8

You can find a didactic exposition of Mirrlees (1971) -- including derivations of optimal tax schedule formulas for different social welfare and utility function -- in section 4.2 of "The Economics of Taxation" by Bernard Salanié (2003, First Edition). I bet it is still somewhere in the second edition too, but I do not have a copy of it so I don't know in ...


6

There's a fair amount to unpack in the question, so it might be useful to take it step by step, and consider everything from a more abstract, economic theory perspective. ...those who are more hardworking (or, at least, those who are more skilled) are essentially punished.... We should be careful making statements like this for a couple of reasons. First,...


5

It may seem unfair that someone who has already met their tax obligations gets hit with another one after they die. From an economic standpoint, it is very popular. I'll let this economist article explain it... The gut dislike of death duties seems to arise because the tax clashes with heartfelt dynastic instincts Any tax on capital will tend to ...


5

From an equality of opportunity perspective, it is desirable to have some taxes on inheritance. This levels the playing field for each generation to some extent. If real estates are exempt from such a tax, individuals would prefer real estate over other assets, creating a distortion in the asset price market. For a recent contribution to optimal inheritance ...


4

It looks right to me. There's an alternative (but equivalent) way to solve part D: we know that the consumer's choice will satisfy $$ x^* = \frac{ a(m-t)}{ p_x - s} ,\ y^*= \frac{(1-a)(m-t)}{p_y}, $$ or, with a balanced budget, $$ x^* = \frac{ a(m-sx^*)}{ p_x - s},\ y^* = \frac{(1-a)(m-sx^*)}{p_y}.$$ The government wants to maximize $\min\{x,y\}$, ...


4

Question B in the link answers your question: most participants believe that taxable income would not rise enough to offset the tax cut, indicating that they do not believe we are on the wrong side of the Laffer Curve.


3

I think it is the chain rule. Let $w'(w) = w$, since we are looking for revealing mechanisms. The condition $$ \frac{\partial V}{\partial w'} (w'(w),w) = 0 $$ holds for all $w$ because the mechanism is revealing for all types. As the (not partial) differentiate w.r.t. $w$ of the right hand side is 0, the same goes for the differentiate of the left hand size, ...


3

Why are you doing $\frac{\partial^2 V}{\partial w'^2}$ ? Even if it is said that $w^{'}=w$ at the optimum, it should be taken different when you differentiate it for first order conditions. So, you differentiate it according to $w^{'}$ and $w$.


3

Some issues to consider when thinking about this: A) The idea is to think about the equilibrium of an economy with a particular tax system. For example, in equilibrium a change from income taxes to consumption taxes doesn't necessarily change prices or consumption one way or the other. Intuitively, firms would lower the price because they no longer have to ...


3

Well, one advantage to a sales tax is that it affects everyone (even those who don't pay income taxes). However, some people may see that same fact as a problem. This problem lies in analysis of the equity of the tax. When we consider every single person being taxed 30% on everything they buy, we need to think about how that affects different income groups. ...


3

Because the supply of land is essentially fixed, land rents depend on what tenants are prepared to pay, That doesn't make any sense. If more people want to live in a particular place, rents will increase. And if rents increase, then obviously tenants are prepared to pay more. If they aren't willing to pay increased rents, then they don't really ...


2

To be the wrong side of the Laffer curve would require there to be another lower tax rate which produced the same or greater tax revenues That is not what was being said: Question A addressed the sign of the impact on GDP, not on tax revenues; Question B addressed the sign of the impact on tax revenues; nobody agreed and the large majority disagreed ...


2

To obtain $\frac{\partial y}{\partial z_n}=0$, you implicitly assume that each consumer takes its own skill level as given. And in such a case, in reality the consumer optimizes with respect to labor supplied only. Perhaps it would be better to optimaze with respect to $l$ given $n$. Regarding aggregation the discrete analogous would not be what you write ...


2

in America, the higher your income, the higher the percent of it is spent on taxes Progressive taxation is even worse in many European countries. Progressive taxation is marketed by depicting grotesque disparities between the super rich and the poor, but the fact is that modest levels of income (affording modest levels of purchase power) readily fall in [...


2

There is also a good discussion in "Contract Theory" by Bolton and Dewatripont. It is discussed in terms of non-linear pricing in Chapter 2, "Hidden Information and Screening". However, Mirrlees optimal taxation is discussed explicitly in section 2.2.2, "Optimal Income Taxation." This treatment covers the case with only two types. The case with a continuum ...


1

There is something called productive consumption. The coal and the iron a steelmill consumes are productive consumption, as steel cannot be produced without consumption of coal and iron. Plus, the bread and cloth workers for the steelmill consume are also productive consumption, as the workers would not be able to work without eating and dressing. ...


1

On your assumption "I assume that investing is more useful than consuming for society as a whole, at least in the long run." This is not necessarily true. Imagine if all factories were geared towards investment. There would be a lot of heavy industry, to pour concrete, cast steel and make intricate machinery but all of it would go to build new factories. ...


1

The literature on optimal income taxation kicked off with Diamond, Mirrlees (1971). In their model, people differ only by ability, i.e. the highest earning person is the most productive one. As a consequence, any marginal tax rate on this person will be detrimental to production and hence to social welfare (in this model). Therefore, the optimal top marginal ...


1

I don't see how the log-log utility function you specify would justify a regressive tax rate. In a simple setup, where government engaged in lump sum spending that had to be financed by a consumption or labor income tax, the log-log utility function would have all the same properties as more typical linear, quadratic, CRRA, and CARA utility functions. quasi-...


1

Should housing be considered a form of capital for the purpose of capital gains taxation? Chamley-Judd's proposition aims at avoid[ing] unlimited growth in tax compounding as the horizon extends. Criticism of the Chamley-Judd model is centered on the "assumption regarding infinite lives". But I think the distinction between short-term and long-term ...


1

I think there are a few different ways one can go about examining the topic and general question you bring up. For that reason, I'd like to highlight that this isn't my primary field, and so my answer might not align with a more expert view from that field. However, to get the ball rolling... First, we should probably take a short digression and consider ...


1

There are too many questions in your post, and I advise to edit out most of them, especially those that are not answerable (like "is the system just" etc). For just the first question the answer is No, you don't have the same tax rate on income from labor and from capital. Let $\pi$ be profits before tax, $\tau_{\pi}$ the tax rate on profits, $\tau_d$ ...


1

To provide some input (which I do not necessarily endorse), the Tax Foundation has used its "Taxes and Growth" (TAG) model to estimate/simulate the effects on USA Economy of Thomas Piketty's proposal that the tax rate for very high incomes should rise to $80$%. The results can be found on a report freely downloadable from here. Their Key Findings are (...


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