Suppose , and
) Assuming logarithmic utility, what is consumption in the future?

Question

Suppose  , and 
) Assuming logarithmic utility, what is consumption in the future?

Quizplus · Accepted Answer

Assuming logarithmic utility, the optimal consumption in each period is given by the formula:

ln(C1) - γ/(1+r) * ln(C2)

where C1 is consumption in the present, C2 is consumption in the future, γ is the coefficient of relative risk aversion (a typical value for this parameter is 2), and r is the discount rate.

In this case, we have two options with different payoffs in the future:

Option 1: $150,000 in the present, $75,000 in the future
Option 2: $71,428.57 in the present, $142,857.14 in the future

We can plug in the values for each option and compare the results:

Option 1: ln(150000) - 2/(1+0.05) * ln(75000) ≈ 11.183
Option 2: ln(71428.57) - 2/(1+0.05) * ln(142857.14) ≈ 10.856

Therefore, option 1 provides a higher utility and is the best choice.

The consumption in the future for option 1 is $39,375.00 (i.e. half of the $75,000 payoff).