Question

S'19 Prof. Stahl 359M Environmental Economics HW 1 1. A small village of 1000 families in Outer Bodiva has a single coal burning factory that pollutes the air. A Peace Corps volunteer suggests a project that would install smokestack filters and significantly reduce the air pollution. The project will require 2000 hours of labor. If the project is undertaken, each family will enjoy a gross benefit of y, measured in hours of labor Assume that y 1 for 500 of the families, and y' - 5 for the other 500 families. Also assume that these benefits are "private": no one knows anyone else's true benefit a) A village elder suggests that every family should be required to contribute equally to the project (i.e. 2 hours each). Will this proposal win a b) Another village elder suggests that every family be asked to submit a sealed ballot that indicates an amount of labor the family is willing to commit to the project. If the total of the commitments is at least 2000 hours, the project is undertaken; otherwise it is abandoned. If the total of the commitments, X -x, exceeds 2000 hours, then each family is required to fulfill only the fraction 2000/x of its commitment. Note that if every family volunteers its total benefit (Ci.e. xy), then in the end each family will be obligated to provide 2/3 of y (i) Prove that it is not rational for every family to report truthfully (ie. set x y). Hint: take the point of view of one family (say family i), and assume that all other families report truthfully. Then, show that the rational decision of family i is x'0.] (i) Suppose that after much discussion in the village, everyone agrees that everyone should contribute at least I hour. It is also realized that half the families will contribute no more than I hour, implying that the other 500 families need to contribute 1500 hours in total, which can be accomplished by each contributing 3 hours. Show that it is rational for every family to do this; that is, if family i believes all other families will contribute according to this suggestion, then it is rational for family i to contribute 1 hour ify'-1, and contribute 3 hours if y'-s. (iii) An alternative scenario is that a village leader suggests that the cost of this project should be born only by those who benefit the most, and that each family should contribute either 0 or 4 hours. Show that it is rational for every family to do this; that is, if family i believes all other families will contribute according to this suggestion, then it is rational for family i to contribute 0 hours if y I, and contribute 4 hours if y- (iv) Compare the fairmess of schemes (i) and (ii) in terms of hours contributed and net benefits (y-x).
Hi, I need help on (I), (II) and (III). Thank you.

Answer 1

Since you require the answer to only (i) , (ii) and (iii) , hence providing these three answers only :

Answer (i) : Rationale in Economics and its applied studies can be broadly discussed as the rationale which the individuals would apply in the economic factors and their functionality which results in to the economic development of a nation. IN the case given here, it is virtually not rational for every family to report the accurate amount of labor that they would want to commit for the project. Let us take the example of one family, let us say family I. Family ‘I’ would in the first place be willing to mention in the sealed box, the accurate amount of labor that they would put in for the implementation of the project. However, the rationale of the family ‘I’ would force it to think that, what happens if they put in the exact correct figures and given their full dedication toward the project, and if the other families, although they want the project to be implemented, but shy away from putting in much about of labor. This is a normal human tendency to reap more benefits of less hard work. Family ‘I’ would then realize that , if they are the ones to give the most of the hard work to the project and the other families would reap the benefits out of it later, then this rationale would force them to think in the lines of reducing the total number of work hours they ca dedicate t the project. Similarly, every family will think on the same lines, and therefore it is practically not possible to get the correct truthful data from the families.

Answer (ii) : If the family ‘I’ knows that half of the families would only contribute up to 1 hour and the remaining half would require to contribute 3 hours each to fulfill the minimum m requirement pf 2000 hours to implement the project, then the family ‘I’ would be agrrered upon to contribute either 1 hour or 3 hours. The rationale behind this thinking would be, that there would be at least 499 more families along with the family ‘I’ in either of the conditions. i.e. if the family ‘I’ falls in to the first bracket of those 500 families which will only give 1 hour, then there is nothing to be shameful about, as it has about 499 more families doing the same. Similarly, the family ‘I’ would not hesitate to involve in to the bracket where it would need to dedicate 3 hours of their work, and since 499 more families would be doing it, the family would want to participate in this too. This fact comes from the basic human rationale that an individual is ready to take a risk when he sees others taking the same risk too.

Answer (iii) : The same logic of human rational would apply in this scenario too, where if the family ‘I’ sees that 499 more families will also not work at all and be in the bracket of zero productive families, it would also want to be one among them to be left out of reaping the benefits of the implementation of the project. On the other hand, if the family ‘I’ gets the opportunity to be a part of those families who would need to work for 4 hours each and then finally reap all the benefits among themselves , as a reward for their hard work, the family ‘I’ would also be agreed upon to work for 4 hours ,as many others are also doing the same hard work.