As in the previous exercise, consider an initial wealth of 10 and the lottery 𝑋 [-6 or +6, both with probability 0.5]. Assume now that the utility is:
𝑢 = 𝑤 for 𝑤 ≤ 10
0.5 𝑤 + 5 for 𝑤 > 10
a. Draw the utility function. Is it globally concave?
b. Compute the certainty equivalent and the risk premium attached to 𝑋.
c. Can you apply the Arrow–Pratt approximation? Why
d. Consider now the lottery 𝑌 defined in exercise 1.1 [from Eeckhoudt et al., -3 or +3, both with probability 0.5]. Compute the risk premium attached to 𝑌. Is it smaller than for 𝑋? Why?
e. Answer (b) and (d) above if the individual has an initial wealth of 20. How do the risk premia for 𝑋 and 𝑌 compare?