Arrow of time and irreversibility in Economics In physics there is the concept of arrow of time, which states that time only evolves in one direction (forward), and that this should be visible in the material world. As the Wikipedia article states (emphasis mine):

  Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that this is not the case: there is an obvious direction (or flow) of time.

The emphasis above wants to highlight an important question, which I think it is pertinent to economics. Namely, if the direction of time were to be reversed, would the theoretical statements described by these models still hold? This is, are dynamic economic models time-asymmetrical or time-symmetrical?

For example, consider a Solow model. Is there an arrow of time in this model?  To put it differently, draw a Solow diagram of the accumulation of capital. Draw the path of the economy from A to B. Does this imply necessarily a unidirectional time evolution?

This relates to the issue of irreversibility and determinism. If we use deterministic models (as the standard Solow), we can reconstruct "back" everything from "the future". However, complex systems, where uncertainty and stochastic shocks prevails are by definition irreversible.

As this article on the Chemistry Nobel prize winner Ilya Prigogine states:

  Prigogine contends that determinism is no longer a viable scientific belief: "The more we know about our universe, the more difficult it becomes to believe in determinism". This is a major departure from the approach of Newton, Einstein and Schrödinger, all of whom expressed their theories in terms of deterministic equations. According to Prigogine, determinism loses its explanatory power in the face of irreversibility and instability.

Any hints of how this discussion translates into economics?

The question and the answer by user14471 seem to relate to the issue of ergodicity in economic systems and models. Economic systems (in reality) cannot conceivably be ergodic, while some economic models are ergodic (those that do not attempt to reflect any of the non-ergodic properties).

Necessary concepts to answer this question: Ergodicity, microstates, macrostates

Ergodicity is the property of a system to spend approximately equal amounts of time in each of its microstate (if you observe it over sufficiently long times). A microstate is simply the state of a system if you consider every property of every element of the system. Not all microstates are distinguishable. Undistinguishable microstates constitute a macrostate. That is, all macrostates are distinguishable but some have more microstates than others. An ergodic system will be more likely to assume those macrostates with more associated microstates (that is, the macrostates with higher entropy).

Examples

Consider a non-economic example: gas in a container. For the definition of a microstate, the position of every molecule is important, for a macrostate only the distribution of the gas matters. While there is a macrostate in which all the molecules are crammed together on one side of the container, this one is extremely unlikely; a macrostate with an even distribution of molecules across the container is much more likely. Since the gas can, however theoretically assume each of the microstates in the future, independent of which other microstates have been assumed in the past, the system is ergodic.

Now consider an economic example: the distribution of dollars across the population. A microstate considers which dollar is owned by which person, a macrostate only considers the distribution. While microstates are not distinguishable or even measurable (how do you distinguish the different dollars in your bank account?), the number of microstates per macrostate is important. Theoretically, all dollars could be owned by one person (while everyone else has nothing). This is an extremely unlikely macrostate, while a more even distribution across the population is much more likely. Actually the likelihood (and entropy) will be maximized by a Gaussian distribution. (However, if you measure the distribution of wealth, you will find that it is not Gaussian but heavy-tailed.)

How ergodicity, irreversibility, and the arrow of time, are related

Ergodicity can be phrased differently as: every microstate is reachable from every other microstate. It is reversible, it does not have an implicit arrow of time. It is easy to see that this is not the case if the system has an attractor (a stable equilibrium) that captures trajectories (development paths) which will then not be able to leave the attractor again.

Ergodic and non-ergodic models in economics

Armed with these concepts, we can now return to the question of reversibility in economics.

Models of simple exchange of goods etc. are ergodic. Depending on how and according to what prices and preferences the goods are exchanged, every microstate of the system is reachable and possible. What is more, every transaction can be reversed.

In the case of models of growth, developent, or technological change, ergodicity will typically not hold any more (unless you can have degrowth such that the system reverses its growth trajectory exactly). These systems typically have attractors (Solow-Swan models for instance have an attractor once you remove the neutral technical change term) they have production functions that would generally not be considered reversible, and they may not allow for recessions and reversion of technological change. More complex models of technological change and development from evolutionary economics or so will definitely

That said, economic models have a certain tendency to assume ergodicity for whatever is not part of the model. Macro-models (including Solow-Swan models) assume that the structure of the microlevel (that is not modeled) will not interfere with how the model works, that agents are exchangeable (representative agents) and that transactions are neutral. For RBC and DSGE models this is made more explicit by assuming an unbiased i.i.d. stream of shocks acting on a largely homogeneous population of agents. Some varieties (HANK etc.) try to address this, but the heterogeneity those models allow for is extremely limited. Agent-based models address this from a different angle and are able to achieve the non-ergodicity property observed in real economic systems (see last paragraph below), but they have their own problems, as was discussed in a different question.

Ergodicity in real economic systems

In real economic systems, it is obvious that development paths are not reversible. You may suffer a recession, you may even experience an extensive collapse and lose advanced technologies, but you will not be able to dismantle and sell off the associated capital goods (and the human capital) in a way mirroring how they were acquired. Further, humans react vastly different to gaining and losing wealth (loss aversion).

And beyond this, the very distribution of wealth - a heavy tailed, Pareto distribution, not a Gaussian - will show you that the system does not achieve (or even come close to) the entropy maximizing macrostate with the most associated microstates. This is a structural property typically found in complex systems with self-organizing properties (the issues Prigogine wrote about as mentioned in the OP). You will find similar distribution also among firm sizes, regional agglomerations (city sizes), and a ton of other things that are more or less related to economic systems.


Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)? I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30).

However, as the choice $x(p',w')$ is only feasible under the price-income level $(p',w')$ and $x(p'',w'')$ is only feasible under $(p'',w'')$ in Figure 2.F.1(b), why does it still satisfy the WARP definition which requires that a choice (say, $x(p',w')$) should be feasible under two different price-income levels (say, $(p',w')$ and $(p'',w'')$)?

Intuitively, this just says that if the bundle you choose was possible under wealth $w$ and price $p$ but it is not $x(p, w)$, then it must be that you cannot obtain it when price is $p'$ and wealth is $w'$.

It simply does not say anything about case (b) in which $p' \cdot x(p'', w'') > w$ and $p'' \cdot x(p', w') > w''$. Since the first part of the if ... then statement in the definition is false, everything evaluates to true.


Oil price decreases due to supply decrease? I am reading this article on the Financial Times: Oil prices hit as US gulf coast faces hurricane

If the production of oil is forecast to decrease, that means the supply would decrease. Surely the price should rise, not fall?

The article says:
The price of crude oil was driven down on Friday as Tropical Storm Nate was forecast to strengthen and hit the US Gulf of Mexico coast with hurricane force winds on Saturday night, and as traders anticipate disruption to refineries.

What am I missing?

Refineries need oil to produce chemical products. Therefore, it means declining demand for oil and falling prices according to demand supply principles.

The point is refineries which use oil as ingredient.


Neoclassical economic profit and growth theory versus marxian Marxists have a very specific "profit" and "economic growth" theory. According to marxists, profit doesn't come from technology, whose cost will be reflected in the price of whatever commodity the technology owning businessman is selling. Instead, the businessman profits by paying workers low enough for their labor so that they can squeeze a profit (e.g. profit comes from living labor not dead labor (technology)). Some of this profit will in turn be used to invest in more technology which will cause capital growth (capital valorization in marxist speak).

What's the neoclassical parallel to this? It seems in neoclassical models, the market is in equilibrium so the prices reflect marginal costs and there's no "economic profit". What seems to happen is that technological advancement "happens" and this in turn creates economic growth and a new steady state/equilibrium. However, is technological innovation here merely an accident, or does it have a logic in the same way marxian "growth" has (e.g. capitalists accrue profit through living labor and then invest it in technology)?

If there is perfect competition, then yes, you will get zero economic profit, but even then, technology does no poof out of nowhere. Otherwise, you might find very different results.

Let's think of the nature of competition through product differentiation. (We'll get into technology later.) Imagine two firms making their own widgets in Cournot competition, but instead of the normal price function $P = X - q_1 - q_2$, we have

$$P = X - q_i - d\cdot q_{-i}$$ where $-i$ denotes the other firm that is not firm $i$, and $d \in (0,1)$, $1$ being no product differentiation, and $0$ being completely different products sold by the two companies.

If $d = 0$, then the firms aren't really competing since their products are completely different and are acting as monopolists, making economic profit. If $d = 1$, then the firms are competing through regular Cournot and still making profit (probably).

In Bertrand, we can consider product differentiation as part of determining how much of the market you will steal away by undercutting price. The way a normal Bertrand model works is that you set price and then produce (as opposed to Cournot, where you set production, which affects the price). If you have a lower price, and there is no product differentiation, you steal away the whole market, so each firm will push price down to the price under perfect competition, where both firms split the market.

With product differentiation though, you don't lose the whole market when you are undercut, since your product is still a bit different. With full differentiation $(d=0)$ then you get the same result where each firm act as monopolists.

Under each of these models, technology doesn't "just happen", but is reflected through lowering the marginal costs of the firm, which is essential for the firm to be competitive against its rivals. The less technologically advanced the firm is, the more of the market they will lose out on. Economic profit here can be used to invest into research and development or just straight up "technology" to reduce the cost of capital usage over time or other such things like that.

Even in perfect competition with no economic profit, the reason there is no economic profit will partly be because firms have to constantly update their technology to remain competitive, regardless of how differentiated the products are (as long as $d > 0$).


Shouldn't corporate tax be calculated based on EBIT instead of EBT? When I was studying Corporate Finance in university, I was surprised to learn that it is more advantageous for corporations to take more debt (even if they don't need to) because it creates tax shield which leads to a gain for equity holders.
This feels like a distorting incentive. Therefore, wouldn't it be optimal to tax corporations based on earning before interest and taxes rather than based on earnings after interest?

Indeed the debt tax shield is distorting. Any policy that will essentially distort prices to favor A over B will lead to too much A and too little B. So such differentials are (almost) always distorting (unless you actually want less B and more A due to externalities).
Here the tax deductibility makes debt cheaper compared to equity. We know this is distorting from the Modigliani-Miller theorem. It states that a company's capital structure is not a factor in its value, so it doesn't matter how much debt or equity they have. However, the theorem holds in perfect markets without taxes. As you learned, taxes destroy this result.
So what can we do?
We need to not influence the price (cost) comparison between debt and equity in any way. So this leaves two options:

Limit (remove) the tax deductibility of debt (as you propose).
Allow for the cost of equity to be equally tax deductible. This proposal is known as the allowance for corporate equity (ACE).

Both have been tried in different countries.
The issue with the first one is that you are asking firms to pay taxes on money they may not have. Suppose the tax rate is 10% and a firm has EBIT of 10\$ and interest of 10\$. The firm has no money left after paying its interest, but it now owes the Government 1\$ (10% of the 10$ EBIT). Where is the firm supposed to get this money? Borrowing could be difficult as they can barely repay their current debtor's interest. If the firm pays the full interest, it cannot pay the Government taxes and is now essentially in default. If the firm pays the Government first and does not pay interest to its creditors, it is also in default. We don't want that either. It's counterproductive, since one point of removing the tax shield was to reduce debt and default risk in the first place. So eliminating the tax shield would be impractical, but one could try to limit it.
The main issue with ACE is the potential revenue loss. The IMF estimates that if the allowance were given to all equity, corporate income tax revenue would fall by 5-12 %. (I am borrowing this excellent link from a great comment by sba222).
Side note: You propose taxing earning before interest and taxes, but note that all taxes are on earnings before taxes, so its just "EBI" that we're talking about.


If governments can accurately do your taxes for you, why would it overwithhold people's income? Here's What Would Happen if No One Paid Taxes

But don't the majority of people get refunds? And wouldn't that mean it wouldn't be quite so much of a disaster if no one filed?
$\color{red}{\text{There are more refunds; people are overwithheld.}}$ So for those folks, it works as a kind of forced saving. You get a lump sum that you can then spend for some item you may not have been budgeting for on a weekly or monthly basis. A bunch of economists have argued, pretty persuasively, that with modern computers, the government could do your taxes for you with no problem. The computer could do that stuff with the blink of an eye. They would have all your information, so you would either get a check or a bill in the mail.

Overwithholding Definition

Who wouldn't want to get a big tax refund check from the Internal Revenue Service (IRS), right? But think again: When you get a big refund, you’re just getting your own money back; but with no interest. In effect, you're letting the IRS use your own money for most of the year without paying you any interest.

If governments can accurately and automatically do your taxes, why would people be overwithheld and there be more refunds? Can't the government's supercomputers can factor in and compensate you the interest?

This is US specific and more of a political than an economic or technological problem.
In the US, there is a lot of lobbying by tax preparation firms for the antiquated tax system to remain unchanged. See e.g. this 2019 article "Inside TurboTax’s 20-Year Fight to Stop Americans From Filing Their Taxes for Free".
In many other developed countries, the quote from Vice applies: Their governments do simply calculate your taxes correctly (and automatically deduct/credit from/to your bank account the exact amounts). Most taxpayers have to do zero work (all their information on their salaries having already been automatically submitted to the government through their employer). There is also no need to bluntly withhold large and arbitrary sums.


Why do loans drive the economy? Someone was saying: "Why is credit so important? Because when a borrower receives credit (loan), he's able to increase spending. Spending drives the economy. This is because one person's spending is another person's income ".

I think he didn't look at the lender's prospective. When a lender gives his money to someone else, his spending will decrease. So the economy is balanced and this will not drive the economy. The same amount is spent just by a different person.

Am I right?  What am I missing?

The lender is typically supplying loanable funds in the form of ‘savings’. I.e. money she wouldn’t spend until a future date. But the market for loanable funds allows one to earn interest on these savings rather than laying dormant (think about when people would store money under their mattresses). So, with this surplus of funds, another can make use of these funds (for a price, interest) and increase the amount of spending they themselves do. Hence, the total amount of spending would increase because if that person hadn’t borrowed money to increase their spending, the money would sit in savings.


Do carbon taxes in place today apply to carbon embedded in imports? I’m giving the example of Sweden whose carbon tax is highly regarded and which is the highest in Europe.
Source

Sweden has a carbon tax of €110 / t. Source

This tax does not apply to installations covered by the EU ETS. The EU ETS applies to 45% of all carbon emitted in the EU and currently only prices carbon at around €25 / t.
Source1 Source2

Moreover some 45% of primary energy consumed in Sweden is nuclear and hydro making Sweden’s energy supply relatively less dependent on carbon emissions.
Source

As a consequence of the carbon tax and the high share of non-fossil energy generation Sweden’s per capita carbon emissions are low by international standards (5.5 t CO2e / capita / year).
Source

However, when measured by consumption Sweden’s per capita emissions are relatively high (15.4 t CO2e / capita / year). 58% of carbon consumed in Sweden is imported.
Source

This makes me think that there could be tendency for expensive domestic carbon emissions, especially those not covered by the cheaper EU ETS, to be substituted with carbon embedded in imports – unless the carbon tax would apply to imports as well.

I think the answer is generally/overwhelmingly "no" there usually not a embedded carbon (import) tax in most jurisdictions. A 2019 paper says:

  The idea of a BCA is not new. In the US, for example, lawmakers have tabled several proposals to introduce a carbon tax. So far, though, no country in the world has an operational BCA.

Supposedly the EU Green Deal was supposed to include one, but I haven't followed the developments. (There have been arguments against it already. And the US has already threatened to retaliate should the EU adopt it.)


Formula for Effective Discount Rate of Discount Rate Series what is the formula to calculate an effective discount rate of Discount Series? For EX, If Price of Product A is $X and Discount Series is given like 10%,20%,30%,5%,2%. How can we calculate effective discount of this discount series?

https://answers.yahoo.com/question/index?qid=20110703053015AANbTBg

I found something here, but searching for a generalized formula for N number of Discount Series.
Thank you

$$\displaystyle 1-\prod_i(1-d_i)$$ should give you the answer, with the discounts treated as fractions, so for example $10\%$ being $0.1$


General equilibrium regarding on U= max(ax,ay) + min(x,y) Please kindly instruct me on solving the following in a general equilibrium framework with standard budget constraint,
$$ u^{1}\left ( x  \right )= max\left [ \frac{x_{1}}{10}, \frac{x_{2}}{10}\right ]+ min\left [ x_{1},x_{2} \right ] $$
, with $e^{1} = (10,10)$

What would this consumer demand at prices $p = (\frac{3}{4}; \frac{1}{4})$?

Given the other two consumer utilities

$$u^{2}\left ( x  \right )= x_{1}^{\frac{2}{5}}x_{2}^{\frac{3}{5}} $$

$$u^{3}\left ( x  \right )= x_{1}^{\frac{3}{5}}x_{2}^{\frac{2}{5}}$$
, with $e^{2} = (4,6)$ , $e^{3} = (4,4)$

Find one Walrasian equilibrium (and determine both equilibrium prices and the equilibrium allocation).

I have completely no idea how to start with it...

Thank you!

Let us name three consumers A, B and C, and two goods X and Y. Equilibrium price vector $(p_x, p_y=1)$ and allocation $((x_A, y_A), (x_B, y_B), (x_C, y_C))$ satisfy the following:

Optimality Conditions (Allocation must solve the utility maximization problem of the three consumers, i.e. it must lie on the demand functions)

$(x_A, y_A) = \begin{cases} \left(\frac{10p_x+10}{p_x}, 0\right)  & \text{if } p_x \leq \frac{1}{10}  \\ \left(10,10\right) & \text{if } \frac{1}{10} \leq p_x \leq  10 \\ \left(0, 10p_x+10\right) & \text{if } p_x \geq 10\end{cases} $
$(x_B, y_B) = \left(\frac{2(4p_x + 6)}{5p_x}, \frac{3(4p_x + 6)}{5}\right)$
$(x_C, y_C) = \left(\frac{3(4p_x + 4)}{5p_x}, \frac{2(4p_x + 4)}{5}\right)$

Feasibility Conditions

$x_A + x_B + x_C = 18$
$y_A + y_B + y_C = 20$

Solving the above gives price vector $(p_x, p_y) = (1.2, 1)$ that supports the allocation $((x_A, y_A), (x_B, y_B), (x_C, y_C)) = ((10, 10), (3.6, 6.48), (4.4,3.52))$ in equilibrium.


Does 'ethical investing' have any effect? Some mutual funds make a point of only investing in ethical companies (eg avoiding arms companies, polluters, human rights violators, etc).

Or other organisations pressure funds to stop investing in particular industries/companies. (example).

Some organisations involved in ethical investments are particular big. For example the New Zealand Super Fund is worth $20bn, and frequently recieves pressure to divest in certain firms.

The question is - does divesting from unethical firms have any impact on those companies?

No doubt that consumers boycotting what the company is producing would have an effect, as that directly effects their revenue.

Similarly refusing to loan money, or provide additional capital to ethically questionable companies would limit their ability to do business.

But as far as I can see not owning shares in particular companies simply reduces demand for, and thus value of those companies, improving the return on investment for people who are willing to own those shares.

Does boycotting ownership of ethically questionable companies/industries have any effect on those companies/industries?

In a world where capital markets are infinitely deep there shouldn't be any price response to capital and so we wouldn't expect any consequences on firm behavior. There is some good empirical evidence for slow moving capital so that's probably not true. Ethical investing is likely to drive up capital costs at least some. In which case your question boils down to two questions, "can an non-ethical company become an ethical one" and one that may seem quite different, "what is the elasticity of demand for capital with respect to the price of capital?" Tobacco and munitions companies can shift into other business but they can't get ethical investment funds without abandoning that business. Other businesses like fair-trade coffee and certified conflict-free diamonds, may allow ethical investing in the current business with higher costs. The former group really only have one choice, to shrink in response to expensive capital. The latter group have a second option, to shift into ethical investing business models that may be more expensive but less expensive than the increase in the cost of capital.

Let's ignore that first channel for a minute. Let's just consider a world with some ethical industries and some non-ethical ones. One day some people wake up and become ethical investors and this causes a change in the demand for non-ethical securities. If firms have an inelastic demand for capital (lower right graph, moving from $S_2$ to $S_1$) then the quantity of capital demanded changes relatively little from the ethical preference shock and so the  total capital invested in the non-ethical industry changes very little ($Q_2$ to $Q_1$). Instead returns go up a lot ($P_2$ to $P_1$) for those investors who remain invested in non-ethical industries.

On the other hand, if capital demand is quite inelastic (lower left graph, moving from $S_2$ curve to $S_1$)), the return on capital changes very little ($P_2$ to $P_1$) but the total capital invested in  non-ethical industries falls a lot ($Q_2$ to $Q_1$). In that world the ethical industries crowd out the non-ethical ones because the profits aren't there to preserve their capital supply.

Now consider production shifting. If substitution into ethical practice is more expensive than paying a higher cost of capital, this won't be an important channel. Firms are better of taking their licks in the capital markets. However, if substitution is cheaper (like when capital demand is inelastic and and substitution easy) then behavioral adaption will become the dominant channel.

In practice, according to Does Ethical Investing Impose a Cost Upon the Firm? A Theoretical Perspective by James J. Angel and Pietra Rivoli (1997), the actual effects on capital costs and quantities are quite small, suggesting that neither industry shrinking nor industry transformation are important under prevailing circumstances. If more money shifts into ethical investing this could easily change.


Are social goods and public goods the same thing? I am confused as to they are the same or different?

I guess it might depend on the author. Here's another classification:

  The classifications of public goods associated to agriculture identify two main categories: environmental goods and non-environmental goods (or social goods). In the first category are placed those public goods closely related to
  environmental externalities, such as farmland biodiversity, water availability and
  quality, resilience to flooding and fire, climate stability (mainly carbon storage and
  reducing greenhouse gas emission), agricultural landscape. In the second category
  are placed those public goods more related to the social dimension of agricultural
  activities, such as farm animal welfare and health, rural vitality and food security.

So under this classification social goods are non-environmental public goods.

And for some other authors, public and social goods are entirely synonymous:

  Turning to allocative problems and policies we note first, that the category of good and services provided by government are of the nature of public (or social goods). In the case of private goods, we found that efficiency in the competitive economic sense meant the maximization of individual utility alone [...]

  Public goods are those the consumption of which jointly by all individuals could make any one individual better off but no other individual worse off. Examples of public or social goods are public education, hightways, water and power, the postal system and so on.

There also exists some economic dictionaries, which might reflect the wider usage of the terms.

The Oxford one, in its first edition only defines public good:

  public goods Goods or services which, if they are provided at all, are open
  to use by all members of society. Examples include defence, law and order,
  and public parks and monuments. As nobody can be excluded from using
  them, public goods cannot be provided for private profit. Public goods can
  be and frequently are provided privately, by individuals and voluntary
  organizations, from motives of altruism or ostentation. Really expensive
  public goods such as defence are necessarily provided by government bodies,
  which alone have the power to raise the taxes needed to pay for them.

"Social good" is not defined in that one. There's a newer 3rd ed online of that dictionary, which also doesn't seem to define social good.

Likewise, The Economist defines only public (but not "social") good

  Public goods

  Things that can be consumed by everybody in a society, or nobody at all. They have three characteristics. They are:

  non-rival - one person consuming them does not stop another person consuming them;

  non-excludable - if one person can consume them, it is impossible to stop another person consuming them;

  non-rejectable - people cannot choose not to consume them even if they want to.

  Examples include clean air, a national defence system and the judiciary. The combination of non-rivalry and non-excludability means that it can be hard to get people to pay to consume them, so they might not be provided at all if left to MARKET FORCES. Thus public goods are regarded as an example of MARKET FAILURE, and in most countries they are provided at least in part by GOVERNMENT and paid for through compulsory TAXATION. (See also global public goods.)

They also define

  Global public goods

  Public goods that cannot be provided by one country acting alone but only by the joint efforts of many (strictly, all) countries. Some economists, along with global institutions such as the UN, reckon that such goods include international law and law enforcement, a stable global financial system, an open trading system, health, peace and enviromental sustainability.

There's also a Routledge dictionary of economics, which defines (quoting 2nd ed. of that):

  public good (H4)
  A commodity or service which is available
  to everyone in a particular catchment area,
  cannot be withheld from non-payers and
  is ‘non-rival’, i.e. one person’s consumption
  does not diminish that of others. The
  main examples are national defence, sewerage,
  street lighting, lighthouses, public
  health measures such as mass vaccination,
  and scientific research. As individuals
  cannot be charged according to consumption
  for goods and services collectively
  provided, it is usual to finance their
  production by taxation. Although the
  provision of public goods was small until
  the twentieth century, writers as early as
  PETTY, SMITH and John Stuart MILL argued
  for their existence. It is not always easy to
  distinguish between a public and a private
  good as some private goods gratuitously
  benefit third parties, e.g. maintaining a
  garden in a beautiful condition confers
  pleasure on many people in the vicinity.
  See also: club good; local public good;
  mixed good; private good

  social good (H4) see public good

The MIT dictionary of modern economics has quite long entries, so I'll only reproduce snippets here (from 4th ed.). For public good is says among other things:

  The extreme, or
  'polar', case of a 'pure' public good has been
  defined by Paul A. SAMUELSON as a good
  which is:
  1. non-rival in consumption
  2. has the characteristic of NONEXCLUDABILITY
  - that is, if the good is provided
  the producer is unable to prevent anyone
  from consuming it.

This source also defines "collective goods" (defined by non-excludability alone), "local public good" (public goods may depend on the chosen community), "mixed good". The entry for the latter is quite long, and says in the end

  Mixed goods are certainly more common
  than pure public goods and possibly more
  common than private goods - thus their
  analysis is of great importance. The term
  impure public good is sometimes used to
  describe mixed goods.

The MIT dictionary does not define social good.

The New Palgrave dictionary (which is more like an encyclopedia, with articles/entries contributed by different authors) mentions (in its second edition) that

  The
  distinction between private and public or social goods arises from the mode in which benefits become
  available, i.e., rival in the one and non-rival in the other case (see Public Goods).

So that entry (which is actually on merit goods) considers the terms social and public goods synonymous. They further use the public/social goods interchangeably a few times in their entry on Musgrave. Musgrave himself wrote the "public finance" entry for that Palgrave dictionary, and it too uses social good to mean public good at one point.

Their entry for "public goods" (written by Agnar Sandmo) is basically dedicated to the Samuelsonian approach to the topic. It doesn't define or mention social goods, but it does define a "social welfare function", talks of "social marginal cost of the public good" etc. There's no entry for "social goods" in that Palgrave dictionary (even though it's 7,000+ pages long).

I think the trend from all of these is clear: "social goods" are much more idiosyncratically defined, if defined at all. Most authors who do use the term "social goods" seem to use it synonymously with public goods (unlike what Wikipedia claims, without a citation.)


Is inconclusive region in durbin watson a problem? What to do if my durbin watson is found to be inconclusive?

Do I have to change my model?

There are cases error serial correlation is a disaster. For example, if your model is $y_t = \beta_0 + \beta_1 y_{t-1} + u_t$, then serial correlation in $u_t$ means correlation of $y_{t-1}$ and $u_t$ (in general) and your OLS estimator is biased and inconsistent. In other cases, serial correlation does not cause endogeneity and OLS is still consistent. An example is the case the right-hand side variable is strictly exogenous. Then you can use OLS and heteroskedasticity and auto-correlation consistent (HAC) inferences, e.g., using the Newey-West standard errors.

So my answer is "it depends". If some regressors become endogenous due to the error serial correlation, you will probably want to change your model. Otherwise, you can use OLS and HAC standard errors.

If your model is dynamic ($y_{t-1}$ on the right-hand side), the chance is high that you need to seriously worry about serial correlation in $u_t$. This happens in many time-series and financial applications.

By the way, Farebrother (1980, JRSS Series C) proposed Pan's procedure for $p$ values for DW tests. Inconclusiveness can be avoided.


When big companies invest on a new idea/product? I am graduated in AI field. I love robotics and intelligent systems, so I worked on some new products by myself at home that have new ideas and are interesting(at least me and my friends think!). I decided to apply for a accelerator or incubator, bu I faced whit a question like this in those forms:

  Who are your largest competitors and why? Differentiators? How can you
  defend your business model?

And when I thought about it, there is no competitor at the moment(because of new idea and product), but the large companies like google,apple,microsoft,sony,samsung,etc would become our competitor at AI(Artificial Intelligence) field! And I think they can remove me from the market very soon and very easy!

So, I don't know what should I do? Should I forget my AI field ideas and make a company in that field because of those huge companies?

Is it possible to find that, when does companies enter to a business? Or is it possible to make a deal with them to have our individual company? Or I must try to become their employee and just this(Actually if the accept me :) )?

Legal perspective

Big companies have no reluctance is taking other people ideas:

usually legal systems does not provide protection for ideas themselves,
even if an idea is protected by intellectual protection rights (IP, as a side note please consider long procedure for application for patents, etc.), litigation is costly and long-lasting. You will have significantly smaller resources to be able to protect your idea (even if you win, by the time of the court ruling the market will be taken).

Thus, an idea is not purchasable for big companies. IP, prototype or a small company with IP is.

Business perspective

Even if you will have purchasable IP/prototype/company, big companies still decide which is the most beneficial: to buy or to reproduce. Most often the latter is cheaper. This is because if a larger company can, as you say, remove you from the market very easily, it probably will. If you are considering building your own company, I suggest seeing Michael Skok’s framework, especially chapter ‘Disruptive business models’ and ‘Getting Behind the Perfect Investor Pitch’. In short: if there are no technical barriers for possible competition, make a business model impossible to be replicated by competitors (real life example: Netscape market position was taken by Microsoft’s Internet Explorer because Microsoft could sell IE with every copy of Windows; Microsoft’s lost huge part of the market to the Google, because Google's business model comprised of delivering free products to consumers and profit based on advertisements).

Please also consider that creating a new market takes not shorter than 3 years from the release of the product, sometimes even 7 years (source: S.Blank, B.Dorf, The Startup Owner's Manual).

If you are interested in methods of evaluation return of investment

However, if you are interested how big companies evaluate new ideas for investment (usually for development by themselves), most important factors are soft criteria. Those depend on the project, please find some exemples of such criteria below:

technology (in short: is it the way to go?)
competition (the questions you’ve described can be good examples of some of questions, which companies have to answer before going into investment)
missed opportunities (what would be the better investment, which the company could miss if it will engage in the project at hand?)
profitability in general (how much the value of the company will increase as a result of the investment? when the project will yield return?)
advisability and viability (in general: labour-, capital- and resource- intensity of the project)
means - what is the funding structure (who is bringing their financial contribution? will the gathered means be sufficient?)
in cases when capital is to be transferred to an outside entity (e.g. while investing in smaller company) - credibility of the team, which will lead development works (can they deliver? what were their previous projects? what is their commitment to the project?),
‘extras’ (additional cost-, income-, manufacturing- and/or public image- advantages)

There are many interesting mathematical models to calculate return on investment (ROI, ROE, Payback Period, Accounting Rate of Return, Net Present Value, Internal Rate of Return etc.) but these are only used after all the soft questions can be answered positively.

Hope it helps. I intended to make a small comment, but ended with few paragraph answer :)


Market Power in microeconomic theory What does the term Market Power mean in microeconomic theory

In competition policy (part of microeconomics), market power is often defined as the ability of a firm to raise and maintain prices above the levels that would prevail under competitive conditions (with obvious adjustments if the market power is held by a buyer).  Having market power does not necessarily mean it is used or abused, just that it can be

See for example:

https://stats.oecd.org/glossary/detail.asp?ID=3256
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/284400/oft415.pdf


How important are capital requirements for controlling broad money supply? Interestingly, the Bank of England (BoE) is one of the few central banks that does not have reserve requirements.

Canada, the UK, New Zealand, Australia, Sweden and Hong Kong have no reserve requirements.
This does not mean that banks can—even in theory—create money without limit. On the contrary, banks are constrained by capital requirements, which are arguably more important than reserve requirements even in countries that have reserve requirements. [...]
Even in the United States, which retains formal (though now mostly irrelevant) reserve requirements, the notion of controlling the money supply by targeting the quantity of base money fell out of favor many years ago, and now the pragmatic explanation of monetary policy refers to targeting the interest rate to control the broad money supply.

The first fact, i.e. that the BoE has no reserve requirements is easily confirmed from a 2014 BoE paper by McLeay et al.... which also strongly states the fact from the 3rd paragraph above (monetary policy as the ultimate control on broad money creation.)
On the other hand, the (unsourced) Wikipedia claim that capital requirements are (also) a brake on the creation of broad money is, interestingly, impossible for me to find the McLeay paper. So, how important are capital requirements for controlling broad money supply?
E.g., are there some [semi-]official statements by the major central banks:  Fed, ECB, or even BoE on this alleged importance of capital requirements as a control of broad money supply? (I know the central banks [probably] don't entirely control these capital requirements, in the EU at least. On the other hand, it looks like the Fed does have some control over the capital requirements.)

FWIW, I found a blog which is partially contradicting Wikipedia:

capital adequacy requirements don't limit the ability of banks to create money when the economy is doing well. However, they do limit the ability of banks to create money when the economy is doing badly.

On different banks, and at different times, different regulatory constraints may bind on their ability to create money:

Reserve requirements relate bank lending (bank assets) to the quantity of reserves held by that bank at the central bank.
Capital requirements relate bank lending to the amount of equity capital of the bank.
Liquidity requirements relate the asset market liquidity of a bank's assets to the tenor of a bank's funding.
Stress tests attempt to model the liquidity and/or solvency of a bank under an adverse scenario that affects the value of assets on its balance sheet and/or its funding.

In today’s environment, capital requirements and liquidity requirements are the constraints most likely to be binding on US banks, though stress tests were also binding on some banks in the recent past. Reserve requirements don’t currently bind in the US, as banks are awash in reserves, and as noted in the question, many other countries do not have these requirements.

The fact that capital requirements are a brake on money creation is quite straightforward: if a bank that is constrained by capital requirements wishes to lend more, it must first raise costly equity capital. As a result, capital requirements are by definition a structural constraint on money creation.

Having said that, capital requirements are not a tool that one uses primarily to control the money supply. Instead, they're used as a prudential measure to ensure the solvency of banks. This is because, in the framework of instruments and targets, capital requirements are a very poor instrument with which to affect either of the two main targets of monetary policy, inflation and unemployment.

They're a poor instrument for these purposes for at least three reasons: (1) the relationship between capital requirements and money creation is in no way linear— as noted before, capital requirements are binding on different institutions at different times, so it's difficult to predict the effects of tightening or loosening them; (2) changing capital requirements has a lot of consequences (such as the potential impact on bank solvency, and cost to banks of raising additional capital or shedding assets if a tightening of requirements puts banks over the new, lower limit); and (3) capital requirements affect only banks, while over half of financial intermediation occurs outside banks.

Conversely, interest rates are pretty good at affecting broad money supply, and in a really efficient way, as marginal lending opportunities are compared to the price of money. At the same time, interest rates are pretty useless as a prudential instrument, as demonstrated in the early 2000s.


Relationship of continuous and discrete time models I am trying to understand two comments from a colleague. I have no clue about continuous time models. He said something like "just replace $\delta$ with $e^{-rdt}$ the Poisson process becomes a Bernoulli process."
Suppose I have a discrete time setting with discount factor $\delta$. A buyer receives a constant value $v$ for each period in which he uses a good.
Then, for example, my total value today of using the good for two periods is $v(1+\delta)$. Would the value from having the good over a time interval $[0,d]$ be $\int_0^d v e^{-rt} dt$, or how does it work?
Next, if in one period of length $d$ in expectation $\lambda_d$ buyers arrive and the number of arrivals is Poisson distributed, how do I get to the Bernoulli process? What exactly is the probability? Whatever I wrote down seems to converge to zero.
Do you have a recommendation where I can read up on these basics?

Poisson process can be interpreted as a continuous case of Bernoulli process.
Taking your example, consider that the buyer is consuming the good in batches in fixed intervals of time with probability $p$. So the consumption is allowed only after fixed intervals, and the r.v. $X_t \sim Bern(p)$, where $X_t=1$ indicates that the buyer consumes the good at time $t$. Further, how much she consumes in $n$ periods is distributed as $Bin(n,p)$. The expected level of consumptions in $n$ periods as we know is $np$.
Now consider that the buyer can consume at any instant and just not in intervals. Unlike in previous case where consumption could happen only at $t=1,2,...n$, now it can take place at any $t\in \mathbb{R^+}$. Naturally the probability that consumption happens at some given $t$ is $0$. So comes the rate $\lambda$, i.e., we say that the buyer on average consumes $\lambda$ amount in a given length $n$ of time. Now the total consumption between $t=0$ to $t=n$ becomes $Pois(\lambda)$.
So, $Pois(\lambda)$ is a limiting case of $Bin(n,p)$ as time interval $\to 0$.
Coming to your second question:
The buyer gets value $v$ when he uses the good at a given time, and the value gets depreciated after one time interval by $\delta$. The total value, as you mention, is: $v(1+\delta+\delta^2+..)$
However, if we assume the value is depreciating continuously at rate $r$ we can say:
\begin{align}
rv(t)&=\lim_{\Delta t \to 0} \frac{v(t+\Delta t) - v(t)}{\Delta t} \\
&=\frac{dv(t)}{dt} \\
\end{align}
From this you will get that the value from having the good over a time interval $[0,d]$ be $\int_0^d v e^{-rt} dt$
Lastly, to answer the last part: if you want to go to Bernoulli process from the described poisson process consider that arrivals can happen only in discrete time intervals such that on average in $d$ periods, $\lambda_d$ arrivals take place. So, this translates to the bernoulli process such that arrivals happens at a given time $t$ with probability $p=\lambda_d/d$.


Which income dollar is taxed most heavily, including implicit taxation, in USA? Income is often taxed implicitly by disqualifying deduction or government assistance. For example, if the recent proposal of "free tuition for kids of families making under \$125k" would pass the \$125,001-st dollar earned by the parents of 2 kids attending \$25k/year college would effectively reduce their after-tuition income by \$49,999, or 4,999,900% of that dollar.

Thus the question: which income dollar is currently taxed most heavily in USA, including both explicit federal+ssi+state taxation and implicit taxation by disqualifying deductions and assistance programs? How often it exceeds 100%?

EDIT:

famsy's answer convinces me that the question is too complicated. Therefore I'd like to amend it as follows:

Could you list realistic situations in which marginal income is taxed much more than 100%?

famsy mentioned hard cutoff in various welfare/HUD/etc benefits and a situation when a small marginal income led to \$30k of lost benefits. Assuming that the cutoff was set at the same amount that leads to implicit taxation of 3,000,000% on the disqualifying dollar.

Any other examples of that?

Unfortunately this question is exceptionally complex and depends on factors such has how many children the person has, which state they live in, and which services/opportunities they are taking advantage of.  I read a paper a while back (having a hard time finding it) in which the authors attempted to compute the effective tax rate for all incomes after the various deductions, benefits, alternative minimum tax, and other considerations.  The rate was very nonlinear with many peaks and valleys.  It was not particularly increasing with income.  This is further complicated by state taxes and the fact that states administer many welfare benefits using different criteria from each other.

Most taxes scale in and benefits scale out as income increases.  I believe the most heavily taxed dollar would be the one that takes you from qualifying for one of the various welfare benefits to not.  Many welfare programs have hard cutoffs.  This will vary from state to state, though, and may depend on other factors like what your savings are and how your social worker is feeling that day.

When I was in graduate school I had a stipend of about \$22K and my friend got slightly less.  He qualified for food stamps, WIC, and medicaid, and HUD paid his rent and utilities.  He received about \$30K a year in government benefits (not counting the value of medicaid) on top of his stipend.  I was just over the income line got none of these (well, my wife got WIC when she was pregnant).  So the small difference in our income cost me many thousands of dollars--he lived much, much better than I did.  It was more than an income difference, though.  HUD paid his rent because he had found a cheaper apartment than I was able to and they had a rent-per-square-foot cutoff.  Later I tried restructuring my life in order to qualify for some of these, but the state had changed some of its rules (you had to have less than $2,000 in your bank accounts to qualify).

This is also complicated by the fact that the rules are not applied consistently.  For example, some of the social workers deciding which benefits he got did not count his stipend as income, while all the ones I talked to counted mine.

Your tax rate and marginal tax rate depend on many elements of who you are, where you live, how you file taxes, what consumption choices you make, and luck.


Statistics about music tourism I'm a college student; for my thesis I need some statistics about international classical music tourism.

I need some data about how big international classical music tourism is in terms of spending and how much tourists' passion for music economically affects their behaviour when they travel.

Where/how can I find some useful data (hopefully free)?

The European Commission produces reports on tourism as part of its Eurobarometer surveys, which you can find here: http://ec.europa.eu/public_opinion/index_en.htm. If you do a bit of searching you might find some useful data in these reports. For example, a report of European's attitudes towards tourism can be found here: http://ec.europa.eu/public_opinion/flash/fl_370_en.pdf. I know this is not exactly what you asked for, but there is usually reference to cultural tourism in these kinds of reports and from there you may get further breakdown in terms of music tourism. This, I cannot guaranteed, however.

A second place to look would be on the websites of national tourism offices (they usually have a publications section with reports and statistics) and also on websites of lobbying groups; for example, UK Music has a research section and there they cite numbers on economic impact of music tourism. See here: http://www.ukmusic.org/research/measuring-music-2015/.

Generally speaking, it's quite hard to come by good data for arts and tourism - except maybe in France. Hope my suggestions are helpful and best of luck.

(I made this an answer because it was too long for a comment).


maximize untility AND minimize disutility DISCLAIMER: This could very well be all bogus, I'm talking about my intuition as a beginner/intermediate economics student, you have been warned.

I got the feeling agents do not just maximize utility but minimize disutility as well. Now my understanding is that from the convexity assumption follows that those problems would have the same optimum. But I think it could very well be the case that the utility function does not at all look like the disutility function (also different variables) and optimum of those two functions need not be unique (Am I with the duality gap on the right track?).

If this at all a valid intuition I would appreciate some pointers to empirical studies that examines utility and disutiliy, or some theories that incorporate the notion of disutiliy (not just as an inverse of utility) into preferences.

P.S. I got the idea while reading about The Paradox of Choice from Barry Schwartz (more choices could lead to confusion and in my interpretation disutiliy)

I believe what you're getting at is a concept in economics called "Loss Aversion". It has been used quite extensively in recent economic research, especially in behavioral economics and finance. Another important key word here is "Prospect Theory", which encompasses loss aversion as well.

The basic idea is that people suffer more from a loss of x\$ than they enjoy a gain of x\$ compared to a reference point. The utility function has a different (smaller in absolute value) slope when moving in a positive direction from the reference point than when moving in a negative direction. This is illustrated by the graph below (source: https://upload.wikimedia.org/wikipedia/commons/4/4e/Valuefun.jpg).

Under these conditions,  utility and disutility are different. Otherwise, maximizing untility or minimizing disutility is the same, as you mentioned.

This insight goes back to Amos Tversky and Daniel Kahneman.Kahneman received the Nobel Prize in Economics in 2002 for this work.

A summary of the most important literature can be found for example here: http://loss-aversion.behaviouralfinance.net/


Willingness to accept is different from willingness to pay - is there a name for this Given the situation below, can someone help me identify/name the logical phenomenon?
So I own a laptop that I don’t use…. Someone has offered me £1000 dollars  for it but I decided not to sell it. I myself would NOT pay £1000 dollars for it… I feel like there’s some kind of illogical behaviour going on here because me not selling it for £1000 is financially equivalent to me buying it for $1000. I think in both cases I’m giving up £1000 for a laptop. Do you guys know  if there a word/name for this?

The discrepancy between WTP and WTA is known as the endowment effect, and this has been extensively studied in behavioral economics.


Changing the base year of Real GDP from 2001 Euros to 1990 Geary–Khamis dollars Estimating regional Gdp in Italy (1871-2001):
sources, methodology, and results (Felice, E)

This article has Italian historical regional GDP figures, but they are in constant 2001 euros not in 1990 Geary–Khamis dollars where I can compare them more easily with other GDP figures. Would someone show me how you go about converting 2001 euros to 1990 Geary–Khamis dollars?

In general, real output is  calculated like this:
$$RGDP_{t, b} = NGDP_t \cdot p_{base} / p_t$$
Where $NGDP_t$ is nominal GDP at time t, $p_t$ is the price level in time $t$ and $p_{base}$ is the price level in the base period.

To covert RGDP between base periods, note that the ratio to a common year's $RGDP_t$ in two different base years is:
$$RGDP_{t, b1} / RGDP_{t, b2}  =  p_{base1} /  p_{base2}$$

You can rearrange this equality to solve for what you want:
$$RGDP_{t, b2}  =RGDP_{t, b1} \cdot p_{base1} /  p_{base2}$$


Regarding the role of the Fed in controlling interest rates When it is said that the Fed cut interest rates, does this refer to the discount rate, fed fund rate or both?

It is exceedingly rare for commentators to discuss the discount rate. As such, referring to “rate cuts” typically refers to Fed Funds.

In any event, under normal circumstances, the discount rate is kept at a constant spread to the Fed Funds rate, so they move at the same time.


need help from theorists: proof in Cole, Mailath, and Postlewaite (2001) I have one question in the proof for section 4.1. in Cole, Mailath, and Postlewaite (2001).
$$\lim_{\varepsilon \to 0}\frac{1}{2\varepsilon}\int_{\overline{l}-\varepsilon}^{\overline{l}+\varepsilon} v(\beta(i) + \delta, \sigma(i+\beta^{-1}(\beta(i) +\delta) - \overline{l}-\varepsilon))-v(\beta(i), s(i))di$$

They say the above limit is equal to :
$$v(\beta(\overline{l}+\delta, \sigma(\tilde{l}))-v(\beta(\overline{l}, s(\overline{l})),$$ for $\tilde{l} = \beta^{-1}(\beta(\overline{l})+\delta).$

I am not sure how do they this. I think if $\varepsilon \to 0$, the term inside the integral goes to 0. But, the answer they give us is to substitute $\overline{l}$ for $i$ in the integral. I appreciate if you give some help to figure this out.

This can be achieved with L'Hopital's rule, which says
$$\lim_{x\rightarrow0}\frac{f(x)}{g(x)}=\lim_{x\rightarrow0}\frac{f'(x)}{g'(x)}.$$

The result from Cole, Mailath, and Postlewaite holds fairly generally and is not special to the particular functions in their integrand.

Let
$$f(\epsilon)=\int_{l-\epsilon}^{l+\epsilon}h(x,\epsilon)dx \iff f'(\epsilon)=h(l-\epsilon,\epsilon)+h(l+\epsilon,\epsilon)+\int_{l-\epsilon}^{l+\epsilon}\frac{\partial h(x,\epsilon)}{\partial \epsilon}dx$$

and
$$g(\epsilon)=2\epsilon\iff g'(\epsilon)=2.$$

Then, using L'Hopital's rule:
$$\lim_{\epsilon\rightarrow0}\frac{f(\epsilon)}{g(\epsilon)}=\lim_{\epsilon\rightarrow0}\frac{f'(\epsilon)}{g'(\epsilon)}=\frac{h(l,0)+h(l,0)}{2}=h(l,0).$$

A final word on 'intuition'. You reason, correctly, that the integral goes to zero with $\epsilon$. But the problem is that the denominator, $2\epsilon$ also goes to zero. So, to know what the overall expression does as $\epsilon$ approaches zero, we need to know whether the numerator or the denominator approaches zero faster. In other words, for $\epsilon\rightarrow0$ are we dividing a small number by a very very small number, or are we dividing a very very small number by a small number? This, roughly speaking, is the logic behind L'Hopital's rule.


Normality of residual is violated, How to fix it properly? One of the key assumption of the OLS is that the normality of the residual.

If this assumption is violated, how can we fix it generally?

Especially, I want to make predictions

Use Bayesian regression. It's much more flexible on its assumptions, and much more powerful in its outputs. You'll find that you have to be much more explicit about your assumptions, and you'll have to quantify them.

It's much harder work, and all the work you do, will be valuable.

Normal regression makes it very easy for anyone to do really bad science.

Bayesian regression makes it harder to do anything, but makes it much easier to do good science.


Imbens and Angrist (1994): the $D_i(z)$ variables I'm referring to the Econometrica (1994) paper by Imbens and Angrist. In particular, I don't really understand the random variables $D_i(z)$ (defined on page 468). Could you please provide me with intuition about them and explain why, specifically, for $z\neq w$,
$$
D_i(z)-D_i(w)
$$
can only be either $1$ and $-1$? I understand that, in order to get $1$ or $-1$, the authors are looking at 2 scenarios $0-1$ and $1-0$. But why are the remaining scenarios $1-1$ and $0-0$ excluded?

I hope this meets your idea for intuition, but equation 1 comes from using the Law of Total Expectation with the independence condition (Condition 1). There are four possible values of $D_i(z)-D_i(w)$. $$D_i(z)=D_i(w)=1$$ $$D_i(z)=D_i(w)=0$$ $$D_i(z)>D_i(w)$$ $$D_i(z)<D_i(w)$$. Consider the LHS of (1). $$E[(D_i(z)-D_i(w))*(Y_i(1)-Y_i(0))]$$ From the four possibilities above it is clear that this expectation only takes on a value other than 0 when the last two are true, where the third option gives a value of 1 and the fourth a value of -1. So then using the Law of Total Expectation with the independence condition yields the equality from the paper.


Can we stabilise the price of a cryptocurrency? Currently, the volatile price of cryptocurrencies such as Bitcoin means that they are currently poor stores of value and therefore are unlikely to achieve mass adoption. What can be done to stabilise the price of a cryptocurrency, apart from pegging the cryptocurrency to a fiat currency?

First it might be useful to list the reasons behind cryptos' volatility.

One of the reasons is that cryptos have no underlying value. In contrast to other assets like oil, gold, company shares, etc. that you could make use of them, cryptos are similar to fiat currencies in that they're not fully backed... but in the case of fiat currencies, at least (in my understanding) there are laws that make them valuable ("these notes can be used to settle debts" or something similar.)

Value of most cryptos are determined, therefore, by "investors"' beliefs.

To "fix" this, you could, as you suggested, peg it to fiat currency (or basket of currencies), or you could back it up with other assets/commodities.

Other reasons (you could Google why cryptos are volatile) include having many retail investors holding a significant portion of the asset, not having that many institutional players in the market, etc. could be analyzed accordingly to make cryptos more stable.


Intuition for the CES consumption index in New-Keynesian DSGE models I don’t understand, from an intuitive point of view, the CES aggregator in the context of a New Keynsian DSGE model. I understand that the consumption index Ct is the sum of all consumption goods and we conceive of a continuum of goods over the interval (0,1) and, as such, have;

I understand that we are making assumptions here about the imperfect substitutability of goods and that this is what gives firms market power in the monopolistic setting of the DSGE models in question.

What I do not understand is the intuition of how levels of consumption of all different goods maps onto the expression for Ct above. How can we represent this using an integral over a range? I do not understand the intuition, and nowhere seems to provide a decent explanation. I would be very grateful if one of you could possibly explain it to me?

Many thanks in advance.

Heuristically, you can think of the integral as just a sum:

$$ \bar{C} = \left( \sum_{i=1}^n C_i^{1-\frac{1}{\epsilon}} \right)^{\frac{\epsilon}{\epsilon - 1}} $$

where $\bar{C}$ is an index of aggregate consumption, and utility is given by $u \left( \bar{C} \right)$.

It's easy to check that the marginal rate of substitution between goods $j$ and $k$ is given by

$$ \text{MRS}_{jk} = \left( \frac{C_j}{C_k} \right)^{-\frac{1}{\epsilon}} $$

which means that the (absolute value of the) elasticity of substitution is $\epsilon$.

With a continuum of goods, the analogue of summation is integration, and you can (loosely) think of the MRS between goods $j$ and $k$ as

$$ \left( \frac{C_t (j)}{C_t (k)} \right)^{- \frac{1}{\epsilon}} $$


General Equilibrium with Perfect Substitutes I came across the following problem:
The quantities of an economy’s only two goods are denoted by $X$ and $Y$; no production is possible. Ann’s and Ben’s preferences are described by the utility functions
$u_A(x,y) = X+Y$ and $u_B(x,y) = XY$.
Ann owns the bundle $(0,5)$ and Ben owns the bundle $(30,5)$. Determine the Walrasian equilibrium
price(s) and allocation(s).
It is quite easy to determine B's offer curve (with the price of $Y$ ($p_2$) normalised to 1): $$OC_B = \left(\frac{30p_1 + 5}{2p_1}; \frac{30p_1 + 5}{2}\right)$$
However, I don't know how to proceed now, since consumer A is indifferent between good X and good Y. The general Marshallian demands for a function of the form $u_A(x,y) = \alpha X+ \beta Y$ are (if we assume that the consumer consumes the same quantities in case we have $p_1 = \frac{\alpha}{\beta}p_2$) are the following:
$$
X^{M} = \left\{
    \begin{array}{ll}
        m/p_1 & \mbox{if } p_1 < \frac{\alpha}{\beta}p_2 \\
        m/2p_1 & \mbox{if } p_1 = \frac{\alpha}{\beta}p_2  \\
\ 0 & \mbox{else}
    \end{array}
\right.
$$
and
$$
Y^{M} = \left\{
    \begin{array}{ll}
        m/p_2 & \mbox{if } p_1 > \frac{\alpha}{\beta}p_2 \\
        m/2p_2 & \mbox{if } p_1 = \frac{\alpha}{\beta}p_2  \\
\ 0 & \mbox{else}
    \end{array}
\right.
$$
So if we replace exogenous income with the endowments $\omega = e_1p_1 + e_2p_2$, and normalize the price of Y to 1 again, our offer curve would look exactly the same as the one of consumer B (since $\alpha = \beta = 1$), because we are in the case where consumer A splits his consumption equally (by assumption), since we have that $MRS_A =  \frac{1}{1} = 1$. And since $MRS = \frac{p_1}{p_2}$ in equilibrium, we must have that $p_1 = p_2 = 1$ if I'm not mistaken.
$$OC_A = \left(\frac{30p_1 + 5}{2p_1}; \frac{30p_1 + 5}{2}\right)$$
Solving for the Walrasian Equilibrium, we would get that $p_1 = 1/6$, which corresponds to our price ratio, since $p_2 = 1$.
This somehow doesn't seem right to me, because the fact that consumer A wants to consumer both goods equally if $p_1 = \frac{\alpha}{\beta}p_2$ is just an assumption that we have made to be able to define that case. In reality, however, consumer A is totally indifferent between goods X and Y, so he can freely switch between the two and does not have to consume them $50:50$. Also, what makes this approach very confusing to me as well is the fact that the prices are endogenous within this framework. So the prices should be able to adjust freely according to demand, which makes the above definition of the Marshallian demands redundant.
My second question is that given this logic, would it even make sense to look at what happens if $p_1 \neq \frac{\alpha}{\beta}p_2$? As I said, the prices are endogenous, so we cannot impose certain prices in the beginning already. How do you approach such a problem with perfect substitutes in general then? Say we have for example $u_A(x,y) = 2X+3Y$ and $u_B(x,y) = XY$. Does the result change?

To solve for competitive equilibrium, we can first find the demand :
Demand for commodity $X$ by A is $x_A = \frac{5}{p_x}$ if $p_x < 1$, $x_A \in [0,5]$ if $p_x = 1$, $x_A = 0$ otherwise.
Demand for commodity $X$ by B is $x_B = \frac{(30p_x+5)}{2p_x}$.
Now we can equate demand and supply and solve for $p_x$.
$x_A + x_B = 30$ yields $p_x = \frac{1}{2}$.


Where to start with social networks? I'm working on my master's thesis in industrial organization and I have a model that is based on social networks. I have had two courses about social networks (one more focused on basic industrial organization questions in networks and the other more about basic graph theory) but as I work more on the model I feel I'm not really using the network in solving the questions that arise and leaving it more as a descriptive structure, and I fear it is mostly due to ignorance.

Can anyone refer to a good book, class notes or papers that might help me learn more deeply the implications of the network structure and/or the pros and cons of modeling a problem as a network? For example on how the network structure might be helpful when trying to determine existence of equilibrium.

The best introduction is, in my opinion, the book by Matthew Jackson. It has a pretty nice introduction (even if you know nothing about social networks) and chapters about many of the applications of graph theory in economics.

Jackson, M. O. (2008). Social and economic networks (Vol. 3).
Princeton: Princeton University Press.

It sounds like you try to model a game on a network (i.e., using game theory with players on a network without changing the network). If this is true, then the following paper might be even more relevant:

Galeotti, A., Goyal, S., Jackson, M. O., Vega-Redondo, F., & Yariv,
L. (2010). Network games. The review of economic studies, 77(1),
218-244.


Difference between social choice functions and social decision functions? A social decision function (SDF) à la Sen (1970) is defined as a collective choice rule whose range is restricted to social preference relations which generate a choice function. From Gaertner (2009), a preference relation $R$ generates a choice function over a set $X$ if and only if $R$ is reflexive, complete and acyclical over $X$. I thus struggle to understand where exactly the difference between a SDF and a social choice function (SCF) à la Gibbard-Satterthwaite lies. A SCF is itself a choice function, so the preference relation $R$ generating it must satisfy the same conditions as the one generating a SDF.

Let $X$ be the set of alternatives.
A social decision function maps profiles of preference orderings to relations on $X$ such that every nonempty subset of $X$ has at least one maximum under this relation.
A social choice function maps profiles of preference orderings to elements of $X$.
Now let $P$ be a profile of preferences, $f$ a social decision function, and $g$ a social choice function.
There might be more than one $f(P)$-maximum in $X$, so $f$, in contrast to $g$, will not always pin down a single choice in $X$.
On the other hand, suppose the alternative $g(P)$ is not available for some reason (say, the winning candidate died). Then $g$ is of no help in finding an alternative from the remaining set of alternatives $X\setminus\{g(P)\}$. But $f(P)$ will allow us to rank the alternatives in this remaining set (provided $g(P)$ is not the only element of $X$), though, again, there might be more than on $f(P)$-maximum in this set.


What do all the distributions that have the same Gini index have in common? According to the Wikipedia article about Income inequality metrics, Gini index have the next disadvantage:

As a disadvantage, the Gini index only maps a number to the properties of a diagram, but the diagram itself is not based on any model of a distribution process. The "meaning" of the Gini index only can be understood empirically. Additionally the Gini does not capture where in the distribution the inequality occurs. As a result, two very different distributions of income can have the same Gini index.

So, I want to ask - what do all the distributions that have the same Gini index have in common? (Empirically, they produce the same area under the Lorentz curve, but what does that mean?)
Thanks!

This is a Lorenz curve.

The Gini coefficient is the area between 'equal wealth' and your chosen line, divided by all the area under the equal wealth curve. There are other illustrations online, for sure, which would explain this.

The Wikipedia article is telling you that the actual distribution of income is not fully captured by the Gini coefficient. The same Gini coefficient could have different distributions of income. For example, it could move equally in the lower region at first and then flatten between 60 and 80 per cent of people. Or it could be that poorer people get nothing and the middle and upper classes are hoovering up the income.

Both examples, if you set up the toy numbers properly, imply very different distributions for poor people, but produce the same Gini coefficient.


L-infinity and weak-star topology While reading economics papers, especially those related to economy with land, I often encounter the terms $L^\infty$ and the "weak* topology". They seem like very basic terms, but I couldn't find a basic explanation of them. Here is a typical paragraph which I am trying to decipher (it is from page 4 at the introduction of A foundation of location theory):

Let:

$$[0,\frac{1}{n}]\cup[\frac{2}{n},\frac{3}{n}]\cup[\frac{4}{n},\frac{5}{n}]\cup...\cup[\frac{n-2}{n},\frac{n-1}{n}]$$

$(n=1,2,...)$ represent a sequence of commodities of increasing utility. If the indicator functions of these sets are embedded in $L^\infty$ with the weak* topology, then the limit is $\frac{1}{2}1_{[0,1]}$, half the indicator function on the interval $[0,1]$. This, indeed, is a natural limit that is not in the commodity space.

So my questions are:

What is $L^\infty$?
What is the "weak* topology"?
What is the meaning of "embedded in $L^\infty$"?

NOTE: I have some basic (undergraduate) knowledge of topology. I have heard about "weak topology" but never heard of "weak* topology". I will be very thankful for a simple, intuitive explanation that will help me continue reading!

$L^{\infty}$: the (Banach, usually) space of bounded measurable functions modulo the equality almost everywhere. Like all function spaces not involving holomorphic functions, it's really a space of equivalence classes.

weak-$^*$ topology: the topology on the dual $X^*$ of any topological vector space $X$ induced by the $(X, X^*)$-pairing.

"embedded in $L^{\infty}$": a (say) topological vector space $Y$ is said to be embedded in $L^{\infty}$ if there is an injective continuous linear map from $Y$ to $L^{\infty}$.

(This is the usual meaning. In your paragraph, "embedded" just means viewing those indicator functions as representatives of their classes. The weak-$^*$ topology on $L^{\infty}$ is given by the identification $L^{\infty} = (C_0)^*$.)


Can futures buying/selling distort price discovery? How credible is the suggestion that specific parties distort price discovery (rig the market) of a given asset by buying/selling corresponding futures contracts or any other derivatives.

Should these position not unwind at some point causing a reversal effect?

Can futures buying/selling distort price discovery?

Yes, that is plausible although will not necessarily be the case. I will focus on put & call options.

Consider the put-call parity, which I rewrite as

$$S+P=C+K*exp(-rt)$$

where S denotes the stock [price], P put, C call, and K the strike price.

Buying enough call options will increase C. If that were the only change in the market (regarding this stock), that would "break" the put-call parity and therefore an arbitrage opportunity would ensue.

Since K is fixed, the only possible changes to offset C's increase are an increase of P and/or of S. An agent who notices C going up is likely to interpret that someone else has information in the sense that S will go up.

Unless that agent also has information in the opposite direction, it would be irrational for him to buy P in his attempt to take advantage of the arbitrage opportunity. Thus, he is likelier to buy S instead of P at least while the put-call parity is restored. Buying S tends increase its price (as is the case with any financial instrument).

Similarly, in the event of C's increase, the agent might set up a strategy that consists of taking a short position on C and hedge it by taking a long position on S (he might have to borrow because C<S, but that is irrelevant to the point). Opening that long position tends to increase S.


Difference between unemployment rate between ILO and bureau of labor statistics Why there are differences between the unemployment rate of the US between the data of the bureau of labor statistics and the ILO (international labor organization). Have they different definitions of labor force? Or is it because they are conducted by the different organizations?

With regards to the concept of 'unemployment' and the 'unemployment rate' it is important to note that, while the general definition (number of unemployed /number labor force * 100) is pretty standard, the exact parameters or "operational criteria", in ILO-speak, for how some of these concepts are defined can vary from place to place, often with large impacts on the final statistic.

Specifically, it is important to consider the criteria what is used to classify people as "employed" and "unemployed", with the latter concept having many different criteria to define--e.g. working age, paid or not, what constitutes "actively looking for work", what constitutes "available for work", etc.

With this in mind, the ILO has a standard definition with specific operational criteria for all of the concepts used to define employement, unemployment, and the labor force, so that calculations of the unemployment rate using this ILO definition are sure to be comparable from place to place.

Now with all of that said, the US BLS uses the Current Population Survey to calculate unemployment rate according to the ILO definition, so the stat should be the same. If you go the the ILO-STAT dashboard for the United States, you can see that the data-source for ILO stats on the U.S. is in fact, the BLS and the US Current Population Survey.

On a more general note, the ILO recently published this very useful, concise guide that explains specifically l their definition, but also, more generally, how to interpret uemployment rates and all of operational criteria and how they can impact rate calculations. You can find the guide to  unemployment rate on the ILO site.


Cholesky Decomposition in R package "vars" I'd like to know if, when running a VAR model in R (package "vars"), the cholesky decomposition matrix is upper triangular (so I should order my variables from more endogenous to less endogenous), or lower triangular (so I should order my variables from less endogenous to more endogenous).

According to page 6 of the documentation for vars, the Cholesky decomposition matrix is lower triangular:

  The long-run impact matrix is the lower-triangular Choleski decomposition of the above matrix and the contemporaneous impact
  matrix is equal to:

  $$(I_K − A_1 − \dots − A_p)Q$$

  where $Q$ assigns the lower-triangular Cholesky decomposition.

In the theoretical literature, Cholesky factorization is traditionally defined as lower-triangular; that is, as $A = L L^{T}$. There is a function is base R, chol(), that returns the upper-triangular Cholesky decomposition of a matrix $X = R^{T}R$.


Difference between Income-Expenditure Identity and the Goods Market Equilibrium condition Is there any difference between the Income-Expenditure Identity and the Goods Market Equilibrium condition. Both are $Y=C+I+G+NX$. If it is an identity, why do we solve for the equilibrium output? Shouldn't it always hold? If someone could clarify this it would be very helpful.

The output defined with spending approach: $Y\equiv C+I+G+NX$ is an identity because it holds by definition. By definition output must be equal to sum of spending, investment government spending and net exports. However, this is actually not the equilibrium condition.
The equilibrium condition is that goods market demand $Z$ must be equal to output in the equilibrium. Hence the equilibrium condition is that $Z=Y$ (this is really just macro version of saying that demand = supply, since output $Y$ is the supply). This is the equilibrium condition not the identity $Y\equiv C+I+G+NX$. However, given that the equilibrium condition is that $Z=Y$ we can from that deduce the following: $Z=Y \implies Z= C+ I + G + NX$ in equilibrium.
This might be easier to explain with graph. Consider the following graph from Blanchard et al. Macroeconomics a European Perspective pp 47. In the graph below the demand is the purple line while the identity $Y \equiv C+I+G$ (they omit net exports for simplicity) is the $45°$ line that just definitionally says output is equal to output.


A possible typo in Herbst and Schorfheide book of DSGE estimation In a state-space representation, the measurement equation is something of this form $O_t=H_t s_t + u_t$, where $O_t$ are the observational data at time $t$, $H_t$ is a possibly time-dependent matrix relating the state $s_t$ and the observational data. We can see $u_t$ as the measurement errors at time $t$.

However, in Herbst and Schorfheide book (Bayesian estimation of DSGE models),

we have $s_t$ dependent on $y_{t}$, but not $y_{t-1}$, while the measurement equations are of the form:

Is this a typo? Should I add the $y_{t-1}$ term to $s_t$?

After asking this same question on the dynare forum, I got the answer that it's really a typo, and I should augment the state vector.

The interesting thing is that afterwards, I rerun the Gensys function of Sims(2002), and I got a solution for an indeterminate model, which is a bit strange.

Augmenting the state vector by a lag from a previously already present variable shouldn't change the model, since I just added the equation y_{t-1}=y_{t-1}to the model. However, the gensys function states that it does.

This makes me wonder if there's something wrong with the code in Sims(2002).

If anyone knows more, please feel free to share. Thanks


Why did Malthus thought that population increases geometrically while resources increase arithmetically? Thomas Robert Malthus is a 18th century demographer and economist that is famous for the study of population growth, especially for the support of laws that would limit the growth of (poor) population. The basis of his reasoning is summarized by Wikipedia:

The main point of his essay was that population multiplies geometrically and food arithmetically, therefore whenever the food supply increases, population will rapidly grow to eliminate the abundance.

On which basis are these two claims in bold funded?
The fact that a population grows geometrically (in other words, exponentially) in a situation of abundance of resources is now classic and known as the exponential growth or natural growth. This Wikipedia page claims that the model was in fact introduced by Malthus himself.
Why did Malthus consider that resources grow arithmetically?
Actually, the same Wikipedia page quotes Malthus (emphasis added):

"Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand. ... The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in the course of a few thousand years. Necessity, that imperious all pervading law of nature, restrains them within the prescribed bounds."

The text does not mention arithmetic but bounded resources. It is more in line with a logistic model with a constant carry capacity, or seasonal variations.
Did Malthus really consider resources growing arithmetically, or is it a later misattribution?

As mentioned in the question the exponential population growth was argued to exist because it is based on the 'natural growth' that can be empirically observed anywhere in nature where the resources are abundant. So you already answered that part pretty much yourself.
When it comes to the arithmetic growth of resources, the word resource is actually not appropriate modern economist would call things like food and shelter output not a resources which are factors of production (the wikipedia in this article uses the word resources improperly see Samuelson & Nordhaus Economics). Resources are inputs not outputs of production.
The reason why Malthus thought that output/production would grow arithmetically is due to diminishing marginal product of factor of production. Diminishing marginal product means that although output increases when you use more factors (resources like land, labor, capital) the output increases at a diminishing rate. The diminishing returns as argued by many economist must apply otherwise even single plot of land could produce enough crops to feed whole world. At some point just throwing more labor and capital at a plot of land will simply lead to smaller output.
Malthus thus reasoned that due to these diminishing returns output will over time grow only arithmetically as given the fact that amount of land is fixed in the world at some point no matter how much machinery and labor force you apply to it at some point the output will increase only minimally (e.g. having 3 tractors for one acre field might increase output significantly compared to having 1 but having 100 tractors as opposed to 97 will not make much difference).
However, Malthus turned out to be wrong because he did not taken into account the effect of technology on production. A Malthusian production function would look something like:
$$Q=K^{0.3}L^{0.2}$$
which exhibits diminishing returns to scale as more and more inputs of labor and capital (resources) are put in the output will always increase but at diminishing rate (in fact if you would plot this curve you would see that as factor inputs increase the output increase becomes more and more ‘flat’ and ‘linear-like’ e.g. imagine a plot of square root function).
However, modern economists realize that technology plays a role in production process too. A modern production function would look like:
$$Q=AK^{0.3}L^{0.2}$$
where $A$ would be the level of avaiable technology. So as long as technology keeps accumulating and growing sufficiently fast enough to keep output with population growth Malthusian trap will not occur.


Does the investment component of GDP (demand side) identity include expenditures by the government and households? In the identity GDP=C+I+G+(X-M) does "I" include expenditures by the government and households?

For example, if a construction firm builds new residential properties and a household buys this property. Is the value of the new residential property allocated as 'firm' expenditure or 'household' expenditure and where in the identity above would these expenditures fall?

Also if a government builds a school or bridge would this go under "I" or "G"?

“I” would be called private domestic investment. (https://apps.bea.gov/iTable/iTable.cfm?reqid=19&step=2#reqid=19&step=2&isuri=1&1921=survey)

Firm and household expenditures for investment both count as private investment.

(https://courses.lumenlearning.com/boundless-economics/chapter/measuring-output-using-gdp/)

Any investment expenditure by a government would be categorized under government spending.

If a government builds a school or bridge it would go under government spending “G”. (https://courses.lumenlearning.com/wm-macroeconomics/chapter/calculating-gdp/)


What is the economic incentive to cheat? How does an experiment capture exogenous deviations? In my undergraduate career an economic experiment was conducted on my class:

one class was the control
two classes were the experimental (I was in an experimental class)

The basic premise was a modified prisoner's dilemma whereas two individuals had to make a decision regarding whether or not to 'cheat'. As this was a two stage game, the first person can choose whether or not they will cheat the second. The second can choose to cooperate or cheat. Each individual are in different classes to prevent collusion.

The monetary value (USD) was 1 for both individuals choosing to cheat, 5 if one cheated the other, and 3 if both cooperated.

Nonetheless, the experiment itself went well with no hiccups. But I approached the PI's of the experiment with the following:

This would a be a poor measure of individuals within a population willingness to deviate from established rules as you've established what the options to cheat are, issues that are prevalent within society are often based upon individuals looking for overlooked loopholes, obscure mechanisms, or outright illegal means to obtain an advantage over their competitors. As a result, the results in this experiment are predetermined and not representative of a random and at times chaotic economic structure.
If you wanted to explore an alternative measurement of behavioral economics, look for individuals who are unique in their attempts to cheat. Who go beyond the rules that you place in front of them and seek alternative means to maximize gains.
An example: Given that the experiment happened sequentially, a student who was in a previous class holds the details of the experiment as leverage in return for a greater monetary reward, threatening to disclose the details (effectively blackmail). The individual-level analysis concludes that the student realizes that there is a greater 'pot' of money that can be had (if the total class sizes is 100, then there is a budget of at least $500 to cover the situation where everyone cooperated) and the options at hand: to play according to the experiment rules (1, 3, or 5 payoff) or not to and blackmail the experimenters for a greater payoff (>5 but <500). From the experimenter's perspective, a slightly higher expense to payoff the rogue student and in the process, preserve the integrity of the experiment (and the research value of the expended monies of conforming students).

Of course, I am in full knowledge that the the deviation itself in the real world would constitute a crime and liable to criminal prosecution then and now. But this does not deter crime given the prevalence of well... crimes committed for monetary gain.

Although the reply was along the lines of "We hope you don't tell the other classes about the experiment" I retorted that my goal wasn't monetary gain, but wanted to learn more about experimental methodology and parameters.

The basic premise remains unanswered. When an economic experiment is designed to have predetermined outcomes of ethical and unethical decisions, how does it address the extreme levels of deviation that is present within historical record? Enron, Bernard Madoff, Arthur Anderson, to name a few.

I am sure I am missing a couple of literary research pertaining to the experiment and would be open to any suggestions.

A couple of comments to your question below:

  When an economic experiment is designed to have predetermined outcomes of ethical and unethical decisions, how does it address the extreme levels of deviation that is present within historical record?

1) External validity --- whether results obtained in the lab can be generalized to settings outside the lab --- has long been one of the main criticisms of experimental economics, and practitioners in this field are well aware of this. In light of this concern, one must therefore exercise caution in interpreting experimental results. Lab results should be extrapolated to an external environment only if the settings of the experiment sufficiently resemble those in that environment. (To some extent, the same can be said about generalizations of results obtained using field data.)

In the experiment that you participated, decisions were labeled as "cooperate" and "cheat". However, the labels could very well be "A" and "B", or "Left" and "Right", or "Aspiring" and "Cautious". The point is that the labeling of the actions is arbitrary, and you shouldn't (over)interpret the results just because the experimenter happen to choose a non-neutral frame.

2) Judging by your very limited description of the experiment --- e.g. you didn't say what the control treatment was like, or whether the subject moving at stage 2 can observe what was chosen in stage 1 --- I suspect that the experiment was more for a pedagogical purpose than a research one. Generally speaking, experiments for research purposes should avoid recruiting subjects from the experimenter's own class, since there are strong outside incentives that may affect/dominate the salience of the payoff from within the experiment. Moreover, experiments should generally adopt neutral framing, since non-neutral frames tend to bias the results in a certain direction.

Therefore, I think you are over-interpreting the results in an experiment that is not very rigorously conducted.


Will periodical increasing and decreasing cryptocurrency supply peg cryptocurrency to dollar effectivelly? As far as I understand, in order to make cryptocurrency pegged to USD we need somebody to take the risks of exchange rates. So, if ratio CRYPTO to USD is at a given time 1CRYPTO:1,1 USD, then we increase cryptocurrency supply by 10% and it will return to 1:1 parity? And conversely, if at a given moment ratio is 1.1 CRYPTO: 1 USD, we decrease money supply by 10% and ratio will return to 1:1, is that right?? Increasing and decreasing amounts of cryptocurrency in existence in response to price fluctuations can effectively peg 1 crypto: 1 USD or not??

No, it's by no means a guarantee of a peg.

The cryptocurrency's actual exchange rate will be determined by people's collective expectations of the present and future value of the cryptocurrency relative to the dollar.

Most importantly, the exchange rate will be driven by how much people trust that they will actually be able to get a real dollar in exchange for a unit of the cryptocurrency.


Intuition behind Euler Lagrange equation in economics When being exposed to the concept of the Euler Lagrange equation as a mathematical concept, many ideas from the physical sciences are used to explain its relevance in terms of choice of shortest path, brachistochrone problem which are great for educational purposes however in the context of economics it is difficult.
The paper that comes to mind which is explict about the Euler Lagrange condition in terms of solving is Grossman 1972 (the famous grossman model of demand for health). The continuous time variant of the model (on page 28-29 of the PDF) has the following condition associated with it (notation changed for simplicity from time denoted by $i$ to being denoted by $t$) we get:
$$\frac{\partial Q}{\partial H(t)}-\frac{\partial}{\partial t}\frac{\partial Q}{\partial \dot{H}(t)}=0$$
or
$$\frac{\partial Q}{\partial H(t)}=\frac{\partial}{\partial t}\frac{\partial Q}{\partial \dot{H}(t)}$$
What is the economic interpretation of this result?

The Euler Lagrange Equation in words in the context of physical capital accumulation states: Any possible accumulation that may occur at the optimum is brought back to a steady state in the next instant due to the law of motion.
This equation communicates the physical properties of our optimum meaning that once we are there no possible improvement from capital accumulation is possible.
This logic carries over for the our case in the context of the continuous time version of the Grossman model this time with health capital.


Equivalence of definitions of continuity One of the definitions of continuity is that the Upper Contour Set and the Lower Contour Set are closed.

I am trying to show that if preference is continuous and $x>y>z$, then there is some $\alpha \in [0,1]$ such that $\alpha x+(1-\alpha)z>y$

Can you help me to prove second one by using closeness?

HINT: it is easier if you go through the intermediate step that the set $\{\alpha \in[0,1]: \alpha x+(1-\alpha) z \succsim y\} $ is closed for every $x,y,z$


Questions about profit function I know that a profit function is defined by $\pi(p;w)=\max_{x\in\mathbb{R}}pf(x)-w\cdot x$ and $\pi$ is a convex function (i.e. $\pi$ is convex in $(p, w)$. My concern is how we can find the max value of the profit function when the profit function itself is convex.

From my previous knowledge on convex function, I also know that a convex function has a global minimum on its domain (correct me if I was wrong), but how can we find the maximum?

Can anyone please explain this for me? I am so confused. Thanks in advanced!

You're probably confusing two things: the objective function $pf(x) - wx$ being used in profit maximization problem: $\max pf(x) - wx$, the objective function is concave in $x$ and thus, you can solve the maximization problem. However, a profit function $\pi(p,w)$ being a result of maximization problem identifies the maximum profit given level of prices and wages $\pi^*(p,w)$ (and it's convex in $p$ and $w$ as you said).


When the federal reserve buys bonds or other assets from banks, do the banks make a profit? My understanding is that the federal reserve is injecting money in the market by buying bonds and debt from banks.   Do the banks make a profit on the sale of their bonds or corporate debt to the feds?  If not, what is their motivation for selling bonds or debt to the feds?

I am not sure about this, but the Fed mainly trades with Primary Dealers. These are often subsidiaries of banks, but could be independent financial entities.

If the dealer is selling from its own inventory, it will make a gain or a loss depending on the price it originally bought the bond at. Since that may be some time ago, there is no certainty about profits.
The dealer may effectively act as an intermediary. It will buy from clients who are bond investors, and then sell to the Fed. If the trading desk of the primary dealer does a good job, they have a good chance of locking in a small profit. (Making recurring small profits by intermediating trades is the business model of investment dealers.)


Market impact function I have the following Dynamical system for market impact function

$$p_{t+1}-p_t=a(d_t-s_t)$$

$$s_{t+1}-s_t=bp_ts_t-cs_t$$
$$d_t=y-rp_t$$

where $s_t$ is quantity supplied, $d_t$ is quantity demanded, $p_t$ is market price, $a,b,c,y,r>0$ are fixed.

What is the name of the model? And most importantly,how can I interpret these equations?

Thanks

This is some dynamic supply-demand model (I am not aware of it having some special name).

The first equation gives you the evolution of prices. It says that there will be inflation if there is excess demand $d_t>s_t$ and deflation if there is excess supply (that’s why the first equation has ($d_t-s_t$).

The second equation tells you how supply changes in response to price in time. It is basically a dynamic version of basic supply curve. If the prices increase supply increases as well

The third equation is a demand function. The $y$ is most likely income - hence higher income the higher demand, and then the demand is decreasing in price