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# eco331h3 - Northwestern University Fall 2009 HOMEWORK 3 DUE...

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Northwestern University Marciano Siniscalchi Fall 2009 Econ 331-0 HOMEWORK 3 DUE MONDAY, OCTOBER 26, IN CLASS. Note These questions are from the midterms I gave in 2007 and 2008, so you can get a sense for the kind of questions I ask in an exam. For your information, there will be two questions, and you will have one hour and fifteen minutes to complete the midterm. Again, it’s open-books, open-notes, open-whatever except for computers or anything with a wireless or wired connection of any sort. 1 Background: Electricity distributors such as ComEd face a rather complex pricing problem. The demand for electricity varies throughout the day, and is random (e.g. demand is higher on hotter days). To make matters worse, power cannot be stored, bringing certain generators (e.g. nuclear power plants) online takes time, and their output can also be random (the obvious examples being solar or wind farms). One way ComEd and other power utilities respond to these challenges is by providing different levels of reliability: they promise almost 100% reliability (i.e. delivery of electricity no matter what the circumstances) to customers (e.g. hospitals) who absolutely require a steady power supply, at a high per-unit price; they offer lower reliability, at a lower per-unit price, to more tolerant customers such as households. This is a neat example of an industry creating an artificially differentiated product out of something (power) that is, in and of itself, relatively homogeneous. This question considers a simplified version of the pricing problem faced by ComEd. We assume that pricing is not per-unit, but is paid upfront. This simplifies the math, but still captures the gist of the pricing approach in the electricity distribution industry. The Question: An individual with Bernoulli utility u ( w ) = - exp( - 0 . 001 w ) wishes to produce a widget that can be sold for 1000 dollars if it is of high quality, and 400 dollars otherwise. You don’t need to know the individual’s wealth. Producing a high-quality widget is facilitated by the use of electrical power, as this enables the use of precision tools. If electrical power is available, quality is high with probability 0 . 8; if instead the individual chooses not to buy electricity, or if the individual does buy electricity but power is not delivered, the quality of the widget is high with probability 0 . 4.

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