Why does the Brexit cause a fall in crude oil prices?

I'd like to extend Lasse's excellent answer.

Fear and uncertainty are driving markets - but they can drive prices in either direction of course.

Specifically what's happening here is that the oil markets are pricing in at least two effects.

Firstly, the UK is an oil producer, and Sterling's slide means that its oil just got cheaper for other countries. This is a small effect, but relevant, as UK short-run marginal extraction costs are close to current prices, so some UK fields are marginal producers and thus price-setters.

Much more importantly, the markets are now pricing in the possibility of a further slump in oil demand, as a result of poor general economic performance. That would be driven not only by a soon-to-be-declining UK economy, but also driven by a (much larger) destabilised European economy; and also driven by the possibility that this vote will mark the turning point, where globally we move away from a consensus on the value of tariff-free international trade, and back towards protectionism and isolationism, which would leave the global economy worse off, as well as leaving most participants individually worse off too.


Are there any drawbacks to a hypothetical climate policy?- Carbon tax for reducing Income tax

Prominent economist Greg Mankiw has been a prominent advocate of the kind of change you describe (he invites people to join "The Pigou Club", named for Arthur Pigou who first proposed these kinds of corrective taxes).

You can find a nice, non-technical summary of his arguments here. In particular, Makiw deals with some of the weaknesses you identify above and argues that they shouldn't be too much cause for concern.

Wikipedia has an article that lists other prominent economists who have jooined the Pigou Club by publicly advocating for a shift towards carbon or similar taxes (including links to many articles where the issue is disccused. It is here.


The name for the amount $56.25 is certainty equivalent.

The expected utility for the individual from taking the bet is calculated as follows:
$$E[U]=\frac12U(100+125)+\frac12U(100-100)=75$$
Suppose the individual can pay an amount of money $x$ so that she can avoid taking the bet (which leads to expected utility $75$). What's the maximum amount of money $x$ she's willing to pay? Well, she would pay up to a point where she's indifferent between taking and not taking the bet.

If she takes the bet, expected utility is $75$. If she pays, her utility is $U(100-x)$. We want her to be indifferent, so that $U(100-x)=75$. Reading off from the blue curve in your graph (the curve describing $U$), we see that
$$U(56.25)=75$$
which means $100-x=56.25$, or $x=43.75$.

So we can interpret 43.75 as the maximum amount of money that an individual is willing to pay in order to avoid the (risky) bet.


Why does nation's total debt matter and not NIIP?

NIIP includes (and in fact is predominantly) personal assets.

The government of Japan could not sell the assets of its citizens to satisfy its sovereign debt.


Percentage of workforce change, with two PPFs

The fact that you are getting a correct answer in D using your method is purely due to algebra and cancelling off of common terms.
Let us first see why the answer is actually 25% :
So why does a PPF shift? A PPF Shifts because of either a change in technology or change in resources. The question clearly states that there is no change in the technique of production or output per worker. This means the change in PPF is due to change in resource - which in this case is Labour.
Now in order to find % change in the labour force, consider that if the entire labour force is used in the production of the good Y ( which is what points on Y-axis denote )
Previous Production = 2000, New Production = 2500 [ from intercepts of your equations ]
Since we know that there has been no change in per-unit labour output hence it remains 10.
Thus Previous total labour force = 200, New total labour force = 2500/10 = 250 .
You can easily compute and see that percentage increase is 25%
Your method:
% change = $\frac{2500-2000}{2000}100= 25$
if you simply divide the numerator and denominator by 10 (which is output per work for y), you get what has been done and explained above.


How can austerity and quantitative easing happen simultaneously?

The division comes from the entities guiding these sets of policies.

The austerity program falls under fiscal policy, which is controlled by Parliament. Quantitative easing falls under monetary policy, which is controlled by the Bank of England.  The policies enacted by these two entities are not necessarily coordinated, and can sometimes work opposite each other's objective.


Why does the nominal interest rate equal 25% in this problem, instead of 16.4%?

Keep in mind that nominal interest rate=Profit/Initial Amount.

The exact relationship that links real interest rate, nominal interest rate and inflation is $(1+R_{nominal})=(1+R_{real})(1+\pi)$ where $\pi$ is the inflation rate (Known as Fisher's identity)

$R_{nominal}=R_{real}+\pi$ is an approximation that works best when those variables are relatively small.


How is workforce guaranteed in basic income system?

Brian's answer surely hit a major part of the issue - the level of the UBI. Yet, there are other aspects of the problem.

People like to work. There is a huge amount of sociological literature showing that people derive considerable non-pecuniary benefits from work, or alternative, that lack of work leads to several personal (and social) undesirables (for example, here, here, and here). As Voltaire said,

  Work keeps at bay three great evils: boredom, vice, and need.

Thus, many people will like to work. This is the supply side of the labour market.

Firms will still need workers. Provided capital and robots do not take over all jobs, firms will still require some workers. If the supply of labour across skill levels is not high enough, then either migration will occur (perhaps politically undesirable, but historically favoured by firms), or wages will go up. The latter will induce more people to work.

The key is, then, not only the level of UBI, but whether there will be enough jobs. Perhaps there will not be, at least not for the current working week. Maybe Keynes' prediction of a 15-hour working week might finally become true.


Does a General Equilibrium here require Pareto Optimality?

Competitive equilibrium is the price vector $(p_x, p_y, w =1, r)$ such that it solves the following system of equations:

Demand for $X$  = Supply of $X$
Demand for $Y$ = Supply of $Y$
Demand for $L$ = Supply of $L$
Demand for $K$ = Supply of $K$

where these demands and supplies are either exogenously given or are derived by solving utility maximization problem of the consumers, and profit maximization problem of the firm in a standard way.

Method 1: One way to solve the posted problem is to find these demands and supplies and solve the resulting system of equations.

Method 2: Another way is to use first welfare theorem. First welfare theorem says that if the utilities are increasing then competitive equilibrium is Pareto efficient. In the posted problem, both the consumers have increasing utility function. So, we can use it to determine the competitive equilibrium prices. Equilibrium prices and allocation satisfy the following:

Efficiency in production: MRTS$^X_{L,K}$ = MRTS$^Y_{L,K}$ = $\frac{w}{r}$. Use this to derive Production Possibility Frontier (PPF).
Efficiency in consumption: MRS$^A_{X,Y}$ = MRS$^B_{X,Y}$ = MRT$_{X,Y}$ = $\frac{p_X}{p_Y}$.

Solution (using method 2): Given the data in question, we see that both the production functions exhibit constant returns to scale and the PPF will be of the form $4x + y =$  constant. Therefore, the price ratio $\frac{p_x}{p_y}$ in equilibrium will be 4 regardless of the initial endowments. This will be true as long as both the inputs $L$ and $K$ are available in positive quantities. Equilibrium can be fully determined once the details about endowments are specified. To find $\frac{w}{r}$ ratio we need to know the total endowment of labor and capital in the economy, and to find the absolute prices of $X$ and $Y$ given $w = 1$ we need the data on how much of the total endowment of labor and capital belongs to each consumer.


Why is capital income taxed differently than wage income?

One reason is the inflationary gain problem.  Let me give an example with simple numbers.  I make \$100 in income and pay 20% tax of \$20.  I have \$80 left, which I invest in a stock.  The stock goes up in value at the same rate as inflation, about 3.5% a year.  After 20 years, it's worth about \$160, but \$160 has the same value now as \$80 did when I earned it.  So in effect, I have made no gain.  If I have to pay a 20% tax on the \$80 nominal gain, then I actually have \$8 less spending power than when I made the investment.  Just in order to keep pace, I would have needed returns of 125% inflation.

Another reason is to encourage investment.  A lower tax on capital should encourage savings, and the US is generally low on savings.

There is also a historical argument that if the income tax rate is 90% (which was the top rate starting in World War 2 and ending in the Kennedy administration), then it is impractical to tax investments at the same rate.  From 1921 to 1986, there was a lower rate on long term capital gains than on other income.  In 1991, capital gains tax was capped at 28%.  In 1997, long term rates were reduced again.

The current system is designed to encourage long term capital investments by decreasing the rate the longer something is held.  This does very little to help with nominal gains but does provide an incentive for long term savings.  It's unclear if it actually increases saving.  It certainly doesn't increase net savings, as the US tends to be fully leveraged, borrowing as much as is saved.

There have been proposals that focused more on the nominal gains issue.  For example, in the late 80s, early 90s there was a proposal to switch investments to working like traditional IRAs:  deductible at the time of investment but taxed the same as any other income at the time of sale or withdrawal.  Since this delayed the original tax to be paid at the same time as the capital gains, there is no separate tax on the nominal gain.


How to interpret the difference between natural level and steady state in Macroeconomic theory

Natural level of output is equivalent to full employment output. This does not mean full employment of all resources, there is always a natural level of unemployment even in full employment output level.

Neoclassical economics: Steady state output is achieved when capital-labour ratio is stable or constant. In steady state, economy is not growing and also not in recession, all variales grow at the same rate i.e. birth rates equal death rates, capital accumulation rates equal depreciation rates, etc.


The instrument in "The Colonial Origins of Comparative Development"

You should include all controls in the second stage, even if they are not instruments.
The entire effect of log(mortality) should be mediated through Exprop.  This does not mean there cannot be other things causing GDP or Exprop, but log mortality cannot have a effect on GDP except through Exprop.


I will answer your question from the economic point of view, not financial. Your question can be understood from several differents positions. Im from Argentina and nowadays Argentina has devaluated the money nearly 50% agains USA dollar. When I analize why, it comes clearly when I see macroeconomics data. Speaking about INDIA, in general terms the relation Country Money/North American Dollar is explained economically with the macroeconomics equilibium result. Lets see what we have in India. The GDP per capita is low, as you can see in the image, meaning that the value added per capita is poor against USA. You can imagine like you do a simple job, may be Rural job, against USA (industrial work) . The Debt (% GDP) is near 68% (think that as you have an important DEBT to attend annually. The Debt Per Capita is near $1183 dollars, so you can imagine that you have that debt. Your Education Expense (% GDP) is 14%, that number is not so great if you want change the economic structural problem and economic development. Health expenditure is near 5%, that is low, so you may be dont have a huge life expectancy, in fact is 68 years!. People in your country tends to Emigrate rather than inmigrate, so imagine that you dont like to much live in India. Each marriage has 2.33 sons and you have a tremendous amount of people to feed (2.400 millons or persons). There is more, you spend the money buying GUNS more than EDUCATION, your Defense Spending %GDP is 14% (very big) and ending, your imports are bigger than your export so you spend more money than you should.

As a conclution, India´s value added is low, so the income is low, India spend few in education and Health but too much in military stuff. India has debt and Buy (gold and crude petroleum) more than sells (diamonds, refined oil). If you have an expensive dollar your petroleum will be more expensive. The value of a Rupia agains USA Dollar is calculated by the Central Bank of India, and it is not easy to explain because it has a complex macroeconomic impact and reasons, but, in general, it needs to be one value that maximize the Indian macroeconomics indicators and gives an improvement trend for the society.


why has the GDP per capita of Ireland grown of almost 30% between 2014 and 2015?

It is an national accounting reason, rather than the Irish people have higher incomes or being more productive

It seems that some companies previously deemed to be foreign are now deemed to be Irish, and so their profits now count towards Irish GDP (and, to the extent they are not a subsidiary of a foreign company and retain their profits, also to Irish Gross National Income).  The Irish Central Statistics Office said a 26.3% increase in GDP and 18.7% in GNI from 2014 to 2015 at constant prices

What may have happened is inversion where United States companies are notionally taken-over by Irish companies (though the old US shareholders remain shareholders of the new merged company), largely to take advantage of Ireland's generous corporation tax regime.  That makes their production/value-added/profits appear to be Irish this year, boosting Ireland's GDP compared with last year

Further reading from 10 months ago when this was noticed:

http://www.irishtimes.com/business/economy/ireland-s-gdp-figures-why-26-economic-growth-is-a-problem-1.2722170
https://www.theguardian.com/business/2016/jul/12/irish-economic-growth-revised-figures-foreign-investment-aircraft
http://uk.reuters.com/article/uk-ireland-economy-idUKKCN0ZS0ZC


For forecasting with VAR in R there are some good tutorials on econometrics with R. This tutorial from Justin Eloriaga also helped me when we had to make VAR for our quantitative macro assignment. PenState also has good sources for econometrics, here are their sources for VAR.


How reliable is BLS / JOLTS data on quits?

Here is a short lists of study’s that looks at the on the reliance of JOLTS data as well as make comparisons to other similar data sets.

Analysis of JOLTS Research Estimates by Size of Firm October 2012-
 Katherine Bauer Klemmer
https://www.bls.gov/osmr/pdf/st120060.pdf

ADJUSTED ESTIMATES OF WORKER FLOWS AND JOB OPENINGS IN JOLTS-  Steven Davis,  R. Jason Faberman, John Haltiwanger, Ian Rucker (2018).
http://faculty.chicagobooth.edu/steven.davis/pdf/MS_ch5_StevenDavis-et-al_p315-370.pdf

Help-Wanted Advertising and Job Vacancies- Rob Valletta – Federal Reserve San Francisco
https://www.frbsf.org/economic-research/publications/economic-letter/2005/january/help-wanted-advertising-and-job-vacancies/

UNDERSTANDING ONLINE JOB ADS DATA  - Anthony Carnevale, Tamara Jayasundera, Dmitri Repnikov
https://cew.georgetown.edu/wp-content/uploads/2014/11/OCLM.Tech_.Web_.pdf

Reliability of JOLTS Estimates
https://www.bls.gov/jlt/jltreliability.htm


First, it is actually not Fed that prevents bank runs. Bank runs in the US are prevented by Federal Deposit Insurance Corporation (FDIC)  which insures deposits that people have at the bank up to \$250000. This is what prevents the bank runs as runs are created when people worry bank will fail and they will loose their deposits. This is because bank never has enough money to let all people withdraw them at the same time as loans are made long term while deposits can be withdrew at a depositors whim and consequently if people worry bank will fail they will all 'run' to their bank in order to make sure they get their money before bank fails and stops paying out deposits.
Second, generally and broadly speaking the literature agrees that there is some rationale for saving banks under two conditions (Hanson, Kashyap & Stein 2011; Osinski Seal & Hoogduin, 2013):

They are systemically important (their collapse would lead to collapse of other institutions).
They are only illiquid not insolvent.

The point 1 is considered to be more important than the second so even illiquid institutions might be considered to be worth saving if they are too systemically important.
Now Fed or other government bodies can't be always $100\%$ sure about how systemically important bank is or whether it is illiquid or only insolvent, but central banks around the world typically create and track some measures of systemic importance of various banking institutions. For example, Fed has whole dedicated unit/department just for researching systemic risk.  In addition they will also try to estimate whether bank is insolvent or just illiquid. Lastly, since no research can give you $100\%$ correct answer at the speed Fed usually has to act there is also some discretion involved in the decision process. So partially it also depends on what decision makers at Fed think should be done in each specific case.
However, if some banks are judged to be insolvent and not systemically important  they are routinely allowed fail. In fact as the data from FDIC show the total number of commercial banks that have to register for deposit insurance (basically any 'ordinary' bank) fell by almost 200 just between year 2018-2019.


Does the hoarding of perishable goods such as pulses and cereals make economic sense?

It does not make economic sense. Disclaimer that I am responding directly to your Thai example, and not talking about economics of storage. Rice can be safely stored for a period of time, and it is in the United States. Many developing countries struggle with proper storage of grain. For example, the World Bank estimates that 10-20% of South Saharan Africa's grain crop is lost to spoilage each year, roughly equivalent the amount of grain that they import yearly which can feed 48 million people.

The Thai government, not traders, where hoarding rice under their rice pledging scheme. The government has lost billions of dollars under the scheme and the Thai prime minister Yingluck Shinawatra faces possible jail time. During the 2011 crop year, the Thai government announced the rice pledging scheme which would establish the price floor and pay growers 50% over market price (subsidy).

The Thai government also greatly reduced exports, so it had a large stockpile of old crop rice (for several years). Part of the plan was to help their producers, the other possibly to have a hold of the global market (large control over the global supply). What ended up occurring was that their new crops had to compete against the old crops. The "alternative" product brought Thai and world prices down.

In addition, this was a very strange way of the Thai government to give aid to producers since it would have been more efficient to directly pay an equal amount of the additional producer surplus gained from the price floor straight to the producers.

A large percentage of the rice did in fact rot, and the government is now auctioning off rice that is not fit for human consumption. Some of it is also not fit for animal consumption and will have to be auctioned off for ethanol producers.


Can the stock market grow faster than GDP indefinitely?

There are trends that has allowed stock markets in advanced economies to grow faster than GDP for a long time:

Branching out abroad. This gives access to faster growing markets in developing countries. This trend will end when all countries are advanced economies.
Fewer private companies. This trend will end when most of GDP is generated by companies listed on the stock market.
Multiple Expansion. Reduced interest rates and increased money supply can reduce returns expectations and increases PE multiples. This trend has worked both ways through time but for the last 10-20 years it has generally acted in an expansive capacity.

In addition, there is a way for the stock market to generate a higher return  without an increase in stock market value:

Dividends. Dividends increase stock market return without increasing its value. Though not really considered growth, dividends are often included when comparing stock market growth with GDP growth.


When a central bank buys government securities, is this exactly equivalent to printing money?

I don't know if you are aware that you are using the word "print" abusively but:

  The U.S. Treasury controls the printing of money in the United States. However, the Federal Reserve Bank has control of the money supply through its power to create credit with interest rates and reserve requirements.

Source : https://www.investopedia.com/ask/answers/082515/who-decides-when-print-money-us.asp

Thus both are correct. Clearly a CB does not increase the money supply by creating credits in order to buy governments securities.

It does so with other goals in mind, such as forging economic cycles, maintaining financial stability, reconfiguring the debt market and/or stimulating money multipliers in the national economy.

A CB (theoretically)(and indirectly) buys government securities in an inflation-neutral manner $\iff$ no money printed $\iff$ it uses the existing "stock of (scriptural) cash".

The difference between your two scenarios is the notion of debt. Strongly putting aside the fact that your ex-nihilo first scenario literally makes no sense without a credit underlier.


The best way how to learn how to create new models is to see how other people create new models and learn from that. If you are already good at math then you could learn this by observing how models are created from some graduate textbook focused on theory such as MWG Microeconomic Theory.
Seeing how models are derived will help you in two ways:

It will help you to see what is the thinking process of an author that motivates model development.

Most new models are created just by tweaking old ones. In order to do that you already need to have an excellent knowledge of the existing models.

Next, the point of models is to create a simplification of a reality which will allow you to think about problem analytically. So when you try to create new model you first need to find some new problem, that has not been modeled yet, and then try to capture it in mathematical form.
For example, let us take equation from that linked Math.SE question as an example and let us think about how it was derived. First we can observe that people in cities seem to be more productive, they usually earn more money even when controlled for difference in price levels, also commercial and industrial activity seems to be located at or around various cities. Cities are by definition places where many people live (each country might have different definition of what city is but usually it will be defined in terms of demography and mainly population), so how could we model such situation?
Well a natural and logical way is to assume that peoples productivity $P$ depends on both some innate productivity $P_0$ and then has also some component which depends to proximity of other people so we can add term that tells us how productivity varies with proximity to other people $\int_APf(r)dA$ which will then gives us the expression derived by user Daniel:
$$P=P_0+\int_APf(r)dA $$
Moreover, this can also serve to illustrate my previous point. Now that we learned about this model we can  also try to tweak it and in process come up with a new model. For example, what else does productivity depends on? I would guess that pollution will also be one thing that affects productivity. And in turn what does level of pollution depend on? Well historically again proximity to other people, cities are more polluted than villages. So based on this observation we can come up with 'new' equation:
$$P=P_0+\int_A Pf(r) - Pg(r)dA $$
where $-Pg(\cdot)$ will be term that captures how productivity is negatively affected by pollution which will again depend on proximity to other people. So we created new model from the old one (although I am not sure if this model already does exist or not in the literature, perhaps we just rediscovered some already existing model but for didactic purposes this serves as an example).
So in conclusion in order to learn how to make new models you should observe how other people create new models. Then you should find problem you are interested in and try to translate the model into math like in example above. Also this can usually be done just by tweaking the old models, most theoretical research does not start from scratch but builds on some preexisting work.


Intellectual property as a retarder of innovation

The cuisine and fashion industries both largely exist without intellectual property protection other than trademarks (n.b., they can use copyright on certain aspects of their work but this is generally thought to give little protection) yet they seem to flourish. How is this possible?

In fashion, it is thought that copying the work of other designers can be good for everyone, allowing the industry to have a color of the year and products like bags and dresses at various quality, fit, and price levels.

There may be related forces at play in cuisine. It is difficult to imagine the Cronut fad lasting as long as it did without other bakeries making very similar efforts to keep customers interested and the product in the news.

This is only one mechanism. Another mechanism giving rise to negative outcomes is barriers to entry. Think of patents as raising the returns and costs both to entry into an industry. They raise returns because conditional on getting greater IP protection you have more economic rents from your IP based monopoly. But because others already have these heavy protections the cost to a new entrant of innovating and litigating in a way that permits entry to the industry will be much higher. The consensus seems to be that at some point the marginal benefits of greater protection fall faster than the marginal costs of entry increase, leading to something like the Tabarrok Curve for patent protection:

Source: Marginal Revolution


Start by establishing $ \epsilon _1 = \epsilon , \epsilon_{t>1}=0$ . Now, epsilon will be your impulse.
You can calculate an expression for $A_t,\bar{A}_t\ \forall t$ . From here, you can either:

Work recursively with each variable and provide an analytic function for them, for every moment on time.
Calculate a value if you are simulating it, using the policy functions at each step.

Notice that, if you log-linearized your equations, $\epsilon=1$ would mean a 1% deviation from the steady state.


How to check whether the production function below is neoclassical or not

C.E.S production functions are indeed tiresome to differentiate, and it is very easy to make a mistake. But hey, this (algebraic manipulation) is part of the job, and one needs to practice moving around symbols , creating common factors, etc.

But there is another way to show that $F_{KK} <0$ in totally abstract terms.

First, prove 4. (linear homogeneity), it is easy.

Second, exploit Euler's Homogeneous Function Theorem, and decompose $Y$ using the first derivatives and the variables (this is a very well known result).

Third, re-arrange the previous to obtain an alternative abstract expression of the first derivative of say, capital.

Fourth, differentiate what you got in step Three, to obtain an expression for $F_{KK}$.

All the above are done using abstract notation $F_K, F_{KK}$,etc and nowhere the actual C.E.S functional form. After step Four, you will need to calculate the cross-partial, which is easy, even for the C.E.S. function.


Questions on comparing GDP between various countries

Answer to question 1:

OER is an actual price set by the government. The real exchange rate or RER (That´s how people typically call it) is a ratio of prices of goods, as you mention.

The arbitrage does not go away because the goods in the RER calculation are not completely tradable. The PPP among tradable goods is closer to 1 (meaning the PPP exchange rate among tradable goods is closer to the OER). You can´t trade hamburgers, they get cold, mushy....

Moreover, goods and services are not the only thing being traded across countries. You also trade capital. So a country that is in vogue for international investors will see lots of demand for its capital, raising the price of everything denominated in its exchange rate. So its goods and services look expensive, but its not that things are in disequilibrium its just a disequilibrium in the goods and services part of the balance of payments, that is balanced by another disequilibrium in the capital part of the balance of payments.

Answer to question 2:

Use nominal GDP, in Dollars or in PPP Dollars. Use dollars if you care about dollars, for example if you want to figure out the likely market size for your good which is produced in the US. Use PPP dollars if you care about local living conditions. PPP adjusted (per capita) GDP is a good way to figure out (economic) living conditions.

Answer to question 3:

High rates should imply higher returns to investors that provide liquidity to the local economy, so they should be connected with a more appreciated currency. High inflation lowers the expected future value of the currency, so it should make holding the currency less desirable instead. This should lead to a more depreciated currency.

However, the answer quickly gets more complicated if you add expectations and monetary policy to the mix. For example, an increase in interest rates that will lead to an expectation of a slowdown in the economy and very low future rates might depreciate the currency; high inflation that will lead to an expectation of a big monetary policy contraction raising interest rates, might appreciate the currency.


Why can't someone have their money restored if someone they paid in advance goes bankrupt?

That’s how bankruptcy law works. Every entity that is owed money - including firms that sold products to the bankrupt, workers - wait inline to get paid back according bankruptcy laws.

The state cannot make everyone whole, as that would just encourage fraud. E.g., create a shell company, get rich friends to lend it money, take the money out and declare bankruptcy. Your friends get their money back from the government, and you get their hands on the proceeds as well. You make it worth their while by passing them money back under the table.

The state could bail out certain groups, but that’s an entirely a judgement call by the legislative body.


Justification for my Random Effects estimation

Your first point is valid for not using fixed effects as you are interested in the entire border not just these 16 roads.  Random effects can be advantageous when you have such a small sample compared to the population for your treatment group.  Also note, if the unobserved effect has a large variance or T is very large then RE will be close to FE anyway.  You can try both and do a Hausman test to see if the two models are different.

Your second point is not convincing.  I don't see this as being a justification for using random effect.  Don't lose site of what you are looking for, the effect of exchange rates on shopping across the border of your two countries.  You don't care about the effect of roadway length on the roadway traffic, so why bother with the idea of holding on to it in your results.  The one thing your distance variable can do is act as a sort of robustness check for you since that is one of the fixed effects you want to control for.  Now I can understand your interaction term with distance as there is probably some sort of cost and benefit for people considering the exchange rate vs the distance they have to drive, but in FE models, your interaction will remain.  Also note, that road dummies would be very similar to FE with your model specification.

I would probably likely try a First Difference approach as well since you are going to have serially correlated errors.  You have controlled for some time-variant factors like seasonality with your months and some economic conditions with consumer confidence, but there could be other factors that change over time: road constructions, localized new regulation, new store openings on one side of the border, etc.  These would create serial correlation in your error term.

As long as you have a good justification for each modeling approach, I would try them all and compare your results.  Just use a straightforward pooled OLS model as your baseline, and then proceed from there.  Don't just blindly try everything, but be thoughtful and understand the assumptions you make in each approach.


Rationalizable strategies and Weak Dominance

In 2-player games, the strategies that survive iterated elimination of strictly dominated strategies are called rationalizable. Note that even if no strategy is strictly dominant, there can be strictly dominated strategies. If you cannot eliminate any strategy, then all strategies are rationalizable.
Only if correlation of players' randomization is allowed, all strategies that are rationalizable (not never-a-best response) are also equivalent to those that survive iterated elimination of strictly dominated strategies in games with more players.
In any case, you can always find rationalizable strategies if a best response exists -- independent of whether a (strictly or weakly) dominant strategy exists.


Economic impact of employer ignorance to cliff effects?

There is generally no effect of employers not formally tracking their employees' subsidies on the labor market. Generally speaking government subsidy is already reflected in the labor market whether employers know about it or not.
A trivial example would be policy that gives unemployed people benefits as long as they are unemployed (let's say ${\\\$}100$). Employees only accept job if the benefits of having job outweigh the costs of having it. Simplifying by assuming that only benefit of job is the money and nothing else (unrealistic but does not affect underlaying mechanism) in the above scenario employee won't accept any job offer that does not pay at least ${\\\$}100$.
So in this case whether employer knows about the subsidy or not job will be created only if employer is prepared to bid for the job more than ${\\\$}100$ and only jobs that pay more then ${\\\$}100$ will be created in the economy. Really the only difference between scenario where employer knows about subsidy or don't is that those employers who don't know will wonder about employees rationale for asking ${\\\$}100$ but that has no additional effect on labor market. Employer has no reason to care about whether the ${\\\$}100$ is being asked because that is the employee's value of free time so employee won't accept less or whether this is because of another competing job offer or government subsidy. This the beauty of price system - you don't need to understand people's motivations or preferences or situation - they will already be reflected in prices they are willing to pay or they ask for (in symmetrical fashion some businesses also get subsidies from government that can be conditional on their size/profitability (e.g. some credit for small businesses) -these could affect labor market but are not dependent on employees actually knowing about these subsidies).
The above generalizes to the situations when subsidies depend on the wage as in your description above. Again such subsidies would have effect on employment/wage or other factors, but generally the employer knowledge of those subsidies would not.


If Germany is the largest exporter, why do Chinese products pervade the the US market?

Intermediate and capital goods used in the production of other goods are often very expensive and made by Germany. Think fancy manufacturing equipment in chemicals, semiconductors, and metal fabrication as well as precisely manufactured consumables like processed chemicals and auto-parts. Chinese goods are ubiquitous because they are skewed towards final goods like toys and white goods we consume at in our homes.

This shows the mix of German exports is heavily intermediate and capital good focused:

This shows that China is more consumer goods focused (but the trend towards this as a shrinking fraction of a growing total):


I think one thing you can think of is this:

Assuming such a thing is possible (Fama may cry never here), one might first define a productive investment as an investment in an asset that is undervalued by the market relative to its fundamental value.

The distinction then between this type of investment and a bubble investment is that bubble investments stray far above the fundamental value of an asset. Bubbles are usually made worse than they might have become otherwise whenever trend investors attempt to play bubbles for profit. And it is generally the realization of this fact (that bubbles have pushed securities beyond fundamental valuations)by market participants that crashes the bubble.

This paper on the topic is nice.


Would a world-wide currency be a good idea?

I agree with the members that have voted to close, but I felt obliged to point out an important confusion in the question. The OP writes

  "A single currency with an enforcing entity controlling entity could use this power to help countries in the desperate need to grow,... By
  retrieving in the form of taxes a percentage of each nation's Gross
  Domestic Product... and then redistributing this to each country, we
  would be in fact spreading resources from wealthy parts of the world
  to the poorest in a fair way."

It appears therefore that the OP focuses on issues of global income/wealth inequality, and he thinks that, under a common currency, redistribution would be easier...

...The OP fails to see that, in order to have a global currency, it would take a "geopolitical will" from the parties involved, which, if it existed, the contribution of a common currency as a "redistribution facilitator" would be negligible.

One important reason of why we do not have a global common currency, has to do with the fact that we do not feel that much "connected", truly "parts of a single whole". Hence, wealth redistribution to the extent imagined by the OP is not something universally desired. Because if such a sense of being part of a single whole was the dominant flavor of human existence, the desire to redistribute would flow rather naturally from it, and then it could actually happen whether we had a common currency or not.

Now I am voting to close also.


How would Greece "temporarily" leave the Eurozone?

There´s several possibilities, but they are all speculative.

My guess is that its not too hard to tell a story like this one: They could leave the monetary union, declare all local deposits and debts to be in drachmas and then move on, printing drachmas and taking them in for tax payments. Later on, when the economy is growing and the fiscal deficit has become manageable, they would apply to be part of the Eurozone again.


Compute Nash Equilibrium in median voter game

The calculations look correct.

For the PSNE, I would just say since there is no mutual BRs in pure strategy, there is no PSNE, and leave it at that.

In the MSNE, A would play $-1$ with probability $\frac{1-s}{2-s}$, $0$ with $\frac{s}{2-s}$ and $1$ with $\frac{1-s}{2-s}$; B would play $-1$ with $\frac{s}{2-s}$, $0$ with $\frac{2-3s}{2-s}$ and $1$ with $\frac{s}{2-s}$.


Why $nominal$ interest increases when inflation is expected to increase?

Better look at the Fisher rule (Fisher equation).
nominal interest rate (i) = real interest rate (r) + inflation (pi) (i = r + pi)


Does Chile have a government owned Export Import bank like the US or India?

Chile joined the OECD in 2010 but does not have an official export credit agency listed by the OECD in its involved in the Export Credit Group

The Inter-American Development Bank is lending US$27 million to the Chilean Finance Ministry to support export promotion and services, but this does not look like financing

So I would assume that financing comes from private sources (in particular Chile has large private pension systems) and foreign export credit agencies, plus the usual market operations of the Chilean central bank to ensure monetary stability and liquidity in the context of a floating exchange rate significantly affected by the world price of copper


Calibration of utility function parameters controlling labor disutility

$\alpha$ handles the conversion between the units in which labor is measured and the the units in which consumption is measured.

Consider the leisure part of the utility function:
$$ - \alpha \frac{n^{1 + \frac{1}{\nu}}}{1 + \frac{1}{\nu}}$$
We can rewrite it like this:
$$ - (\alpha^{\frac{1}{1 + \frac{1}{\nu}}})^{1 + \frac{1}{\nu}} \frac{n^{1 + \frac{1}{\nu}}}{1 + \frac{1}{\nu}} = -  \frac{(n\cdot (\alpha^{\frac{1}{1 + \frac{1}{\nu}}}))^{1 + \frac{1}{\nu}}}{1 + \frac{1}{\nu}} $$
Define $\gamma = (\alpha^{\frac{1}{1 + \frac{1}{\nu}}})$
and rewrite the utility function in terms of $\gamma$ instead of $\alpha$
$$ u(c, n) = \log (c) -  \frac{(\gamma \cdot n)^{1 + \frac{1}{\nu}}}{1 + \frac{1}{\nu}}$$

Written this way, I see $\gamma$ and therefore $\alpha$ as serving as a unit shifter. How many seconds of leisure makes you indifferent over one dollar less consumption? Say it were 60 seconds. What unit is $n$ measured in? Should we put in $n=1$ for minutes, $n=60$ for seconds, or $n=\frac{1}{60}$ for hours? $\nu$ can't answer that question because it controls the shape and curvature but not the scale of the utility function with respect to $n$. However, $\gamma$ can. If the "true" measure of $n$ is in hours and we guess wrong and choose seconds then $\gamma$ should be $\frac{1}{3600}$ and conditional on $\nu$ this implies $\alpha$.
In calibration the true units of $n$ it need not map cleanly to one of our time units. $n$ might be properly measured in units of 15.5 seconds or $\pi$ minutes, but the functional form is flexible enough to handle these cases regardless of if you input the labor in the calibration in any of the more standard units of hours, minutes, or seconds.

As for how to calibrate this, you have to see the bundles of labor/ leisure and consumption chosen by households for given sets of prices. This, combined with the demand functions that follow from this utility setup, should give you the required calibration. The paper A Model of Housing in the Presence of Adjustment Costs: A Structural Interpretation of Habit Persistence (Flavin and Nakagawa (2008), free copy here) shows the way to do this in a different (housing / non-housing consumption instead of consumption / leisure) problem. Their $\gamma$ parameter acts much like $\alpha$ does here.


Would this hypothetical firm exit in the long run?

The firm will not exit: for example inputs $x_1=1,x_2=1$ lead to $y=1, c=5$ and profit $py-c=1$

In general profit is $6x_1^{1/2}x_2-3x_1-2x_2$

As you found with $x_1 =\frac19$, profit is $-\frac13$ which is independent of $x_2$
But with $x_1 \gt \frac19$, profit is an increasing function of $x_2$ and is positive when $x_2 \gt \frac{3x_1}{6\sqrt{x_1}-2}$
For example with $x_1 =1$, output is $x_2$, profit is $4x_2 -3$ and is positive for $x_2 \gt \frac34$
For example with $x_1 =4$, output is $2x_2$, profit is $10x_2 -12$ and is positive for $x_2 \gt \frac{6}{5}$

So there appears to be no  profit maximizing level of $x_2$ because (providing $x_1 \gt \frac19$) profit is an increasing  function of $x_2$. So a profit maximiser will want to increase $x_2$ without limit.  Your partial derivative method did not find this infinite solution

For what it is worth, given a particular $x_2$, the optimal value of $x_1$ seems to be $x_2^2$ making the profit $x_2(3x_2-2)$ which is clearly positive when $x_2>\frac23$ and then again an increasing function of $x_2$


Difference between 'ideal variety' and 'love of variety' - International trade

Basically, the difference is that in the love of variety approach the entry of new varieties in the market does not "crowd" variety space. So, differentiated varieties may exhibit a high or low degree of substitutability, but this is invariant to the number of products in the market. Hence, consumers "love" variety, in the sense that increased variety improves welfare.

In the Lancaster ideal variety approach, entry of new varieties causes "crowding". Goods become more substitutable as more varieties enter the market. So, the marginal utility of new varieties falls as the market size grows.

These two approaches have different implications for welfare of small and large countries as discussed in Hummels and Lugovskyy.


Trouble Understanding the Integral Underlying Random Utility Models

This has nothing to do with any specific model. For any event $A$, let $I_A$ be the indicator function such that $I_A(\omega)=1$ if $\omega\in A$ and $I_A(\omega)=0$ if $\omega\notin A.$
Then $\mathbb{P}(A)=\mathbb{E}[I_A],$
and here the expectation is given in terms of a density function.


How are ties broken in a second price sealed bid auction?

The winner pays the second highest bid, which is 5 dollars, however who the winner is depends on the tie-breaking rule. There are multiple rules one could use. In most cases it is assumed that the winner is selected randomly from among the people who placed the highest bids. But you could also select the winner from this group alphabetically or by checking who submitted their bid first.

In case of a Vickrey auction in equilibrium when multiple players place the same highest bid all such players are indifferent between winning and losing, so the exact tie-breaking rule is usually not very important, it does not affect the players' equilibrium payoff nor the seller's revenue.


Why teach Arrow's impossibility theorem?

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

Arrow's impossibility theorem is a more nuanced theorem. If you have not studied it do read up on it, it is fascinating! (You probably have to get a book on Social Choice to get familiar with the concepts the theorem uses.)

Judgement aggregation is covered in basic micro courses to show that it is not clear which of the efficient allocations a social planer should use, because society may not agree.


Do governments issue debt at low r to pay debt with high r?

The phrase governments "do debt rollover from time to time" is an understatement. The entire stock of Treasury bills is rolled over continuously, as well as the coupon debt. For example, a 3-month Treasury bill needs to be rolled over four times a year.

As for the current situation, it is somewhat strange.

Government fiscal agencies (Treasury, Ministry of Finance) have tended to increase the average maturity of their debt issued. (The answer by Facet_Velvet discusses this, but in order to keep this answer self-contained, I will provide the same link: link to OECD report.)
Many (but not all) developed central banks have been buying government bonds, replacing them with short-maturity governmental liabilities (deposits at the central bank).

These two actions tend to cancel each other out. The only defense of the policy that I can offer in this context is that the central bank is the party taking the interest rate risk. (The central bank has nominally independent finances.) As a disclaimer, I think Quantitative Easing as a policy makes no sense, so I cannot come up with a good rationale for this policy mix.

However, the answer to your question is that we cannot think of the central government as being like a household or business. As the currency issuer, it has a very different perspective on finances, and minimising interest costs is actually not an important policy objective.

For example, it is extremely easy for the government to minimise interest costs: it just needs to set interest rates at 0% by legislative fiat. (Some may object that this is impossible; the experience with interest rate pegs during and after World War II show that the policy is feasible.) However, just because we can minimise interest costs does not mean that it is a good idea. In order for monetary policy to work, the government needs to have bonds that set the rate of interest at a positive level, which can then be varied by the central bank to help control the business cycle.

The primary interests of the government in issuing bonds are:

Create a yield curve that act as a benchmark for private sector borrowing. When Australia was running large surpluses, I believe that the Australian banks pleaded for continued government bond issuance to keep the yield curve liquid. (I do not have a reference.)
Have a liquid Treasury bill market that gives risk-averse investors a place to park cash. In particular, central bank foreign exchange reserve managers are not willing to take large amounts of interest rate or credit risk, and so you need a liquid Treasury bill market if you want foreigners to hold your currency as foreign reserve assets.
They need to meet the demands of institutional investors for long-dated credit risk free bonds.

These competing demands imply a continued juggling act to balance out issuance at various maturity points.

Finally, governmental debt managers do not want to lock in their portfolio of issued bonds as long-dated instruments, as they can do nothing about them. Unlike mortgages, almost all government bonds cannot be repaid early. (The U.S. issued some 30-year callable bonds in the early 1980s.) If the debt is termed out, and the the government has a fiscal surplus (which happened for a brief period in the late 1990s), the government would end up with no Treasury bills outstanding and a surplus of liquidity. It would have to go into the private markets and lend to private sector entities with that surplus, which the government does not want to do. Hence, they need to have a sizeable amount of short-dated paper that can be run off in such a situation.


That type of demand is called an Isoelastic demand function, because the elasticity of demand is constant, so it does not depend on prices.

You have not done any mistake. But you just need to move forward one more step. Notice that at the moment your derivative has both p and q in it. Try to get rid of q. This is, try to have $\epsilon=f(p)$, and not $\epsilon=f(p,q)$. This hint should be enough for you to solve the question.


Such data can be found on Quandl, for example:

https://www.quandl.com/data/ISM/MAN_PMI-PMI-Composite-Index


If the government builds a bridge, how do we know it's the best possible usage of real resources (i.e. steel, labor, etc) at the time?

A short answer is that in case of provision of public goods in real-life we can never be completely sure if they are provided in optimal quantity due sheer difficulty of quantifying all costs and benefits, measurement problems when it comes to underlaying utility, due to uncertainties involved and many other factors.
However, this does not mean that no evaluation of public projects can be done. Most developed countries will have some dedicated analytic unit. In the Netherlands where I live that would be Centraal Planbureau [Bureau for Economic Policy Analysis] (CPB)  in the US it is Congressional Budget Office (CBO).
These units routinely engage in cost-benefit analyses of public projects and then make recommendations based on whether the projects net present value is positive. The net present value would be given as:
$$ NPV = B_0 - C_0 + \frac{B_1-C_1}{1+r} + \frac{B_2-C_2}{(1+r)^2} + ... + \frac{B_T-C_T}{(1+r)^T} $$
Where $B$ are benefits of the project, $C$ are costs and $r$ is discount rate or you can interpret it as a required rate of return.
The benefits and cost try to capture actually underlaying changes in utility. They will be usually estimated using hedonic pricing or various discrete choice models that can tell us something about peoples preferences and utilities based on observing their actions. For example, from the way how housing prices vary in cities with high congestion we can estimate how much people value time lost in traffic. The required discount rate is usually set to be equal to interest rate on government/municipality bonds or rate that government could obtain if it had invested the money into wealth fund. Of course, the way how these parameters are estimated or assumed is always a point of contention as this can't be done with infinite precision and complete certainty (this holds even in cases when we do ex-post cost-benefit analysis as most benefits and costs are virtually never directly observable and have to be estimated).
The above is, of course, just a short overview as providing an exhaustive review of how public cost benefit analysis is done is unfortunately beyond scope of SE. A good and highly cited example of public cost-benefit analysis is: Leape, J. (2006). The London congestion charge. Journal of Economic Perspectives, 20(4), 157-176.
Furthermore, just because project passes cost-benefit analysis it does not necessary means that the outcome is pareto efficient or even that it maximizes utility. However, it is reasonably good guard against completely frivolous spending.  This being said, advice given is not advice taken and such analyses are often ignored by politicians, as pointed out by Giskard public officials are not necessarily benevolent.


Doesn't the semi-strong form of the EMH conflict with expecting stock indices to increase in the long run?

The two propositions here are:

EMH: I can't predict which stocks will do better than average.
The average stock will increase in the long run.

1 does not contradict 2.

Analogy: I am in a room full of babies.

EMH: I can't predict which of these babies will be the tallest in 20 years.
Nonetheless, I can predict that in 20 years, these babies will be taller than they are today.


Slutsky Decomposition from Indirect Utility Function

Since you already know the demand correspondences, you can use use the duality principle as follows: $v(\textbf{p},e(\textbf{p},u)) = u.$ Using this we get $\frac{4e(\textbf{p},u)}{p_1p_2}=u$, or $e(\textbf{p},u)) = \frac{up_1p_2}{4}.$ Now, using Shephard's Lemma, we can obtain the Hicksian demands as: $\frac{\partial e(\textbf{p},u)}{\partial p_i} = h_i(\textbf{p},u)).$

However, the job is not yet done. You might get stuck with the $u$ while evaluating the Slutsky's equation. In other words, you need to find the utility function as well. The demand correspondences are(I hope you've obtained the same expressions) $x_1(p_1,p_2,m)=m/2p_1$ and $x_2(p_1,p_2,m)=m/2p_2$. Since the indirect utility function is homogenous of degree zero, you can further write it as $v(p_1,1,m)=v(p,m)=m^2/4p=(m/2).(m/2p).$ From the demand correspondences obtained, you have to represent $m/2$ and $m/2p$ in terms of $x_1$ and $x_2$ ($p_2=1$, as a consequence of homogeneity of $v(p_1,p_2,m)$), and substitue it back into the indirect utility function. Thus, we obtain the the utility function $U(x_1,x_2)=x_1.x_2$(since we obtain the indirect utility function by substituting the walrasian demands into the given utility function, backtracking the same steps gives us back the utility from the indirect utility). I think now one can easily evaluate the Slutsky's Equation.


What is the relationship between S&P500 and the US dollar

You're doing the traditional mistake of people not familiar with Econometrics: You mistake correlation and causality.

You look at a change in the USD, assume it to be exogenous, and then predict an impact onto the S&P.

However, changes in the USD are not exogenous. For example, an increase in US productivity (compared to the productivity of firms in other countries) will both increase the S&P and valuate the USD.

For what you're trying to do, you need to separate different effects, which is virtually impossible - or look for random variation in the USD, of which I'm also unfamiliar with.


Did I calculate maximum price of machine correctly?

The thing you are missing in your calculation is that the roubles the machine produces in year 1 are more valuable than those in year 2.  Think about 2 different machines with different production schedules

Machine 1 - 440 roubles year 1, 0 in year 2
Machine 2 - 0 in year 1, 440 in year 2

Using your calculation the value of both of those machines would be the same about 306 roubles, but machine 1 produces the goods in year 1.  So in year 2 you can put those roubles in the bank and earn 20 percent interest on them.  So at the end of 2 years you actually have 528 roubles instead of 440.

What the NPV calculator is doing is taking into account the production in year 1 is worth more than the production in year 2 by dividing it by a smaller number, $(1+0.2)$ instead of $(1+0.2)^2$.

Regarding the part about $i$ meaning different things.  $i$ is how we tell how muc we value a dollar today relative to tomorrow.  In the real world inflation makes things in the future cost more so we discount future dollars by that amount.  In your problem a dollar I save today is worth 1.20 tomorrow so if I invest that money in a machine I better earn at least that much otherwise I'd rather put it in the bank.

Explanation of NPV:
Think of there being 2 different machines.  One gets you 240 in one year.  The second gives you nothing in the first year but 200 in the second.  Using your calculations you would say you'd pay
$$ \frac{240}{(1+0.2)} = 200 $$
for machine 1 and
$$ \frac{200}{(1+0.2)^2} \sim 138.9 $$
for machine 2.  Thus you better be willing to pay 338.9 for a machine that does the work of machine 1 and machine 2. That is all NPV is doing here.


How to show that the estimator is consistent?

Remember that consistency describes how the estimator behaves in the limit as N asymptotically approaches infinity. Assuming no errors in your math up to this point, you need to consider how your error terms $U_i$ behave asymptotically as well.


I used to work for a major online advertising network, and it's pretty much an open secret in the industry that a substantial portion of ad impressions are either bot-generated, scams to exploit misleading search engine results, or both.  There are typically several layers of "middlemen" involved between the company whose products are being advertised and the websites running the ads, and everybody has a financial incentive to keep their mouths shut about the rampant fraud involved.

The basic economics is this:  an unscrupulous website joins an advertising network (which often have insufficient resources dedicated to their review/approval process for new websites joining their network) and then either purchases botnet traffic (at a lower price than they're receiving in ad revenue) or tries to pull in search engine traffic through misleading search terms, for as long as they can get away with it.  They're typically caught fairly quickly, but by that time they may have made several hundred (or several thousands) of dollars in profit.  Then they register a new scam website and repeat the process.  Remember:  websites are typically paid for the ads that appear on their website, even if nobody ever clicks on them.

Since nobody in the entire industry is really interested in exposing this aspect of the business, it may be difficult to find actual studies.  I'll take a look though, and would suggest that "fraud in online advertising" is the appropriate search phrase.

Update: It looks like the Wikipedia article on Ad Fraud has a number of references that may serve as a good starting point.  An online search turns up a good number of results as well, although many of them appear to be marketing material for software that claims to help prevent/stop ad fraud.


How to account income from the informal sector?

Check this interesting report of the International Labor Office on Measurement of the Informal Economy. They raise and discuss the Key Challenges:

The paucity of data
Why is measurement important?
Conceptualizing the informal economy (Employment in the informal sector and informal
sector enterprises)


What econometrics book or textbook should I use?

I'm not an econometrician but here is my guide on some books I found helpful (and still do).

My opinion is that a nice place to start is with an advanced undergraduate textbook. These are often helpful even for postgraduate students to build intuition and brush up on mathematical techniques. For books at this level I would recommend Introductory Econometrics: A Modern Approach by Wooldridge, Introduction to Econometrics by Stock and Watson and Introduction to Econometrics by Dougherty.

You mention a dislike of maths and stats. Do you have much in the way of familiarity with matrix algebra? If not, I recommend A Guide to Modern Econometrics Verbeek and the older Econometric Methods by Johnston and DiNardo. These two books are pitched at the more basic end of the graduate level and have excellent appendices on matrix algebra. Either of these would be an excellent starting point for you.

More advanced books include Greene's Econometric Analysis and my favourite; Econometrics by Fumio Hayashi. The latter textbook centers on the Generalised Method of Moments as an organizing principle which really helps illuminate the material. Econometric Analysis of Cross Sectional and Pannel Data Wooldridge is a classic at the graduate level. It may also be worth considering the online textbook by Bruce Hansen. It's available on his website https://www.ssc.wisc.edu/~bhansen/econometrics/ These textbooks could be considered rather mathematical on the first reading. For example, the large sample properties of estimators require some sophisticated mathematical machinery. All the textbooks mentioned above give a fairly digestible but somewhat superficial treatment of these topics. To get a good understanding of these topics a course in measure theory and integration would be a great help!

After these come the more specialized books in Panel Data / Microeconometerics and Time Series. The books mentioned in the previous paragraph generally do have an introduction to these topics but it's rather limited. In terms of Time Series a great textbook is Applied Econometric Time Series by Walter Enders. This book is much more focused on Time Series in real world applications and is lighter on the technical details. I would recommend this to you if you're still interested in VAR, ARCH, GARCH and error correction models etc. In stark contrast is Time Series Analysis by James Hamilton. A very thorough textbook but quite a hard read. In terms of Microeconometrics, I like Microeconometrics by Cameron and Trivedi and Baltagi's Econometric Analysis of Panel Data. There are many, many more excellent textbooks in these fields but they're too numerous to mention. Remember, these books are advanced and would only be used once you've taken the standard grad econometrics courses.

Lastly, every economist should have a copy of Angrist and Pischke's Mostly Harmless Econometrics A great guide to econometrics as a discipline.


The only relation I see is that they are both named after Vilfredo Pareto. The Pareto curve is related to efficiency, and I see no way of connecting the Pareto chart to the same concept. Since Pareto was an engineer before becoming an economist, it seems most likely to me that its just that two distinct techniques from two different fields were named after him. I suppose you could use a Pareto chart as a tool to make efficient engineering decisions, so they are minimally related.


Calculating optimal level of negative externality

Almost correct. Setting $W(h)=0$ is wrong (but inconsequential for the solutions). Checking the SOC for completeness should be included, but is somewhat obvious here. Correctness of 3. holds only under the assumption that the consumer owns no shares of the firm, which seems to hold in this exercise.


Citing non-economics studies in an economics research paper

As long as the main results/conclusions of your paper don't rely solely on the non-economics literature you cite, you should be okay. In other words, it's perfectly fine to use non-economics literature to motivate or even as part of the support for your thesis, as long as you also include proper economic arguments, i.e. theoretical models or econometric analyses.
For example, Bidner and Eswaran (2015) theorized about the origin of the Indian caste system and cited quite a few sociological, anthropological, and biological literature to motivate their model.
Likewise, Caplan and Dean (2008), which provides axiomatic foundations for a neuroscientific hypothesis (that dopamine encodes the "reward prediction error"), is full of references to the psychology and neuroscience literature. The paper even includes an extended review of the non-economic literature and explains how they are relevant for economic decision-making.
Similar examples are plentiful, and they end up in high-rank journals because, notwithstanding their non-economics citations, those papers contain substantive economic contributions.


First Order Condition for Profit Maximization in Gambling Industry

The expression in question is in footnote $11$ of the referenced article. Reading the paper, we see that the decision variable here is "the payout rate", which is the reciprocal of $P$. So equivalently, we can solve the maximization problem with respect to $P$ (and not w.r.t. $Q$). More over, "price elasticity of demand" involves the derivative of $Q$ with respect to $P$, and not the other way around:

$$E_{PQ} = \frac {dQ/dP}{Q}P $$

and we expect it to be negative (higher price means lower payout rate leading to less demand for the quantity measure here, i.e. less "demand for prizes").

We can write the maximization problem as
$$\max_{P}N = \max_{P}\left[P\cdot Q(P) - Q(P) - C(Q(P))\right]$$

The  first-order condition is

$$\frac{\partial N}{\partial P} = Q + P\cdot Q'  - Q' - C'\cdot Q' = 0 \tag{1}$$

Multiply throughout by $P/Q$:

$$Q\frac PQ + P\cdot Q'\frac PQ   - Q'\frac PQ  - C'\cdot Q'\frac PQ  = 0$$

$$\Rightarrow P +P\cdot E_{PQ} - E_{PQ} - C'\cdot E_{PQ}=0$$

$$\Rightarrow -E_{PQ} = \frac {P}{P-1-C'} \tag{2}$$

This makes sense. Plugging in the values presented in the reference, we have

$$-E_{PQ} = \frac {2}{2-1-.12} = \frac {2}{0.88} \approx  2.27 $$

which is very close to the value resulting from the equation presented by the authors. I haven't been able, by whatever algebraic manipulations I tried, to replicate their formula, but eq $(2)$ is correct in any case. If a reconciliation comes up, I will update.


What is the name and the mathematical model of this effect

I know that this is called price “stickiness”. Price “flexibility” is when something such as interest rates would bring prices to equilibrium quickly. Price stickiness in this case could have a delayed effect as you mentioned. We could also call this “elasticity”. For simple models rise over run can measure price elasticity. For example, a 5% change in interest rates, and it’s corresponding impact on prices could be measured by slope (rise/run).


These guys (paper) claim the distribution is still power-law, but steeper in recessions and flatter in booms.

[Content added after suggestion]

  While it is well known that the distribution of firm sizes (in the US
  at least) looks like a power law distribution, these guys look at
  whether it changes in shape over the business cycle.

  They show that (in log-log space) the distribution is actually a power
  law in both recessions and expansions, but its not the same power law,
  its steeper in recessions and flatter in booms, meaning that large
  firms become relatively larger in booms than in recessions, or
  alternatively that there is  a lot of entry of small firms in booms.


How to decide the best bid in an auction?

To understand the economics of auctions a little better, I'd recommend taking a look at "Auctions: Theory and Practice" by Paul Klemperer. This book has a number of advantages:

with the exceptions of some non-essential appendices, the book is non technical and therefore more accessible to lay-readers. Other texts on auctions tend to be aimed at economics graduate students or above.
the book was motivated by Klemperer's experience designing radio spectrum auctions in the UK and discusses applications for public sale/procurement auctions at some length.
the book emphasises the main considerations and intuition behind the analysis and design of auctions, rather than the details that are more likely to be of interest to academics rather than participants.

The book can be read free of charge on Klemperer's website here. Alternatively, it is available in print; here is the publisher's page.


I cannot find for this Simple shared effort level game

You are right, there is no equilibrium for $s\leq \frac{1}{4}$. Note that Nash's theorem only guarantees the existence of an equilibrium in finite games (which this game is not). (Also note that $0$ is not in the best-response set of any of the two players, so we know that, if there were an equilibrium, it would not contain zero effort by any player.)

To get an intuition of what is going on, consider the plot below, which shows the best response functions for the two players, with  $s=\frac{1}{4}$. As you point out, the lines do not intersect. Suppose we start at point $(0,0)$, and let each player revise their action in turn, holding the other player's action constant (dashed line). Player 1 will update their action to $e_1=2$, the best response to $e_2=0$. But then, player 2 will update their action to $e_2=\frac{3}{2}$. This goes on ad infinitum, never reaching an equilibrium.


Theories that complement/contradict prospect theory?

A good place to start would be the book Prospect Theory: For Risk and Ambiguity, by Peter Wakker (2010, Cambridge University Press).  There is an entire area of economic theory called decision theory which studies models of decision making under uncertainty --typically, models which deviate from the classical expected utility maximization model in some way.  Decision theory involves both theoretical results and experimental tests.  Prospect theory is only one among many models that decision theorists consider.


Why is a Normal Yield Curve a sign of a healthy economy?

The prevalent hypothesis for the normal slope of the yield curve is due to a combination of the expectations hypothesis, and a liquidity premium.
Recall what the yield curve is measuring- it graphs Yield to maturity against a bond of maturity t, for different time horizons t. This yield to maturity is generally thought of as the interest rate.
First, the assumption is that we hold constant the risk profile of the bonds in question- think of just looking at the yields of T-Bills for different horizons.
The expectations hypothesis is straightforward: it specifies that the yield to maturity (upto an approximation) of a two year bond is the average of the current yield and the expected future yield. As such, if the yield curve is flat, this would mean that the interest rates are not expected to change. Generally speaking, the yield curve is upward sloping. This can still occur under constant interest rate expectations, because people have a preference for liquidity. As such, not having liquidity for 2 periods is more costly than 1, and hence this premium is reflected in a liquidity premium on the yield curve. However, if the yield curve has a sharp upward slope, the economy is expected to do well. This is because first, output is positively correlated with interest rates. This is, in part, due to the fact that a boom is correlated with increased spending, leading to inflation, and the government controlling money supply (inflation) by raising interest rates.


How do Marxist economists solve the Diamond-Water Paradox?

The Labor Theory of Value has been replaced by the theory of Marginal Utility, which was already accepted by Marx time. In fact he acknowledged:

  "nothing can have value, without being an object of utility"

-Wikipedia: Marginal Utility - The Marginal Revolution and Marxism

Marginal Utility addresses the diamond - water paradox by explaining that the more of a resource or commodity one has ready access to, the less one needs access to even more. The declining marginal utility means that because water is nearly ubiquitous and easily accessed it has very little "value" per unit to an individual because they know they have access to many many units.

"Modern" analytical Marxists, including John Roemer have built a strong foundation (if somewhat heterodox) based on the theory of marginal utility.


How would banking in EU change if taxpayers withdrew their support for Deposit Guarantee Scheme?

Based on the discussion in comments, the core of your question appears to be "What would happen if European governments stopped providing deposit insurance?"

The question and answer about the US deposit insurance program here provides useful background, but the short answer would be that we would expect bank runs to be more likely, though how much more likely would be a function of the institutional relationships between banks, banks' access to liquidity backstops, the extent of bank regulation, and economic fundamentals. This is because (as discussed in the linked answer) private deposit insurance doesn't entirely relieve depositors of monitoring burdens, and private deposit insurers lack the ability to discipline the banks they insure without potentially creating bank runs.

Theory aside, it's not difficult to find examples (particularly historical examples) where deposit insurance has not existed, and while bank runs were generally more likely in those cases, they were not always common, as emphasized by Calomiris and Gorton (1991). Institutional arrangements such as credit mutuals, where shares in the depository institution are allocated based on deposits, can mitigate run risk, for example. A decent review of banking from an industrial organization view can be found in Neuberger (1998).


Taxes levied on sellers = Taxes levied on buyers

Whether the tax is imposed on the buyer or the seller doesn't make any practical difference. It's just an accounting detail. One might even say, it's just an accounting trick.

I haven't read this particular book but I imagine what he was driving at with the "bowl" example was this:

Suppose that instead of filing tax forms, etc, the government collected taxes on the spot: There is a tax collector standing beside the counter with a bowl to collect the tax money. The price not including the tax is \$10. The government charges a \$1 tax.

So, scenario 1: The government declares that the buyer must pay the tax. So when you buy the product, you hand the seller \$10, and then you drop \$1 into the tax man's bowl.

Scenario 2: The government declares that the seller must pay the tax. So the seller increases the price to \$11. When you buy the product, you hand the seller \$11. He then drops \$1 into the tax man's bowl, and keeps the remaining \$10.

Either way, the buyer has \$11 less cash, the seller has \$10 more cash, and the tax man has \$1 more cash. Whether the buyer hands the tax money directly to the tax man, or the buyer hands the money to the seller and the seller hands it to the tax man, makes very little practical difference.

We could discuss what portion of the tax is really born by the seller and what portion by the buyer. If today the tax is zero and tomorrow the government begins imposing a \$1 tax, it doesn't necessarily follow that the seller can continue to collect \$10 and the buyer will pay \$11. Increasing the cost to the buyer to \$11 would mean that fewer units are sold -- some number of people will not buy or will not buy as many for \$11. So the seller may conclude that to maintain sales sufficient to maximize his profits, he must drop the price to, say, \$9.60, so with tax the total price is now \$10.60, and the seller is paying 40 cents of the tax while the buyer is paying 60 cents. Or he may have to drop the price further, or not drop it as much. But whatever the optimum price ends up being, whether the government nominally collects the \$1 from the buyer or from the seller has nothing to do with how the tax is really being split between buyer and seller.

There is the technicality that there may be costs involved in record-keeping or other mechanics of the tax. Like if the seller is required to collect the tax and turn if over to the government, then the seller has additional book-keeping costs. If the buyer is expected to keep records and pay the tax, then the buyer has book-keeping costs. But this isn't the main point.


My guess is because they are denominated is Euros and their yields respond to the European Central Bank monetary policy decisions.


Do mainstream economic models use the blank-slate view of humans?

Standard economic treatments of skill generally assume that people have some baseline level of skill (human capital) which varies over people, and also that skill (human capital) can be improved via education or other methods.

Most of the time, models don't specify why baseline skill varies over individuals, but heritability would presumably be one reason. There are certainly some generational or evolutionary models that assume that parent and child baseline skill levels are correlated, which is in effect a heritability assumption.

As for GDP forecasting specifically, most GDP forecasting methods focus more on education level as the primary (or only) measure of human capital (both the average level and its distribution), but this is likely because baseline skill can't be measured very well, and can be proxied pretty effectively by education anyway because of selection effects.

So, in short, no, economic models aren't blank-slate, although using education as the only measure of human capital, which is sometimes done for pragmatic reasons, does look a tiny bit like a blank-slate assumption.


Aggregate production function, factor shares and cointegration

Intuitively, you test for cointegration because if two variables are cointegrated, they represent only a "one dimensional" family of data points - even if you have a million data points from that sample, they will all fall close to the same subspace, and in general that will mean that you will have many values of parameters for your regression problem which will give a good fit (spurious regression).

Consider the linear regression case - say that you have $ y = Ax + \varepsilon $ as your regression problem, where $ x $ is a column vector, $ A $ is a row vector and $ y $ is a real number. Let's say further that the "structural" relationship we are looking for is $ y = Bx $, where $ B $ is also a row vector. Take an extreme case of cointegration - $ x $ is $ 2 $-dimensional, and we have a linear relationship between its coordinates, i.e $ x_2 = c x_1 $ for some constant $ c $. In this case, any linear functional $ A $ which is equal to $ B $ when restricted to the subspace spanned by $ (1, c) $ will give a perfect fit, and the regression won't be able to distinguish between them. (There's a one dimensional family of such functionals, i.e row vectors $ A $.)

What VECM analysis does is to take advantage of deviations when the relationship is not perfect. In real econometric applications, you never have a relationship that's as clean as $ x_2 = c x_1 $ (or $ y = Bx $) for your entire dataset - cointegration allows for transitory white noise in the linear combination $ x_2 - c x_1 $. If the variance of the white noise is relatively small, a standard regression will still return similar $ R^2 $ values for many different operators. Instead, what you do is look at first differences: a good fit should also fit these, i.e we should have

$$ Ax_{t+1} - Ax_t \approx y_{t+1} - y_t $$

where the subscripts denote the time of observation. Running the regression this way allows you to capture the white noise in the cointegration process and use it to your advantage - it's a way of capturing the information which a naive linear regression is going to miss.


What is a good way te represent analytically two markets with different price elasticities of demand?

How about constant elasticity demand: $Q(p)=p^a$, where $a<0$?

Such functions, as their name implies, have the advantage that the price elasticity of demand is constant along their entire length:

$$\eta=Q'(p)\frac{p}{q}=ap^{a-1}\frac{p}{p^a}=a.$$

Since the elasticity of the demand function is directly controlled with a single parameter, such functions are often convenient when performing comparative statics exercises in which the objective is to show the effect of varying the elasticity of demand upon equilibrium.


Is my reasoning about economic growth and environmental sustainability correct?

It is on a correct track but I would not say it is 100% correct as you miss the main source of growth which is technological progress. Consider the following Cobb-Douglas production function with all 4 main factors of production, capital ($K$), human capital ($H$), labor ($L$), land ($M$) then the standard production function would look something like:

$$F(K,H,L,M) = A K^{\alpha}H^{\beta}L^{\gamma}M^{1 - \alpha - \beta - \gamma}$$

Well you are correct to say that production $F$ increases if either more capital is put to work, or more labor hours are employed ($K$ or $L$ increases). However, there can be limits to how far you can push capital accumulation and still be sustainable.  Machines after all need some raw materials. Also, people only have 24 hours a day so there is a limit there. Land is for all practical purposes fixed (at least before we can make an effective use of real estate on moon or mars - and I am saying that just half-jokingly). However, you missed one important factor of production: human capital. That is things like better education which as far as I can see can increase almost without bounds.

Second thing you missed is $A$ that is the total factor productivity, which makes any factor more productive and loosely speaking it is the technology avaiable. For example, thanks to our better understanding the computer technology modern computers are more faster than the old ones yet they are produced with the same amount resources (or sometimes even less resources - think of the old bus size punch card computers). This does not apply just to capital, thanks to telecomunication technology you can make better use of your human capital, thanks to better management techniques better use of labor, thanks to agricultural techniques like crop rotation better use of the same land.

Also some things that were not correct in your answer:

Comparative advantage (unless you are considering some dynamic endogenous growth effects) generally does not lead to higher economic growth. It will increase the efficiency so GDP will have one time jump from lets say 100 to 200, and sometimes the jump may take several years so on yearly accounts it looks like growth, but its really just increase in level - that is still good but its not really long run growth.


How to work out Price with only the Derivative of Profit Function?

This question seems to be unanswerable. Even assuming a linear inverse demand function $p(Q) = a - bQ$ and a linear cost function $C_i(Q_i) = cQ_i$ the best response function will take the form
$$
q_i = \frac{a-c}{2b} - \frac{1}{2}q_j.
$$
From the information given, you cannot know if say $c=10$ and $a=55$ or $c = 0$ and $a = 45$, so it is impossible to infer the inverse demand function and the price. (And this is assuming linear functions everywhere.)

Also, notice that the exact market structure (Cournot or Stackelberg) is only given in question c). Yet this would also affect market price. Hence, the question is unfortunately just of bad quality and cannot be answered.


How to make deliberate devaluation or depreciation of a currency?

A country can increase the supply of its currency, through some combination of increasing the amount of base money, or loosening the capital / reserve requirements of banks.

It can decrease interest rates.

It can decrease the supply of the currency it wants to depreciate against (for example by buying and holding lots of that currency, or equivalent instruments).


This question is heavily reliant on the context of when it was asked. A lot has happened since February with respect to the Australian Dollar.

A currency devaluation can be caused by quite a few factors. In the case of Australia, the devaluation is occurring with respect to the USD. The AUD remains strong but the US is currently experiencing a surge in consumer confidence. There is also a few larger factors at play. The USD is seen as basically the safest investment one can make. In recent history, govt bonds have been less attractive. As a result, Australian Sovereign bonds have been more attractive as they are very safe. In short, the AUD devaluation has more to do with the strength of the US than any domestic weakness (although Australian economic performance has been underwhelming).
Another key factor relates to the resources boom in Australia. This has primarily been driven by an increase in demand from China instead of an increase in mineral output. The resources book has been a key driver of economic growth. In March/April, the iron ore price took a big hit, partly due to weakening demand from China. As a result of the change in price, the value of Australia's exports dropped very quickly. This directly reduces our Terms of Trade. Manufacturers are pretty happy about this and it is expected they will pick up some of the slack from the stagnating mining sector.

This devaluation has a few flow through consequences. Exporting to the US is cheaper. Importing from the US in particular is more expensive. A good way to think about it is if you are Australian and are thinking about travelling to the US for a holiday, you would be pretty upset. Your trip just got a lot more expensive very quickly. If you own a hotel and you cater to a lot of American tourists, you will be very happy. It will be cheaper for them to come. This change is good for our exporters, including natural resources, manufacturers and services.

The RBA typically responds to these issues very well. Their main instrument of monetary policy is the interest rate.
There isn't much need for a monetary policy response to the devaluation of the dollar. The RBA targets inflation rate which is preferred to Exchange Rate Targeting by many governments.
With respect to a fiscal policy response, The IMF has a working paper on Fiscal Policy and the Real Exchange rate. It doesn't answer it perfectly, but it is definitely worth a read. The key point is that the effect depends critically on (i) the composition of public spending, (ii) the underlying financing policy, (iii) the intensity of private
capital in production, and (iv) the relative productivity of public infrastructure

There should be very low immediate pressure on the standard of living. It gets more expensive to import into Australia, but Australian produced products are more competitive in the international marketplace.


Quarterly regression, year-fixed effects

I guess there's no easy answer. It depends on what you think the data generating process is.
Let $y$ be year, $q$ be the quarter and $c$ be the country.
Then $S_{y,q}$ is the USA shock at year $y$ and quarter $q$, $X_{c,y,q}$ is the observable covariates of country $c$, at year $y$ and quarter $q$ and let $Y_{c,y,q}$ be the variable of interest.
From reading your question, your basic regression looks like this:
$$
Y_{c,y,q} = \alpha_0 + \alpha_1 S_{y,q} + \alpha_2 X_{c,y,q} + \alpha_3 (X_{c,y,q} \times S_{y,q}) + \varepsilon_{c,y,q}.
$$
The underlying assumption is here that:
$$
\mathbb{E}(\varepsilon_{c,y,q}|S_{y,q}) = \mathbb{E}(\varepsilon_{c,y,q}|X_{c,y,q}) = 0
$$

A first thing you might be worried about is that $Y_{c,y,q}$ might be (systematically) different depending on the country in addition to what you observe in $X_{c,y,q}$. In this case, you should probably add country fixed effects.
If you think that $Y_{c,y,q}$ might differ according to the year $y$ in addition to what is explained by $S_{y,q}$ and $X_{c,y,q}$ then you should add year fixed effects.
If you think that $Y_{c,y,q}$ might change with $q$ (e.g. seasonality) in addition to $S_{y,q}$ and $X_{c,y,q}$ then you can add quarter fixed effects.
In principle you coud add country$\times$year fixed effects or country$\times$quarter fixed effects if you are worried about a combination of these problems. If you add year$\times$quarter fixed effects you loose identification for $S_{y,q}$.

Which of these options is best will depend on what exactly you are looking at (i.e. what is $Y_{c,y,q}$) and how you think this changes by factors not included in your regression.
If you decide to add year fe, then the identification of the coefficient on the shock $S_{y,q}$ (and the interaction) only relies on intra-year variation in $S_{y,q}$ and $Y_{c,y,q}$. So if you think there is a lot of yearly variation in $Y_{c,t,q}$ explained by $S_{y,q}$ then you will not be able to capture those when using year fixed effects.
There is also the (subtle) issue of how you define the year. For example, you could define a year from "Januari year $x$" to "December year $x$". An alternative could be, for example, to define the year from "April year $x$" to "March year $x +1$". Depending on this choice, your results might vary.


Hint: Simply apply integration by parts to the integral on the LHS. Simplify and you should arrive at the following expression:
\begin{equation}
(1-R)-\int_{R-k}^1G(\theta)\mathrm d\theta.
\end{equation}
Add and subtract $k$ to obtain:
\begin{equation}
(1-R+k-k)-\int_{R-k}^1G(\theta)\mathrm d\theta = (1-(R-k))-k-\int_{R-k}^1G(\theta)\mathrm d\theta.
\end{equation}
Observe that $(1-(R-k))=\int_{R-k}^1(1)\mathrm d\theta$. Substitute that in and collect terms, you'll get the RHS expression.


So Lets use a present value Hamiltonian here:

$H=e^{-pt}u(c)+\lambda(\dot k)$

FOC:
wrt c: $0=e^{-pt}u'(c)-\lambda$

wrt k: $-\dot\lambda=\lambda[(1-\tau)r -g]$

Take the FOC from consumption and differentiate wrt to time:

$\dot\lambda =-\gamma c^{-\gamma-1}\dot c e^{-pt+gt(1-\gamma)}e^{(1-\gamma)v(n)}+c^{-\gamma}e^{-pt+ gt(1-\gamma)}e^{(1-\gamma)v(n)}[(1-\gamma)(g+v'(n)\dot n)-p]$

Then substitute back in the FOC for consumption:

$\dot\lambda =-\gamma c^{-1}\dot c\lambda +\lambda[(1-\gamma)(g+v'(n)\dot n)-p]$

Then substitute this guy into the Foc for capital:

$g-(1-\tau )r=-\dot c/c\gamma+(1-\gamma)[g+v'(n)\dot n]-p$

leading to:

$r(1-\tau)=p+(\dot c/c +g)\gamma+(1-\gamma)[-v'(n)\dot n] $


risk aversion and convexity of indifference curve

It would seem that both options are correct given the specific mean-variance utility function.
Use $\mu$ to denote the expected value. In the $(\sigma,\mu)$-plain, an indifference curve representing a particular utility level $\overline U$ is given by
\begin{equation}
\overline U=\mu-\frac12 A\sigma^2.
\end{equation}
Applying implicit differentiation, we can obtain the slope of the indifference curve to be
\begin{equation}
\frac{\partial \mu}{\partial \sigma}=A\sigma,
\end{equation}
which is increasing in $A$, the parameter of absolute risk aversion. This shows that option (a) is correct.
Moreover, if we measure the degree of convexity of the indifference curve by the value of its second derivative, we'd get
\begin{equation}
\frac{\partial^2\mu}{\partial \sigma^2}=A,
\end{equation}
which is again increasing in $A$. This suggests that option (b) is also correct.
This conclusion seems consistent with the graph you show: within risk aversion, the indifference curves with higher curvature are also the ones with steeper slopes.


First of all, you can differentiate between static (essentially all players move simultaneously and only once) and dynamic (essentially non-static) games.

An extensive-form game is essentially a game tree. This form of presentation makes sense when looking at games where players move sequentially. However, you could also represent a simultaneous-move game in a game tree. It just doesn't add any insights over the normal form (matrix).

Game trees are a great tool to present dynamic games such as standard sequential-move games with perfect and complete information (player 1 moves first, player 2 observes the move and reacts, and so on), and they can also be used to present games of incomplete information or games of imperfect information.

Repeated games are dynamic games in which the same static stage game is repeated multiple times. Such games are dynamic but usually not represented in extensive-game form. If the stage game is not always exactly the same, but instead the game to be played in each period depends on a state, we speak of a stochastic game. How the state transitions from one state to the other can depend on the actions played before (and pure chance). Strictly speaking, A repeated game is a stochastic game with only a single state.

I have never heard the term "evolutionary game" without "theory" following. I am not sure if there is a definition of "evolutionary games". However, I see evolutionary game theory as a subfield of game theory that deals with certain forms of dynamic games and also different underlying assumptions. In particular, there is often no "common knowledge of rationality" and often players find their "optimal" strategy by trial and error without really knowing what they are doing.


What is time inconsistency in monetary policy?

In a nutshell, time inconsistency occurs whenever a policy maker can publicly commit to a certain policy action in a non-binding way. This is an issue in several settings (commitment vs. discretion settings and, as you see, policy coordination settings). You've run across the issue of time inconsistency in the context of policy coordination across interdependent economies. One can summarize the issue as follows: I promise in $t-1$ to deliver policy action A in period $t$ but instead deliver policy action B once we arrive in period $t$.

Consider, as does the paper you cite here, a simple two-country model where the policy actions in a domestic country impact the loss function of the foreign economy and vice versa. Under certain first order conditions (laid out in the very paper you quote) there are obvious gains available to the policy makers of these nations if they are able to arrive at a coordinated equilibrium rather than the Nash equilibrium. However, in a dynamic game with no commitment device aside from reputational concerns it might be the case that one country will promise to play the coordinated equilibrium and then deviate unilaterally to the cheater equilibrium. As you can see, time inconsistency in this context means (literally) for one to be inconsistent over time with promised and realized policy actions.

Further, see Luchonacho's references in his comment. Both links are quite helpful here and themselves could serve as an answer to your question.


Should free market consumers have the maximum information easily available?

There is an argument to be made that markets work better if there is as little information asymmetry between buyers and sellers as possible. In fact this is so basic insight that you will see it mentioned in pretty much any economics 101 textbook, for example see Mankiw Principles of Economics chapter on asymmetric information.  This is in fact the economic rationale for why modern product packages come with such a cornucopia of information about the content of a product you buy (especially when it comes to food).
However,  in the example above signaling and providing information is essentially costless (companies usually already know what they put into their products - and labels are orientational which is accurate enough - its not that every package of cereal is examined in lab individually). When it is very costly to determine how exactly the goods are produced, the case is less clear cut (it would depend on empirical comparison of cost & benefits). For example,  due to complex supply chains company in US subcontracting to China might not necessarily know about conditions of subcontractor. Requiring all firms by law to have full and complete monitoring of all supply chains might lead to costs that potentially outweigh the benefit of such regulation (again this would require some empirical investigation).
In addition, while it is completely true that:

Obviously companies won't advertise the fact they use slave labour voluntarily

the converse does not hold. Firms have incentive to advertise that they do not use slave labor and so on and hence why so many firms pay money to external auditors to get the privilege of  putting 'fair trade' or 'bio' labels on their products.
This does not mean that government regulation of such labels could not potentially be welfare enhancing. That would require further investigation of particular case, it just means it is not necessary a priori without any further investigation to assume it necessarily requires additional regulation (although my guess is you could probably justify it in non-trivial number of cases after empirical investigation).