Let's define $C_k$ such that:
$$
\mathbb{E}(y_{t+k}|y_t) = C_k y_t.
$$
Then:
$$
\begin{align*}
\mathbb{E}(y_{t+k+1}|y_t) &= \phi_1 \mathbb{E}(y_{t+k}|y_t) + \phi_2 \mathbb{E}(y_{t+k-1}|y_t),\\
&= \phi_1 C_k y_t + \phi_2 C_{k-1} y_{t},\\
&= (\phi_1 C_k + \phi_2 C_{k-1}) y_t
\end{align*}
$$
This gives us the following recursive second order difference equation:
$$
C_{k+1} = \phi_1 C_k + \phi_2 C_{k-1}.
$$
Or, updated one period:
$$
C_{k+2}- \phi_1 C_{k+1} - \phi_2 C_k = 0.
$$
This is a second order homogeneous difference equation, which is of the form $C_k = \alpha a_1^k + \beta a_2^k$. Computing $a_1$ and $a_2$ can be done by solving the following characteristic function:
$$
(a^2- \phi_1 a - \phi_2) = 0
$$
This gives the following two roots:
$$
a_1 = \frac{\phi_1 + \sqrt{\phi_1^2 + 4 \phi_2}}{2} \text{ and } a_2 = \frac{\phi_1 - \sqrt{\phi_1^2 + 4 \phi_2}}{2}.
$$
So in general we have:
$$
C_k = \alpha a_1^k + \beta a_2^k
$$
To find $\alpha$ and $\beta$, we need two starting values, say $C_0 = 1$ and $C_1 = \phi_1$. In other words, we assume that $\mathbb{E}(y_t|y_t) = y_t$ and $\mathbb{E}(y_{t+1}|y_t) = \phi_1 y_t$.
This gives the following two conditions:
$$
\alpha + \beta = 1\\
\alpha \left(\frac{\phi_1 + \sqrt{\phi_1^2 + 4 \phi_2}}{2}\right) + \beta \left(\frac{\phi_1 - \sqrt{\phi_1^2 + 4 \phi_2}}{2}\right) = \phi_1.\\
$$
Solving this system in terms of $\alpha$ and $\beta$ gives:
$$
\beta = \frac{\sqrt{\phi_1^2 + 4 \phi_2} - \phi_1}{2 \sqrt{\phi_1^2 + 4 \phi_2}}\\
\alpha = \frac{\phi_1 + \sqrt{\phi_1^2 + 4 \phi_2} }{2 \sqrt{\phi_1^2 + 4 \phi_2}}
$$
This gives the following closed form expression condition:
$$
\begin{align*}
\mathbb{E}(y_{t+k}|y_t) &= C_k y_t,\\
&=\left[\begin{array}{ll} &\frac{\phi_1 + \sqrt{\phi_1^2 + 4 \phi_2} }{2 \sqrt{\phi_1^2 + 4 \phi_2}}\left(\frac{\phi_1 + \sqrt{\phi_1^2 + 4 \phi_2}}{2}\right)^k\\
+ &\frac{\sqrt{\phi_1^2 + 4 \phi_2} - \phi_1}{2 \sqrt{\phi_1^2 + 4 \phi_2}} \left(\frac{\phi_1 - \sqrt{\phi_1^2 + 4 \phi_2}}{2}\right)^k\end{array}\right] y_t
\end{align*}
$$


Which institutions are in the eurodollar market?

Eurodollars are, by definition, held (on the liability side) inside the banking system. They're US dollar deposits held either outside the US or inside the US via an International Banking Facility. On the asset side, eurodollars are typically lent by nonbank financial institutions. This means that the eurodollar market links the two segments of financial markets: it's typically nonbanks providing short-term funding to banks.

For an introduction to nonbank financial intermediation, I'd recommend "Shadow Banking" (Pozsar, et. al., 2010).


How long do stock markets usually take to process complex new public information?

I used to work for a company called Value Line, which is noted for its stock ranking system. Through a number of tests, its statistics department came to the conclusion that it took up to six months for new information (e.g. earnings) to be reflected in stock prices. So they introduced a time decay factor that would reduce the value of information to zero over a six month period in calculating their rankings.


Models for online markets with reputation system

I would suggest you start by looking at

  C. Dellarocas. "The Digitization of Word-of-Mouth: Promise and
  Challenges of Online Reputation Systems". Management Science 49
  (10), October 2003, 1407-1424.

for a review of relevant literature and

  Friedman & Resnick "The Social Cost of Cheap Pseudonyms". Journal of
  Economcs and Management Strategy. 10 (2), 173–199.

and

  "Sustainable Reputations with Rating Systems," 2011. Journal of
  Economic Theory, 146, 2, 479-503

for some models of online reputation systems that comes to mind. If I think of any others, I will update this answer.


Probably this question is better placed at stackoverflow. Technically, in order to predict out of the sample, you need the full set of variables in the estimation. So after carrying out the estimation, you could do something like this. I assume your last observed year is 2010.

* expand US data for the last observed data point.
expand 20 if country == "US" & year == 2010
bys country year: replace year = . if _n > 1
bys country (year): replace year = year[_n-1] if year == .
estimates restore panel_estimation
predict outcome_var
* check whether that worked
tw line outcome_var year if country == "US"

This will predict a value based on your panel estimation also for the newly created observations. I am not judging whether it makes sense to extrapolate a time-trend over three years to twenty years ;)


What are some results in Economics that are both a consensus and far from common sense?

The principle of comparative advantage

As Paul Samuelson (1969) put it:

  thousands of important and intelligent men ... have never been able to grasp the doctrine [of comparative advantage] for themselves or to believe it after it was explained to them.

Example

  Imagine that an American worker who devotes all his time to soybean production can produce up to 100 tons of soybeans per year. And if he devotes all his time to steel production, he can produce up to 4 tons of steel per year.

  In contrast, the corresponding figures for a Chinese worker are 30 tons of soybeans or 3 ton of steel.

Maximum possible production

          American  Chinese
Soybeans     100      30
Steel         4        3

A layperson could reason:

  An American worker is literally more productive than a Chinese worker at everything. So why aren't we simply producing all of our own soybeans and steel?

  Instead, we're doing the foolish thing of importing steel from China!

This reasoning is "common sense". It is also wrong.

Although the American worker is "better at everything" (we say he has the absolute advantage in producing both soybeans and steel), the Chinese worker has the comparative advantage (CA) in producing steel. This is because by producing 1 ton of steel, the American forgoes 25 tons of soybeans, while the Chinese forgoes only 10 tons.

And so, by the principle of CA, the American should focus on producing soybeans and the Chinese on producing steel. The two can then trade to mutual benefit.

Numerical example:

Say that without trade, the American spends a quarter of his time producing steel and the rest producing soybeans. The Chinese spends half his time on each. Hence:

1. Consumption without trade

          American  Chinese
Soybeans     75       15
Steel         1       1.5

But they can do better by specializing and trading. The American, whose CA is in soybean production, should specialize in soybeans. And the Chinese, whose CA is in steel production, should specialize in steel.

2. Production after specialization but before trade

          American  Chinese
Soybeans     100       0
Steel         0        3

The American can then trade, say, 20 tons of soybeans for 1.2 tons of steel. End result:

3. Consumption after specialization and trade

          American  Chinese
Soybeans     80       20
Steel        1.2      1.8

Comparing Scenarios #1 and #3, we see that with specialization and trade, both the American and Chinese workers are strictly better off.  Remarkably, each gets to consume more of both soybeans and steel than they did without trade.

Thus, even though the American is "better at everything", the principle of CA offers a powerful rationale for why he should still import steel from China and be "dependent" on the Chinese worker.


An important field in current research is the yet unexplained

Equity premium puzzle

originally published by Mehra, Prescott (1985). Considere a multiperiod investment consumption equilibrium model (CCAPM) with its important result:
$$E_t\left[m_{t,j}\right]=\frac1{\left(1+R_{F,t+j}\right)}$$
where $E_t\left[m_{t,j}\right]$ donates the expected value of a stochastic discount factor (sometimes also referred to as a pricing kernel) and $R_{F,t+j}$ a riskless rate of return.

The model states, that the maximized Sharpe-Ratio $SR_{max}$ can be represented as the ratio of the standard deviation of the optimal stochastic discount factor $\sigma_{m^*}$ to its mean:

$$SR_{max}=\frac{\sigma_{m^*}}{\overline m}$$

Linking this result with common time separable power utility function shows, that the above equation is approximately the risk-aversion coefficient times the standard deviation of the logarithm of consumption.

The problem

The average risk premium of the market measured in units of risk is far too high to be explained by any consumption-based representation of the stochastic discount factor. As Cochrane(2001) notes, the Sharpe ratio measured in real terms has been about 0.5 on the basis of the past fifty years (in the US). This implies, that investors are very risk averse, with a coefficient of risk aversion at least 50.

What does that number mean? Suppose an individual faced with a 50-50 gamble of doubling or halving his savings. With a level of risk aversion of 50, he would pay 49% of his savings to avoid the loss of 50%. This individual would forgo a 50% chance of doubling his money and accept a certain loss of 49$ to avoid losing an additional 1% more.


How will asteroid mining impact the economy?

I doubt that asteroid mining will hugely increase ROI. Price is endogenous so it will fall as a response to increase in supply and hence ROI will fall.

Assuming that space mining is not natural monopoly, or will not be monopolized by government it will decrease the price of those metals by shifting supply to the right in their individual markets (as mining them from space would not be done by profit seeking firms if it is cheaper to do on earth).

Decrease of price in these resources will also decrease the prices of goods that use these metals as inputs shifting supply of those goods as well.

Assuming this will happen for large enough number of markets it can also shift the whole aggregate supply in the economy. This means that the aggregate output will be higher at a lower price level (see the picture below). It will also raise welfare of consumers primarily in the main industries affected by the lower prices of those resources but also throughout the whole economy.


What does long-run level mean for exchange rate

The long-run in economics is a technical term. It means, roughly "without any short-run constraints". What are short-run constraints? Well they're fixed costs like any contracts you've signed (like, say, your lease, your employment contract) and any capital that you've accrued or lack would be short-run constraints.

To give an illustrative example, a barbershop may want to increase profits and considers potential options. In the short-run he can increase the prices of haircuts or decrease his hours of operation. In the long-run he can move to another location where he'll have more room for additional chairs and such.

For currency exchanges, I'd imagine fixed costs would include trade contracts and debt. At any rate hopefully this answers your question.

edit: and "level" in this context just means the exchange rate itself. Since it is numeric, it can be said to have a level. You could change the word 'level' for 'rate' and it'd be the same meaning.


Interpretation of the Cross Partials of the Cobb-Douglas

The interpretation of the cross partial here is the change in the return (or marginal productivity) of labor when capital increases marginally. Similarly, it can be interpreted as the change in the return of capital, when labor increases marginally.

We often only want to interpret the sign of the cross-partial and not the exact value. Here we see that the productivity of one factor increases with the other factor. Interpreting the exact value is more difficult, but also not really interesting for most economic applications.

Furthermore, it is not correct to say that the return to labour increases as $\frac{1}{K^a}$ with capital. How did you arrive at this conclusion?


In panel data application, when using Fama and MacBeth regression is preferable over the fixed or random effect model? thought

I cannot precisely answer your questions because I do not know which exactly regressions you want to perform as @jmbejara says and which papers are you referring to that use Fama-MacBeth regression. Are they on financial or other literatures? I haven't seen Fama-MacBeth on other literatures (I do not follow any other literature to be exact), so please post the papers. Obviously, if in other literatures one can justify the analogy of the risk-premia concept, Fama-MacBeth can be applied there, too.

I answer your three main questions in reverse.

3. It would be very kind of you, if you guide me through a link or book dealing whit this subject?

If you are interested in financial panel data, there are plenty of resources to consult. Some are:

The amazing book of Bali, Engle, and Murray (2016). "Empirical Asset Pricing: The Cross Section of Stock Returns", because it explains the Fama-MacBeth procedure (among others) step-by-step and I find it the most important of all the resources (ToC available here).
For more information on the standard errors, Petersen (2008, published in the RFS) with his article "Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches" (it also seems available online here) compares different approaches and highlights their intricacies. This paper is crucial for any financial panel data research paper!
Goyal (2012) in "Empirical cross-sectional asset pricing: a survey" also explains the Fama-MacBeth approach with different applications.
Chordia, Goyal and Shanken (2015) in "Cross-Sectional Asset Pricing with Individual Stocks: Betas versus Characteristics" because it has an extensive discussion for the Errors-in-Variables problem of the Fama-MacBeth procedure.
Jagannathan, Skoulakis and Wang (2010) (also a draft) contains more "mathematical/econometric" formalization.

2.  In Fama and MacBeth regression can individuals under study be different in different time periods?

Yes, and this is one of the reasons that Fama-MacBeth is appealing, since you can run it on unbalanced panel datasets. In a balanced panel, every individual has data for the same/every time period, while in an unbalanced this is not a requirement.

1. In panel data application, when using Fama and MacBeth regression is preferable over the fixed or random effect model? Is there a statistical test shedding light on this issue?

Usually, in finance, a fixed effect concerns a firm effect (dummy for firms), while Fama-MacBeth is designed to account for a time effect (Petersen (2008)).
Random effects are rarely used in the financial literature (Petersen (2008)). As he says: "When the residuals of a panel regression are correlated, not only OLS standard error estimates are biased but also the coefficient estimates are inefficient (the estimates do not exploit all of the information in the data). Researchers can improve efficiency by estimating a random effects model using a GLS approach."

To sum up:

I find Fama-MacBeth appealing for accounting for time-effects (it's easy to calculate time-varying betas, for example)
it has easy intuition for the financial literature, and
it can be applied to unbalanced panels.

People use the Hausman test to decide between fixed/random effects models, but I find the intuition and justification of the choice of the proper model more appropriate. I am unaware for a specific test which includes Fama-MacBeth but I am far from an expert in the field.


Understanding a multi-player Tragedy of the Commons game

what does  exactly represent? Is a threshold?

Yes, $n$ is the threshold above which the benefit $B$ realizes. Think of this as a situation where a public good with benefit $B$ is provided only if more than half of the population votes for it. $C$ is the cost of voting, and $n=\lceil\frac12N\rceil$ is the smallest integer greater than half of the population size ($N$).

  Why would rational players prefer everybody to cooperate?

While a rational player would choose $\mathbf{D}$ regardless of what others would choose, he/she would still prefer the outcome with benefit $B$ to the outcome with $0$ benefit. Hence, he/she would prefer everyone else chooses $\mathbf{C}$, i.e. bearing the cost of providing benefit $B$, while he/she enjoys $B$ without incurring any cost by choosing $\mathbf{D}$.

Additionally, suppose there are $N$ players, and that $n<N-1$. Then with all the other $N-1$ players playing $\mathbf{C}$, it doesn't really matter if the remaining player chooses $\mathbf{C}$ or $\mathbf{D}$. So arguably it's less morally objectionable for the last player to choose $\mathbf{D}$.


A paper just out of the oven provides a very comprehensive analysis of market power in the US for more than 50 years, using mark-up data from three different sources. The key graphs below:


GDP simple question got me confused: the sale of a capital asset

No, the sale of a capital asset doesn’t count in GDP, as the cost of the asset was already accounted for when the plane was first sold to Delta. To your second point, if a broker somehow provided a service by facilitating the sale, that would count towards GDP, but the sale itself would not.


Determinants of economic growth in ARDL model - nominal or real variables?

My experience is that most of the papers estimating these sort of regressions use real variables, all of them deflected with the same index. As Roy says, you not want to confound an effect by inflation.

For example, assume the "true" model is that with variables in real terms:

$$ Y_t = \beta_0 + \beta_1 X_t $$

Converting into nominal variables, you get:

$$ Y_tp_t = \beta_0 p_t + \beta_1 X_tp_t $$

Then, a correct estimation of the "true" model when using nominal variables would require you to add prices as a regressor (or inflation if using log of differences). Thus, you have a further robustness check of your model by estimating it in nominal terms and adding inflations as a regressor.

Someone could rightly ask, what if the "true" model is in nominal terms? That is slightly odd though. Such model would be something like

$$ Y_tp_t = \alpha_0 + \alpha_1 X_tp_t $$

But say that there is a change in $p_t$ and in $X_t$ such that $X_tp_t$ remains unchanged. And yet, $Y_tp_t$ would change because of the change in $p_t$, withouth any right-hand side variable changing - a clear inconsistency.


Autonomous or non-autonomous optimal control system?

What about rewriting the problem in the following way?

$$\underset{\left\{ c_{t}\right\} }{max}\int_{t=0}^{\infty}\left[u\left(c_{t}\right) e^{y_t}\right]e^{-\rho t}dt$$

with the new state variables defined as

$$\begin{align}
\dot{k_{t}}=f\left(k_{t}\right)-c_{t}\\
\dot{y}_{t}=-h\left(k_{t}\right)
\end{align}$$

given the initial conditions $(k(0),y(0))=(k_0,0)$.


We start with a production function: $f(k,l)$, which tells us what quantity will be produced if we use $k$ units of capital and $l$ units of labour. Suppose that we cange that quantity of capital by $dk$ units and change the quantity of labour by $dl$ units. If this change is chosen so that we stay on the same isoquant then it must be that the total production doesn't change:

$$\frac{\partial f(k,l)}{\partial k}dk+\frac{\partial f(k,l)}{\partial l}dl=0.$$

Rearranging, we get

$$\frac{dk}{dl}=-\frac{\frac{\partial f(k,l)}{\partial l}}{\frac{\partial f(k,l)}{\partial k}}.$$

This is the marginal rate of technical substitution, the slope of the isoquant. It has the same interpretation as any other slope. It means that if I increase labour by one unit then I can decrease capital by $$\frac{\frac{\partial f(k,l)}{\partial l}}{\frac{\partial f(k,l)}{\partial k}}$$ units.

Example Suppose we have a Cobb-Doublas production function: $f(k,l)=k^a l^{1-a}$. We have

$$\frac{\partial f(k,l)}{\partial k}=ak^{a-1}l^{1-a}$$

$$\frac{\partial f(k,l)}{\partial l}=(1-a)k^{a}l^{-a}$$

$$MRTS=-\frac{(1-a)k^{a}l^{-a}}{ak^{a-1}l^{1-a}}=-\frac{1-a}{a}\frac{k}{l}.$$

Now we can plug some numbers in to this example to see how it works. Suppose $a=1/2$, and we currently have $k=4$ and $l=1$. Then, we have

$$MRTS=-\frac{1/2}{1/2}\frac{4}{1}=-4.$$

So, for each unit increase in the quantity of labour employed, we can decrease the quantity of capital employed by 4 units.

This works backwards too, so every unit decrease in $l$ would demand a 4 unit increase in $k$ to keep us on the same isoquant.


For linear quadratic approximation of RBC model, why does matrix $P$ of value function $V = F^TPF$ has to be negative semi-definite matrix?

P being negative semi-definite would imply that V is a concave function. The reason you would restrict P so that V would be a concave function is because of some of the assumptions you've made about about the model previously tell you that V must be concave.

In general, some of the typical assumptions that imply that the value function must be concave are something like the following:

the graph of the constraint correspondence is convex,
the period return function is concave,
other assumptions about the stochastic transition function having the Feller property and being monotone,
etc...

Sorry I'm not giving the full details, but you can read more about them in chapters 4 and 9 of "Recursive Methods in Economic Dynamics" by Stokey, Lucas, and Prescott. The point that I'm making is that the assumptions of these kinds of models usually imply that the value function is concave. Therefore, if you check the assumptions and they indeed do so restrict the value function, then you can restrict your search to look only for matrices P that are negative semi-definite.


When action and strategy differ in game theory

If you happen to know that the "normal form" is sometimes also referred to as the strategic form, you'd most likely not be surprised that it doesn't help you distinguish between the notions of action and strategy. The normal form is precisely used to represent strategies (not actions) in a game. To appreciate the difference between strategies and actions, it's probably best to consider another form of game representation: the extensive form.

Suppose 2 players move sequentially, and that Player 2 observes Player 1's choice before making his decision. The scenario can be represented using a game tree as follows:

Here we can call $\{A,B\}$ Player 2's actions (actually the correct jargon here is behavior strategies, but I sense that this level of nuance is unnecessary at this point). However, they are not his strategies, for strategies in this case is a "full contingent plan" that specifies an action at each information set the player moves. Since Player 2 moves at two information sets (one after $L$ and the other after $R$), so one of his strategies would be

  "choose A if Player 1 chooses L and choose A if Player 1 chooses R", or simply denoted as AA.

So, Player 2 has four (pure) strategies: $\{AA, AB, BA, BB\}$. In comparison, since Player 1 only moves at one information set (at the beginning), her actions and strategies are identical: $\{L,R\}$.

To represent this game using the normal/strategic form, we'd have

It's not a 2-by-2 game, but 2-by-4, precisely because strategies and actions are not the same.

Lastly, a note on Prisoners' Dilemma (PD) and other similar one-shot simultaneous-move games. If you consider the extensive form of PD, you'd see that each player moves at only one information set, and so their set of actions and set of strategies coincide (just like Player 1 in the above example). This is why you can use the two terms interchangeably in those games.


Why would a natural monopoly lose money when MC=P, but a competitive firm would get positive accounting profit?

I found the answer in "Intermediate Microeconomics" by N. Gregory Mankiw.

  When a firm’s average-total-cost curve continually
  declines, the firm has what is called a natural monop-
  oly. In this case, when production is divided among
  more firms, each firm produces less, and average total
  cost rises. As a result, a single firm can produce any
  given amount at the smallest cost.

...

  By definition, natural
  monopolies have declining average total cost [due to economies of scale, I suppose]. As we first discussed in Chapter 13, when average total cost is declining, marginal cost is less than average total cost. This situation is illustrated in Figure 10, which shows a firm with a large fixed cost and then constant marginal cost thereafter. If regulators were to set price equal to marginal cost, that price must be less than the firm’s average total cost, and the firm would lose money. Instead of charging such a low price, the monopoly firm would just exit the industry.

From other book:

  If demand is large relative to the minimum efficient scale, a competitive market is likely to result. If it is small, a monopolistic industry structure is possible.

Of course there must be the point where MC=ATC, but if the demand will ever become big enough to go beyond this point, then it will probably mean that our natural monopoly isn't natural anymore, that it makes sense to (re)introduce competition because now we have diseconomies of scale. Although it can be exactly MC=ATC, but it will be just coincidence and as such is unlikely.


That's an entertainingly specific question to ask! I don't know the answer, but my thoughts are this.
You're looking at an aggregate demand curve, which is a result of all the demand curves of individuals in this economy. Now, individual demand curves are fairly easy to understand. Each individual takes prices to be fixed, and then they maximise utility. When the price changes, for instance because the economy moves from point P1 to point P2, everyone adjusts their consumption behaviour. How much they'll change their consumption is then a question of their utility functions, and hence is specific to the product and to the economy.
So, this is my answer: I think either could be true, it just depends on the product, prices, and utility functions.


According to the U.S., what constitutes as fair subsidies?

One potential approach to this question would be to look at the agreements made under the WTO, of which both China and the US are members.

According to the WTO there are two different categories of non-allowable subsidies.

  Prohibited subsidies... require recipients to meet certain export targets, or to use domestic goods instead of imported goods. They are prohibited because they are specifically designed to distort international trade, and are therefore likely to hurt other countries’ trade.

There are also "Actionable subsidies" which are not permitted if the complaining country can show that these subsidies cause damage.

  The agreement defines three types of damage they can cause. One country’s subsidies can hurt a domestic industry in an importing country. They can hurt rival exporters from another country when the two compete in third markets. And domestic subsidies in one country can hurt exporters trying to compete in the subsidizing country’s domestic market.

Both the US and China have brought complaints about each other's subsidies to the WTO in the past. However the present US administration has expressed a lot of mistrust towards all forms of multilateral institutions including the WTO. By taking unilateral action instead, the US effectively dodges the question of defining fair versus unfair trading practices in a  clear and rational way.


Estimating the rental rate of capital from data

Time series on rental price of capital can be estimated using $$r=\frac{P_k}{P}(i-inf+\delta)$$
here, $P_k$ is the price of capital goods (price index for capital goods), $P$ is a deflator, $i$ is nominal interest rate, $inf$ is an inflation rate and $\delta$ is depreciation rate of physical capital stock.


Transforming an indirect utility function into an expenditure function

There is no error in your calculations. The problem is with the indirect utility function that you were given.

An indirect utility function should satisfy $v(\alpha p_1,\alpha p_2,\alpha y)=v(p_1,p_2,y)$. In other words, if income goes up and prices go up by the same factor then everyone is as well off as they were before.

Unfortunately, in this case $v(\alpha p_1, \alpha p_2, \alpha y)= \frac{1}2\alpha^2\frac{y^4}{p_1p_2}$


Which foreign workers in USA who send remittances to family are getting the best bang for their buck?

A good start would be The Economics of Migrants' Remittances by Hillel Rapoport and Frédéric Docquier. They both work extensively on this topic. In this paper, they review the  theoretical  and  empirical  economic  literature  on  migrants' remittances.

They review six theories decomposed into two broad categories individualistic motives (altruism, exchange, inheritance, and the strategic motive) and two types of familial agreements (on insurance and investment).

In all of these six theories, except one, migrant's income is indeed a very good predictor of remittances. However, other motives matter and may differ across "foreign national workers grouped by country of origin". For instance, some societies are more altruistic than others, and assuming  that  altruism  decreases  with  time  of arrival, the size of remittances should be negatively related to this variable in the altruistic case.

They also predict contrasting effects concerning the distance from family. For instance, in the inheritance theory, the amounts remitted are expected to be closely related to the probability of receiving inheritance in the origin country. If, as they assume there is a negative correlation between the distance from family and the probability of receiving inheritance, a Mexican worker will remit more than an Ethiopian worker, other things being equal. This could even be true if the Ethiopian worker has "the most income per capita after living expenses".

To sum up, migrant's income is a crucial variable but other variables, which may differ by country of origin, may also be of first-order importance to understand remittances.


Ranked choice preference with ties - Arrow's Impossibility Theorem

Allowing indifference will not solve the problem of the effect of the independence of irrelevant alternatives (combined with the unanimity and transitivity requirements).
You have said $b >_1 c$ and $c >_2 b$ should lead to $b =_s c$
Now consider  $a >_1 b$ and $a >_2 b$, which should lead to  $a >_s b$ by unanimity

so $a >_1 b >_1 c$ and $c >_2 a >_2 b$ should lead to  $a >_s b =_s c$ by transitivity
and thus $a >_1  c$ and $c >_2 a $ should lead to   $a >_s c$ by the independence of irrelevant alternatives

And also consider  $c >_1 a$ and $c >_2 a$, which should lead to  $c >_s a$

so $b >_1 c >_1 a$ and $c >_2 a >_2 b$ should lead to   $b =_s c >_s a$
and thus $b >_1  a$ and $a >_2 b $ should lead to   $b >_s a$

Combining these means $b >_1 a >_1 c$ and $c >_2 a >_2 b$ should lead to $b >_s a >_s c$

but that implies $b >_1 c$ and $c >_2  b$ should lead to $b >_s  c$

inconsistent with your $b >_1 c$ and $c >_2 b$ leading to $b =_s c$


Is there a name for this type of problem?

I take from your comments that you are interested in airline seating prices.

The subject of airline pricing is very complex:

There are different seating classes at different sizes, where the offered quantities vary over time
There is overbooking, because more expensive tariffs allow "last second changing" into and out of a specific flight, and companies try to accommodate for that
Demand for the same flights vary with season and even day of the week. Typical example: There is higher demand on short distance flights for Thursday Evening/Friday Afternoon and Sunday night / Monday morning flights
Elasticities vary with the distance: The more short term flights are being booked, the "more desperate" customers are, and the higher the faires are that companies can charge them. However, at the "last minute", the companies potentially become "desperate" to fill seatings themselves, and offer low prices themselves

I remember sitting into one, two lectures on this when a professor of Business Administration was treating the subject. The elasticities part of could equally well be treated by Economists, but most who look at the subject are BAs involved with logistics and similar - I would refer you to look for their literature (I have none at hand) for more detailed information.


Difference between shocks, innovations and disturbances

In Greene "Econometric Analysis" the disturbance of linear regression,
$$\epsilon_t = y_t - \mathbf{x_t}\boldsymbol{\beta}$$

is estimated with the residual,
$$e_t = y_t - \mathbf{x_t b}$$

In the text, disturbances $\epsilon_t$ are also called innovations. Qualitative events in an economy that impact a process or model's variables or error term are shocks.


How does high U.S. federal debt affect its citizens?

Rather than have a long comment thread, I will give a partial “answer” here.(Really a direction on how to ask a new question, or what existing questions to search for.)
The first thing to note is that this is a broad question, and hard to answer. The other thing is that answers can easily veer into opinions. Questions of this form are often closed.
The preferred format would be to ask about the linkage of debt levels to one topic of concern. The most common seem to be as follows (“it”=high debt levels).

Does it need to be paid back?
Does it imply a risk of default?
Will It cause GDP growth to slow?
Will it raise inflation?
Will it cause the currency to fall in value?
Will it cause interest rates to rise?

Each one of these is a somewhat complicated question, and it would be best to look at existing questions, and see whether they match your interests.
To what extent I can offer an answer, the safest general statement is that nothing has to happen immediately - Japan providing a data point (or even the US after World War II). Beyond that, you need to ask something more specific, as too general answers turns into opinions.


Fair voting procedure when there are many issues

That's interesting: the flavor of the frequentist approach to probability used for a socio-political fairness criterion: if my measure as a population group is $0<p<1$, and known, then my opinion should be accepted by the whole at the same measure, as number of issues goes to infinity. In other words, current observed acceptance rate should be a consistent estimator of theoretical acceptance rate, and equal to my measure.

Then it is very easy to create such a decision rule, while saving public money: no need to hold one referendum after another, just construct a die, with as many sides as there are "uniform groups", with the die's weight distributed in such a way that the side representing uniform group $i$ will have probability of turning up equal to $p_i$. It won't be difficult to construct, and publicly and objectively test it for the desired properties.

Then, wherever an issue comes up for voting, just roll the die. And ok, spend some money for a suitable public ceremony.

Whenever there is a census, the relative size of each uniform group can be re-measured and a new die can be constructed.

Why do I have the feeling though that no uniform group is likely to ever accept such a scheme?

(This of course puts aside the importance of each issue, in general, for each uniform group, etc, but I took that from the OP which concentrates on number of issues, irrespective of what the issues are about, and to whom they matter and how much they matter, and how do we measure that etc).


Consider:

Proposer offers $0$
Receiver always rejects the offer regardless of the amount

You should be able to argue that this is a pair of mutually best responding strategies for $T=1$. The $T>1$ cases follow a similar logic.


The process of printed money reaching the government?

1) The phrasing you use is somewhat non-standard, but it seems close to the correct view.

The U.S. Treasury borrows by issuing bonds. What people loosely call “printing money” (a badly defined phrase) is that the Federal Reserve buys those bonds from their owners. The original owners of the bonds “lent” the Treasury the money, and the Fed just takes the loan of their hands. The Fed pays for the bond by creating a deposit at the seller’s bank (the central bank is a bank which takes deposits from private banks), and that deposit is considered to be “money” (technically, part of the monetary base).

The Treasury owns the common equity of the Federal Reserve, so to a certain extent, it is one arm of the government dealing with another.

There are plenty of questions on here that discuss “quantitative easing” and give longer explanations.

2) The Fed buys and sells bonds in the market, so it is a market rate.


What does the sun product of price times quantity divided by average price

Note that $Q_i P_i$ is the total revenue from good $i$. So dividing total revenue from all goods by the amount produced of all of them should give us something like "average revenue per item produced"?


What is meant by the sentence in the context of "Monetary Policy in India"?

From the first Google hit I got, The tools of macroeconomic policy—a short primer:

Macroeconomic policy is concerned with the operation of the economy as a whole. In broad terms, the goal of macroeconomic policy is to provide a stable economic environment that is conducive to fostering strong and sustainable economic growth, on which the creation of jobs, wealth and improved living standards depend. This brief outlines the nature of each of these policy instruments and the different ways they can help promote stable and sustainable growth.
[...]
Fiscal policy operates through changes in the level and composition of government spending, the level and types of taxes levied and the level and form of government borrowing. Governments can directly influence economic activity through recurrent and capital expenditure, and indirectly, through the effects of spending, taxes and transfers on private consumption, investment and net exports.
[...]
Monetary policy decisions are implemented by changing the cash rate (the interest rate on overnight loans in the money market).
[...]
By changing the cash rate the RBA is able to influence interest rates across the financial system. Changes in interest rates in turn can influence economic activity by affecting savings and investment behaviour, household expenditure, the supply of credit, asset prices and the exchange rate.
[...]
Exchange rate policy is concerned with how the value of the domestic currency, relative to other currencies, is determined.
[...]


What is the difference between comma and plus in the bellman equation?

You should be careful about the way you wrote your two equations because the $\max$ operators are different. In the first equation, you maximize an objective function on a set, meaning you look for the best value of $y$ given that $y$ belongs to a known set. You did not define this set. In the second case, you choose the maximum among two values. Contrary to the first equation, $y$ is predefined and is not a parameter to find given your notations.

If I abstract from the notation mistakes, I think you want an example to understand the difference between a classical cake-eating problem (your first equation) and a stopping-rule problem (probably your second equation).

Consider the following framework. Time is discrete. There is one good in the economy.
We are interested in the problem of a consumer.
At each period $t$, the consumer has access to a stock of good $x_t$. She faces a standard inter-temporal saving problem; she has to decide how much to consume, $c_t$, and how much to save for the next periods, $x_{t+1}$.
The consumer enjoys a flow utility $u(c_t)$ and discounts future consumption with a factor $\beta$.
To close the model, a saving technology must be defined. We can consider two different cases:

(i) There is an interest rate $r$. The consumer can freely withdraw any amount from the saving account.
(ii) There is an interest rate $r$. The consumer, however, cannot withdraw a quantity of good without closing the saving account.

Let's write the optimization problem in the two cases:

(i) $$V(x_t)=\underset{0\leq x_{t+1}\leq (1+r)x_t}{\max} \{u((1+r)x_t-x_{t+1})+\beta V(x_{t+1})\}$$

(ii) $$V(x_t)=\underset{x_{t+1}= (1+r)x_t \text{ or } 0}{\max} \{u((1+r)x_t-x_{t+1})+\beta V(x_{t+1})\}$$
Consumption $c_t$ is equal to $(1+r)x_t-x_{t+1}$. We can make an analogy with what you wrote. My $x_t$ and $x_{t+1}$ are your $x$ and $y$, and $F(x,y)=u((1+r)x-y)$.
In the first case, the consumer has to choose the amount to save $x_{t+1}$ in the interval $(0,(1+r)x_t)$. In the second case, she can only choose whether to keep on saving, $x_{t+1}=(1+r)x_t$, or to close the account, $x_{t+1}=0$. By normalizing $u(0)=0$, the second case can write:

(ii) $$V(x_t)=\max \{u((1+r)x_t),\beta V((1+r)x_t)\}$$

In the first problem, the consumer eats a share of the cake (which is expanding at a rate $r$) and keeps the remaining for the next periods to maximize her inter-temporal utility. In the second problem, the consumer has to decide when to eat entirely the (growing) cake, which defines the stopping rule.


Homogeneity of degree zero and normalization

Demand $x(p, m)$ is the solution to the utility maximization problem:

$\max\limits_{x\in\mathbb{R}^n_+} \ \ u(x) \\ \text{s.t.} \ \  p\cdot x \leq m$

where $p\in\mathbb{R}^n_{++}$ is price vector, and $m$ is the income.

When we multiply both sides of the constraint in problem above by $\lambda > 0$, and look at the revised problem we get

$\max\limits_{x\in\mathbb{R}^n_+} \ \ u(x) \\ \text{s.t.} \ \  \lambda p\cdot x \leq \lambda m$

Since this operation does not affect the constraint, the solution remains unaffected i.e. demand satisfy $x(\lambda p, \lambda m) = x(p,  m) $ which shows that demand is homogeneous of degree 0 in $(p, m)$. So, this is always true for demand function. Given that $p_1 > 0$, we can take $\lambda  = \frac{1}{p_1}$, and find $x\left(\frac{p}{p_1}, \frac{m}{p_1}\right)$ to get $x(p, m)$.

It is helpful to note that for any function $f(p)$ that is homogeneous of degree $k > 0$, it is the case that $f(\lambda p) = \lambda^k f(p) \neq f(p)$ for $\lambda \neq 1$.


I feel this barely qualifies as an answer, but doesn't Shiller have house prices data on his webpage? Currently here.

Specifically:

  Historical housing market data used in my book, Irrational Exuberance [Princeton University Press 2000, Broadway Books 2001, 2nd edition, 2005], showing home prices since 1890 are available for download and updated monthly: US Home Prices 1890-Present.

I don't have much experience with this data directly, and am only aware of it through  Khandani, Merton, Lo (2013) ("Refinancing Ratchet Effect"), where they use this and many other data sources to construct a (very long) housing dataset for their simulation analysis.

Details of Case Shiller Series Construction methodology (from the end-notes of the 2006 edition for chapter 2):

  Even though there were no regularly published home price indexes
  before the 1960s, some economists were constructing indexes of home
  prices that cover most of the years since 1890. We found home price
  indexes from 1890 to 1934 and from 1953 to the present that used in
  their construction some device to attempt to hold the quality of the
  home constant.

  The nominal home price index 1890–1934 is from Leo Grebler, David M.
  Blank, and Louis Winnick, Capital Formation in Residential Real
  Estate: Trends and Prospects (Princeton, N.J.: National Bureau of
  Economic Research and Princeton University Press, 1956). It is a
  repeated-measures index based on a survey of homeowners in twenty-two
  U.S. cities, who were asked to give the value of their home in 1934
  and the date and price of the purchase of that home. Since it is based
  on repeated measures of individual homes, the series is protected, in
  contrast to the simple median price, from any bias from changes in the
  mix of houses sold or of the increasing size and quality of newer
  homes. Its shortcoming is that it depends on memories of the surveyed
  homeowners for the earlier purchase price.

  The nominal home price index that we constructed for 1934–53 is a
  simple average over five cities of median home prices advertised in
  newspapers. The cities are Chicago, Los Angeles, New Orleans, New
  York, and Washington, D.C. My students collected the data from
  microfilmed newspapers at the Yale University library, collecting
  approximately thirty prices for each city and year, except that for
  the fifth city, Washington, D.C., 1934–48, data came from a median
  price series from E. M. Fisher, Urban Real Estate Markets:
  Characteristics and Financing (New York: National Bureau of Economic
  Research, 1951). The median series for 1934–53 does not make any
  attempt to correct for home quality change, as do the indexes we use
  for the other subperiods. Improvement in home size and quality gives
  median home price an upward bias, and this is why I avoided using
  median price outside the 1934–53 interval.

  The nominal home price index for 1953–75 is the home purchase
  component of the U.S. Consumer Price Index (CPI). The Bureau of Labor
  Statistics collected data on home prices for those years for homes
  that are held constant in age and square footage. In the 1980s they
  discontinued this index when they switched to a rental equivalence
  basis for housing in the CPI. They made this change to correct what
  was considered a conceptual flaw in the housing component of the CPI:
  the CPI is supposed to be a price of consumption goods and services,
  not of investment assets. For our purposes, however, the old home
  purchase component is acceptable. There are, however, some
  shortcomings in the home purchase component, notably that it is based
  only on homes with certain government-subsidized mortgages, and the
  procedure that the Bureau of Labor Statistics used to correct for
  changes in the ceiling on these mortgages was not optimal. See J. S.
  Greenlees, “An Empirical Evaluation of the CPI Home Purchase Index
  1973–8,” American Real Estate and Urban Economics Association Journal,
  Carnegie-Rochester Conference Series on Public Policy, 17 (1982):
  203–38.

  The nominal home price index for 1975–87 is the U.S. home price index
  published by the U.S. Office of Housing Enterprise Oversight (OFHEO),
  which is available on their Web site. It is a repeat sales index, and
  thus controls for quality change. The nominal home price index for
  1987–2004 is the repeat-sales U.S. home price index produced by Fiserv
  CSW, Inc., successor to Case Shiller Weiss, Inc.

  Since 1987, the CSW and the OFHEO series have shown very similar
  patterns through time, though the sharpness of the increase is
  slightly more pronounced in the CSW series, an observation we
  attribute to the fact that our series is based only on actual sales,
  while the OFHEO series also uses both actual sales and appraised
  values as if they were sales. Appraised values are somewhat sluggish
  to respond to new market conditions.


The Oil hike of the 2000's: Did it go unnoticed, and why?

I consider the very rapid growth of infrastructure in the BRIC countries to be a strong driver of the high oil prices (as well as other building commodities) in the mid-2000s.  It takes a lot of energy to build roads, mine copper and iron, make cement, etc...

I would disagree with two of the implications in the statement: "in the 2000's we witnessed the greatest increase in oil prices ever, even when compared to the 70's oil shocks. To most of us, this fact went a bit unnoticed..."  I disagree with the comparison of the early '73 OPEC oil embargo and the oil spike in 2008, and I disagree that it went unnoticed.  This is not an apples to apples comparison.  In 1973 there were times that you could not buy gasoline.  In 2008, gasoline was always available, it was just more expensive.  And I, and all of my acquaintances, noticed it, and we complained about it, but we always had it available.  That's a very big difference to not being able to buy something crucial to your livelihood.

That being said, I would agree that increased lending in the mid 2000s and a very strong world economy may be a reason that the spike of oil prices in 2008 wasn't considered a crisis.

I would also agree that oil prices did not cause the late 2000s recession.  The recession was caused by an abrupt evaporation of interbank lending and a hasty tightening of credit.

Since you are a student of Economics (and I assume of markets), let me say something that wasn't clear to me until I spent 30 years working in investment management: the economy and markets are very different.  The economy is 7 billion people a day waking up and having to be productive to survive.  It is real, and it is very hard for any government to derail it, as hard as they might try.  I have huge faith in the economy. The securities markets, rather, are places built on fear and greed, two very intense emotions that are self-reinforcing, meaning that the more the emotion is fed, the stronger it becomes, thus feeding that emotion even more.  That is why we get bull market bubbles and bear market cliff dives that do not correlate in their magnitude with the underlying economy.

The stock market is a leading indicator of economic direction, but not of magnitude.  Keep this in mind.

Alright, sorry for the preachiness.  Good luck.


Restrictions proving quasiconcavity of utility function

Since $u$ is twice differentiable, it is quasi-concave if and only if its marginal rate of substitution declines as $x_1$ increases and $x_2$ falls. You can then compute
$$
MRS = \frac{\frac{\partial u}{\partial x_1}}{\frac{\partial u}{\partial x_2}} = \frac{1}{\gamma x_2^{\gamma - 1}} = \frac{x_2^{1 - \gamma}}{\gamma};
$$
which is increasing in $x_2$ (so quasi-concave) if and only if $\gamma < 1$. [We assume throughout that $\gamma > 0$ since $u$ is increasing.]


No, cointegration occurs when two series have the same stochastic trend. In order to have a stochastic trend, they should be nonstationary. Stationary variables do not have a trend. You can perform standard inference.


What are the economic ramifications of rent control?

Well, rent control is the classic example used in many economics textbooks when talking about price ceilings. A price ceiling is a maximum price one can pay for a good, and is set by a governing body. There are many cons to price ceilings and not many pros.

$\textbf{Pros:}$

1) Because tenants of the property know that apartments are in short supply, they will have an incentive to take good care of the place in order to stay on the renter's good side because they may not be able to get another apartment if they get kicked out of this one.

2) Tenants who get apartments will have lower rent costs and will therefore be able to spend/save more of their money. If they choose to spend it, that can boost the local economy because more money will be spent in local businesses.

$\textbf{Cons:}$

The graph above depicts a binding rent control. By this, I mean that the rent controlled price is below the equilibrium price. In this example, the rent controlled price is $1,000$ and the equilibrium price is $1,500$. What this causes is a shortage of apartments. Looking at this graph, we can see that at the price of $1,000$, $Q_D=2,100,000$ and $Q_S=1,900,000$. Using this, we can see that the shortage will be:
$$Q_D-Q_S=2,100,000-1,900,000=200,000\;apartments$$

What this means in words is that there are more people who want apartments than there are people who are willing to supply apartments. What might be the side effects of this?

1) Rationing: There are a couple of ways rationing may occur, but in the market for apartments the only way which makes sense is rationing through discrimination by sellers biases. What this means is that the renter may give the apartment to someone who doesn't value it as much as another person based on their biases.

2) Illegal activities: One thing which may occur due to rent control is under-the-table deals. Basically, people may pay the seller some money under the table to ensure that they get an apartment.

3) Homelessness or relocation: We need to look at what we mean by the quantity of apartments demanded is greater than the quantity of apartments supplied. What this means is that people who want/need to buy apartments will not be able to (in our example 200,000 people at least). What are the two outcomes of this? The first outcome would be homelessness because people cannot get apartments, and they may have nowhere else to go. The reason why this is not desirable is pretty obvious (we don't want people to have to live on the streets). The second outcome would be relocation of current residents. What this means is that people will need to move out of the area. This will hurt the local economy because less people will be spending their money in local businesses.

One last thing to keep in mind is that over time this shortage will get worse. In the short run, the sellers may not be able to take the apartment off the market. However, in the long run, sellers may decide to sell the apartment complex, which will cause the supply of apartments to decrease even more. This will exacerbate the problems I listed above.

$\textbf{Edit:}$ Another problem caused by rent controls was mentioned (quite astutely) by $\textbf{AdamBailey}$. He pointed out that landlords may not make enough money to maintain his or her rental properties, and over time the quality of such rental properties may depreciate drastically. This shows that, not only will the quantity of apartments decrease, but the quality may decrease as well. This is another perfect example of how rent controls can hurt those that it is trying to help.


How many people in the world were living below 15 dollars a day in the last decades?

Most of the "official" statistics compiled in international organisations use some thresholds like the one shown in the graph. Common for instance are the one by the World Bank (data here and report here).

Therefore, unless you find such data already computed, it is not possible to tell.

There is one imprecise alternative though. You can use this online tool to compute global poverty based on any threshold you like (using annual income in £). For example, 15 US dollars correspond to roughly to £11.64 (as of 31/08/17, 13:25 BST), which amounts to a yearly (365 days) income of £4,250, which yields:

As the FAQ explains, this analysis is based on data from the World Bank, is valid for 2008, and assumes a population of 6.69 billion. Therefore, based on the above result, 5.34 billion people lived below $15 a day in 2008. This is "sort of" consistent with the data in the graph you posted, in my opinion.

Unfortunately, such analysis is only valid for 2008.


https://www.desmos.com/calculator/m3yzlrz1rs

Here, as you can see when $2x>y$, $U=y+y=2y$ (Right hand side to the line of kink of $2x=y$
and when $2x<y$, $U=2x+y$
So, the Black curve denotes the utility function of 10 level of utility but you can draw for any with the kink line as $2x=y$.


Reference request: Development economics

Development economics has a distinct flavor among subfields in Economics, in that it usually opts for a more socio-economic, geopolitical and historical approach rather than mathematical modelling.
But they do use rigorous quantitative methods as regards empirical studies.

Anyway a book that can certainly show you how this subfield thinks is E. Wayne Nafziger's "Economic Development" (850 pages long - in hardcover, the book weighs 1.5 Kgr!)

See also the scientific journal "Journal of Development Economics"


Will Chinese yuan be a key international currency someday?

"SDR inclusion does not mean... that the renminbi will rival the dollar as an international currency, at least not any time soon. The dollar is widely used globally in trade, in international borrowing and lending, and as the principal currency for official reserve holdings (about sixty percent of global reserves are held in dollars). Importantly, the dollar’s global status is a market outcome, not the result of a decision by any international body or of an international agreement. Private investors and governments freely choose to hold dollars because the markets for dollar-denominated assets are, by far, the deepest and most liquid of any currency; because the United States imposes no restrictions on capital flows in or out of the country; because of the quality of U.S. financial regulation; because the Federal Reserve has kept inflation low and stable for the past thirty years; and because the United States is large, prosperous, and politically stable."

This is the quote from Ben Bernanke's blog. Ben Bernanke is the former chairman of the Federal Reserve.


Why do top professional sport players get usually paid so much?

tl;dr There is a lot of demand for what they produce.

A proper answer should have some evidence, perhaps I will add that when I have more time.

Even within a category, say, football (soccer) players, you see a lot of discrimination: Top players at top clubs in top leagues get most of the cake. This is anecdotal evidence for the demand side story:

Only the best leagues earn much money through television rights, because only there is most of the demand (how much media coverage do you have for your national third league anyways?)
Only the best teams in these leagues get most of this money, mostly because leagues partly pay teams based on their performance ranking wise
Only the best players get the highest share, which is a combination of the previous two facts, and that these guys are quite unique and have hence an even higher demand:

They make more marketing money (people really want to see them)

Due to their uniqueness, they can bargain better deals with teams and sponsors

Note that the last point is really the only supply-side story. If you ignore super stars, the supply of good players is huge. Most of the twist really comes from some of them being marginally better / lucky, making it into the better leagues, which happen to be the one that mass media demand, and get the high compensation.


Fannie Mae and Freddie Mac as substitute benchmark bonds

Fannie Mae and Freddie Mac bonds have long been viewed as having an implicit government guarantee, and though they received government support during the crisis, they never missed a payment to bondholders. This implicit guarantee was strengthened in July 2008 when Congress passed the Housing and Economic Recovery Act of 2008, which created a channel through which the Director of the Federal Housing Finance Agency could place them in conservatorship, which was done in September 2008. The GSEs remain in conservatorship today, and have access to lines of credit with the US Treasury. So while it's true that they still do not have an explicit guarantee today, it's easy to see why they're viewed as having a guarantee, at least implicitly.


How is reserve money 'multiplied' by the banking system?

This overlaps an existing question: Can money multiplier happen within a single bank? The mechanics is described in there, and I think it addresses some of your questions.
My guess as to what is happening in the explanation you found is that there is an added behavioural assumption: banks only make loans up to the size of their excess reserve position. This means that if there is an injection of reserves, there can only be a loan of the same size as the injection, then a sequence of smaller loans. You then end up with diagram result. The reality is that this is not how banks operate, and they could just make a single loan and use up the excess reserves in one shot. (Obviously, could be done in smaller steps.)
The “sequence of small loans” story was probably in an old Economics 101 textbook, and it has been repeated many times. I have not seen a formal version of this model, so I have no idea why the non-existent constraint on loan size is imposed in the money multiplier model explanation.


Economic concept where turning something down heightens emotional attachment

It's called reference-dependent preference, a notion belonging to the intersection of economics, psychology, and neuroscience. Here is a set of brief introductory slides on the concept


Complementarity in CES Production Function

Total investment in terms of how much capital is augmented, is always $I = I_{b} + I_{h}$.

$(I_{b}^K + I_{h}^K)^{\frac{1}{K}}$ is equal to the amount of the intermediate good $Y$ that we need to allocate for investment. And given the formulation and when $K>1$ we see that we economize on the amount of the intermediate good $Y$,

$$Y_I = (I_{b}^K + I_{h}^K)^{\frac{1}{K}} < I_{b} + I_{h} = I$$

Further, if we split investments equally, we achieve the maximum possible economy (i.e. the minimum $Y$ required for given total $I$ to be achieved).

So inherently, the formulation "pushes us" to keep the two investment levels close, because the further apart they are (for given total $I$), the more $Y$ we will require, reducing consumption. This "closeness of levels" is what the author refers to as "complementarity" (perhaps confusingly, if one has the micro/demand-production theory meaning of the term in mind).

Fisher, J. D. (1997). Relative prices, complementarities and comovement among components of aggregate expenditures. Journal of Monetary Economics, 39(3), 449-474.


What was "Pareto's proof of the immeasurability of utility"?

I think the "immeasurability of utility" refers to what we know today as the non-uniqueness of utility representation. The word "utility" also has a slightly different meaning there. As Pareto notes in the mathematical appendix to his 1909 book, Manual of Political Economy (limited preview on Google Books), the "utility" measure is

  the measure of pleasure provided by the combination [of quantities of consumption goods], or [...] the measure of the value in use, the utility, the rareté (Walras), the ophelimity of this consumption.

He goes on to prove that there is a lack of a one-to-one correspondence between quantities of consumption and the indices of indifference curves (which are the candidate for measuring utility). Therefore he concludes that indifference curves are merely the index of utility (i.e. pleasure), not the measure of it.


Why is economic growth measured exponentially rather than linearly?

Growth as is meant here "must" be nothing in particular. It is a specific metric, the percentage change in yearly GNP/GDP, and it is what it is.
In Blanchard and Fischer 's "Lectures on Macroeconomics", in the introductory chapter 1, page 2, Figure 1.1, the logarithm of USA GNP 1874-1986 is graphed: and it is impressively linear , bar a disturbance around World-War II (a dive before it that was roughly equally compensated immediately after). But this means that

$$\ln Y \approx at \Rightarrow Y \approx e^{at}$$

(for the US Economy, $a \approx 0.030\;\; \text{to} \;\;0.037$ for the period).

It is the data that told us that "growth was exponential" during this period.
(Note that "exponential growth" usually includes the concept of constant growth rate, while  in informal language, "exponential" may also refer to exploding paths, paths with increasing growth rate).
And so economic models were deemed relevant if they could replicate to a respectable degree the observed data.

The question "can this go on forever?" is an altogether different issue, starting with the meaning of the word "forever".


Cournot model with piecewise inverse demand

In the book Sushko, I. (Ed.). (2002). Oligopoly dynamics: Models and tools. Springer.

there is a chapter,

Puu, T., Gardini, L., & Sushko, I. (2002). Cournot duopoly with kinked demand according to Palander and Wald. (pp. 111-146).

where the authors examine in detail a specific numerical example, among other variants.  They arrive at the best response functions and find that there exists two Cournot equilibria, for which, as they write

  "...both equilibria, the Cournot points, are locally stable. They hence coexist with each its proper basin of attraction in the space of
  initial conditions."

The authors are concerned with dynamics, hence the mention of "initial conditions". If one wanted to turn their conclusions into the static case with just one move to equilibrium, one should consider in which "basin of attraction" does the zero output vector belongs.


The world bank group has a Urban Transport Data Analysis Tool (UT-DAT) located here: https://www.worldbank.org/en/topic/transport/publication/urban-transport-data-analysis-tool-ut-dat1

It has an excel file that has some data.  There is also Data.world  https://data.world/datasets/transportation

There is Global Mass Transit website but its a paid service with some free options:   https://www.globalmasstransit.net/index.php

This Wiki site here might be a better option for you on free public transportation data links:
https://www.transitwiki.org/TransitWiki/index.php/Publicly-accessible_public_transportation_data

The world bank has Public private partnerships investment in transport (current US$).
Which are contractual relationships typically between a state or local government, who are the owners of most transportation infrastructure, and a private company.

https://data.worldbank.org/indicator/IE.PPN.TRAN.CD

This looks like a hard find.


Recommended reading to understand American economic history

Found this to have more breadth on the overall US economy: The Rise and Fall of American Growth: The U.S. Standard of Living since the Civil War


Creating a pragmatic, useable (not theory heavy) proxy for a currency basket for a set of economies

There is an economic literature on optimal currency areas. However, that is related to the adoption of a single currency.
As described in the question, a basket is just a new asset that is a weighted allocation to underlying currencies.
Once the weightings are fixed, the fair value of the basket is the weighted value of the component currencies, which can be updated in real time.
The only way that this basket changes anything in the real economy is that entities are willing to hold it and trade it.
The issue is straightforward: people and firms want their local currencies, not the basket. What they want is to translate the foreign currency to theirs.
Banks can offer quotes for any currency pair. It is only in the worst case that the quotes would have a bid/ask that is as wide as doing a pair of transactions versus a major currency (often USD, EUR). The only way a basket can improve matters is to have a tighter bid/offer versus the national currencies than they have versus the major currencies. How plausible is that outcome?
The weighting could be done in any number of ways, but the basket has to meet the constraint that people want to own it. The weighting has to reflect the ability to buy short-term financial assets in the underlying currencies. Realistically, that determination has to be done by the entities managing the basket.


Can Direct Taxes on the consumers have a impact on the Demand (rather than supply)?

In microeconomics you can analyze tax incidence on supply demand graph. If you levy tax on consumers this will shift demand curve to the right.

However, this does not mean that whole tax burden rests with consumers. The tax drives a wedge between the price that consumers pays and the price that consumers receive. The whole tax burden is the triangle ABC and you can see that this triangle is split in half by original price. The upper half that cuts into consumer surplus is the tax incidence on consumers and lower half tax incidence on producers.

The tax incidence depends on elasticity of supply and demand. The more inelastic demand relative to supply the more tax burden is shifted to consumer and the more inelastic supply the more tax burden is shifted to producers.

I am not familiar with Singapore’s real estate market but usually the housing market is thought to have elastic demand and relatively inelastic supply so the tax incidence should fall more on suppliers.

Now to your macro question. First of all tax on a single market should not even had any macroeconomic impact in general. When we talk about increasing taxes in macroeconomic classes we usually mean that across whole economy for example increasing VAT that affects all markets.

But let’s for now suppose in Singapore housing market is such a great share of GDP that taxes there have macroeconomic impact. Well this would first in short run shift aggregate demand to the left to new equilibrium with lower prices and GDP but in a long run the equilibrium GDP will be determined by long run supply curve of the economy. As firms adjust to the new prices GDP will go eventually back to the same level but at lower overall price level.

Here is the example of macroeconomic effects of aggregate demand shifts. In the picture demand shifts due to decrease in investment but taxes would work the same way.


Did the Marshall Plan cause Western Europe's economic expansion after WWII?

Barry Eichengreen is one of my favourites for this period. So, I am just going to let him explain it.
From : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.207.1592&rep=rep1&type=pdf

Our central conclusion is that the Marshall Plan did matter. But it
did not matter in the way that the “folk wisdom” of international
relations assumes. Milward (1984) is correct in arguing that Marshall
Plan aid was simply not large enough to significantly stimulate
Western European growth by accelerating the replacement and expansion
of its capital stock. Nor did the Marshall Plan matter by financing
the reconstruction of devastated infrastructure, for as we show below,
reconstruction was largely complete before the program came on
stream.
The Marshall Plan did play a role in alleviating resource
shortages. But this channel was not strong enough to justify the
regard in which the program is held. By 1948 and the beginning of
Marshall Plan aid bottlenecks were scarce, and markets were good at
alleviating their impact. Rather, the Marshall Plan significantly sped
Western European growth by altering the environment in which economic
policy was made. In the immediate aftermath of World War II
politicians who recalled the disasters of the Great Depression were
ill-disposed to “trust the market,” and eager to embrace regulation
and government control. Had European political economy taken a
different turn, post-World War II European
Wartime relief, post-World War II UNRRA aid, and pre-Marshall Plan
“interim aid” may well have significantly speeded up the
reconstruction process. ... recovery might have been hobbled by clumsy
allocative bureaucracies that rationed scarce foreign exchange and
placed ceiling prices on exportables to protect the consumption of
urban working classes. Yet in fact the Marshall Plan era saw a rapid
dismantling of controls over product and factor markets in Western
Europe. It saw the restoration of price and exchange rate stability.
To some degree this came about because underlying political-economic
conditions were favorable (and no one in Europe wanted a repeat of
interwar experience). To some degree it came about because the
governments in power believed that the “mixed economies” they were
building should have a strong pro-market orientation. Marshall Plan
aid gave them room to maneuver in order to carry out their intentions:
without such aid, they would have soon faced a harsh choice between
contraction to balance their international payments and severe
controls on admissible imports.
To some degree it came about because
Marshall Plan administrators it pressured European governments to
decontrol and liberalize even when they wished to do otherwise. In
post-World War II Western Europe the conditions imposed, formally and
informally, for the receipt of U.S. aid encouraged the reductions in
spending needed for financial stability, the relaxation of controls
that prevented markets from allocating resources, and the opening of
economies to trade. Marshall Plan “conditionality” pushed governments
toward versions of the “mixed economy” that had more market
orientation and less directive planning in the mix. While postWorld
War II European welfare states and governments are among the most
extensive in proportion to economic life in history, they are built on
top of, and do not supplant or bypass, the market allocation of goods
5 and factors of production. The Marshall Plan should thus be thought
of as a large and highly successful structural adjustment program.


Variance of $\hat{\beta _0}$ in case of homoskedasticity

They are certainly not the same, since the first contains an expected value while the second does not contain an expected value but a sample mean.

Of course, they are very closely connected, and one can see this if one writes down the definition of the variance of a random variable.


Inability of a long-term bond market intervention to contribute to achieving a peg

The issue isn't so much that intervening in the long-term market wouldn't help, but rather that under rational expectations all the return rates on government bonds are determined by the same process, and thus have to be consistent with each other and converge to the same rates. What D'Amico et al. seem to be suggesting is that the Federal Reserve tried to enforce mutually inconsistent rates on bonds with different maturities, such that there was a sequence of operations on bonds with short-term maturities (what I think they're calling "an expected path for the short-term rate") which would yield a return either above or below that of bonds with different maturities.

What it seems that they're really saying is that, under rational expectations, the FED would have had really just one policy instrument: the interest rate at any time. Bonds with different maturities just had to conform to that rate. But in practice, the FED tried to enforce a set of different rates, one each for each kind of maturity, which the authors think it's doable because the variance of bond prices is lower than what would be expected under rational expectations (hence the "the slightest fluctuation in expectations of the short-rate path would immediately imperil the peg" bit).


how to measure the funding liquidity, i.e., equivalent U.S. TED spread, in the Australian market?

it is measured by the swap spread, the difference between the 3-month bank bill swap rate (BBSW3M) or 3-month bank bill rate and the 3-month overnight indexed swap rates (OIS3M) captures the inherent bank credit risk and therefore funding liquidity in the inter-bank lending market.


Is China at the golden savings rate s? If so, what is it?

To partially answer this question, in Advanced Macroeconomics by Romer, question 1.5(c) asks

  "What saving rate is needed to yield the golden-rule capital stock?"

Answering this tells us what $s_{gold}$ is.

But before we can find this we must find the golden rule level of capital stock $(k_{gold})$.  Which we shall derive with the following equations: The intensive form of the production function, the dynamics of capital in the Solow Model, and consumption per unit of effective labour

\begin{cases}
Y_t = (A_t L_t)^{1-\alpha} K_t^{\alpha} = A_t L_t \left( \frac{K_t}{A_t L_t} \right)^{\alpha} = A L k^{\alpha} \\
\Rightarrow Y/AL = y = k^{\alpha} \\
\dot{k} = s y - (n+g+\delta) k \\
c = (1-s)y \\
\end{cases}

Under the balanced growth path, $\dot{k}=0$ so

$$ \displaystyle s k^{* \alpha} = (n+g+\delta)k^* \Rightarrow k^* = \left( \frac{n+g+\delta}{s} \right)^{\frac{1}{\alpha-1}} $$

We maximize $c^*$ with respect to $k^*$ to implicitly define the golden-rule level of capital per unit of effective labour

$$ \displaystyle \frac{\partial }{\partial k^*} c^* = \frac{\partial }{\partial k^*} (1-s)k^{* \alpha} = (1-s)(\alpha k^{* \alpha - 1}) $$

$$ \displaystyle = \alpha (1 - s) \left( \frac{n+g+\delta}{s} \right)^{\frac{\alpha-1}{\alpha-1}} $$

Next replace $s$ with $(n+g+\delta)k^{* 1-\alpha}$

$$ \displaystyle = \alpha (1 - (n+g+\delta)k^{* 1-\alpha}) \left( \frac{n+g+\delta}{(n+g+\delta)k^{* 1-\alpha}} \right) $$

$$ \displaystyle  0 = \alpha (k^{* (\alpha-1)} - (n+g-\delta)) \Rightarrow k^*_{gold} = \left( \frac{\alpha}{n+g+\delta} \right)^{1/(1-\alpha)} $$

We can finally compute, $s_{gold}$

$$ \displaystyle s_{gold} = (n+g+\delta) k_{gold}^{*1-\alpha} = (n+g+\delta) \left( \frac{\alpha}{n+g+\delta}\right)^{(1-\alpha)/(1-\alpha)} = \alpha $$

So for a Cobb-Douglas production function the golden-rule saving rate should be whatever $\alpha$ is.


First lets correct some misconceptions  "Economic theory says that interest rates fall in recessions." Economic theory (at least mainstream economic theory) does not say anything like that.
In fact in IS-LM AS-AD model, which is one of the workhorse models of modern macro, during recession if central bank would be passive and not do anything in recession interest rate would increase. This is because when an economy enters recession, demand for liquidity increases but the supply of credit decreases and hence ceteris paribus interest rate should increase.
Second, while adjustable rate mortgage (ARM) interest usually increases at the beginning of a recession it will usually quickly starts falling as data show. The reason for this is that in real world ceteris paribus condition is not realistic. During recession central bank will not be passive but it will actively try to stimulate economy by lowering its interest rates and by injecting extra liquidity into the economy which affect all other interest rates in economy including ARM and put downward pressure on them. Hence the interest rates will tend to eventually fall during recession as a result of central bank intervention if the intervention is successful.


DSGE models (Dynare) are only based on simulations and approximations? (without data)

Short answer

It doesn't seem like you've tried very hard to find estimation using Dynare (google results of "Dynare estimation"). Dynare is in fact capable of doing estimation and typically people use some sort of data to estimate the parameters that govern their model.

Longer Answer

What is a DSGE model?

A DSGE model is a series of equations (and variables and parameters) that describe a "model" economy. Once you write everything down and take into consideration the optimizing decisions made by the agents, it is simply a system of stochastic difference (differential) equation that you can imagine writing in some form along the lines of:

$$ E_t F(y_{t+1}, y_t, y_{t-1}, u_t) = 0$$

What does Dynare do?

The majority of introductory examples only use Dynare to solve the model and run some simple simulations. In addition to being able to solve the model, Dynare is also capable of doing Bayesian estimation of the parameters that make up the model by feeding in data.

Solves and simulates the Model

Dynare takes this system of equations (and the given parameter values) and solves them using perturbation methods. One of the outputs of the solution is a law of motion for all of the variables in the economy -- i.e. one can write something along the lines of

$$y_{t+1} = F(y_t, u_{t+1})$$

This law of motion allows you to generate model analogues of the data that you are interested in -- i.e. capital, labor, consumption etc...

Estimates the model

Once Dynare has a law of motion and has obtained simulated moments, it can compare the output of the model to data that you have provided. Dynare uses Bayesian estimation (though it is possible it does other types, but I'm not familiar with it) to estimate parameters which means that you need to provide it with a prior for each variable that you would like to estimate. It then uses a simple Metropolis Hastings algorithm to obtain estimates for the distribution over parameter values.

References

I would recommend you read both of the following references.

Tommaso Mancini Griffoli. Dynare User Guide: An introduction to the solution & estimation of DSGE models. 2007-2008. found here
Stefanie Flotho. DSGE Models - solution strategies. December 2009. found here


Calculating mean variance portfolio with risk aversion parameter

Here's how you would account for risk aversion.

First of all, I think this problem is usually set up using weights as the variables (see here http://www.math.ku.dk/~rolf/CT_FinOpt.pdf, page 141). If you want to use dollar weights, you will have to transform the result.

The optimization problem is:

$$ \max_w \quad  w'\mu −\frac{\gamma}{2} w'\Sigma w$$

Weights add up to 1:

$$ w'e = 1 $$

Where you have $N$ assets, $w$ and $\mu$ are $N\times1$ vectors, and $\Sigma$ is an $N\times N$ matrix. $e$ is an $N\times1$ vector of ones.

The Lagrangian for the problem is:

$$ \max_w \quad  w'\mu −\frac{\gamma}{2} w'\Sigma w + \lambda (w'e - 1)$$

To optimize, we take the gradient of the objective function, and set each element equal to zero. So we will have an $N\times 1$ vector equation:

$$0 = \mu - \gamma \Sigma w + \lambda e$$

This can be solved for $w$:

$$w = \left(\gamma \Sigma\right)^{-1} \left(\mu + \lambda e\right)$$

Plugging this back into the constraint, we get:

$$ \left(\left(\gamma \Sigma\right)^{-1} \left(\mu + \lambda e\right)\right)'e = 1$$

The transpose reverses the order of the terms, and has no effect on the symmetric $\Sigma^{-1}$ matrix:

$$ \left(\left(\mu' + \lambda e'\right)\frac{\Sigma^{-1}}{\gamma} \right)e = 1$$

This can be simplified to:

$$ \mu' \Sigma^{-1} e + \lambda e' \Sigma^{-1} e = \gamma$$

Solving for $\lambda$, we get

$$ \lambda = \frac{\gamma - \mu' \Sigma^{-1} e}{e'\Sigma^{-1} e} $$

So the overall formula for the weights is:

$$w = \left(\gamma\Sigma\right)^{-1} \left(\mu + \frac{\gamma - \mu' \Sigma^{-1} e}{e'\Sigma^{-1} e} e\right)$$


Reductionism, value and market economics

You are mistaken. Economics doesn't actually concern itself with measurable quantities, but rather with the behavioral functions that give rise to measurable quantities (such as price, investment, etc). The most obvious example of this is the utility function, as they are unique up to scale – meaning that there are several (actually infinitely many) which nonetheless do the same thing.

Consider the prisoner's dilemma, for instance: we might introduce for each player a scale factor which multiplies his whole payoff matrix. But no matter how we change those payoffs, so long as the structure of those matrices is preserved so will be the behavior of the prisoners. So nothing really changes. But that is fine, because what we're not interested in modelling is the value of the choices to each player, but how the players choose.

So it isn't necessary to introduce any concept of the measurable economic value of anything so long as we might say that it is preferable to something else. Which is to say that we might model the behavior of any agent without introducing a cardinal measure: we can do fine if his choices are merely ordered (this is the idea behind Revealed Preference, which was initially formulated by Paul Samuelson as an alternative to utility functions, but which was later on found to be equivalent to them).

But to answer what's bugging your mind: there isn't practically anything even mildly relevant to human life which economists won't deal with. Because in so far as people's choices are observable, they can be treated by an economic model. For instance, there's a chapter in the Handbook on the Economics of Leisure which is called The Economics of Sleep and Boredom. I've also seen a paper once on the economics of suicide (there's actually a small literature on this). Another example – though less odd and more important – is Becker's theory of crime, which takes crime out of the domain of other social sciences (which might explain it in terms of marginalization, poor education, etc) and into the domain of expected utility and choice theory (i.e. what are the odds the guy think he has of getting away given the circumstances).

Contrary to popular opinion, dealing with money and crunching numbers is often the least important and most boring part of an economist's job. Most often economists are concerned with figuring out why people would do what they do.


Sources of historical cross-country government debt to GDP data

Using the World Bank's International Debt Statistics you could calculate the ratio of PPG, bonds (AMT, current US\$) to GNI (current US\$):

  PPG, bonds (AMT, current US\$): Public and publicly guaranteed debt
  from bonds that are either publicly issued or privately placed. Data
  are in current U.S. dollars.

  GNI (current US\$): GNI (formerly GNP) is the sum of value added by all
  resident producers plus any product taxes (less subsidies) not
  included in the valuation of output plus net receipts of primary
  income (compensation of employees and property income) from abroad.
  Data are in current U.S. dollars.

These data go back to 1970's for some countries, but the data only covers 1970-2013. The OECD numbers go back to 2000 but are even easier to work with. You can link right to them. For some rich countries the data go back quite a bit farther (like G7 countries like  the UK, France, and the USA). For a large panel of countries.  I don't know of sources better than the World Bank and the OECD. You could check the IMF data page but all I found were links back to the World Bank data.


Translated Selten Subgame Perfect Eqm Paper

Do you mean this article?

Selten, R. Reexamination of the perfectness concept for equilibrium points in extensive games, Int J Game Theory (1975) 4: 25.


"$\backslash$" notation question in definition for Nash equilibrium

Informally, a (possibly mixed) set of strategy choices is a Nash equilibrium if no player can expect to benefit by changing strategies while the other players keep their strategies unchanged.

Here I would interpret your definition as $\Delta$ being the set of all possible strategy choices across all players, $\sigma^*$ being a set of strategy choices which will be a Nash equilibrium if it satisfies the conditions, $i$ being a player, and $\sigma^* \backslash \mu_i$ being a change in player $i$'s strategy while the other players' strategies stay the same.  So I would take $\backslash$ having a type of "not included" interpretation.


How to make sense of so many conflicting theories and ideas in the field with an open mind? Is every school of economic thought as valid as the rest?

This is how I view it. At the very core of economics, is each and every human on this earth making decisions he or her thinks are in his or hers best interest. In real life, we do not calculate utility before making a decision or compute any expected values; we do what feels right at the moment.

Taking the cross-section of human decisions, economists try to make sense of it all, and ultimately deduce some theory that resembles a law of physics to shed light some basic insight into the human condition.

This is a mighty hard task; near impossible. Its amazing to me we've made any progress at all, yet here we are.

As a field of knowledge, economics will never explain the world perfectly in whole, because the nature of what we study is far from perfect and certainly stochastic. There will never be a unified theory of economics, but that does not mean the small pieces of insight each economics paper tries to uncover is trash. It is still valuable to use what the data can tell us, to the best of our ability, to guide our future decisions, and analyze the decisions we've made in the past.

If anything, its interesting as hell.


is there a difference between E[e|x]=0 and E[e|d=1]-E[e|d=0] in continuous vs discrete case in regressions?

It is very unclear what you are asking. But in most regressions it is assumed that the error term (I assume "e" is the error term) is assumed to be iid for all values of x. In particular, in the discrete case $E[\epsilon|d=1]=E[\epsilon|d=0]$, but this can be generalized by saying $E[\epsilon|x]=E[\epsilon|x']$ for all $x, x'$. Now if your regression also includes a constant term, it is without loss of generality to assume that the expected value of $\epsilon$ (which is the same for all values of x) is equal to zero. Thus, the importance of the assumption $E[\epsilon|x]=0$ is not so much the "equal to zero" part, but the fact that is the same for all values of x.


Interpretation of the World Bank's definition of Portfolio equity inflows

Yes given that ownership of 10 percent or more of the ordinary shares of voting stock is the criterion for determining the existence of a direct investment relationship. This threshold of 10 percent establishes a controlling interest, per guidelines established by the Organisation of Economic Co-operation and Development (OECD).

According to the OECD Portfolio investment is the category of international investment that covers investment in equity and debt securities, excluding any such instruments that are classified as direct investment or reserve assets.


Has any person ever actually planned his or her consumption according to Modigliani’s LCH?

The life-cycle hypothesis as a model doesn't need to explain people's behavior perfectly to be of use in understanding the economy or the decisions that individuals make. Recall the old saying that "all models are wrong but some are useful." As a quick example, note that many people do in fact borrow when they are young (e.g., for college, save while their income is relatively high (e.g., a lot of people save for retirement), and dissave when they're older---just as would be predicted by this theory.


What are the advantages of using demand systems estimation? How is this different from individual demand estimation for product?

One advantage of considering demand systems is that more data is available for identifying the degree of income effects and substition between commodities. A second advantage is the possibility to impose and test microeconomic restrictions (which are between equations). An introduction to the estimation of demand systems with an historical perspective is provided by:
Berndt, E. R., 1991, The Practice of Econometrics: classic and contemporary, Addison Wesley.
More recent treatments are available in most econometric textbooks.


Central Banks are not made to make profit. They are there to stabilize the price (inflation) and avoid crisis.

But to do that, they sell and buy assets. If they do a good job, they must purchase assets when they are undervalued and sell when they are overvalued. By doing that they are making profit.

This is good because Central Bank's infrastructure does have a cost. If they were not making profit, they would have to be financed by the taxpayer. When a central bank is making profit, they typically give this money back to the state, lowering the amount of needed taxes.


Does cornering a market has any "bad" economic consequence?

You already have your answer in the last sentence. A monopoly can be established and that leads to well known "bad" economic consequences, i.e. economic inefficiencies.


What's the name for this type of non zero sum game?

As far as I know the definition is yet to be extended beyond two person games, but you seem to be looking for some notion of antagonism.

A two player game is antagonistic if given any two outcomes A and B, if player one prefers outcome A then and only then player two prefers outcome B.

Read more here.


Why would minimum rent under franchise arrangements for McDonald's decrease year by year?

Suppose McDonald's has 2 franchisees. Franchisee A under its current franchise arrangement has to pay \$100 a year of minimum rent until the current arrangement expires in 2025. Franchisee B, on the other hand, has to pay \$75 a year but its arrangement expires in 2019.

The future minimum rent due to McDonald's in 2018 is $\$100 + \$75 = \$175$. This continues until 2020, where the payments then drop to only \$100 a year after Franchisee B's arrangement expires. Although, we would expect a high renewal rate with McDonald's franchisees, the table only shows future cash flows under contracts existing today, or as they say in the annual report

  "The following table summarizes...future minimum rent payments due to the Company under existing franchise arrangements as of December 31, 2014."

Note that these values are not discounted. In our simple example, McDonald's is owed \$100 a year from 2021 to 2025 by Franchisee A and then gets $0 a year after 2025 since there are no more arrangements left. \$100 a year from 2021 to 2025 sums to \$500 for the thereafter row.

These tables of contractual obligations and future cash flows are helpful to analyze the future cash needs of a business. Often times companies may have a lot of debt due in a specific year when a bond issue matures. While companies often refinance ("rollover") that debt, it is helpful for investors to know that that debt maturity is coming up since if the company cannot refinance (say it is a lousy retailer or there is a financial crisis) and does not have enough cash on hand, the company could be forced into bankruptcy.

This future minimum rents table provided by McDonald's tells investors how much cash is contractually coming in the door, and also sheds light on the remaining life of McDonald's franchise arrangements.


About gross domestic product at factor cost

The best practice would be to use definitions from recognized international institutions such as the World Bank or the Organisation for Economic Co-operation and Development (OECD). In this document The OECD classifies three types of gross value added (1) at  basic  prices, (2) at producers' prices and (3) at factor cost.

Let first define gross value added at  basic  prices  as  output  valued  at  basic  prices  less  intermediate consumption valued at purchasers' prices. Then, gross  value  added at  factor  cost  can  be  derived  from  gross  value  added  at  basic  prices  by subtracting other taxes less subsidies on production.

As an example, GDP  at  market  prices  for  the  United  States  in  1992  was US\$ 6,234 billion.  As GDP at factor cost removes all net taxes on production, it would equal \$6,234 billion less \$506 billion or \$5,728 billion.

GDP at factor cost is thus a way of measuring gross value added at some prices. So, as far as I understand, it makes sense that depreciation get cancelled and finally becomes GDP (at factor cost) = Gross value added (at factor cost).

Why is depreciation added to Net value added? According to your source, if we deduct depreciation from Gross Net Product (at factor cost), we get Net National Product (at factor cost). So, if we add depreciation to NNP we get GNP.


Effects on transit system shutdown based on local workforce end-of-day times?

That's a fascinating idea, and I'd thoroughly suggest additional research into the matter (especially because you might be able to conduct a quasi-experimental analysis using instances of changing public transportation schedules on labor market factors, such as Boston's temporary decision to keep the MBTA rapid transit open later).

As far as your interest in other academic studies, I'd ask for a bit more clarification for a complete answer: what is the outcome variable(s) you are most interested in? Are you thinking about the impacts on the labor market (the distortionary effect on which groups are able to take jobs in the later shifts of retail, for example)? Or are you more interested in the potential for economic growth if hours were extended?

If you clarify the above a bit more, I can try to search for more resources. However based on what you've mentioned, there are a few academic studies I found that might be of interest:

This Study by Fan, Guthrie and Levinson looks at the impact of light rail service on labor market outcomes for various types of workers. They cite two other articles (here and here) that also look into the impact of public transportation on labor market outcomes for different groups of workers. There are other citations in all three documents that you might find interesting along that dimensions.

This article by Guthrie and Fan Examines the impact of public buses on economic development in the Twin Cities, Minnesota. This study is one conducted by the American Public Transportation Association (so I might take some of their findings with a dose of skepticism) and details a variety of the economic impacts public transportation investment can have in the surrounding area.

There are a few other studies that are more tangentially related to what seems to be your central question, but still might be interesting. This article, by Bauernschuster, Hener and Rainer looks at the impact of public transportation strikes on traffic, health outcomes, pollution, and other factors. The impact on traffic is also examined in this NBER article by Anderson.

It may also be worthwhile (again, not entirely sure what your main research question is on specifically) to look outside some of the normal "econ research channels." This study in PubMed looks at the impact of Strikes in London's Underground on bicycle usage.

I hope some of those helped. If I can refine my answer further to better assist, just let me know!!


Why is there less price transparency in some industries (especially healthcare) than in others?

Obviously nursing homes are a.smaller market...

Large, liquid markets with frequent buying and selling of standard products have the most information.

Also, Zillow is bad, home assessors exist for a reason.


Repo is the short abbreviation for Repurchase agreement, as per Investopedia (https://www.investopedia.com/terms/r/repurchaseagreement.asp).


Monopoly - Where is the Markup formula derived from?

It is just a missing parenthesis issue. The expression

$$\text{(P-MC/P)= -1/η}$$  should have been written

$$\text{((P-MC)/P)= -1/η}$$