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Assignment 1: guidelines In the first assignment, you are asked to calculate the excess burden (deadweight loss) as a function of the tax rate in two simple scenarios. The first question examines a linear utility function in which the two goods are perfect substitutes. Verify that in such a case the consumer will buy the cheapest good of the two options (a corner solution). You should draw the three budget lines: the original no-tax line, the after-tax line and the benchmark case where a lump-sum tax is levied (a parallel shift of the original budget curve). You need to calculate the actual tax revenues (AT) and the potential tax revenues that would have been raised under a lump- sum tax regime (which attains the same level of after tax utility, U1) (PT). The excess burden (EB) is given by EB=PT-AT. In the first question, you should distinguish between two cases: (i) in the first case the tax on good y is small enough such that the consumer still prefers to consume only y (what should be then the relevant range of the tax, t, in this case?); (ii) in the second case, the tax levied on y is sufficiently large, such that the consumer switches and spends her entire income on the other good, x. You should obtain an excess burden function, EB(t) which is a step-function distinguishing between the two cases described above (a step-function means that the EB is fixed over a given range and then jumps discontinuously to another range over which it is fixed again). In the second question a firm has to choose between two mutually exclusive projects: a risky one and a certain one. As the government does not deduct losses, the firm is effectively paying a higher tax rate on risky projects that on certain ones. This is the source of inefficiency and hence deadweight loss. You should first verify that in the absence of taxes, the expected-profit maximizing firm will choose to invest in the risky project. Next you need to demonstrate that when the tax rate, t, is high enough the firm will change her choice and switch to the certain project. The excess burden measures the substitution effect, namely the fact that although the risky project is more profitable, the firm is switching to the other project even when it receives the tax revenues back as transfer from the government. You can again use the same methodology used in class. Calculate the actual tax revenues then find the after tax expected profits of the firm and define it as U1. Finally find the lump sum tax that will maintain the same level of profits for the firm (remember that with a lump-sum tax the firm’s decision will remain the same). Then you will need to calculate the potential tax revenues and compare them with the actual revenues. The difference is the excess burden. You are supposed to obtain again a step function for EB(t), due to the discrete choice of the firm (only two options).
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