-- Imperfect Information

An electric utility is considering two programs, B and N, that would encourage residential customers to cut back on their air conditioning use during the hottest days of the summer. It knows that twenty percent of its customers (20%) are highly flexible (type H) and would react strongly to a policy, while the remaining 80% have low flexibility (type L) and would react little. Policy B is a broad one-size-fits-all approach that would cost the utility $90 per household. When applied to an H household it would produce a gross benefit to the utility of $300 but when applied to an L household the gross benefit would be only $50. Policy N is a new approach specifically tuned to the needs of H households. It would cost the utility $150 per household and would produce a gross benefit of $450 when applied to an H household but a $0 gross benefit when applied to an L household.

1. Suppose that initially no information is available about the type of any given household. Which policy should the utility use, if any? (It could choose not to do either B or N).
2. Now suppose that a large, detailed dataset is available that can be used to test whether any given household is type H or type L. If the utility uses the test, it could then apply policy B or N, or no policy at all, to the household. (To be clear, it can use different policies with different households.) The evaluation would cost $10 per household but would not be infallible. It has a 20% risk of reporting that a type-H household is type L, and 10% chance of reporting that a type-L household is type H. Please determine whether the utility will use the test. If it does, how would it use the results?