  We study the optimal design of electricity contracts among a population of
consumers with different needs. This question is tackled within the framework
of Principal-Agent problems in presence of adverse selection. The particular
features of electricity induce an unusual structure on the production cost,
with no decreasing return to scale. We are nevertheless able to provide an
explicit solution for the problem at hand. The optimal contracts are either
linear or polynomial with respect to the consumption. Whenever the outside
options offered by competitors are not uniform among the different type of
consumers, we exhibit situations where the electricity provider should contract
with consumers with either low or high appetite for electricity.
