Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now
39

This is a good question. To be concrete, I think it's easier to pick a single number - this is arbitrary, but I'll go with the figure of $10,000 offered in the proposal by Charles Murray (one of the most prominent conservative supporters of a universal basic income). I'll assume that this is offered to every adult in the US age 18 and over, expanding ...


16

I see the important lesson of the impossibility theorem as establishing that it is not generally speaking possible to have nicely behaved preferences of groups, even if individuals have nicely behaved preferences. Therefore a social welfare function may not exist . Attempts to improve aggregate welfare by maximizing the outcome of a preference aggregation ...


15

What you describe has not much to do with Arrow's impossibility theorem. This is called the Condorcet paradox. The preference profile you gave is used to demonstrate that even if all individual preferences are transitive group judgement may not be. Using majority voting y beats z, z beats x and x beats y. Arrow's impossibility theorem is a more nuanced ...


13

I strongly suspect that an emerging important area for applications of measure theory will be in approximate dynamic programming techniques. Approximate dynamic programming (aka "reinforcement learning" in the computer science literature) has been the direction of research work in the last ~10-20 years of the dynamic programming literature. Economics is only ...


13

There is a temptation for economists to be utilitarians - to go around trying to maximise some measure (total, average, minimax as in Rawls ...) of utility. I think this happens even to economists who've never studied any moral or political philosophy because we often end up using welfare tests. It seems to me that Arrow is very useful (more useful than ...


9

There is quite a bit of work being done in that area. One very recent example is Straub and Werning's working paper "Positive Long Run Capital Taxation: Chamley-Juff Revisited." The point seems to be that we need to consider the rate of convergence to the steady state. Also, there is other literature that gives some competing results (e.g., "the new ...


9

Thanks to densp for identifying this paper. It refers to a major pilot project undertaken in Namibia Background: The Basic Income Grant (BIG) pilot project took place in the Otjivero-Omitara area, about 100 kilometres east of Windhoek. All residents below the age of 60 years receive a Basic Income Grant of N$100 per person per month, without any ...


8

This was too long for comment. "Post 1960" seems an arbitrary and very high bar for an applied field, including micro theory. Most of the topics you name would not be considered contemporary mathematics. For example, measure theory started with Lebesgue's thesis and is over a century old. Topology is even older and started with Poincare, who introduced ...


6

The assumptions are different. First one states that if a bundle is better than the optimal one the consumer cannot afford it. The second one states that if a bundle is as good (not necessarily better) than the optimal one it has to cost as least as much, not less. Consider a space with just one type of good, $x$, and a utility function $U(x) = 0$. Let the ...


6

Ljungqvist and Sargent (2004). Recursive macroeconomic theory 2n ed. (ch. 15) present and review the issue. In the Concluding Remarks section, they mention two environments, where the "zero-optimal-capital tax rate" does not hold: Aiyagari(1995) presents a model with heterogeneous agents, incomplete insurance markets and borrowing constraints (i.e. a "...


6

Firstly, suppose we take a utilitarian welfare standard that is linear in money. That is to say, suppose that both utility and profits are linear in the amount of money that consumers and firms have (but not necessarily linear in anything else). In that case, the Pareto standard and the utilitarian social welfare criterion coincide exactly! You can see a ...


5

As you pointed out, the problem of inefficient supply by a profit maximizing monopolist can be solved via subsidizing the monopolist to increase his marginal revenue. The subsidy can be paid by the consumers or by a central government. Consumers unfortunately perceive the problem as a collective action problem: The marginal utility gain from subsidizing the ...


5

Here is an answer based on the following interpretation of the SWF : there is no "true" SWF, but SWFs are observable in principle, they simply represent the preferences of the policy decision maker. Under this interpretation, the policy recommendation are relevant despite depending on the specification of the SWF, precisely because different decision makers ...


5

Measure theory is widely used in the problem of fair division (aka "cake-cutting"). See the many papers about fairness in economics journals. For a particular example, see Tatsuro Ichiishi and Adam Idzik, "Equitable allocation of divisible goods", JME 1999.


5

Loeb spaces have been used to model situations with a continuum of agents. See http://eml.berkeley.edu/~anderson/Book.pdf and the chapters by Sun on economic applications in the book Nonstandard Analysis for the Working Mathematician.


5

I feel like I do not understand the exact meaning behind the notion of the Pareto optimality. It's not you. There are different senses of the phrase "Pareto Optimal," and you have to figure out from context which one is being used. The dictionary definition of Pareto Optimal is something like "An allocation from which any feasible change which makes any ...


5

Suppose you have a product that you can distribute for constant marginal cost $c$. For every $v\geq0$ assume there are some consumers who value the good at $v$. The net welfare created when someone consumes the good is their value minus the cost of production. Thus, if we want to maximise the total social surplus (net of costs), we should give the good to ...


5

There are at least two other examples of SWFs that satisfy these conditions. The first is a positional dictatorship. Let N be the number of individuals (assume it is fixed). For any k between 1 and N, the kth positional dictatorship SWF orders social alternatives in terms of the preferences of the "kth best off" agent. Formally, given any social ...


4

A new report by the Roosevelt Institute answers exactly that using a Keynesian, Stock-Flow-Consistent model calibrated to the US. According to their result, when distributional changes are considered, an UBI would considerably stimulate the economy. The Executive Summary reads: How would a massive federal spending program like a universal basic income (...


4

Perhaps you have heard the competitive equilibrium referred to as the Arrow-Debreu equilibrium. The idea of the theorems existed earlier but Arrow introduced the theorems formally in a way that is equivalent to what we today call the first and second welfare theorem in 1951 in his paper AN EXTENSION OF THE BASIC THEOREMS OF CLASSICAL WELFARE ECONOMICS. ...


4

Here is a chart from the OECD, which shows the net fiscal impact of migrants on their recipient country (i.e. by how much to they contribute or withdraw from the welfare state, albeit excluding in-kind benefits such as healthcare). For most Western countries, Denmark included, migrants are modest net positive contributors ("they pay in more than they take ...


4

The second welfare theorem does not necessarily involve a government as such. It does not matter for the theorem who redistributes the resources. Nevertheless, in practice this will most likely often involve the government.


3

In general, yes it's an externality: it's a cost borne by others. How do we know it's a cost with real economic value? Because in general, properties with good light and better views tend to attract higher purchase prices and higher market rents. And there's a difference between "view/light might be obscured some time in the future" versus "they are ...


3

I think you are looking for data on real median incomes. If this concept is unknown to you, you can read about it on wikipedia. According to the data the real income of most households decreased after the financial crisis but is still above the 1995 level. This means that most households do live better. I don't know if the number of people on welfare would ...


3

One thing such funds get spent on is corruption: Do Public Fund Windfalls Increase Corruption? Evidence from a Natural Disaster (Nikolova and Marinov (2015)) We show that unexpected financial windfalls increase corruption in local government. Our analysis uses a unique data set on flood-related transfers, and the associated spending infringements, ...


3

This is from the end of the first chapter in the book Public Finance in Canada 4th edition by Harvy Rosen. This book is a primer for welfare economics. The book states gives a list of: Journal of Public Economics Canadian Tax Journal National Tax Journal Public Finance Public Finance Quarterly International Tax and Public Finance Journal of Public ...


3

Q1 Optimal usually means one of two things: Pareto optimal (there's no way to change the outcome such that everyone is at least as well-off, but someone is strictly better-off). Optimal in the utilitarian sense (we maximise the sum of everyone's profit/utility). If utility/profit is quasilinear then the two concepts coincide. This paper appears to be ...


3

Convexity of the production set is indeed not needed for the proof of the first welfare theorem but for the proof of the second welfare theorem. It is not a necessary condition though. It is possible to interpret this as an existence issue. The first welfare theorem is about all competitive equilibria and holds trivially if there are none. The second ...


3

In my view, this is not a well defined question since it isn't very clear what you mean by 'feasible': If you mean 'are developed countries in principle able to pay for a UBI?', then the answer is trivially yes. Perhaps you mean 'politically feasible'? Obviously, that depends on the political constraints on redistribution, attitudes towards 'handouts', etc. ...


3

Consumer surplus is their willingness to pay minus the price they pay, and producer surplus is the price they receive minus their willingness to receive. So if you are assuming that consumers are forced to buy at a price of 100, yes the consumer surplus is negative. and according to your example, the producer surplus will be zero. You are right it does not ...


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