Question

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, e.g. GDP. Suppose, the tax rate t is reduced by fraction c, where 0<c<1. For example, if c-0.05, then the new tax rate is t,-t(1-c)-0.95t, 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 1-c is the new reduced tax rate, and g is the rate of increase in income Y that results from the tax cut. Thern t(1-c) Y(1+g) > tY (1-c-g >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, let's 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 g > c 0.075. 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 we try to modl. 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 need a model with more than one tax rate, and then have a tax cut which affects only the top rate. To that effect, let ti and t2.0 < tl < t2 < 1, be two tax rates at which all of the national income is tax, and P1 and P2 are proportions of income which which are taxed at ti and t2, respectively (natural bounds on P and P2 are 0 < P1 < 1 and P2 = 1-Pl). Then tax revenue is TR = ti (YP) + t2 (Yp2). The condition TR' > TR leads to Your assignment is simplify this last inequality as much as possible with an eye to obtaining a nice relationship between rate of income increase g and tax cut fraction c. Then interpret, or restate, the found condition in plain English, e., what does it mean? And, drawing on your general knowledge of the U.S. economy and its recent history, determine the likelihood of the relationship being true in reality (and, by extension, whether we can expect the tax cut pay for itself or budget deficit to increase). This is what we have done with the simpler model during the first class.

Answer 1

As it has been discussed in lecture Toulmin's Model is that good, realistic arguments typically will consist of six parts.

Data: The facts or evidence used to prove the argument.
Claim: The statement being argued (a thesis).
Warrants: The general, hypothetical (and often implicit) logical statements that serve as bridges between the
claim and the data.
Qualifiers: Statements that limit the strength of the argument or statements that propose the conditions under
which the argument is true.
Rebuttals: Counter-arguments or statements indicating circumstances when the general argument does not
hold true.
Backing: Statements that serve to support the warrants (i.e., arguments that don't necessarily prove the main
point being argued, but which do prove the warrants are true.)

In practice student is encouraged to apply the model as a criterion and a heuristic during his/her work on the paper. He/she should not just apply it microscopically, looking at individual sentences in her text and checking for data or warrants for claims that occur in it. The student, we suggest, should primarily apply the model to his/her evolving draft in a top-down manner, asking herself, "Does my draft contain material that will fit into each of the six boxes which constitute the model?" As a general rule, "default" good academic paper contains material which fulfills certain criteria by which it fits into each of the six boxes.

The Claim in a typical academic paper will usually be found in its conclusion. But in many papers, as we all know, the claim cannot be located to one single passage. Even so, a good paper does make a claim. There are a many criteria for this claim, but the first one is simply that it should be there. The student should have something to say--a statement that is his/hers, not just a reiteration of statements made by one or several scholars he/she has studied.

Data usually constitute the body of the paper. Data should support the claim. Data that are irrelevant to the claim should be omitted. Data may be of at least three kinds; what a specific paper, including the present one, has to prevent by way of data is often a combination of all three types:

1) Theoretical data, i.e., theories, concepts, definitions drawn from authorities, either esteemed individuals (for example, "Habermas says ... ") or current paradigms (for example, "it is generally assumed in Generative Grammar ... "). Such general assumptions belonging to a current paradigm that the writer subscribes to are often, as mentioned a moment ago, presupposed rather than stated.

2) Specific data, drawn from studies by others.

3) Specific data, drawn from one's own study.

Specific data may include, according to field, textual evidence, conceptual analysis, examples, qualitative or quantitative empirical data, and many more.

The Warrant has always been problematic. Among the chief difficulties, according to Fulkerson, is the problem of what to understand by warrant. Especially in the micro-analysis of individual arguments, we all know how hard it can be to decide what the warrant is, and whether a given statement is data or warrant.

We believe it is precisely one of the defining features of academic writing that the writer should carefully discuss the warrant for the data he/she uses, whereas debaters in practical argument are rarely required to do so--which is probably part of the reason why we find it so hard to teach the proper understanding of warrant in practical, extended argument.

Backing, according to Toulmin, is what we come up with if we are asked "why in general this warrant should be accepted as having authority". That is, the "backing" box should contain something about how we are justified in interpreting our data in support of our claim. And that implies discussing and defending not only this way of interpreting, but also the way we collect and select our data. Here again we have various options. We may refer to authority, either authority figures or a current theory or paradigm that sanctions such an interpretation; or we may point to parallel studies where a similar method has borne fruitful and reliable results. This discussion will often imply an assessment of our method that is less than categorical. For example, historical sources that we interpret in a given way may only be so interpreted with a certain degree of probability or on certain conditions; the discussion of backing should address not only the question of whether a warrant or method has authority, but also what degree and kind of authority it has.

Rebuttal indicates "circumstances in which the general authority of the warrant would have to be set aside". The criterion that there has to be something in the rebuttal box means that the paper must show awareness of what counts against allowing the step from data to claim. This may take many forms, according to field. If, for example, a student has used a group of readers' responses in discussing the interpretation of a poem, the step from such data to any claim about the poem is one that many literary scholars in the current paradigms would raise doubts about. Therefore, one important value criterion of the paper is the awareness it shows of these doubts, and how well it answers them.

In a case like this the doubts would be of a general nature concerning whether claims supported by a certain type of data have any warrant. Such doubts might lead into fundamental problems of theory or paradigm common to many fields, for example on whether the study of human phenomena is better or worse off by limiting itself to the observation of behavior, or whether introspection is allowable or preferable, and the like. In other situations, there might be specific, practical or even ethical questions that might be raised about the warrant of the data used. What we see generally is that awareness of what might be.