4. (Lehr #6.10) Shockingly Bad Timing (Loewenstein 1987). Consider the timing of a future bad outcome...

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4. (Lehr #6.10) Shockingly Bad Timing (Loewenstein 1987). Consider the timing of a future bad outcome (v < 0), like receiving a non-lethal, but strong electric shock. Figure 6.6 shows two possible plots of U(T, v), as given by equation (6.8). T A U(T, v): = +8+ - A Total Discounted Utility, U(T,v) 3 6 9 D C Periods Outcome is Delayed, T 12 Figure 6.6 Anticipatory Utility of a Bad in Exercise 6.10 a. Consider the two curves. i. If U(T, v) looks like curve C, when is the optimal time T to receive the shock? If U(T, v) looks like curve D, when is the optimal time T to receive the shock? ii. 15 (6.8) b. Now suppose you must receive the shock by period 9 at the latest. Re-answer the two questions from part (a) given this constraint. c. Observe that U(T, v) looks like curve C if and only if U(1, v) < U(0, v). i. Apply equation (6.8) to this inequality to derive a bound on A for which U(T, v) looks like curve C. ii. Provide intuition for the connection between this condition and your results in parts (a) and (b). 4. (Lehr #6.10) Shockingly Bad Timing (Loewenstein 1987). Consider the timing of a future bad outcome (v < 0), like receiving a non-lethal, but strong electric shock. Figure 6.6 shows two possible plots of U(T, v), as given by equation (6.8). T A U(T, v): = +8+ - A Total Discounted Utility, U(T,v) 3 6 9 D C Periods Outcome is Delayed, T 12 Figure 6.6 Anticipatory Utility of a Bad in Exercise 6.10 a. Consider the two curves. i. If U(T, v) looks like curve C, when is the optimal time T to receive the shock? If U(T, v) looks like curve D, when is the optimal time T to receive the shock? ii. 15 (6.8) b. Now suppose you must receive the shock by period 9 at the latest. Re-answer the two questions from part (a) given this constraint. c. Observe that U(T, v) looks like curve C if and only if U(1, v) < U(0, v). i. Apply equation (6.8) to this inequality to derive a bound on A for which U(T, v) looks like curve C. ii. Provide intuition for the connection between this condition and your results in parts (a) and (b).