During deflation, is there any risk on 'printing' money?

You should be confused by Japan's version of QE. No one knows the long term implications, it has never been done before.

I don't know that much about Japan's QE other than the monthly totals, but the concept behind QE is simple.

Normally, when a central bank wants to stimulate economic activity, they will do so by reducing the returns on saving and therefore incentivize consumption. To do this, they need to lower market interest rates.

In the past, they usually did so by controlling the rate at which banks lend to each other, or to the central bank. In the US, this is the Federal Funds Rate. But what happens when you have reached the zero lower bound of the central bank's rate and you need to further influence market rates. In the case of the US and Japan, the answer, in part, was to have the central bank buy debt. But it was not just a small amount like they normally would to change their rate, QE saw the central banks buying huge amounts of debt.

This debt purchasing was designed to serve a singular purpose: drive down long term interest rates. Why would this be helpful? Well with low short term rates, the market for interbank lending would be very liquid, and would not risk the so called "crunch" of credit that occurred during the recession of 07-08. But that was done almost immediately as the crisis revealed itself.

When QE kicked in in earnest, long term rates did begin to go down, but it did not have the immediate effect that central banks thought it would. Unlike short term lending, the long term market is much more slow to adjust to changes in prices, and to some extent the Fed got around that issue in the US by providing forward guidance on their plan to continue QE "For an extended period of time". Even now in the US, QE rolls on, but under the guise of reinvesting the proceeds of original QE assets into even longer term securities.

But Japan started QE earlier! They practically invented it! Why didn't they recover as quickly as the US?

Well they kind of did. In 2010 they posted 4.2%gdp growth after -5.4 the year before. Unfortunately they didn't maintain it.

The reality is that most highly developed countries, (US, Germany, Japan, ect.) are in a period of stable but slow growth. In fact this is the norm in history. It was only the massive upheavals of the 20th century that allowed for massive GDP growth in developed countries. I think it is unreasonable to expect an average of 4% GDP growth in developed countries in the current epoch.

But we've also seen a positive side effect of more sedate GDP growth: lower inflation. There are plenty of theories as to why inflation is lower in developed countries than it has ever traditionally been. I like parts of all of them. One is that globalization and fewer barriers to international trade has lowered prices of goods and services globally by increasing efficiency.

Another theory is that the strategies of central banks are more effective at maintaining low inflation than they are at bringing down high inflation. In particular, inflation targeting regimes, such as the one currently employed by the Fed, seem to be effective at maintaining well anchored market expectations, and help to reduce market shocks.

As to whether a country can become richer by printing money without inflation the answer is: kind of...

There is interest rate risk to QE. If rates go up, QE loses money for the central bank. But since the central bank controls interest rates, they don't really have to worry about it. The Fed will make money on QE, and the BOJ will probably make money on their QE (although they bought non-government assets in addition to government, so I'm not as sure about those). Does making money on QE make the country richer? Not really. But does lowering the yields on government bonds make a country relatively richer? Yes. With cheaper government debt, the government is more able to conduct expansionary fiscal policy without having to worry about too much interest. In the case of QE it is even better because your own central bank owns the securities so you practically are performing seigniorage!

Of course this assumes that the government then uses this money to improve the production of the country, but if you throw enough money at it, it can't help but make your country richer.

Now, the final question is: what happens in the long term as a result of QE? Is there a risk of inflation as QE securities mature?

I've thought about that question a lot in the last few years, and I think that in the case of the US there is limited risk of inflation from maturing securities. The fed can roll them off at a very slow rate, and by tapering the reinvestment of the securities, they can ensure a slow, gradual decrease in the size of their balance sheet, and low inflation.

In Japan the issue of the types of securities is more of an issue. The US only did QE through government backed securities and mortgage backed securities (to a lesser extent) and both are flexible with their maturity schedules.

I have not looked at the maturity schedules of the BOJ's QE securities, but I hope that they have the same flexibility to reinvest at least some of the proceeds of maturing securities.

Regardless, monetary policy has certainly entered a new era of complexity, and there are risks to the new strategies in terms of accurately communicating the intentions of the central bank in a timely manner. The biggest risk of inflation isn't anything financial, it is the risk of the wrong signals being sent to the markets of the world by the communications of central banks.

I'll try to add citations at a later date (I have several which I was thinking of as I wrote this answer).


A profit maximization problem (whole problem has been solved, I just have question about interpretation)

Your production function is basically a Cobb-Douglas function of the form $y=A(t_m-a)^\alpha(t_l-b)^\beta$. Therefore, the parameters $\alpha$ and $\beta$ measure the intensity with which inputs are needed for production. The smaller the value of such parameters, the smaller the marginal productivity of the inputs is. In your context, the company is more labor intense than managerial intense, since $\alpha=m<1$ and $\beta=1$. Finally, the parameters $a$ and $b$ measure the minimum level needed by the company of each input in order to operate. In your case, $a=0$ so the company needs a management to operate. However, $b=-n$ so the company can produce even if $t_l$ was equal to zero. Notice that the larger the $n$, the less the company needs of labor.

In fact, though you found two equations that characterize equilibrium I think you want to solve for $t_m$ and $t_l$ in terms of parameters only (you will see that if  $n$ is very large, the optimal $t_l$ is zero. After that, I would plug in the results into the profit function, that will tell you how much profit the manager will get if he decides to enter the industry, and you can compare that to the outside option.

Solution:

For the manager to operate the company, the profit function must be larger than the outside option. I will assume that if she operates the company, since she is the manager, she does not need to pay herself, so the costs are only $w_lt_l^*$, but her outside option is equal to $w_mt_m^*$, the labor income she will earn working for a similar company  that would demand the optimal management labor.  Therefore, she operates the company iff the profit $\pi =\rho t_m^m(n+t_l)-w_lt_l-w_mt_m\geq 0$.

Case 1: (Assume that $t_m^*,  t_l>0^*$)

Solving the FOC's, we get $$t_m^*=\left(\frac{w_l}{\rho}\right)^{\frac1m} \qquad t_l^*=\frac{w_m}{m \cdot w_l}\left(\frac{w_l}{\rho}\right)^{\frac1m}-n$$

$$\pi^*=\frac{w_m}{m}\left(\frac{w_l}{\rho}\right)^{\frac1m}-w_m\left(\frac{w_l}{\rho}\right)^{\frac1m}-w_l\left(\frac{w_m}{m\cdot w_l}\left(\frac{w_l}{\rho}\right)^{\frac1m}-n\right)=w_ln-w_m\left(\frac{w_l}{\rho}\right)^{\frac1m}$$
Therefore, $\pi^*\geq 0$ iff  $$w_ln\geq w_m\left(\frac{w_l}{\rho}\right)^{\frac1m}$$ However, we assumed that $t_l^*>0$ so
$$\frac{w_m}{m}\left(\frac{w_l}{\rho}\right)^{\frac1m}\geq w_ln$$

The two inequalities can hold since $1 > m$. These are necessary conditions for the manager to operate the company and demand strictly positive labor. I would interpret them as $w_ln$ needs to be intermediate.

Case 2: ($t_m^*>0$ and $t_l^*=0$)

This case occurs if
$$\frac{w_m}{m}\left(\frac{w_l}{\rho}\right)^{\frac1m}\leq w_ln$$
Notice that (after doing some algebra) the optimal profit function $\pi^*$ is still bigger than zero iff
$$w_ln\geq{w_m}\left(\frac{w_l}{\rho}\right)^{\frac1m}$$
In this case, if the first inequality is satisfied, the second holds too.

Conclusion Putting the two cases together we conclude that the manager operates her company if and only if
$$w_ln\geq{w_m}\left(\frac{w_l}{\rho}\right)^{\frac1m}$$
She will sometimes hire workers in her company (if $w_ln$ is not  too large) and sometimes she will not.


Strictly increasing but not convex preferences

Take $u(x,y)=x^2+y^2$ on $\mathbb R_+^2$. The function is strictly increasing in both $x$ and $y$, but the indifference curves are concave to the origin. Hence the preference it represents cannot be convex. For example, $u(1,0)=u(0,1)=1$, but the average of the two bundles is less preferred:
\begin{equation}
u\left(\frac12,\frac12\right)=\frac12<1=\frac12u(1,0)+\frac12u(0,1).
\end{equation}
The indifference curves for perfect substitutes are straight lines. They still represent a convex preference, although not a strictly convex one.


The Bank Rate / Discount rate is the interest rate charged by the central bank to member institutions for loans from the central bank. These are typically thought of as emergency funds to meet the liquidity needs of solvent banks with illiquid assets, thought since Bagehot to be properly set at a penalty rate to discourage abuse.* In contrast, the repo rate is the interest charged on repurchase / rehypothecation transactions, which are short term over-collateralized (e.g. \$100 collateral to borrow \$95) loans where a much larger set of institutions including banks, insurance companies, hedge funds, and others can participate on similar financial terms.

The discount rate is a policy rate where the repo rate is an emergent market price for funds. These rates are linked but not in a mechanical way. For example, if the discount rate were set very low, banks would prefer to borrow from the central bank than the collateralized loan market at the repo rate and therefore quantities and rates in the repo market would likely fall. Or it would if there weren't generally speaking a stigma to using the discount window to borrow at the discount rate. But if it were profitable maybe that stigma could be overcome. And there may be other differences like changes in terms or the suitable assets usable as collateral that make comparisons of rates imperfect.

* -

  This penalty explains the positive difference between the fed funds
  rate and the discount rate. If there were no penalty, banks would be
  indifferent between borrowing from other banks and the Fed’s discount
  window.

Is the Discount Window Necessary? A Penn Central Perspective (Calomiris (1993))

That is, banks would rather borrow from the Fed than each other, so the Fed sets its policy rate higher to push banks back into market sources of funds. Then only those shut out of such markets will avail themselves of such funding.


Euclidean spaces,vector spaces,metric spaces,commodity spaces,Cartesian spaces

I will try to do this at an intuitive level without being technical. If you want rigorous definitions of any of this I can edit my post.

We need a way to mathematically model the consumption choices that an agent faces. To accomplish this, we use $\mathbb{R}^L_+$ to denote the agent's level of consumption of each of 1,2,..,L goods.

Vectors tie into this because we want to think about how much of each good an agent chooses when optimizing over her preferences. So we don't just think about how much of good $i$ the agent wants. We want to think about how much of good 1 the agent wants, good $2$ he wants, etc. simultaneously. So, there are tons of different "mixes" of these goods that an agent can afford (that belong to this agent's budget set given some prices and wealth) and one of those "mixes" (vectors) represents how much of each of the L goods an agent chooses to consume when maximizing his or her representative utility.

Now - Cartesian space. You should actually discuss the Cartesian coordinate system on Euclidean space. We use Cartesian coordinates to denote a point in Euclidean space. We could, for example, instead use polar coordinates to denote points in Euclidean space.

A metric space is a bit more complicated  but you can think of it (this is very simplified) as a space where the distance between any two points is well defined. The distances themselves are called a metric. Having a metric space allows us to use topological methods (for example, the concept of open balls when discussing the local non-satiation of preferences). The most common example of a metric space is three-dimensional Euclidean space.


Why does the answer not include increased negative unplanned stock investment?

Scenario “C” does not specify “unexpected.” Since greater growth was expected, planned inventory investment would rise to meet higher expected demand.


What happens to interest rates when they are already at (near) zero and the stock market crashes?

They would be just pushed to their lowest possible level. Recent experience in Switzerland and Germany shows the interest rate can be slightly negative but that’s it. Once the interest rate hit (zero) lower bound it can’t be pushed further as long as there is cash that carries implied zero interest. At that point central bank would have to resort to other policy instruments such as QE, helicopter money, forward guidance etc.

However, if some western country would decide to go completely cashless it would be possible to have arbitrary negative interest rate. In that case the interest rate would just get pushed further down.


Difference-in-differences with long time horizon and repeated treatments

This question is related to a post I addressed on CrossValidated. The "generalized" difference-in-differences (DiD) estimator is amenable to settings with multiple groups and multiple exposure periods. Take the following specification:
$$
y_{it} = \gamma_{i} + \lambda_{t} + \delta T_{it} + \epsilon_{it},
$$
where $\gamma_{i}$ and $\lambda_{t}$ denote unit (i.e., individual, entity, county, state, etc.) and time (i.e., day, month, year, etc.) fixed effects, respectively. You may also see this referenced as a ‘two-way’ fixed effects estimator. The variable $T_{it}$ is a treatment dummy, indexing the $i$ units affected by the policy/intervention during periods $t$, 0 otherwise. In practice, $T_{it}$ can take on any pattern. Thus, it can more than handle intermittent exposure periods.
Your main policy dummy $T_{it}$ is your interaction term, but you must instantiate it manually to account for the different entities moving into and out of a treated status across time. Thus, $T_{it}$ 'turns on' (i.e., equals 1) if two conditions are met: (1) the entity is in the treatment group and it is in the post-treatment period. Be careful because $T_{it}$ does not demarcate a precise treatment group. Rather, it a discrete indictor for adopter entities and only during those adopter periods. Any 'off' period of treatment should be coded 0.
The problem in your setting is you have a large number of treated units with staggered adoption periods, making it exceedingly difficult to demonstrate a common trend across groups. Centering all units on their adoption date is insufficient as a subset of treated units have multiple treatment regimes. I wonder if you could work on subsets of your data where most treated entities enter into the treatment epoch at more or less the same time. However, this might be difficult with repeated, transient post-exposure periods. Pre-trends might also be violated in settings with irregular exposure periods and heterogeneous treatment effects, a point noted in a recent working paper. In sum, while the "generalized" DiD estimator will work in your setting, you must be cognizant of the downsides of using this approach.
I have previously evaluated policies that were introduced and repealed on several occasions over time. The only difference is the policy dummy turned 'on' and 'off' at the same time for all units. While a different subset of entities were treated in each iteration of the policy, the exposure period was standardized. Thus, I was able to focus on subsets of my panel and assess trend equivalence before each adoption period. I would be happy to share this research if it offers any further insight.
You might also find this working paper an interesting read.


The Neo-Schumpeterian literature models firm behavior with "an search and select" approach. Nelson and Winter (2009) where the pioneers in the subject, it is a pleasant and interesting reading.

Nelson, Richard R.; Winter, Sidney G. An evolutionary theory of economic change. Harvard University Press, 2009


The government does not need to gather capital via tax and Treasuries to spend? According to MMT

There are a number of points in this question, and I do not want to write too long a response that goes too far into opinions. I will note that I am a proponent of Modern Monetary Theory (MMT).

I will first address two questions. I will write from the MMT perspective, and note that I am referring to a sovereign that controls the currency it borrows in (examples: the United States, Canada, Japan). Countries that borrow in a foreign currency (or a currency it does not control, like the euro bloc), face the same financial constraints as a household or firm.

  Does the government really not need taxes and debt to spend since it
  can just print money?

Technically, the government does not "need" to tax to spend, but that ignores a side effect that is also part of MMT: taxes create a demand for state money, and without taxes, government spending would be highly inflationary. (Some countries might be able to achieve the feat of abolishing taxes by having large natural resource endowments exploited by a government-owned enterprise, but I will ignore that.)

A less controversial way of stating this is that a central government does not need to tax before spending, which is undoubtedly true.

As for bond issuance, MMTers observe that spending is implemented by the government issuing cheques (or making bank transfers), which has the effect of creating "reserves" (bank settlement balances at the central bank) in the banking system. It can do this (within institutional limits) without prior borrowing. Bonds can then be issued, which eliminate these reserves that are created.

  Are taxes really only for reducing money supply. Are Treasuries only
  for controlling interest rates?

Although taxes eliminate "reserves", that is not their primary role, rather it is inflation control.

Treasuries drain "reserves," and allow for interest rates to be able the interest rate paid on excess reserves (which used to be zero in the United States).

This post by Bill Mitchell (one of the co-founders of MMT) discusses the lack of necessity of government debt issuance. Link to website. This subject is also covered in Chapter 21 of the textbook Macroeconomics by Mitchell, Wray, and Watts.

I will then turn to:

  Is this common knowledge?

I do not think there is a way of avoiding opinions on this question. In my view, the number of informed dissents to the MMT view in 2020 are very few, the issue is almost entirely how the statements are worded. Conventional economists would refer to this discussion as "money-financed expenditure," and the practical effects of this under conventional theory are hard to distinguish from MMT's description. There is a debate about the inflationary effects of such a policy.

  He says they are spending first and only after that the bonds get
  sold. But what if nobody buys the bonds then it is a problem, right?

The statement "nobody buys the bonds" is probably better expressed as: can a floating currency sovereign default on its debt? That is a difficult question, as the institutional regime in each country is different. The MMT argument is that any institutional arrangements that could lead to a default are self-imposed, and could be eliminated by the government whenever it wishes. I think you would need to ask a separate question on that topic for a country of interest.


What is the difference between Margin and Markup?

Markup is how much the seller is adding to the cost to get the price of sale.

Margin is how much of the sale price is available for overhead and profit.

You would tend to use markup when you are more concerned with costs than the sale price.  You would use margin when you are more concerned with the sale price than costs.

$$\frac{\text{markup}}{\text{margin}} = \frac{\frac{\text{Price}-\text{Cost}}{\text{Cost}}}{\frac{\text{Price}-\text{Cost}}{\text{Price}}} = \frac{\text{Price}}{\text{Cost}}$$

Since cost is generally less than price, markup will generally be larger than margin.

Profit (both accounting and economic) will be no more than margin.  So if you want to talk about profit, you might start by considering margin.

$$\text{markup} = \frac{\text{Price}}{\text{Cost}} - 1$$
$$\text{margin} = 1 - \frac{\text{Cost}}{\text{Price}}$$

One reason you might use markup rather than margin is that you may not know the price.  If you have something that costs one unit and you want 100% markup, then you find out that the price is two units.

$$\text{Price} = \text{markup}\cdot\text{Cost} + 1$$


Misleading vertical axis in foreign exchange graphs analyses?

The convention in finance is that any currency pair "currency1/currency2" is to be interpreted as the number of units of currency2 needed to buy one unit of currency1, or alternatively, as the number of currency2 you get from selling one unit of currency1.

For instance, as of 13th of Match of 2017, the currency pair rate of exchange between the £ and the US $ (GBP/USD) was roughly 1.22. This means that you need 1.22 US dollars to buy £1.

Under this convention, a fall/increase in the GBP/USD means a depreciation/appreciation of the British Pound with respect to the US Dollar.

So, using your example, if the GBP/USD goes up from 3 to 5, then the British Pound appreciates with respect to the US Dollar.

By contrast, the convention in economics is to define the exchange rate as £x/\$1, meaning that you need x British Pounds to buy 1 US Dollar, or that you can sell 1 US Dollar for x British Pounds.

Under this convention, an increase/fall in £x/\$1 means a depreciation/appreciation of the British Pound with respect to the US Dollar.

In other words, the interpretation is exactly the opposite.


Is money mostly created (out of nothing) by banks making loans?

The monetary base (MB) contains what might be called "public money creation", Notes and coins in circulation (outside Federal Reserve Banks and the vaults of depository institutions), Notes and coins in bank vaults (vault cash), and Federal Reserve Bank credit (required reserves and excess reserves not physically present in banks). The broadest available government measured US monetary measure is M2, which does not contain all the elements of MB, but still is an approximation of the total of private and public money creation, which includes currency, plus time, savings, and demand deposit accounts. So, what is MB/M2? What fraction of money is created by the government of the total?

FRED: (Monetary Base; Total)/(M2 Money Stock*1000)
The answer is less than half. Crudely, money is mostly privately created in the US. The "out of nothing" aspect of your question is more complex. In my personal view, and I guess that's only an opinion, is that because banks are government regulated and insured institutions, forced to back each loan with reserves, and regulated to have capital for each of those loans, they cannot really be said to make this private money out of nothing.


I think what you are looking for is known as overselling.


What are all the countries that have a value added tax?

No, many countries do not. For example. the United States does not have a VAT. According to the paper The Consequences of the Value-Added Tax on Inequality in Developing Countries (Alavuotunki and Pirttilä (2015)) here is an extensive list:

A4 – Countries and introduction year of VAT. (Source: IMF)
Asia-Pacific
1977    Korea, Republic of
1985    Indonesia
1986    New Zealand
1986    Taiwan Prov.of China
1988    Philippines
1989    Japan
1990    Pakistan
1991    Bangladesh
1992    Thailand
1994    China,P.R.: Mainland
1994    Singapore
1997    Nepal
1998    Mongolia
1998    Sri Lanka
1999    Cambodia
1999    Papua New Guinea
1999    Vietnam
2000    Australia
2005    India
no VAT  Brunei Darussalam
no VAT  China,P.R.:Hong Kong
no VAT  Lao People's Dem.Rep
no VAT  Malaysia
no VAT  Myanmar

Small Islands
1973    San Marino
1990    Iceland
1992    Cyprus
1992    Fiji
1994    Samoa
1995    Malta
1997    Barbados
1998    Vanuatu
2004    Cape Verde
2007    Antigua and Barbuda
2007    St. Vincent & Grens.
2010    St. Kitts and Nevis
2012    St. Lucia
2013    Seychelles
no VAT  Bahamas, The
no VAT  Comoros
no VAT  Grenada
no VAT  Maldives
no VAT  Solomon Islands
no VAT  São Tomé & Príncipe
no VAT  Timor-Leste
no VAT  Tonga
no VAT  Tuvalu

Americas
1967    Brazil
1968    Uruguay
1970    Ecuador
1973    Bolivia
1973    Peru
1975    Argentina
1975    Chile
1975    Colombia
1975    Costa Rica
1975    Nicaragua
1976    Honduras
1977    Panama
1980    Mexico
1982    Haiti
1983    Dominican Republic
1983    Guatemala
1990    Trinidad and Tobago
1991    Canada
1991    Jamaica
1992    El Salvador
1993    Paraguay
1993    Venezuela, Rep. Bol.
2006    Belize
2007    Guyana
no VAT  United States

North Africa and Middle East
1976    Israel
1985    Turkey
1986    Morocco
1988    Tunisia
1991    Egypt
1992    Algeria
2001    Jordan
2002    Lebanon
2008    Iran, I.R. of
2009    Djibouti
no VAT  Afghanistan, I.R. of
no VAT  Bahrain, Kingdom of
no VAT  Iraq
no VAT  Kuwait
no VAT  Libya
no VAT  Oman
no VAT  Saudi Arabia
no VAT  Syrian Arab Republic
no VAT  United Arab Emirates
no VAT  Yemen, Republic of

Sub-Saharan Africa
1960    Côte d'Ivoire
1980    Senegal
1986    Niger
1989    Malawi
1990    Kenya
1991    Benin
1991    Mali
1991    South Africa
1993    Burkina Faso
1994    Madagascar
1994    Nigeria
1995    Gabon
1995    Mauritania
1995    Togo
1995    Zambia
1996    Guinea
1996    Uganda
1997    Congo, Republic of
1998    Ghana
1998    Mauritius
1998    Tanzania
1999    Cameroon
1999    Mozambique
2000    Chad
2000    Namibia
2001    Central African Rep.
2001    Rwanda
2002    Botswana
2003    Ethiopia
2003    Lesotho
2004    Zimbabwe
2009    Burundi
2010    Eritrea
2013    Swaziland
no VAT  Angola
no VAT  Gambia, The
no VAT  Guinea-Bissau
no VAT  Liberia
no VAT  Sierra Leone
no VAT  South Sudan

Europe
1967    Denmark
1968    France
1968    Germany
1969    Netherlands
1969    Sweden
1970    Luxembourg
1970    Norway
1971    Belgium
1972    Ireland
1973    Austria
1973    Italy
1973    United Kingdom
1986    Portugal
1986    Spain
1987    Greece
1994    Finland
1995    Switzerland

Central Europe and the ex-Soviet
1988    Hungary
1992    Armenia
1992    Belarus
1992    Estonia
1992    Georgia
1992    Kazakhstan
1992    Kyrgyz Republic
1992    Latvia
1992    Lithuania
1992    Moldova
1992    Russian Federation
1992    Tajikistan
1992    Turkmenistan
1992    Ukraine
1992    Uzbekistan
1993    Czech Republic
1993    Poland
1993    Romania
1993    Slovak Republic
1994    Bulgaria
1996    Albania
1998    Croatia
1999    Slovenia
2000    Macedonia, FYR
2003    Montenegro
2003    Serbia, Republic of
2006    Bosnia & Herzegovina
no VAT  Kosovo, Republic of


How startup early valuation influence later funding stages?

No why would it? The valuation should solely be based on the future expectations of the company. Perhaps during this one year, the startup has taken on 100x more customers than it had before, or earning 200 times more, and seemingly have an even brighter future than it did one year ago. Why would the previous valuation affect the new one?

This is at least true for rational investors.


Topology on the space of measurable functions

Not really. There are many compact metrizable topologies you can put on this space, but none that relate meaningfully to the structure of the problem.
Let's look first at the case $A_1=[0,1]$ and $A_2=\{0,1\}$. Consider the elevation function $e:A_1\times\Sigma\to\Delta(A_2)=[0,1]$ given by $e(a,\eta)=\eta(a)$. If you want the ultimate action choice of player $2$ to be continuous in player $1$'s action and the strategy choice of player $2$, you need $e$ to be continuous. In particular, $e$ should be measurable when you endow $\Sigma$ with the Borel $\sigma$-algebra. That never works:
It follows from the main result (Theorem D) in Robert Aumann's 1961 paper "Borel structures for function spaces." that there is no Borel $\sigma$-algebra on $\Sigma$ that makes $e$ jointly measurable. For consumers,  I would recommend to read Aumann's 1963 article "On choosing a function at random." instead.
To make this a bit more digestible, let $F$ be the set of measurable functions from the unit interval to itself. Let $e:[0,1]\times F\to [0,1]$ be given by $e(x,f)=f(x)$. If we endow $[0,1]$ with the Borel $\sigma$-algebra and $F$ with any (!) $\sigma$-algebra, $e$ will necessarily be nonmeasurble. Now, by Kuratowski's isomorphism theorem, all uncountable separable and complete metric spaces are isomorphic as measurable spaces. This will include $A_1$ (if uncountable) and $\Delta(A_2)$ (if $A_2$ has at least $2$ elements).


Is it possible to derive indifference curves given marshallian demand function?

Yes, under some conditions. This is the classic integrability problem: for detailed discussion, see some excellent notes by Kim Border.

Several other technical conditions are required, but the most economically substantive condition is that the Slutsky matrix must always be symmetric and negative semidefinite. To be concrete, if we define the $ij$th element of the Slutsky matrix at $(p,m)$ to be
$$\sigma_{ij}(p,m)=\frac{\partial D_i(p,m)}{\partial p_j}+D_j(p,m)\frac{\partial D_i(p,m)}{\partial m}$$
then we must have $\sigma_{ij}(p,m)=\sigma_{ji}(p,m)$ for all $(p,m)$, and also for any vector $v$ we must have for all $(p,m)$
$$\sum_i \sum_j \sigma_{ij}(p,m)v_iv_j \leq 0$$
The necessity of these conditions follows immediately from basic consumer theory, which shows that if Marshallian demand is derived from constrained maximization of a utility function, then the Slutsky matrix is symmetric and negative semidefinite. But the sufficiency of these conditions (in conjunction with some other technical assumptions) for us to back out a utility function is a more complicated matter, and to get the details I recommend Border's notes or some other advanced micro source.

If, assuming that the Slutsky conditions hold, you want a rough practical way (ignoring the technical subtleties) to back out indifference curves in the typical two-good case, the simplest way is probably to use your knowledge of demand to determine the compensating change in expenditure that is necessary to adjust for a given change in prices. Specifically, for either $i=1,2$ use the identity
$$\frac{\partial e(p,u)}{\partial p_i} = h_i(p,u) = D_i(p,e(p,u))$$
which, given knowledge of the Marshallian demand function $D$, is a differential equation in the expenditure function $e$. Starting with some initial values $(\bar{p},\bar{m})$ that produce some unknown utility $\bar{u}$, we know that $e(\bar{p},\bar{u})=\bar{m}$. Then, varying $p_1$, we can integrate the above differential equation for $i=1$ to obtain $e(p_1,\bar{p}_2,\bar{u})$ for any $p_1$. And then we can get the Hicksian demand vector
$$h(p_1,\bar{p}_2,\bar{u})=D(p_1,\bar{p}_2,e(p_1,\bar{p}_2,\bar{u}))$$
for any $p_1$.

Since these Hicksian demands all correspond to the same utility $\bar{u}$, they are on the same indifference curve. By varying $p_1$, we will be able to trace out many different points on this indifference curve. In fact, if demand is sufficiently well-behaved, then we can trace out the entire indifference curve by varying $p_1$ enough in either direction. (By the way, "tracing indifference curves" is all we can do in any event: since the cardinality of utility is irrelevant to Marshallian demand, we can only retrieve ordinal properties like indifference curves and their ordering.)


Elasticity with perfectly inelastic / elastic demand

In the title you ask about perfectly inelastic demand; in the text it is about perfectly elastic demand. I guess you want to know about the latter. So you can skip one of the paragraphs.

Let us define PED as this absolute vale
$$\varepsilon_p = \left| \frac{d Q / Q}{dP / P} \right|,$$
(otherwise it is a non-positive value, this is just a convention).

In general, both perfectly elastic and inelastic demand are defined in the limit. As always, the math gets a little fishy when $\infty$ is involved (or if you want to divide by zero). To stay sane, it helps to think of an "infinite quanity" as it is used in economics as "very, very, very large approaching infinity" or as "as much as possible". Similarly, think of a good with an "infinite price" as a good that "nobody can buy".

With perfectly inelastic demand, price changes do not affect demanded quantity $q$.
As an example, think of a life-saving drug. How must the price change that you demand $q'<q$ instead of $q$? Well, you always demand $q$ - it doesn't happen. How can we express "it doesn't happen"? We can say that you would only consume less than $q$ if the price becomes some number that is larger than any real number. Now think about a limit approaching this benchmark case of a vertical demand curve, some sequence of very steep declining lines. Then for any $dQ/Q<0$ it must be that $dP/P$ approaches infinity. Similarly, for a demanded quantity $q'>q$, i.e., $dQ/Q>0$, "the good has to be thrown at you". For a meaningful sequence approaching the perfectly inelastic demand, you have to ignore the restriction that prices are positive -- it must be that $dP/P \rightarrow - \infty$. Hence, $\varepsilon_p \rightarrow 0$.
Alternatively, don't think in limits, but ask the reverse question. Instead of "how must the price change that my demanded quantity changes", ask "how do I change my demanded quanity if the price changes"? The answer is, not at all: $dQ/Q =0$ for any $dP/P$, making the PED always zero.

With perfectly elastic demand, an arbitrarily large quantity can be sold at some market price $p$. As an example, think of a \$100 bill or a (hypothetical) perfectly competitive market. "Arbitratily large" does not mean infinity, which is not a real number.
Again ask, how does the price have to change that my demanded quantity changes? By definition, any quantity is demanded at price $P$. That is, the price does not have to change at all. Hence, $dP/P=0$ for any $dQ/Q$. Then $\varepsilon_p$ is not well-defined (you divide by zero), but you can think of a sequence of very flat declining lines that approach the horizontal demand such that $dP/P\rightarrow 0$ and $\varepsilon_p \rightarrow \infty$.
You can again also ask the reverse question: how does demanded quantity change when the price changes. For this just consider the limit again (and ignore the restricion to positive quanitites). If a \$100 bill is offered at \$99.99, demanded quantity goes to infinity. If a \$100 bill is offered at \$100.01, demanded quantity goes to minus infinity -- you would want to sell your bills. That is, $dQ/Q \rightarrow  \mbox{sign}(dP/P) (-\infty)$ and $\varepsilon_p \rightarrow \infty$.


In economic modelling, how are we sure the linearized equilibria behave similarly to original equilibria?

Many macroeconomists have a somewhat cavalier attitude towards checking the validity of linearization methods, but definitely not all of them. For an example of the approximation issues being taken seriously, see Appendix A.3 on "Log-Linearization and Determinacy of Equilibrium" in the book Interest and Prices by Michael Woodford.


GDP is a measure of economic activity. One typical way to look at the question is the way shown in another answer. Here I want to put some assumptions in place in order to give a bit more structure.

It is widely accepted that economic output is created through capital and labor, and facilitated by technology. For the sake of answering this question, we can assume that somehow we can aggregate all the decentralized small economic activities into one aggregate economic activity. For our economy then, GDP $Y$ is produced using labor $L$, capital $K$, and technology $A$, and some sort of production function $F$.

$$ Y = F(A, K,L)$$

This entails all ways that growth can happen, and I shall walk quickly through them.

Labor

When there is more work being done, we produce more. This includes both the intensive margin (each worker spending more time per week, month, year on on his job(s)), and the extensive margin (there being more workers, due to larger population).

Note that it is unlikely to get persistent growth from the intensive margin - eventually people are working as much as they can. The extensive margin, however, can give you persistent growth.

One can also think about $L$ as effective labor, in the sense that human capital also influences output. A stronger man can harvest more fields than a weak one, and a smart man can design more bridges. If workers get more skills that are useful in their economic activity, that will also stimulate growth.

Capital

When there is more machines, we can produce more, for the same amount of labor. $K$ in that equation entails both quantity and quality of machinery, similar to the human capital point.

Capital is part of economic output. Hence, in order to create GDP, we need GDP. We also need people to actually decide that saving previously earned GDP and "transforming it into capital" is better than consuming it.

Capital naturally depreciates. This is because technology may change, and hence old tools might be of less use, but also naturally due to fatigue etc. Hence, even if we don't want to grow, we still need to consistently devote a share of GDP towards investment. If we want positive growth, we need to invest further.

Technology

Technically, technology incorporates both $A$ and $F$ in the previous equation. If we have a large population, but only little capital, creating technologies that make more efficient use of labor, and need less capital, will increase growth. Regarding $A$, using technologies that allow us to produce at a higher level of efficiency we can produce a higher level of output for the same amount of inputs.

So then, what are good policies/channels?

Increase investment

Higher investment means more capital, and hence more to produce. An example policies to increase investment are decreasing capital taxation, and anything that increases the return to capital.

Increase effective labor

We cannot get persistent growth from increasing the working hour per person, although this may be a valid policy in the short run. Increasing the labor force (more immigration, higher fertility) is a  second. Be cautioned, that that also means that the population gets a smaller share of the GDP, as we have more people to split the cake.

Increasing human capital hence seems like the natural way. Policies that allow people to become better at their jobs will increase growth. That could be

better education
training on the job
couching of unemployed

Increase technology

This is a no-brainer, and most likely the most important driver of economic growth over the past century. In effect, many people are worried that the time of big growth is over, just because the time of big inventions and technological booms appears to be over. Policies that incentivize research and development will increase growth. Such as

Patents (but they are a double edged sword) and anything else that will increase the returns to research
Better education, make "research" more attractive
Technological/research hubs, similar to silicon valley: Anything that facilitates research


Financial Smart Contract on Ethereum: can an Ether Futures contract be priced in Ether?

Futures and Options are all about exchanging something for something else. These kind of derivatives all involve exchanging different 'kinds' of goods so it doesn't make sense to have both sides denominated in the same currency: When you have X Ethereum which you are willing to give up for Y Ethereum later, what you have is a loan. Loans aren't going to do much in terms of managing volatility, which is essentially, how much is Ethereum worth in terms of other stuff.

So the futures contracts needs to be exchanging Ethereum for that other stuff that happens to be volatile relative to Ethereum or vice versa. (could be dollars, could be Bitcoins). Of course since we can't predict the future there will be a winner and a loser. It's the nature of this sort of thing, however supposedly both parties are gaining a loss of volatility.

If you want to manage the downside, you can structure it as an option. An example of this would be, You pay \$1 now to have the right to exchange \$300 for 1 Ethereum in 90 days. (or vice versa). If the Ethereum ends up being worth more than \$301 then you end up winning on that deal, and if Ethereum ends up being worth less than \$301, you don't buy it. This benefits both parties: The person selling the option gets \$1 either way, and if Ethereum drops the purchaser of the option doesnt't lose more than \$1. This type of option is called a 'call option'. If structured the opposite way (you pay \$1 for the right to exchange 1 Ethereum for \$300 in 90 days) then the opposite happens: you 'win' if Ethereum drops below \$299, and you don't exercise the option if Ethereum rises in value, in which case you're simply out \$1. This is called a 'put option'.

No matter what, there will be a winner and a loser come the time to exercise the option. This is inevitable. However, the big idea is that the buyer of the option has a certain expectation on the market trend but wants to protect themselves against the opposite trend (in the case of call, fixed loss and unlimited upside, in the case of a put, guaranteed gain if there is downward movement vs. fixed loss if there is upward movement). The opposite side, the side selling the option, makes money off of the fee to purchase the option and is hoping that the volatility works out to less than the cost of the fee.

You are right about fixed futures (where the price and quantity are fixed and there is no option to back out): they will definitely have a winner and a loser. However, both parties get a guaranteed price, and that may be more valuable than any potential gains or losses. For example, say I am a multinational corporation where most of my profits come in USD but have just built a factory in Kenya and have taken out a loan to do so from a local bank. To pay off the loan, I need to guarantee I can get a fixed amount of Kenyan shilling every month, and it may be worth it to set price in USD so I don't have to worry about exchange fluctuations causing the loan to cost more USD than I expect one month, leaving me short; in that case I won't care too much if I lose out on the potential for the USD/Kenyan Shilling rate to move in my favour. Maybe the same thing could apply for someone who has contracts denominated in Ethereum, who knows.

On the other hand, any kind of investment based on expected future trends is just a smarter form of gambling, when you find someone to take the other side of the bet of course someone will win and someone will lose.

Enforceability of such contracts is a separate measure, it would be the same problem for any futures market and ideally that is what contracts, reputation and the rule of law is for.


How are disaster effects calculated into GDP?

GDP is just a partial measure of flow. There are lots of changes to the stock of a nation, its capital, that are not captured by GDP.

Destruction of assets in natural disasters isn't recognised as a loss in GDP. It gets worse: the rebuilding would actually be a positive on GDP. NB any loss in economic output from, say, destruction of factories, would appear as a negative on GDP - the loss of the factory's output.

Changes in natural capital aren't captured either.

GDP is just a measure of volume of transactions. It gets misused as a proxy for economic wellbeing. That's not the indicator's fault, it's the fault of those who misuse it.


please help describe a) what exactly is the Paradox of Profits , b) what is the argument of these papers exactly

You largely answered this question yourself: you provided this reference to a Gennero Zezza paper: (link to paper)

Zezza states in the second paragraph that most of the thinking about the Paradox of Profits was mistaken, as the authors used models which were not stock-flow consistent (flows disappeared). If people are arguing that there is a paradox, but do the accounting wrong, it is difficult to explain the error - since their arguments are internally inconsistent.

I am not familiar with Marx’s arguments, but based on the question, he is making an argument about a fixed money supply. This adds an extra constraint, that is probably not addressed in the Zezza papper.

For a single time period, there is no difficulty in generating profits. The business sector starts with \$100, pays \$90 in wages, \$10 in dividends, and then the household spends all money received to buy goods - generating \$10 in profits, which is enough to cover the dividend. Profits can be achieved also by the business sector investing in fixed capital or inventories. In any event, this can be achieved with a fixed money supply.

The only challenge is generating a steady state. Can a fixed money supply co-exist with a growing economy in steady state? This is perhaps a challenge, but the reality is that even non-financial entities can issue instruments that are used as money if the money supply is constrained. (For example, the pre-Confederation Canadian colonies had a perpetual shortage of coinage, and a wide variety of entities issued tokens that circulated as money). Since it is hard for a society to survive without government, government-issued money is normally issued in a way to grow in line with the economy.

Marx was writing in an era before fiat currencies had shown much ability to survive. My understanding is that his thinking did not take into account the flexibility of fiat systems.

In summary, since the argument that profits are paradoxical is based on faulty logic, it’s difficult to explain where the problems lie. One would need to delve into the details of each argument, and determine where they made the error - and it’s not necessarily always the same error.


So in modern English, a commodity is a raw material for production or basic agricultural good that can be exchanged for money. Labor, by this definition, is neither a raw material, no one grinds humans up to build stuff, I hope; an agricultural good, similar reasoning; nor exchangeable for money, as slavery and indentured servitude is illegal and efficient in most places. (Letting people make their own work decisions, or at least not forcing them to work, is good, generally speaking.)

Even with a more generously wide definition of a commodity, commodities are generally seen to be fungible, which means you cannot easily differentiate between the good/service based on region, or that they all of each type of commodity is seen as equivalent. So if you are willing to say that all labor is equivalent...

Basically, labor is generally not seen as a commodity.


What is a substitute/complement in terms of mixed partial derivatives?

It is very important here to note that there are multiple, mutually inconsistent, possibilities for how to define a substitute/complement.

One way is to say that $x$ and $y$ are complements if an increase in $y$ raises the marginal utility of $x$ (or, given symmetry of mixed partials, vice versa):
$$\frac{\partial^2 U}{\partial x\partial y}>0\tag{1}$$This is the suggestion in foobar's answer.

Another way is to say that $x$ and $y$ are complements if a decrease in the price of $y$ raises the Hicksian (aka compensated) demand for $x$. Since Hicksian demand is the derivative of the cost (aka expenditure) function by Shephard's lemma, this can also be expressed as a condition on mixed partials:
$$\frac{\partial^2 C}{\partial p_x\partial p_y}<0\tag{2}$$
This is the suggestion in snoram's comment, and it is the notion more commonly taught in micro classes.

These definitions are not equivalent! Indeed, in any case with only two goods, those two goods must be substitutes according to (2), regardless of whether the cross-partial of $U$ in (1) is positive or not.

One can give fruitful labels to these concepts (though these labels are more common in the case of production rather than utility functions). Following Hicks, we can call complements by definition (1) q-complements: if $x$ and $y$ are q-complements, an increase in the quantity of $y$ leads to an increase in the marginal value of $x$. Meanwhile, we can call complements by definition (2) p-complements: if $x$ and $y$ are p-complements, a decrease in the price of $y$ leads to an increase in the demand for $x$. See, for instance, Seidman (1989) for a brief overview.

Both concepts are useful in different situations - it depends on what you're interested in!

More technical note: you might notice that (1) and (2) do not seem very similar to each other: (2) is a compensated concept, keeping us on the same indifference curve, while (1) is not. This is a valid criticism, and indeed there is an alternative notion of "q-complements" that is compensated, and a notion of "p-complements" that is not.

The compensated notion of q-complements, which is probably more relevant for most consumer theory applications than (1), asks whether the marginal return to $x$ increases as we increase $y$, while staying on the same indifference curve. (It's more relevant for consumer theory because it doesn't depend on the inherently ambiguous cardinality of $U$. Indeed, apparently Hicks introduced this as the consumer-theory definition of "q-complements" in his 1956 Revision of Demand Theory, though I don't have a copy of it myself.) This notion also has a mixed partial characterization, in terms of something called the distance function, which is a cool micro theory tool that no one learns anymore; the matrix of mixed partials of the distance function is called the Antonelli matrix, and it is a generalized inverse of the beloved Slutsky matrix.

If we wanted to think about other versions of p-complements, there are several options. One way is to hold income constant, and say that $x$ and $y$ are complementary if a decrease in the price of $y$ increases Marshallian demand for $x$. This is a valid notion (called "gross" complementarity rather than "net"), but it's not very nice because it's not symmetric (due to income effects) and hence doesn't have a mixed partial characterization.

Another, nicer way is to hold marginal utility of wealth constant (this is called "Frisch" demand, and is the consumer theory analog of profit maximization, which holds price of output constant), and then ask whether a decrease in the price of $y$ leads to an increase in the demand for $x$. This depends on entries in the inverse of the Hessian matrix of mixed partials of $U$, revealing an inverse relationship with (1) (which depends on the Hessian matrix itself) that parallels the inverse relationship noted above between the Antonelli and Slutsky matrices.


Do products which are only produced and consumed locally contribute to GDP value?

Yes.

1. You seem to believe that goods and services that are not exported may not be counted.

This is false. (Almost) all goods and services are counted, even if they are not exported.

2. The only exception is (intangible) services produced for one's own consumption.

Examples: Mowing one's lawn, making one's meals, and cleaning one's home are not counted in GDP.

Note that (tangible) goods produced for one's own consumption are counted in GDP. For example, the crops produced and consumed by a rural household are counted in GDP, even though they are not sold on the market.

(There is one exception to the exception, which is that housing services "generated" by one's home is counted in GDP.).


When people talk about “Companies Hiding Money Overseas” to avoid taxes, what does this really mean?

Re: main question.

It can range from a) companies fraudulently charging above/below market prices among departments/subsidiaries in order to fraudulently lower tax liabilities in a particular jurisdiction, to b) companies retaining profits and associated capital in the foreign country that the profits were earned in.

Most often, it refers to locating headquarters in a lower-tax jurisdiction regardless of whether the corporation has a substantial presence in that jurisdiction for its main area of business activity.

The other questions are all very complex and can have extremely numerous caveats and/or special cases, etc. The questions are also prone to predictable divisions along ideological lines.

However, here are some general points relating to each:

1) An empirical point of reference on the role of taxation in governmental capacity to address market imperfections: Somalia's tax-to-GDP ratio is about 10% (too low), while the tax-to-GDP ratio of the USA is above 30% (too high or too low?) and that of France approaches 50% (commonly viewed as too high). If all profits go overseas and are not taxed domestically, this could reduce the ability of government to correct market imperfections.

2) Does it add value elsewhere? Here you could enter into debates about what does it mean to "add value" (the most obvious assumption would be that you refer to "value added" as determined by monetary amounts representing value at different stages of production) or different views on "efficiency" (e.g., profit maximization of firms as compared to social welfare maximization in a society). I think you'd really have to get a handle on the main positions of the debate about those concepts, in addition to their most commonly used statistical indicators, in order to be sure of what exactly you're asking and/or want to ask.

3) Ignoring useful theories about things happening instantaneously and always equaling out in a way that is optimal across all uses: a) liquidity is needed both to undertake any investment opportunity that arises (including buying rivals for the purpose of enjoying monopoly profits or possibly for cost savings) and also to protect against liquidity shocks such as those related to a major fall in the value of capital assets across an economy (e.g., 2008-09); b) the case of holding a lot of cash should be compared to opportunities which exist for them to deploy liquidity to earn profit - for example, corporations should not be expected to engage in explicitly redistributive zero-value digging and filling of ditches (leaving specifically redistributive questions to the larger tax pool via government, which can more easily re-capture the value of human capital growth), and it is not desirable to "excessively" promote companies to deploy cash holdings in a pro-monopoly anti-competition manner.


I think this is due to how terminology surrounding ZLB changed/evolved over time.
In most models ZLB is actually mathematically zero lower bound in a way that is closer to a boundary solution as you put it (see examples in Romer Advanced Macroeconomics chapter 11 and more importantly sources cited therein for the models including ZLB). Nonetheless, the ZLB result hinges on many simplifications such as that there is no cost to holding cash money. Such assumptions might be fine for model building purposes but when it comes to practical policy making those storage costs can easily result in the effective lower bound being let's say $-0.5\%$ or some other value that would have to be empirically estimated.
However, in the mean time zero lower bound somehow acquired separate meaning as being the term for the idea that interest rates cannot fall beyond zero, even if originally the terminology coincided more closely to what mathematicians would consider biding constraint. Colloquially, at least from my own experience, when people discuss ZLB at conferences/workshops they often do it in a sense of referring to the result or even sometimes just as referring to idea of lower bound rather than trying to follow mathematical terminology.


Can value be defined as any increase in consumer or producer surplus?

The standard (finance) definition of EVA is only related to the producer's side of the market. Broadly speaking, it is defined as profits minus the cost of capital.

This is closely related to the concept of producer's surplus in microeconomics which is defined as profits (P) minus fixed costs (FC). In micro-economics, fixed costs most of the time refers to the cost of capital, capital being the fixed factor of production (and labour the variable factor of production).

Producer's surplus (PS) is defined as total revenues (TR) minus variable cost (VC, cost of using labour, in an easy model VK=w*L, with w=wage; L=labourinput). Profits are, of course, total revenues minus total costs (TC), with total cost equalling fixed plus variable costs.

So, it is easy to show from these two definitions that PS really looks like the finance EVA, because, as I said, FC can be seen as the cost of capital, the fixed factor of production.

PS=TO-VC

W=TO-VC-FC

<=> W = PS - FC <=> PS = W + FC

Therefore, the PS (or, for the finance guys: EVA) is only measuring value that is created (surplus) for the producer. Just add consumper surplus (CS) to the PS and you get the total surplus of an exchange. Two remarks:
1) to get the CS you need to measure utility, CS = Utility of the goods bought - price paid for the goods. Unfortunately, this is quite impossible to measure.
2) I use "exchange" since surplus is only created when a seller sells his stuff to a buyer. CS refers to the surplus of total utility derived from the consumption of the goods above the price paid for the goods, PS refers to the benefit of producing (and selling) goods above the situation of not producing. This interpretation is equivalent to PS = TO-VC. When the producer produces and sells his product, he has profits TR-VC-FC. When he doesn't produce, but disposes of the production capacity (the capital), his profits are -FC (no revenues and no variable cost, but having the production capacity at his disposal means he has to bear the cost of capital, the FC). The producer will be producing when is PS is positive, that is, when producing creates a surplus (more profits than if he would not produce).

Notice how I prefer to use surplus (instead of added value) to adress this kind of measure for the value of an activity. This is because, in economics there is the concept of added value, which may be closer to what you're looking for. It is defined as outputs - intermediate inputs (net outputs), and thus measures the value that the producer 'adds' to his inputs when producing. It can be easily measured and is, in fact, GDP.

To sum up, these all the measures discussed:

EVA, the finance equivalent of PS;
total surplus = PS + CS, but with CS being unmeasurable;
GDP, or value added.


Why do we use mostly two-tailed Student's t-statistics to find if an explanatory variable is significant in a regression?

We'd like to test if an variable $x_j$ is relevant in the respect of the model

means that we want to test its "statistical significance", so the null hypothesis is  $$\text{H}_0 : \beta = 0$$

(by the way, historically, that's why it is called the "null" hypothesis: a hypothesis of "null"-zero- effect).

The $t$-statistic for this test is

$$t=\frac{\hat{\beta_j}}{SE(\hat{\beta_j})}$$

Using a two-tailed test does not constrain us as regards the sign of the coefficient (the direction of the effect, if it exists). It may be positive or negative. If it is positive, the null if it is rejected, will be because the $t$-statistic takes a large positive value. But if the effect is negative, then the $t$-statistic will take a high negative value. So we want to test against either case, and this is why we use a "two-tailed" test.


Constraints on a symmetric pareto allocation under uncertainty

The idea is that since agents are ex-ante identical, they should have the same (ex-ante) expected utility.

Ex-ante identical means that even the agent does not know what's his type until resolution of type at date-1. Because they have the same preferences each agent's consumption profile must be identical. And the analysis can then focus on symmetric equilibrium.

What symmetric means, as explained in the footnote, is that the consumption profile must be identical. The consumption profile $(C_1, C_2)$ represents the consumption for the agent at date 1 (if he is type-1) $C_1$ and the consumption for the agent at date 2 (if he is type-2) $C_2$. Otherwise stated $(C_1, C_2)$ does not depend on the type and each agent has the same $C_1$ and $C_2$. Since the types coincide with the date it's a little bit trivial but it really says nothing more than that.

For the constraint, there is a mass-1 continuum of agents, each endowed with one unit of wealth, so the total wealth is 1. Then from that total wealth an amount $I$ will be invested in the productive technology whose return is $R$ per unit invested. Then it follows that :

at date 1, an amount $1-I$ is available, and the demand will be $\pi_1C_1$, so this yields : $\pi_1C_1 = 1-I$
at date 2, an amount $RI$ is available, and the demand will be $\pi_2C_2$, so this yields : $\pi_2C_2 = RI$


How does 'building land' fit into economic modeling?

Land would fit into production functions or many economic models the same/similar way as other factors of production.

An example of general Cobb-Douglas function with land would be:

$$Y(K,L,T) = A K^{\alpha}L^{\beta}T^{1-\alpha-\beta}$$

Where $K$ is capital, $L$ labor, and $T$ land. Into most economic models land can be integrated rather easily as the example above shows. The land improvements necessary to clear land for building can be in principle modeled as capital accumulation with depreciation but for some general production functions there is not that much difference made between the inputs.


Relaying from @lumi's answer to this question (not a duplicate though) we see that

As @lumi writes

  ..."if we look at the Greek money supply figures, and we know that that there are essentially three ways for liability deposits to
  decrease as shown - loan repayment, loan write-off and cash
  withdrawals, we can deduce pretty easily that Greece is experiencing a
  massive outflow of cash. We can assume that some of it is cash
  withdrawals particularly recently, but some of it also debt repayment
  to debt owners outside of the Greek banking system."

For the last months, I would increase a bit the emphasis on "people withdrawing funds and taking them out of the country".


Find Price Elasticity of Demand for p = 0

The Answer can be found in the comments by user brunosalcedo:

"Remember that elasticity measures percentual rates of change. How does q change per unit of percentual change of p? If $p=0$, then any percentual change of p results in no change at all because 0 multiplied by any number is 0. The elasticity is not just 0 at p=0, it is also continuous at $p=0$. If you compute the elasticity for small but positive prices, and then take the limit as p goes to 0, the limit is 0."


Why did the inverse correlation of stocks and commodities stopped working in 2008?

The problem in your question is the "and vice versa".

To give a very simplistic view, the problem in the 2008 crisis was not on production side - companies had enough to produce, but no-one to sell to. Given this, excess commodities found no buyers, even as the price lowers. The inverse correlation of stocks and commodities supposes full capital use, which is not the case during the 2008 crisis.

Globally, the correlation between commodities and other stocks is around 0, though during full capital use periods it does tend to be negative, there is usually a positive correlation during crisis.


Defn: A function $h:\mathbb{R}^2\rightarrow \mathbb{R}$ is homogenous of degree $k$ if for every nonzero $\alpha$, $h(\alpha x, \alpha y)=\alpha^k h(x,y)$.

Defn: A function is homothetic if it is a monotonic transformation of a homogenous function.

Lemma: If $f$ is homothetic, i.e. $f=g\circ u$ for some strictly increasing $g$ and homogenous $u$ then
$$
\frac{\frac{\partial f}{\partial x}}{\frac{\partial f}{\partial y}} = \frac{g'(u(x,y))\frac{\partial u}{\partial x}}{g'(u(x,y))\frac{\partial u}{\partial y}}=\frac{\frac{\partial u}{\partial x}}{\frac{\partial u}{\partial y}}
$$
is homogenous of degree zero.

Let

i) $u_1(x,y)=x+y$,

ii) $u_2(x,y)=\log(2x+y)$

Then, $u_1$ and $u_2$ are homothetic functions since they are monotonic transformations of homogenous functions (of degree 1). Let

iii) $u_3(x,y)=x+y+log(2x+y)$. Then

$$
MRS_{u_3}=\frac{\frac{\partial u_3}{\partial x}}{\frac{\partial u_3}{\partial y}}=\frac{1+\frac{2}{2x+y}}{1+\frac{1}{2x+y}}=\frac{2x+y+2}{2x+y+1}
$$
which is not homogenous of degree 0.

Hence, sum of homothetic functions is not necessarily homothetic.


Can one bank be the correspondent bank of itself?

Yes it is possible, I worked for a big bank subsidiary in a different country. We had a nostro account with the parent bank, and with its other subsidiaries. I cannot comment on the benefits/limitations of this though.

EDIT:
I remember we did not pay fee for the nostro accounts held with the parent and subsidiary banks. Moreover, these accounts were necessary as we had to deal with transactions involving various currencies. If let's say a client wanted to deposit in EUR, the bank should have a EUR nostro otherwise, the bank would not accept euro deposits.


Just like a Production function, in Economics, a Cost function is not an "engineering relation", but a "best response", reflecting minimum cost to produce a given quantity $q$.

Cost-minimizing firms are at first assumed not to determine their scale of operations -what they decide upon is the demand for production inputs,given the inputs' prices.

Still, by duality, the profit-maximizing condition should also hold -these are for-profit private companies, not, say, some public utility without a profit motive. If the firms are price-takers in the diamonds market, this relation is well-known, and provides the answer to a) (remember that there are functions, and then there are inverse functions).

As for b), I see in the question that the suppliers are assumed identical.


It's probably easiest to insert everything into Utility $U = U(R)$, such that it depends only on one choice variable:

$U(R) = 48R + Rr(L^{*}-R)-R^2$

Deriving w.r.t. $R$ yields the first order condition:

$48 - Rr + r(L^{*}-R)-2R \overset{!}{=} 0$

Rearranging yields leisure in terms of the wage rate:
$R(r) = \frac{48-L^{*}r}{3+r}$

Labor Supply $l(r)$ is hence given by:
$l(r) = \frac{3L^{*}+2rL^{*}-48}{3+r}$

Deriving this by $r$ should yield what you're looking for:

$\frac{d l}{d r} = \frac{3L^{*} + 16}{(r+3)^2}$


The irony of Marx's criticism is that Communism is just as, if not more, available to become a "legalization of thievery", due to the elimination of the "invisible hand" of the market.

To your question, I would point to the Chicago School's consideration of Antitrust government intervention as a defense of the intuitions of Adam Smith, albeit a modification of strict faith in the ability for the "invisible hand" to unrestrictedly manage the fairness of the markets.

Michael S. Jacobs discusses the rise of the Chicago School's antitrust perspective, in his 1995 article in the North Carolina Law Review, "An Essay on Normative Foundations of Antitrust Economics". For Chicagoans, Antitrust actions are a tool to protect the free market. This is aligned with Adam Smith's concept of economic systems, via the application of the strict guideline that "consumer welfare, narrowly conceived in explicit economic terms, should be the only object of inquiry" in considering antitrust intervention (Jacobs, 1995. e.g. Herbert Hovenkamp, 1985). These tools are only to be used with the strict attention to preserving efficiencies of the market - an allusion to the foundational premises of Smith.

The topic of Antitrust Legislation provides an example of the role of government to intervene in the free market, while respecting the need for it to be enacted in a minimized way.

Additional reference material can be found in the article - it is highly notated.

LINK: "An Essay on Normative Foundations of Antitrust Economics". Michael S. Jacobs, North Carolina Law Review, 1995.


Is indefinite exponential economic growth possible?

As Steven Landsburg pointed out, indefinite anything isn't possible given the eventual heat death of the universe.

Von Neumann posited machines capable of indefinite growth in population (and theoretically production and consumption), so in theory, it would be possible for a time.

Sagan's Response however argued if such things existed that we would have already observed them, and that they would destroy whole galaxies en masse.

That's probably the closest answer you can get to a question like this.


Your example is faulty

You have 10 and spent it on Inputs (Let's assume just wages)
Now you have 0 and people have 50 (40 + 10 wages you paid them)
People buy your goods for 20. You have 20 and people have 30
You pay a tax of 5. You have 15, people have 30, govt has 55
Govt pays salaries (Only to its employees). You have 15, people have 50, Govt has 35

In this case, the govt ended up with less money than it started with. This is called a "Fiscal Deficit" when the govt spends more than it earns. A deficit can be funded in many ways
 - loan from international institutions
 - Monetary financing (Printing Money)

But a deficit is a choice the govt makes. It is by no means inevitable if the govt has budgetary discipline. It just needs to keep its expenses controlled w.r.t its income


The 'long run' assumption is not about whether the firms already on the market are price takers (perfect competition) or oligopolists but whether entry to the market is free. If entry to the market is free then in the long run profits tends toward zero, as a profitable market makes it tempting for more firms to enter.

If you have special asymmetric conditions where some entrants have different cost functions than the new ones the zero profit condition may not hold even in the perfect competition case.


Homothetic preferences and weak separability

EDIT: Seems to that after your most recent edit the answer is still no.
A relatively simple counterexample is:
$$
U(x,y,z) = \sqrt{x} + \sqrt{y} + \sqrt{z}.
$$
This is clearly seperable and homothetic. But $D_z$ is is not independent of $p_x$ and $p_y$. I think this is clear just by looking at the utility function, as it is not of the Cobb-Douglas type. If you have doubts you can calculate $D_z$ from these equations:
\begin{eqnarray*}
MRS_{xz}(x,y,z) & = & \sqrt{\frac{z}{x}} = \frac{p_x}{p_z} \\
\\
MRS_{yz}(x,y,z) & = & \sqrt{\frac{z}{y}} = \frac{p_y}{p_z} \\
\\
m & = & p_x \cdot x + p_y \cdot y + p_z \cdot z.
\end{eqnarray*}
Then
\begin{eqnarray*}
m & = & p_x \cdot x + p_y \cdot y + p_z \cdot z \\
\\
m & = & p_x \cdot z \cdot \left(\frac{p_z}{p_x}\right)^2 + p_y \cdot z \cdot \left(\frac{p_z}{p_y}\right)^2 + p_z \cdot z \\
\\
\frac{m}{p_z}\frac{1}{\frac{p_z}{p_x} + \frac{p_z}{p_y} + \frac{p_z}{p_z}} & = & z.
\end{eqnarray*}
As you can see both $p_x$ and $p_y$ appear.


It's a proportional rate - 5% p.a. means 5% per annum, i.e. 5% per year


Easy to understand explanation of deflation and what causes it

Krugman's classic story of a babysitting co-op never uses the word "deflation" but describes it perfectly. Go read it first.

Basically, if you think of money as a thing that has a price level, just as other things have prices, it's possible to imagine that price level falling relative to other goods (inflation) or doing the reverse (deflation). Inflation is, for some reason, easier for people to understand— it means that if you hold on to a $100 bill for a year, that bill will buy you less stuff next year than it'll buy you right now.

In contrast, if you're in a deflationary world, the money in your wallet will be able to buy more stuff a year from now than it can today, giving you an incentive to hang on to your money and wait to spend it. The problem is, if everyone does that, then the fact that everyone is trying to hold on to cash means that the value of cash continues to go up relative to goods (more deflation), which is known as a liquidity trap.


How did the derivatives market 'collapse' in 2008?

The question is quite complex and an answer should be far beyond looking only at the structure of the derivatives, but i try my best.

The initial situation:

Between 1998 and 2006, the price of the typical American house increased by 124%
Global saving glut due to the dotcom-bubble in the early 2000s, seeking institutions for alternative investments, cutting out financial risks
The Community Reinvestment Act which helped low- and moderate-income Americans to get mortgage loans

These points led to a situation, where in fact everyone could get a mortgage to buy a house, not only for using them as own-property, but as a financial asset. Also people with "no income, no job, no assets", leading to the term Ninja-Loan, were granted loans and mortgages. Times were great, as long as house prices increased. The US financial markets were flood by money from investors, wanting to become part of that upswing. How they took part, answers how the derivatives look like, and how their structure led to the financial crisis:

CDOs and CDSs

Lets take a look an a classic CDO:

CDOs pay investors in a prescribed sequence, based on the cash flow the CDO collects from the pool of mortgage loans. There are several tranches, which catch the cash flow of interest and principal payments in sequence based on seniority.

As CDOs became popular, some investment banks repackaged selected tranches into yet another iteration, known as CDO-squared, a complex and intransparent structure of financial derivative.

A CDS (credit default swap) is a financial agreement that the seller of the CDS will compensate the buyer in the event of a loan default. It can be considered as an insurance for a creditor of the referenced loan.

Synthetic CDOs

Synthetic CDOs are CDOs, which do not only bundle the mortgage loans in the picture above, but also other assets and derivatives. Up to 2008 it was popular to construct CDOs, bundling single CDSs, rather then mortgage loans. This is the structure of a synthetic CDO, created in times before 2008.

  How did defaults of mortgages hit investors twenty fold?

Synthetic CDOs described above can be considered as a bet on the performance of CDSs, rather than the performance on a real mortgage security. In fact, the derivatives were detached from a single mortgage due to repeated securization in CDOs and there use as an underlying for CDSs. They became solid derivatives offering high returns.

As stated in the New York Times (1), from 2005 through 2007, at least $108 billion synthetic CDOs were issued, but the actual volume can be much higher because synthetic CDO trades were unregulated.

Debate and further topics

Synthetic CDOs are well known for their destructive character during the financial crisis. They were easy to construct, barely supervised or regulated and offered high returns. As the former Citigroup CEO said, referring to the leveraged lending practice: "As long as the music is playing, you’ve got to get up and dance. We're still dancing." As long as there was a market for these derivatives, they were constructed. Current research address the missing incentives for each, buyer and seller of CDOs, CDSs and synthetic CDOs during the time before the financial crisis: As long as the risks of defaulting mortgages could be transfered to other parties, the credit-worthiness of a borrower does not matter any more. Furthermore, speculatives without any real insurable interest could invest in these derivatives, which increased the demand for these derivatives additionally.

For further information to the structure of the derivatives mentioned above see here or (2). On the role of rating agencies see (3).

(1): The New York Times, Banks Bundled Bad Debt, Bet Against It and Won,  by Gretchen Morgenson and Louise Story, Published: December 23, 2009

(2) Joseph R. Mason, Josh Rosner: Where Did the Risk Go? How Misapplied Bond Ratings Cause Mortgage Backed Securities and Collateralized Debt Obligation Market Disruptions,  May 14, 2007

(3): Markus K. Brunnermeier, DECIPHERING THE LIQUIDITY AND CREDIT CRUNCH 2007-08, NBER Working Paper No. 14612.


Could Depreciation of Capital $=\delta(K(t))^{\theta}$ with $\theta<1$ Be a Realistic Assumption?

For zero investment, $\delta = 0.05$ and $\theta =1 $ and $\theta = 0.9$ we get

We see that it is still a slowing depreciation, which reflects the assumption that capital is more productive in its first years of usage (since depreciation is the mirror image of productive contribution), an assumption good enough for capital equipment with moving parts (and for human capital), and perhaps also for roads, but not necessarily for buildings and things like furniture (here perhaps the Straight-Line method, widely used in Accounting, would be more appropriate -but it creates the need to keep track of capital vintages, since depreciation in that case is a fixed percentage of initial acquisition cost).

So it appears to be a quantitative/empirical matter. With $\theta <1$ capital depreciates slower, but the qualitative behavior is the same, and for smaller values of $\theta$ it can even mimic the Straight Line method, which, as said, is realistic for some forms of capital. So yes, we can have $\theta<1$, it does not appear to contradict any fundamental assumption.


I leave for another thread the issue "What is the justification of using the arithmetic operation of multiplication and so the product of two variables in order to model the concept of interaction?"

Practically, product-terms come from the tradition of the Translog regression specification, which is a second-order approximation to any actual specification, and produces such products.
They are therefore considered "second-order" effects, meaning that they are included in a specification alongside the stand-alone variables. This means that their importance is judged after the effect of the stand-alone variables has been taken into account.

I have not seen in the literature a situation where "interaction terms" are included alone, without the stand-alone presence of the two variables forming the product.

So for the specific study mentioned by the OP, conventional practice would ask "why not include also interaction terms?"

Nevertheless, it appears intriguing to argue convincingly that in a certain case, we should only include the "interaction term" of two variables.


You don’t. CPI is a proxy for the fantastical concept of a real price. Any measure will have theoretical implications (Australia’s CPI makes some very funny housing assumptions, for example).

As the measure is a proxy for a theorised but unreachable category, and as the measure is only available at its noted frequencies you can’t create a line. Part of the measure is its frequency.

This is impossible for two reasons:

proxies are just that
a measure which is grounded in theoretical assumptions and produced with a frequency can’t be resolved smaller than that frequency

You might look into producing a new measure acting as a proxy with a desired frequency, but only state agents and historians tend to go about these windmill fights.


Are any of these tax dodging schemes actually realistic or exclusive to billionaires?

I understand the core point of your question as, "Do people with extremely high incomes pay proportionately less in taxes than average Americans?"

Yes, extremely-high-income individuals do pay a lower percentage of their income in taxes than do upper-middle-class and high-income households, and even more than many middle-income households, but they tend to pay more in taxes than low-income households.

This is due to a number of reasons, but it has less to do with elaborate tax strategies than it does the simple fact that people with very high incomes tend to derive a larger share of that income from dividends and capital gains than from normal cash compensation. Both of these have lower marginal tax rates than are paid to people who receive relatively high cash compensation— the top tax rate on dividend and long-term capital gains is 20%, which is roughly equal to the effective marginal income and payroll tax rate paid by the top 20% of income earners.

From the Brookings Institution/Urban Institute Tax Policy Center, we can see the total average effective tax rates for different groups (for 2011, the most recent year for which detailed data have been released, but things haven't changed much since then):

   Quintile  Avg Eff Tax Rate
      0-20%:  1.9%
     21-40%:  7.0%
     41-60%: 11.2%
     61-80%: 15.2%
     81-90%: 18.6%
     91-95%: 21.1%
     96-99%: 24.3%
     Top 1%: 29.0%
    Top 400:  <20%

The last line of the table is from the IRS Statistics of Income division, which publishes a distribution of the average effective tax rates for the 400 taxpayers with the highest adjusted gross incomes:

 Rate    Number
 0-10%    32
10-15%   147
15-20%   123
20-25%    40
25-30%    28
30-35%    30
  >35%     0

So you can see that the average effective tax rates rise sharply as you go from the poor to the middle class, then more slowly as you move from the upper middle class through to the top 1%, but once you get to the very top, the 0.1% and 0.01% of income earners, they do actually pay less proportionately in taxes than many middle-income families.

Finally, it's important to note that these statistics will tend to understate the degree to which people with extremely high incomes pay lower taxes than those with moderate incomes to the extent that those with high incomes make use of schemes (like the ones in the linked article) that lower their AGI.

To quickly answer your more specific questions:

No, regular people can't borrow against unrealized capital gains, because by definition, regular people don't own large amounts of capital.
Federal income taxes don't apply to a swap of similar assets (i.e., real estate for real estate). You're probably thinking about "barter clubs," which do trigger tax consequences, but those aren't like-kind exchanges, they're barter exchanges (they're not similar assets).
These aren't "fake" charities that are being described, they're real charities (if I recall correctly, they're required to spend 1% of their endowment annually on charitable purposes, which is more than offset by gains on capital income in most years). This is in fact a real and common tax-avoidance strategy that is entirely legal.
No, a regular person could not legally do this— there has to be a business justification for something to count as a business expense, and while a taxi home from work when working late counts as a business expense, personal autos don't meet the test.
If a tax strategy hasn't been determined to be illegal before it's tried, only civil penalties (i.e., no jail time) apply if it's ruled to be invalid.
The tax benefits they describe in #8 accrue to corporations, which are disproportionately owned by wealthy individuals. (See page 156 of this FRB chart deck on the results of the most recent Survey of Consumer Finances for a quick overview of who owns financial assets in the US.)
You're right that IRA plans benefit all very-high-income individuals equally, but they do provide greater benefits to high-income individuals than middle-income individuals (who are less likely to be able to contribute the maximum).


What will happen to bank loans in the event of hyper inflation?

If the loan is indexed to inflation, "nothing" would happen. The remaining loan payments would simply increase.

If the loan is not indexed to inflation, when inflation occurs, the debtor's wage would most likely increase with the inflation rate. Hence, he would very quickly have the money (in nominal terms) required to pay back the debt (which is now less worth, in real terms).

Consider the loan $L$ in monetary terms, and denote the price level by $P$. The lender was expecting $L/P$ when he formulated $L$. Now, instead, he is getting $L/P_2$ in real terms, which is (for the much larger price level $P_2$) a much smaller real value.

Which leads us to the conclusion that in this case (and very often), higher inflation is a redistribution from lenders to debtors.


If petrol/gas prices were locked down, how would normal consumers and the producers be affected?

If the price is higher than the market price it will lead to less people buying gasoline. If the price is lower, more people will buy gasoline. The inverse is true of sellers.

In the first case, there will be over supply of gasoline, leading to a growing inventory.

In the second case, there will be more buyers than sellers, leading to a shortage.


Why is the long-run average production cost not necessarily the same as the minimum average total cost?

Denesp's comment is your full answer: it's a badly-drawn chart which fails to do its one job, that was to illustrate that the long-run cost curve consists of joining up the minima of the short-run cost curves.


What does Hayek mean at the end of the first paragraph of The Use of Knowledge?

Your marginal rate of substitution between (say) eggs and wine is the number of eggs you'd be willing to trade for one additional bottle of wine.  This marginal rate of substitution can reflect your preferences (if you're a consumer) or the state of technology (if you're a producer who can, for example, substitute three eggs for one wine in your production process).

Suppose your MRS is three eggs per wine and my MRS is two eggs per wine.  Then there's an opportunity for a mutually beneficial trade:  You give me two and a half eggs, and I'll give you a wine.  You thought the wine was worth three eggs, and you got it for two and a half --- that's a win.  I thought the wine was worth two eggs, and I sold it for two and a half --- that's also a win.

Whenever your MRS differs from my MRS, there's an opportunity for a mutually beneficial trade.

Therefore, if our MRS's differ, it means that an opportunity for mutually beneficial trade has been missed.

So in order for resources to be used efficiently --- that is, in such a way that all opportunities for mutually beneficial trade have been exploited --- the MRS between any two commodities must be the same for you as it is for me or anyone else, regardless of how we're using those resources.


Was there resistance, historically, to the idea that human behavior deviates from rational decision making theory?

I would recommend reading Thaler's Misbehaving, which chronicles the development of behavioral economics as a field and its struggle to gain recognition by mainstream economists. Several of its chapters (particularly, 6, 17-20) would directly answer your question regarding the historical context and partly the "why".

I share my own personal view below.

I believe the "as if" argument as advanced by Milton Friedman in his Essays in Positive Economics plays an important role in countering the move towards a relaxation of the rationality assumption. In a nutshell, the argument says that a theory should be judged by the accuracy of its predictions, not by the realism of its assumptions. Therefore, while the assumption of a rational decision-maker is not entirely realistic, the theory is doing a good job as long as it generates sufficiently accurate predictions (in the sense that they match what actually happens in the real world) based on such an assumption. Friedman describes a simple of model of billiard players that I think nicely illustrates his idea:

  Consider the problem of predicting the shots made by an expert
  billiard player. It seems not at all unreasonable that excellent
  predictions would be yielded by the hypothesis that the billiard
  player made his shots as if he knew the complicated mathematical
  formulas that would give the optimum directions of travel, could
  estimate accurately by eye the angles, etc., describing the location
  of the balls, could make lightning calculations from the formulas, and
  could then make the balls travel in the direction indicated by the
  formulas. Our confidence in this hypothesis is not based on the belief
  that billiard players, even expert ones, can or do go through the
  process described; it derives rather from the belief that, unless in
  some way or other they were capable of reaching essentially the same
  result, they would not in fact be expert billiard players.

Thaler, and Kahneman and Tversky before him, mounted copious evidence that people  consistently deviate from the behavioral benchmark set by the homo economicus. But to people like Friedman, this is not a sufficient cause for a change of paradigm, unless one brings conclusive evidence to show that the predictions made by rational choice models are wrong. It didn't help that experimental economists like Vernon Smith were successfully showing that (in the market context) people's collective behavior leads to outcomes consistent with rational choice theory. (In this regard, it does seem a bit ironic that Smith would share a Nobel with Kahneman).

Another reason against the paradigm shift could be in the interest of parsimony. Including more realistic behavioral foundations in economic models inevitably makes the models more complex. But if the simpler, albeit less realistically-founded, rational choice model can get things right just as well, there is a philosophical reason for favoring the latter. In a way, this is similar to the if-it-ain't-broke-don't-fix-it mentality.

Eventually, however, rational choice theory were found to fail to predict a lot of phenomena. For example, Nash equilibia are notoriously inaccurate in predicting how people actually behave in many games (e.g. Prisoners' Dilemma, ultimatum game, public goods game, and so on). And adding behavioral assumptions/relaxing the rationality assumption seemed like a natural way to "fix" existing models to increase their predictive power. Hence we have the rising popularity of behavioral economics these days. Still, these "behavioral patches" are often met with skepticism from of many traditional "rationalists". See this post for example.


Where the economic growth of a society come from?

I can see how a new product can value more than the sum of its parts, but I don't understand how this can increase the wealth of a society.

The wealth of society, in material sense, consists of what it can produce. Production of more products or services is the wealth. Economic growth is by definition a continuous increase in production. In fact the way how we most commonly measure economic growth is to just measure output per person by measuring GDP per capita.

Wealth is not money, money is just a measurement stick for value, storage of that value, and tool to simplify exchanges, but it’s not wealth in itself. However, because it is so ubiquitous many non economists equate it with wealth itself but that is just ‘money illusion’. If you would have billion \$ but could not buy even a loaf of bread with it you would be poor compared to a person with 0 dollars who has access to any goods or services they wish.

  let's say a person can spend only what she earn as wage, so when a new product come out, this product is competing with all the pre existing products, someone should lose to someone else to win.

In competitive market economy people  earn approximately what is their marginal product. When you go to work you either create goods or services for someone directly or indirectly and in competitive market you will get for that money equal to the worth of your marginal product. If you can produce more with  the same or less inputs you will also earn more money.

The reason why for example Solow-Swan model shows that economic growth depends on technology is that technology makes people continuously more productive year after year and allows them to produce more. This increases production is the real wealth, but besides that if people are more productive they also get pay more.

In real life not all markets are competitive so the above holds only approximately but empirical evidence shows that real wages indeed track net productivity over long term.

Besides increases in technology endogenous growth theory suggests that also savings rates and support for basic R\&D and human capital can accelerate economic growth. The mechanism there is different than in Solow model but ultimately again what delivers growth is how the above boosts the productivity and output.


You can use the filtered components as many researchers have done before in researching the equity risk premium and consumption-based asset pricing. However, you may want to use the unsmoothed variables for some models -- since the variation may contain useful information for asset pricing or inferring volatility. For an example about how unfiltered NIPA was more informative, see Kroencke (2017).


What does my lecturer mean by "economic calculation"?

The historical economic calculation debate, between Mises and Hayek on the one side and people like Oskar Lange on the other, was about the extent to which accurate trade-offs can be made in a world without meaningful prices, like the world the naive socialists seemed to envision.  For example, if I am looking to buy a car I observe the prices and characteristics of various models, I evaluate the utility I will expect to receive from the various packages of automotive characteristics on offer, compare that utility with the utility I'd expect to get from other uses of the money that I would spend on the car, and make my choice accordingly.

I assume that the question above is asking about the nature of my utility calculation.  It is usually, not literally correctly but not too incorrectly either, assumed that the in the above car buying scenario I am considering my utility exclusively, ignoring the way the utility of others might be affected by my choice in obvious (pollution) and not so obvious (how I would alternatively arrange my life based on my choice of car).

What "separate aesthetic medical industry" is supposed to mean is outside of my expertise.


If all firms in an economy are in monopolistic competition with constant elasticity of substitution, can they profit-maximize at $MC=MR=AC$?

The long-run picture for a firm in monopolistically competitive industry should look like this:

The level of production is pinned down by where MR=MC. Price will be equal to AC at that point, so the firm has zero profits.

If the firm was producing at the point where MC=AC, it would have positive profits, which would encourage entry into the industry, shifting the demand in and reducing profits to zero.


What does Battigalli really mean by "Players can not choose strategies, they can only choose actions."?

The idea is precisely that players do not chose actions, but only chose one action at the time at every node at which they play, based on their beliefs about the way other players and themselves will play at future nodes in the game (where beliefs are conditional on the history that led to that node).

The interpretation is letting players choose full-fetched strategies is equivalent to letting players rely on a computer program to plays the game in their place. That is, they can commit via this computer program to playing a given action at each node.

Such games with commitment devices are in essence very different from games in which the actual players have to repeatedly chose an action at each of their decision nodes. When actual players play at nodes, players have to form beliefs about the way other players and themselves will play at future nodes, and these beliefs may depend on the history that led to future nodes.

For instance, in a Stackelberg game, the leader could believe that the follower will be rational (i.e., utility maximizing) if the leader plays "Low production", but will be irrational (i.e., non utility maximizing) if the leader plays "High production". Maybe the leader anticipates that the follower will be angry if the leader plays "High production", and that, blinded by her anger, the follower then then want to retaliate.

If the follower could have committed through a strategy, the game would have been completely different. Maybe the follower could have committed not to retaliate before she gets angry, and she cannot help her desire to retaliate anymore. But here the idea is that the actual follower has to choose an action later in the game given what the leader chose at the root node. Therefore, the behavioral rule through which the follower chooses an action at a node (e.g., utility max vs. non utility max), and the beliefs of the leader about these procedures may depend on the history that led to that node too.

This opens the way for many new outcomes of the game that would not have emerged from classical game theory. From a conceptual point of view, it also switches the focus from solution concepts to epistemic and behavioral assumption (i.e., from classical game theory to epistemic game theory). Instead of identifying a set of reasonable outcomes (e.g., Nash equilibrium outcomes) and look at the strategies that match these outcomes, one identifies reasonable properties of players' behaviors and beliefs (about each others' beliefs and behaviors), and derives the conclusions of these epistemic and behavioral assumptions for the outcome as the game unfolds.

Now, this is just to give some meat and intuition to Battigalli's framework, and it is does not do justice to the richness of the framework (in part because I don't know much about his work other that the video you linked to). If you haven't done it yet, I strongly recommend that you watch the whole video. I think Battigalli does a great job at making his framework accessible. He also present helpful and intuitive examples to connect his epistemic approach to "classical" game theory by identifying simple conditions on players beliefs and behaviors that allow to recover classical solutions to games such as backward induction.