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Question: please explain each process as im completely lost in solving...

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Please explain each process as I’m completely lost in solving this problem. Thanks! :)
1. During the first class I have mentioned that the course will be centred around the study of several, progressively more complex, models of trade. To give a tangible experience what that might be like, a simple example of tax cuts was provided. Below are the details of that example and a short assignment left for you to finish Various governmental administrations often propose a tax cut that is argued to be not just revenue- neutral but actually tax revenue enhancing. The idea is that a tax cut will leave more money in the hands of consumers and firms, which will increase consumption, investment, and production. This will lead to increase in aggregate national income, i.e., GDP. And this increase will be so large as to increase tax revenue, despite the new lower tax rate at which the income is taxed. The argument is certainly a tempting one and makes some sense. The question is, does it work in practice? To get a handle on the answer, we propose a simple model consisting of one equation that relates tax revenue, income, and tax rate: TR t-Y, where TR is tax revenue, t is tax rate, and y is aggregate income, eg. GDP. Suppose, the tax rate t is reduced by fraction c, where 0 < c < 1. For exarnple, if c = 0.05, then the new tax rate is t = t (1-c) = 0.951, i.e., the rate is reduced by 5% and the new rate is 95% of the old one. Then the proposition of increased tax revenues as a result of tax cut takes definite mathematical form. For the new tax revenue to be greater than before we have where t(1 -c) is the new reduced tax rate, and g is the rate of increase in income Y that results from the tax cut. Then 1(1-c)-Y(1+3) > tY (1- c) +(1 -cg> 1 Thus, if the new tax revenue to exceed the old one, the increase g in income Y has to be greater than tax reduction fraction c. Now, lets consider how likely this to happen. When the Trump administration implemented tax, it reduced top marginal rate from approximately 40% to 37%, or (37% 40%/40% -0.075-a reduction of 7.5%. To compensate for this reduction in tax rate, our model requires that c0.075. But we know that mature advanced economies, like that of the U.S., do not grow at such high rates. So, it is highly unlikely that the tax cut will lead to higher tax revenues and much more likely will lead to increase in budget deficit. Now, the simple model we introduced is, perhaps, overly simple and misses some crucial aspects of reality try to model. In particular, when the tax cut was implemented by the Trump administration, it is the top marginal rates have been substantially reduced, not all the rates. Thus, we nèed a model with more than one tax rate, and then have a tax cut which affects only the top rate. To that effect, let ty and t2, o < tǐ < t2 < i, be two tax rates at which all of the national income is tax, and pi and P2 are proportions of income which which are taxed at ti and t2, respeptively (natura] bounds on pi and pa are 0 < i < 1 and p-1-Pi). Then tax revenue is TR-t (Yp)+ t2 (Ypi). The condition TR TR leads to
Your assignment is simplify this last inequality as much as possible with an eye to relationship between rate of income increase g and tax eut fraction e Then interpret, or found condition in plain English, ie, what does it mean? And, drawing the U.S. economy and its recent history, determine the likelihood of the relationship being true in and, by extension, whether we can expect the tax eut pay for itself is what we have done with the simpler model during the first eclass obtaining a nice on your general knowledge of reality or budget deficit to increase). This 2. Solve the following rational equation z z-1 5 +8r
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