It is October and Sam has won a price of $9000. She has the following two options: • Option A: receiving the entire amount in October; • Option B: receiving the price in three equal installment, that is, receiving $3000 in each of the following months (October, November, December). Sam decides to distribute her price over time by choosing Option B. Assume that Sam has constant marginal utility of money. Prove mathematically that Sam’s preference for Option B cannot be explained by hy- perbolic discounting (the β − δ model). Assume 0 < δ < 1 and 0 < β ≤ 1.
It is October and Sam has won a price of $9000. She has the following two options: • Option A: receiving the entire amount in October; • Option B: receiving the price in three equal installment, that is, receiving $3000 in each of the following months (October, November, December). Sam decides to distribute her price over time by choosing Option B. Assume that Sam has constant marginal utility of money. Prove mathematically that Sam’s preference for Option B cannot be explained by hy- perbolic discounting (the β − δ model). Assume 0 < δ < 1 and 0 < β ≤ 1.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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It is October and Sam has won a price of $9000. She has the following two options:
• Option A: receiving the entire amount in October;
• Option B: receiving the price in three equal installment, that is, receiving $3000 in each
of the following months (October, November, December).
Sam decides to distribute her price over time by choosing Option B. Assume that Sam has
constant
Prove mathematically that Sam’s preference for Option B cannot be explained by hy-
perbolic discounting (the β − δ model). Assume 0 < δ < 1 and 0 < β ≤ 1.
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