Question

The utility from wealth $(w)$ for an individual is given by $u(w) = \sqrt{w$. The individual owns a risky asset that is equally likely to yield either Rs. 400 or Rs. 900. The risk premium of the asset (in Rs.) is}

• A. 5
• B. 25
• C. 625
• D. 650

Hint:

For risk-averse individuals, the risk premium equals expected wealth minus the certainty equivalent — it’s always positive when the utility function is concave.

Answer 1

The Correct Option is B

Step 1: Compute expected wealth and expected utility.
Expected wealth: \[ E(w) = \frac{400 + 900}{2} = 650. \] Expected utility: \[ E[u(w)] = \frac{\sqrt{400} + \sqrt{900}}{2} = \frac{20 + 30}{2} = 25. \]
Step 2: Find the certainty equivalent (CE).
Certainty equivalent is the certain amount that gives the same utility as the expected utility: \[ u(CE) = E[u(w)] \Rightarrow \sqrt{CE} = 25 \Rightarrow CE = 625. \]
Step 3: Risk premium.
Risk premium = $E(w) - CE = 650 - 625 = 25.$
Step 4: Conclusion.
Thus, the risk premium of the asset is Rs. 25.