Problema 1 · Economia de L'empresa UPF Setembre 2012

Tema: Decisió econòmica racional i biaixos · Del examen Setembre (2012)

Enunciado

Short Question 1 (6 points). Unhappiness and Asymmetric Value Function

Imagine that a year ago, an acquaintance entrusted you with €120,000 to invest on their behalf, but the entire amount has now been lost. Aware that your friend will be devastated, your goal is to minimize their distress. Assuming that your friend assesses utility according to prospect theory's asymmetric value function, should you break the news all at once (informing them that the entire €120,000 has been lost), or should you divide the blow by telling them each month over the course of a year that an additional €10,000 has been lost? Justify your recommendation.

Enunciado: Problema 1 · Economia de L'empresa UPF Setembre 2012

Solución

Según los criterios oficiales de corrección

Should you break the news all at once, or should you divide the blow by telling them each month?

Solución: Break the news all at once (entire €120,000 at once)

Justify your recommendation.

Solución: In prospect theory, the value function is convex in the domain of losses due to diminishing sensitivity (v′′(x)>0v''(x) > 0 for x<0x < 0). Consequently, each additional euro lost creates less marginal disutility. A single integrated loss of €120,000 results in less subjective unhappiness than the sum of twelve separate €10,000 losses (∣v(−120,000)∣<12⋅∣v(−10,000)∣|v(-120,000)| < 12 \cdot |v(-10,000)|).

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