A player has $100 today that he needs to consume in the next three periods, t = 1, 2, 3. The utility of consuming Sxt in period t is given by the utility function u(x) = In(x), and in period t = 1 the player values his net present value of all consumption as u(x1) + \delta u(x2) + \delta 2u(x3), where \delta = 0.9. a. How does the player plan to spend the $100 over the three consumption periods? b. Imagine that the player knows that in period t = 2 he will receive an additional gift of $20. How will he choose to allocate his original $100 initially and how will he spend the additional $20?
A player has $100 today that he needs to consume in the next three periods, t = 1, 2, 3. The utility of consuming Sxt in period t is given by the utility function u(x) = In(x), and in period t = 1 the player values his net present value of all consumption as u(x1) + \delta u(x2) + \delta 2u(x3), where \delta = 0.9. a. How does the player plan to spend the $100 over the three consumption periods? b. Imagine that the player knows that in period t = 2 he will receive an additional gift of $20. How will he choose to allocate his original $100 initially and how will he spend the additional $20?
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.1P
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Transcribed Image Text:A player has $100 today that he needs to consume in the next three periods, t = 1, 2, 3. The utility of
consuming Sxt in period t is given by the utility function u(x) = In(x), and in period t = 1 the player values his net
present value of all consumption as u(x1) + \delta u(x2) + \delta 2u(x3), where \delta = 0.9.
a. How does the player plan to spend the $100 over the three consumption periods?
b. Imagine that the player knows that in period t = 2 he will receive an additional gift of $20. How will he choose to
allocate his original $100 initially and how will he spend the additional $20?
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