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: Compute the expected value of each of Bablu's four options.
First option: \(0.1 \times 1000 = 100\). Second option: \(0.25 \times 400 = 100\). Third option: \(0.5 \times 200 = 100\). Fourth option: \(1 \times 100 = 100\). All four options give exactly the same expected value of $100.

Step 2: Apply the expected value hypothesis strictly, as the question asks.
Under the expected value hypothesis, options are ranked purely by this single weighted-sum number, and options that tie on that number are treated as EQUALLY good, this hypothesis has no built-in way to prefer a 'safer' or 'riskier' tied option, because it never looks at curvature or risk attitude at all, that machinery belongs to expected utility, a different theory.

Step 3: Check option A against this.
Calling Bablu 'risk taking' is a conclusion about his personal utility function's shape, which is an expected UTILITY concept, not something the expected VALUE hypothesis, on its own, is equipped to conclude just from seeing which tied option he picked. So option A overreaches what expected value theory alone can tell us.

Step 4: Check options B and C.
'Concave' and 'convex' describe the curvature of a UTILITY function, not the expected value calculation itself, which is just a linear, weighted average of outcomes and probabilities, it has no curvature to speak of. So describing 'the expected value function' as concave or convex is a category error, both B and C are wrong.

Step 5: Confirm option D.
Since all four options are exactly tied at an expected value of $100, the expected value hypothesis is genuinely indifferent between them, so, strictly from this hypothesis's point of view, it does not matter which of the four options Bablu picks.

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