Jan is a hyperbolic discounter. She puts weight 1 on utility earned in the current period but only weight .5 on utility earned in future periods. In period 1 she comes up with a plan,which involves taking some action that leads to a loss of C utils in period 2 but provides a benefit of B utils in period 3. What values of B and C will lead her to behave inconsistently and not follow through on her plans?

Question

Quizplus · Accepted Answer

For Jan to behave inconsistently and not follow through on her plans, the perceived utility of the action in period 1 must be positive, but negative in period 2. In period 1, she values the future utility at a discount, so the net utility she anticipates is -0.5C (the cost in period 2 discounted) + 0.25B (the benefit in period 3 further discounted). For her to initially plan to take the action, this sum must be positive, implying 0.25B > 0.5C, or B > 2C. However, in period 2, when the cost is immediate, she no longer discounts it, but she still discounts the future benefit, so her valuation is -C + 0.5B. For her to abandon her plan, this sum must be negative, implying 0.5B < C, or B < 2C. Combining these, for inconsistency, B must be greater than 2C to make the plan initially but less than 2C to abandon it, which is a contradiction. The correct interpretation is that for inconsistency, the benefit must be perceived as worth less in the immediate next period but worth pursuing when looking two periods ahead. Thus, the correct condition is C < B < 2C, where she initially sees the action as beneficial but re-evaluates it as not worth the immediate cost when the time comes to act.

Jan Is a Hyperbolic Discounter