Today, Tomorrow, or the Day After: A player has $100 today that needs to be consumed over the…

Today, Tomorrow, or the Day After: A player has $100 today that needs to be consumed over the next three periods, t = 1, 2, 3. The utility over consuming $xt in period t is given by the utility function u(x) = ln(x), and at period t = 1 the player values his net present value from all consumption as u(x1) + δu(x2) + δ2u(x3), where δ = 0.9.

a. How will the player plan to spend the $100 over the three periods of consumption?

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 extra $20?

 

 

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