2. 1000 identical residents of Beefalo New York have demand for harmburgers of D = 10 - P. The cost of producing each harmburger is 2, and there are many producers who sell harmburgers for their marginal cost. Unfortunately, the production of beef is associated with an externality (the town smells like manure) so that each harmburger consumed causes a total harm of e=2, spread among all the residents of Beefalo. The well being of each resident equals their consumer surplus minus the harm of pollution W = CS-ex X/1000 where X is the total number of harmburgers consumed by all the residents of Beefalo. Notice that each harmburger harms each resident 2/1000. Each consumer currently chooses to consume 8 Harmburgers. JB considers reducing his consumption of Harmburgers by one unit. What is the change in JB's welfare W? (Calculate his welfare when consuming 8 and welfare when consuming 7) Consider a tax t = 1 that causes all consumers to reduce their consumption. Now all consumers consume 7 Harmburgers. The tax revenue is rebated so that each consumer receives 1/1000 of the total tax revenue (your rebate does not depend on your consumption). Calculate JB's welfare. Explain why JB (and everyone else's) welfare improved when there was a tax on harmburgers, but JB was worse off when he changed his behavior on his own. (You could use the idea of pigouvian taxes, or the tragedy of the commons, from your Principles of Microeconomics class) Optional (for fun): Using JB's consumption q, take the derivative of JB's welfare with respect to q. (For double plus fun: why is W written this way?) WJB = (8)(8) -(8 -q)(8 -q) -2* (792 + q)/1000 = 169-9" - 1584+2q 1000 2