Why did Germany use hyperinflation to free itself from an external debt? Im reading about how Germany used almost any solution To free itself from its WWI debt: hyperinflation, calculating payments on the basis of the economy's potential, rescheduling annuities and finally cancellation outright. But i didn’t understood why they used hyperinflation. I understand it neutralized the domestic debt, but did they had that much ? Why did they did so if they had to reimburse the external debt that was imposed after Versailles congress?

Hyperinflation certainly neutralizes the domestic debt, but the collapse of the mark makes the external public debt unbearable.

The issue is that they did not had much other choice as the war and war reparations made German hyperinflation virtually inevitable.
As given by quantity theory of money a price level, change in which gives you inflation, is given by:
$$P = \frac{MV}{Y}$$
so the change in price level $P$ depends not just on quantity of money $M$, but also velocity $V$ and real output of an economy $Y$.
Even if Weimar Republic would not resort to printing money arguably the fall in real output caused by war, loss of population and territory and horrendous reparations, would be very inflationary in themselves. However, in addition it is true that Weimar Republic also resorted to heavy use and abuse of printing presses exacerbating  the inflation even further leading to hyperinflation. But question is what was the alternative?
Every state must spend at least some minimum amount of money in order to pay police/bureaucrats that enforce the laws of the government. Famously, Weber defined government as a monopoly on legitimate use of power in certain area. Well that is costly, and we are talking about bare minimum for state to exist ignoring that Weimar Republic had also other welfare spending that was likely necessary to keep people 'in line'.  What was the Weimar Republic to pay these costs when virtually all of her productive capacities were destroyed by war, loss of territory, loss of population etc.? Non-trivial amount of German output had to be given to Allies to pay for the reparation itself and debt owed as reparations could not be discharged (in past it was common to extort external debts even at the point of threat of armed conflict). Arguably, the only option was to print more and more money to at least eliminate the domestic debt and keep 'chugging along' or to let the state disintegrate.
The heavy burden of reparation's have to really be emphasized here. As documented by Keynes in his famous book 'The Economic Consequences of the Peace' the war reparations Germany was forced to pay were simply too horrendous.
For example Keynes reports that the treaty demanded:

Germany has ceded to the Allies all the vessels of her mercantile
marine exceeding 1600 tons gross, half the vessels between 1000 tons and
1600 tons, and one quarter of her trawlers and other fishing boats.[9]
The cession is comprehensive, including not only vessels flying the
German flag, but also all vessels owned by Germans but flying other
flags, and all vessels under construction as well as those afloat.[10]
Further, Germany undertakes, if required, to build for the Allies such
types of ships as they may specify up to 200,000 tons[11] annually for
five years, the value of these ships being credited to Germany against
what is due from her for Reparation.[12]

Further it was stipulated that:

(2) Germany has ceded to the Allies "all her rights and titles over her
oversea possessions."[13] This cession not only applies to sovereignty
but extends on unfavorable terms to Government property, all of which,
including railways, must be surrendered without payment, while, on the
other hand, the German Government remains liable for any debt which may
have been incurred for the purchase or construction of this property, or
for the development of the colonies generally.[14]

in addition,

In distinction from the practice ruling in the case of most similar
cessions in recent history, the property and persons of private German
nationals, as distinct from their Government, are also injuriously
affected.

As crazy as it sounds even private German nationals, who might not even have anything to do with war, were subject to the reparations. Furthermore, as reported by Keynes the property, both private and public, in German colonies and Alsace-Lorraine was to be expropriated by Allies. Setting moral considerations aside this greatly diminishes potential tax base upon which Germany could have draw resources from otherwise.
Also this is all in addition to the reparations itself which according to Keynes were set in a way that Germany could not simply inflate them away as:

The Reparation Commission is empowered up to May 1, 1921, to
demand payment up to $5,000,000,000 in such manner as they may fix,
"whether in gold, commodities, ships, securities or otherwise."

As if all of the above was not enough the treaty also forced Germany to give certain amount of resources coal/iron to Allies

i.) To France 7,000,000 tons annually for ten years;[42]
(ii.) To Belgium 8,000,000 tons annually for ten years;
(iii.) To Italy an annual quantity, rising by annual increments from
4,500,000 tons in 1919-1920 to 8,500,000 tons in each of the six years,
1923-1924 to 1928-1929;
(iv.) To Luxemburg, if required, a quantity of coal equal to the
pre-war annual consumption of German coal in Luxemburg.

And this is after ceding Alsace-Lorraine from which,

...Almost exactly 75 per cent
of the iron-ore raised in Germany in 1913 came from Alsace-Lorraine.[53]
In this the chief importance of the stolen provinces lay.

There are further provisions in the treaty but I think the above is enough to get some picture.
The monetary reparations were also extremely large relative to the Germany's GDP (although as a source below shows in the end even Allies realized the whole debt will not be realistically payed). As reported by Albrecht Ritschl

Taken in isolation, the A bonds amounted to 20% of German GDP of 1913, a burden that was
equivalent to France’s reparations to Germany in 1871 (Ritschl, 1996). Adding the B bonds generated
a reparations burden of 100% of 1913 GDP. Including also the C bonds raised the reparations burden
to over 260% of 1913 GDP. However, it was communicated to the Germans that the C bonds would
not have to be paid under any realistic conditions. The Germans had anticipated a burden of 30-40bn
gold marks. Hence, the realistic part of the reparation bill was not entirely beyond the imagination of
German policy makers (Feldman, 1993; Ferguson, 1998)

The purpose of the treaty was literary to destroy the economy of Germany. Furthermore, it was very bad for the international economic order in general. As Keynes reports:

The Treaty includes no provisions for the economic rehabilitation of Europe,– nothing to make the defeated Central Powers into good neighbors, nothing to stabilize the new states of Europe, nothing to reclaim Russia; nor does it promote in any way a compact of solidarity amongst the Allies themselves; no arrangement was reached at Paris for restoring the disordered finances of France and Italy, or to adjust the systems of the Old World and the New.
... Reparation was their main excursion into the economic field, and they settled it as a problem of theology, of politics, of electoral chicane, from every point of view except that of the economic future of the States whose destiny they were handling.

Thus to sum up, Germany was out of options. It lost non-trivial portion of its production capacity and taxable territory and population. It was up for enormous reparation bill that had to be paid either in gold or in assets or products, and it still had to run its own government somehow. Given such situation arguably the choice was to print money or stop paying its government employees and other domestic obligations.


Can You Use Filtered Variables in OLS? I have two variables that are non-stationary and contain stochastic trends. I used the Hamilton filter( an improvement over the HP filter) to remove the trend and isolate the cyclical component. My question is can I use these filtered variables (i.e. the cyclical component of the original data) in a standard OLS regression? Although the variables are now stationary will the application of the filter bias the estimates or generate spurious regression results? I know this is the case with the HP filter, although the Hamilton filter should correct for that.
The reason I am doing this is because I want to preserve the long-run properties of the data for my analysis. If I first difference the data to make it stationary all of that long-run information is lost. I am trying to figure out the best way to preserve the long-run information while making the variables stationary. Any other suggestions are welcome.
Thanks in advance!

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


Are the EU funds coming from EU citizen's taxes as well? I was trying to understand how the EU is funded using their official website, but my limited understanding of economy makes it very hard to understand the money pathways from a single unit (the citizen) to the big organization (the EU). I know that each country contributes with some percentage from GDP, but I'm missing links.

So my questions is, is the EU funded (also) from citizen's taxes? Can anyone please help me to understand how one person's taxes are reaching or converted into EU funds? I would appreciate very much if someone can describe this path step by step.

The main four sources of EU revenue are:

Custom duties and levies - EU calls this its 'Traditional own resources'. These are however not collected directly but member states collect it on the EU's behalf and are allowed to retain (currently) $20\%$ cut from these. These duties are ultimately, at least partially, payed by the EU citizens either directly or indirectly through tax burden incidence (save for special cases where the tax burden incidence might fall on non-EU citizen or company owned by non-EU citizens).
VAT - After EU harmonized the VAT collection rules among the member states a small percentage of VAT was set up to be directed towards the EU budget (between $0.15-0.30\%$ - however this rate has many asterisks and caps attached to it for complete rules see here). The VAT is again not collected directly by EU but by the member states on its behalf but it is for the most part payed by the EU citizens. Of course, part of it might be payed by people on vacation - especially for consumption of non-durable goods as with durable goods its often possible to get VAT rebate.
National contributions from member states - EU calls this 'Gross National Income-based own resource' since it is calculated from member state's GNI and is currently capped at $1.2\%$ GNI. The member states themselves decide how to raise this money - some of them might come from non-EU citizens or firms not owned by EU nationals but empirically most nations raise revenue primarily by taxing their own citizens. For example, most EU countries raise large portion of their revenue through income taxes so when EU citizens pay their income tax little bit from it is forwarded to the EU budget. Of course, most modern nations levy a plethora of different taxes to see exactly where individual members raise their revenue you have to look at their individual budgets.
Other sources - these include fees and fines EU issues, or contributions of non-EU countries to research projects, or taxes on EU staff etc. and other items. Again some of these are presumably collected from EU citizens.

Moreover, note in case of all of the above even some non-EU countries have to contribute, such as Norway for example, for accessing the common market.


What is the definition of a "Stackelberg leader-leader equilibrium"? I have encountered the equilibrium concept of "Stackelberg leader-leader equilibrium" while reading Product Line Rivalry (AER, Brander and Eaton (1984). They say "we define a Stackelberg strategy as one which involves taking into account the contemporaneous reaction of one's rival in setting one's own strategy". That definition does not really help me.

They also mention that this equilibrium concept is another way of interpreting the original Stackelberg model (which I know).

Does anyone have a reference or an explanation ? Of course, Google only returns results on the leader-follower game.

A leader-leader Stackelberg is a situation in the Stackelberg model where both firms believe they are leaders. This leads to global production being much higher than expected by both firms, as they anticipate small production by the other firm in response to their high production.


Conditions for an additive value function In a standard problem of fair cake-cutting, there is a real interval which is called "cake", and it has to be divided among $n$ partners. Each partner $i$ has a subjective value function $v_i$, which is an additive function on subsets of the cake. This means that, for every two disjoint subsets $A$ and $B$:
$$v_i(A\cup B)=v_i(A)+v_i(B)$$
Suppose that, instead of a value function, each partner has a preference relation $\succeq_i$.
A preference relation $\succeq_i$ is represented by a value function $v_i$ iff:
$$A\succeq_i B \iff v_i(A)\geq v_i(B) $$
What properties on the preference relation guarantee that it can be represented by an additive value function?
NOTE: The Wikipedia page Ordinal utility describes some conditions under which a preference relation can be represented by an additive value function. But, it deals with preferences on bundles of homogeneous goods. Here, the preferences are on subsets of a heterogeneous good.
EXAMPLES:
$$u_1(A) = \text{len}(A)^2$$
$u_1$ is not additive, but the preference relation it represents can be represented by the additive function $v_1(A) = \text{len}(A)$.
$$u_2(A) = \min[\text{len}(A\cap[0,4]),\text{len}(A\cap[4,8])]$$
The preference relation represented by $u_2$ cannot be represented by an additive function. Proof: suppose by contradiction that the preference relation is represented by an additive function $v_2$. Then, because:
$$u_2([0,1])=u_2([4,5])=u_2(\emptyset)$$
this must also be true for $v_2$:
$$v_2([0,1])=v_2([4,5])=v_2(\emptyset)$$
By additivity:
$$v_2([0,1]\cup[4,5])=v_2(\emptyset\cup\emptyset)=v_2(\emptyset)$$
This must also be true for $u_2$:
$$u_2([0,1]\cup[4,5])=u_2(\emptyset)$$
a contradiction.

This is only a partial answer because it does not exactly fit your framework, but I hope it will still be helpful (and it's too long for a comment).

If you are ok with discretizing your cake into (possibly arbitrarilly small) pieces of cake, then you will find an answer in

Kraft, C. H., Pratt, J. W., & Seidenberg, A. (1959). Intuitive Probability on Finite Sets. The Annals of Mathematical Statistics, 30(2), 408–419.

the bulk of which is very well summarized in the introduction of

Fishburn, P. C. (1996). Finite linear qualitative probability. Journal of Mathematical Psychology, 40(1), 64–77.

Althought the setup of the papers is in terms of probability jugments, it can be reinterpreted from a preference point of view as follows :

A finite set of objects $S = \{1,2,\dots,n\}$ (in your problem $S$ could contain the pieces of the cake)
A preference relation $\succeq$ over $2^S$ the set of subsets of $S$.
The question : when is $\succeq$ representable by an additive utility function $U$ on $2^S$.

A classical conjecture by de Finetti's was that the following conditions should suffice (here I follows the presentation in Fishburn (1996)):

(Order) : $\succeq$ on $2^S$ is a weak order,
(Nonnegativity) : $A \succeq \emptyset$ for every $A \in 2^S$,
(Nontriviality) : $S \succ \emptyset$,
(Additivity) :  For all $A,B,C \in 2^S$, if $(A\cup B) \cap C = \emptyset$, then $[A \succ B] \Leftrightarrow [(A\cup C) \succ (B\cup C)]$.

de Finneti observed that these were necessary but could not determine whether they were sufficient. Eventually, Kraft, Pratt & Seidenberg (1959) provided a counter-example as well as an additional condition which, together with the four others implied the existence of an additive representation:

(Strong additivity) : for all $m\geq 2$ and all $A_j,B_j \in 2^S$, if $(A_1,\dots,A_M)$ and $(B_1,\dots,B_M)$ contain the same number of replicas of each elements of $S$ (i.e. if $s_1$ appears three times in all the $A_j$ sets, it also appears three times in all the $B_j$ sets, etc) and $A_j \succeq B_j$ for all $j<m$, then we do not have $[A_m \succ B_m]$.

The last condition is often referred to in the literature as the "cancelation" property. Now (Strong additivity) is not the most intuitive condition. In general, it can be hard to to check and navigate, which has spurred a large literature on alternative sufficient condition. I can send you a reading list if you are interested. Unfortunately, I don't remember of any paper directly tackling preferences over subsets of infinite sets, like your real interval.

From my experience with these kinds of problems, changing the domain over which preferences are defined makes a huge difference in terms of the results that hold and the proof techniques you can use. If a result is not already out there in the literature, it is rarely easy to derive it from apparently similar results on different domains.


Question regarding Carlstrom and Feurst (1997) I am reading through Carlstrom and Feurst's 1997 paper Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis and had a question, although it could apply to other papers as well. In the paper the authors derive 9 equations that uniquely derive an equilibrium in their model. Then in the next section they run empirical tests by starting at a steady state and then hitting the system with productivity and wage shocks to see the dynamics.

What I am confused about:

The equations that uniquely describe the solution already have shocks in them, so I am a little confused about what the steady state in the empirics section is. Here is the best answers I could come up with: They taking out the shocks, deriving the steady state, and then seeing how the shocks will move the system away from the steady state and then back over time.
If anyone could confirm or deny this answer that would be great. This is a problem I have come across before when reading these papers with general equilibrium models with shocks.

What you address (and what is done in your referred paper) is called
Model Calibration
Many economic models use this method to determine one or more parameters:

Calibration is a strategy for finding numerical values for the parameters of artificial economic worlds.

As the widespread use of this technique, let me explain it with a universal example and order your statements to the correct steps here:
The Model

In the paper the authors derive 9 equations that uniquely derive an equilibrium in their model.

Let us construct a simple model to explain some dependent variable $y$. The only independent variable to explain $y$ is $x$. The only restriction in our model is, that $\frac{dy}{dx}=1$ must hold for any observation.
The steady state
Without any further requirements, it is simple to derive the whole model:
$$y=x + \mathbf{t}$$
What can be seen, is the appearance of an unknown variable t. As our model contained a differential equation, such additional variables occur. How to deal with them?
Calibration

Then in the next section they run empirical tests by starting at a steady state and then hitting the system with productivity and wage shocks to see the dynamics.

Make use of your economic model and calibrate t to your data. Thats exactly what the authors do in order to see the dynamics. Lets assume you have the following three observations:

|    y    |    x    |
---------------------
|    3    |    1    |
|    4    |    2    |
|    5    |    3    |

Calibration finds an optimized solution for our yet unknown parameter t. For the three observations above, t would have a value of $2$. Now, you have your full model given with the formula:
$$y=x+2$$
Further information
I recommend to read this paper, which discusses the use of calibration techniques in economic models. The authors discuss concrete various macroeconomic models on their critical use of calibration and offer more details and best practices on this technique.


How much should it cost to close the beach? For most of the past week a private surfing contest has closed off Steamer Lane
- one of California's most popular waves - while paying only a few hundred dollars in permit fees. I think this is far too cheap.

Consider the following thought experiment: If somebody were to set up
at the beach and offer \$1 to each surfer who stays out of water they'd
all decline. However, if the amount were upped to \$100, several would
accept. To me this indicates that the price to close off the beach should be tens of thousands of dollars rather than a few hundred.

Is this a reasonable way to price externalities? Is there some other model where it would make sense to charge only a few hundred dollars for beach closures?

The best way to find out the competitive value of the temporarily privatised beach would seem to be to auction licences, charge a tax based on the self-assessed value for holding them, and require the holder to relinquish them at the self-assessed value. This is basically the idea of Eric Posner & Glen Weyl’s Radical Markets (2018).

Given that the organiser of the contest has to commit to a suitable date (presumably during the right season, at the weekend, etc.) she will be willing to pay a tax for holding the licence based on a self-assessed value high enough to deter other (groups of) surfers from buying out her licence for that particular date. The other surfers will likely have less propensity to pay the assessed value of the contest organiser than to pay nothing for using the beach the following day.

That said, the public authority would likely need a mechanism for guaranteeing that the beach remains public in principle. This could be achieved by limiting the number of days per year that the beach could be privatised, or requiring qualitative criteria (such as an event) for issuing a licence. In any case the public condition is mutually exclusive with privatising the beach for dwelling.


Proof Based Math Education in Economics One of the things I've experienced as a graduate student is really the lack of math being a main factor in holding me back from approaching more advanced materials in microeconomics and macroeconomics. Often I find myself playing a lot of catchup. I primarily express this with reference to the lack of training in proofs based mathematics.
My question is: as economics educators what is the rationale for not exposing students to proof based mathematics at the undergraduate or masters level? (a basic intro to proofs class can go a long way).
Note: this question excludes those programs that are specialized PhD stream feeders.

I believe there are different goals to undergraduate and (research-oriented) graduate programs.
Most undergraduate students will not pursue a career in research. For them, different proof techniques may not be of first-order importance. In my eyes, they should learn basic stuff like incentives matter; thinking in terms of marginal changes; supply and demand; market power can be bad; what can be done with OLS; although the market is great it can fail with externalities or public goods; why does inflation matter; how to model asymmetric information; correlation and causality; solving a dynamic game backwards and credible threats; and so on. All of that can be taught without using heavy mathematical machinery. There are enough important concepts to teach and you can only do so much. However, I agree that it should be made clear that taking a few math classes can be very helpful if a career in research is planned.
Moreover, I think that I would not have enjoyed pure math without economic applications as an undergraduate. Usually, I become interested in some economic problem which then incentivizes me to learn new mathematical techniques. My impression is that most undergraduate students have even stronger feelings about that. I fully understand that it is hard to catch up on basic mathematical ideas as a grad student, but it would not have been much easier as an undergrad without a conviction to do research.
Different institutions have different approaches. Therefore, most PhD programs have a mandatory first-year that is quite heavy on proofs and mathematical techniques. Often there is also an additional math camp. The idea is to get everyone on a similar level.


Soft question: How do you create/draw/plot economic graphs digitally? Obviously I'm talking about a theoretical graph not one where you can just plot the data. The only two options I can think of are just using shapes in word/powerpoint or using TikZ in Latex which is very time consuming.
I would be interested to know what your preferred methods are for drawing good looking digital graphs.

Give @Giskards comments I'll put up my answer in the comments as answer. I usually fake the data and then use my favourite plotting program. For example here is the requested income substitution graph challenge created with R and GGplot2. For completeness I add the code, but given that it's quite long I add it to the end of my answer. Added bonus of GGplot/R is that if one is well versed with it it is simple to include LaTEX annotation.

Making a similar graph in Excel is also doable. I'll admit though that Excel becomes a pain once we want multiple axes and scales, and the same probably applies to GGPlot. And of course Excel doesn't work well with LaTEX.
Code to generate graph (all parameters can be adjusted, the only thing that needs to be fixed afterwards is the vertical position of the arrows and the text).
#Packages
require(ggplot2)
#Parameters
#Using a CD utility function for convenience and because it generates easy demands
#As the A in that function is just for scaling we'll set it to 1
#Exponent on utility function
alpha <- 0.5
#Price of goods
p_x <-1
p_y <-1
#Price of x after price increase
p_x2 <-4
#Budget
M <- 10

#Basic numbers as input
df<-data.frame(x_amount=seq(0,M/p_x,by=0.1))

#Budget constraint 1 & 2 (formulated in y-x plane)
df$BC_1 <-(M-p_x*df$x_amount)/p_y
df$BC_2 <-(M-p_x2*df$x_amount)/p_y

#Calculating utility for correct indifference curves
#By the marginal spending rule alpha/(1-alpha)*(y/x)=p_x/p_y
#Therefore y=((1-alpha)/alpha)*(p_x/p_y)*x
#By the budget constraint y=(M-p_x*x)/p_y
#Using that and solving gives x=(M*alpha)/p_x and y=((1-alpha)*M)/p_y
#Utility indifference curve 1
U1<-((M*alpha)/p_x)^alpha*(((1-alpha)*M)/p_y)^(1-alpha)
#Utility indifference curve 2
U2<-((M*alpha)/p_x2)^alpha*(((1-alpha)*M)/p_y)^(1-alpha)

#Indifference curve 1
df$indif1<-(U1/(df$x_amount^alpha))^(1/(1-alpha))
#Indifference curve 2
df$indif2<-(U2/(df$x_amount^alpha))^(1/(1-alpha))

#To find the final budget constraint first identify the x and y value
#To do this we set the first derivative of indifference curve 1 equal to
#the new -p_x2/p_y and find its root
f1 <- function (x) -alpha*(U1/x^alpha)^(1/(1-alpha))/((1-alpha)*x)+p_x2/p_y

Solution_x <- uniroot(f1,c(0.1,20))$root
Solution_y <- (U1/(Solution_x^alpha))^(1/(1-alpha))
#Determine the intercept

f2 <- function(M) M-p_x2*Solution_x - p_y * Solution_y
M2 <- uniroot(f2, c(0,30))$root

df$BC_3 <- M2/p_y - p_x2/p_y * df$x_amount

#Reshaped dataframe to long format
df_2 <- data.frame(x_amount=rep(df$x_amount, times=5),
                   y_variables=c(df$BC_1,df$BC_2,df$indif1,df$indif2, df$BC_3),
                   role=factor(rep( colnames(df)[2:6], each=length(df$x_amount)))
)

ggplot(data = df_2) +
  aes(x_amount, y_variables,colour=role)+
  geom_line(size=1)+
  ylim(0,20)+
  geom_vline(xintercept = Solution_x, size=1, linetype=3)+
  geom_vline(xintercept = (M*alpha)/p_x , size=1, linetype=3)+
  geom_vline(xintercept = (M*alpha)/p_x2, size=1, linetype=3)+
  geom_segment(x=(M*alpha)/p_x, y=3,yend=3, xend=Solution_x, colour="black", arrow = arrow(length = unit(0.25, "cm")))+
  geom_segment(x=Solution_x, y=5,yend=5, xend=(M*alpha)/p_x2, colour="black" ,arrow = arrow(length = unit(0.25, "cm")))+
  geom_segment(x=(M*alpha)/p_x, y=0.8,yend=0.8, xend=(M*alpha)/p_x2, colour="black", arrow = arrow(length = unit(0.25, "cm")))+
  annotate("text",x=3.2, y=3.7, label = "Substitution effect", size=3)+
  annotate("text",x=1.9, y=5.3, label = "Income effect", size=3)+
  annotate("text",x=3, y=1.2, label = "Total effect", size=3)+
  ylab("Amount of y")+
  xlab("Amount of x")+
  theme(legend.position = "none",
        panel.background = element_rect(fill = NA),
        panel.border = element_rect(linetype = 1 , fill = NA))


Do conceptual ideas that become standardised ever make money? TL;DR - Do standardised concepts ever make money?

Recently I have been wondering if conceptual ideas ever make money, more specifically whether a conceptual idea that is standardised ever makes money? If so, how does it do this? If not, why do they not make money?

An example of a concept that has become a standard is the OSI model, the OSI model is a conceptual idea which governs how traffic passes through a network from the physical layer (layer 1) right up to the application layer (layer 7). This concept has become a standard idea and guideline in networking so much so we now "speak in OSI" what that means is, if there's a cable issue it's a "layer 1 problem" and if there is a routing issue it's considered to be a "layer 3 issue"

This question is hard to answer because it can take so many perspectives. The only way I find to approach it is using examples.

Could John Nash profit from his paper in game theory? Could Einstein profit from general relativity? Yes, with prizes and recognition, but not everytime the concept is used. Not in a way analog to the copyrights of music or publishers.

If you talk about standard methodologies or standardized concepts, in the business world, several organisations strive for developing and enforcing standards, notably ISO and GS1. They do have revenue, mostly from consulting or memberships, but they are not-for-profit organisations, as having profit can drive standardisation away.

The history of Thunderbolt demonstrates how trying to make money of a standard (through royalties) can sometimes drive consumers to use another standard which is free, even if inferior.


What does it mean if the controls in my IV model are correlated with my instrument? I am seeking to understand what it means for my 2SLS IV model if my controls are correlated with my instrument (such that when I add additional controls to my model that are positively correlated with Y, the coefficient on my instrument declines).

Is it correct to conclude that my instrument is "invalid"?
Or is my instrument still valid, and this is normal?

I am having difficulty locating an answer. Thank you!

This would not make instrument necessarily invalid. For some 2SLS instrument model of form:
$$y_i  = \beta_0 + \beta_1 \hat{x_i} + \beta_2 k_i +\epsilon_i$$
$$x_i = \pi_0 + \pi_1 z_i + \pi_2 k_i +e_i $$
where $y$ is dependent variable, $x_i$ is the endogenous regressor, $k$ some controls and $z$ instrument the main conditions for instrument validity are:

$z$ has to be correlated with the $x$ variable $cov(x,z)\neq 0$ and have causal effect on $x$

$z$ can affect the $y$ only through $x$ and $z$ itself has to be exogenous $cov(z,\epsilon)=0$

Furthermore, instrument should not be weak which would invalidate inference from the regression and so 1st stage should have $F$-statistics higher then $10$ as a rule of thumb (although some new results suggest that actually correct rule of thumb would be having $F>105$ - see Lee, McCrary, Moreira, & Porter 2020).
You can find more rigorous proof of these conditions in econometric hanbooks such as Verbeek (2008) guide to modern econometrics or Angrist & Pischke (2009) Mostly Harmless Econometrics. The point is that none of the conditions directly say instrument cannot be correlated with other controls as long as it does not violates any other of the conditions. In fact omitting them could lead to omitted variable bias violating the condition that instrument should be endogenous if they are important. However, having highly correlated variables can inflate the standard errors of your model due to multicolinearity, this being said multicolinearity does not lead to bias it only reduces the precision of the estimates and reduces statistical power.


Collapse of Lehman Brothers: What did they have in their books? What kind of products did Lehman Brothers have on their books that caused the collapse? Do we have access to data on this topic?

We do have information on this topic. I’d recommend starting with the Financial Crisis Inquiry Commission report chapter on it, and review the New York Fed article on its resolution. Detailed information on the assets should be available from bankruptcy filings, though those will involve quite a bit of work to obtain.


How to demonstrate that a game always have a subgame-perfect equilibrium in pure strategies? If I have an specific extensive game, with only a finite set of strategies, how can I demonstrate that the game always have a subgame-perfect equilibrium in pure strategies? My first intuition was to show that in every subgame a pure strategy it's a solution to the problem (maybe not unique) and then there is always a pure strategies equilibrium. But I'm not sure.

You could represent the game in simultaneous form (matrix) to see all possible equilibria. If there is only one, then that's your subgame-perfect Nash equilibrium (since there are no other equilibria). If there are multiple equilibrias in the simultaneous representation, the extensive form allows you to see if some paths would never be reached given the structure of the game.

Essentially, the extensive form "proves" which paths would never be reached through ruling them out. The one path that is reached is your SPNE. An SPNE has a more strict definition. There is really no shortcut around the arithmetic in the extensive form since the definition of SPNE forces you to check for the one viable path.


Is there a name for this type of problem? I am having trouble formulating the concept I am thinking about. It has to do with looking at observed behavior of the sales of a particular product during each hour of the day, and trying to adjust prices accordingly.

If you have a time series of 24 pairs of values, $(x_1,y_1), (x_2,y_2), \ldots, (x_{24},y_{24})$, where $(x_t,y_t)$ represents the data at time $t$ o'clock: $x_t$ is the number of sales and $y_t$ is the average price paid (both at time $t$).

Given this information, is there anything that can be deduced about how the product should be priced? What about by the hour?

My background is not in economics, so I don't know if there is a framework 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.


Assets, Liabilities, Equity I am writing a business plan based on some old notes from a master in economics.

However I am I bit confused. Can you please confirm the following is right? (above all what's marked in bold)

Assets: anything I can sell and make money from (patents, real estates, the product I sell, etc. <-- the price I have paid them on the first place)
Liabilities: all my costs (salaries, leasings, equity given to investors, ...)
Equity: what I own (possibly not already paid) = actual money I get from selling these things, without subtracting costs (i.e. liabilities) ==> e.g.  the economic value of selling patents, real estates, my product etc. (possibly higher than the original assets cost)

You are confusing your balance sheet with your income statement, and putting a few things in the wrong bins. The basic accounting identity is:

$$ Assets=Liabilities+Owners' Equity$$

Assets are generally valued not at cost (or as you put it, "the price I have paid them on the first place"), but at either their hold-to-maturity value (i.e., the present discounted value of all future cash flows from the asset), or their mark-to-market value (what you can sell the thing for).

Liabilities are money owed to others that is unpaid as of the date of the financial report— salaries do not generally appear on the balance sheet, except for a small amount that has accrued but hasn't been paid out yet. Salaries will primarily appear on the income statement. Lease accounting is complicated, but if you have capital (not operating) leases, those will show up on both sides of the balance sheet under GAAP.

Equity (including equity held by investors other than yourself) is simply the residual once the value of outstanding liabilities is subtracted from the value of assets. It is definitely not the "actual money [you] get from selling these things without subtracting costs."


I bought a house on a mortgage. If its price changes later, how will it affect the ease of repaying the loan? I had some difficulty in understanding this paragraph in an article explaining the movie, 'The Big Short':

  Most of us when buying a house take out a loan (mortgage) and pay back
  the purchase price over time. We also usually hope that the value of
  the house we buy will go up not down. In the US, many people had
  come to assume that house prices would always rise, because they’d
  risen without fail for many years. This attitude saw mortgage lenders
  offering riskier and riskier loans to people who’d only be able to
  make payments if the price of their house continued to increase.

https://www.ecnmy.org/engage/the-big-short/

If a mortaged house decreases its market price after the mortage was made, the bank is in risk in case of default - it might be unable to recover the amount it loaned. In practice this doesn't change the amount you owe to the bank or the monthly payment -  you owe the same regardless of the value of the house after making the mortage.

I believe the author meant that the people the banks were lending to would only be able to afford to pay the mortages if the economy kept on booming, and they would remain employed.


Steady state Solow model with exogenous technological change Consider the following question:

So, assume the standard function for production:

$$Y_t = A_t K^\alpha_tL^{1-\alpha}$$

where $L$ is fixed.

Then, the growth rate of output is:

$$g_Y \approx g_A + \alpha g_K $$

Case without technological change

In the standard Solow model with constant $A$, $g_A=0$. In the steady state, $sY=dK$ (investment equal depreciation), and $g_Y = g_K = 0$, consistent with the above equation.

Case with exogenous technological change

Here, $g_A=2\%$ (as per the question). But then, there is clearly no steady state, as the marginal product of capital is permanently increasing, thereby expanding capital. In the standard diagram, this means a shift of the function $sY_t$ upwards every period, meaning an ever increasing "steady state", which is never achieved. Hence, to me the question does not make sense.

Finally, here is the official answer:

Now, to me this answer is wrong. How can $Y$, $A$, and $K$ growth at the same rate? The equation of growth written above denies this!

Is the question and/or answer wrong? Am I missing something? Am I wrong?

To simplistically answer your question, use the following:
$Y = K^\alpha (AL)^{1 - \alpha}$

In order to prove all three can be equal:
We will assume that technological progress is labor augmenting (Harrod Neutral) or "labor saving", while holding the following true:

Returns to capital are roughly constant over time.
Capital share of income is roughly constant over time.

The Harrod Neutral is associated with a capital-output ratio that is constant (K/Y) in our "steady state".

Capital Accumulation
In the basic Solow model, (1).
$$ \frac{\dot{k}}{k} \equiv s\frac{y}{k}-(d+n)$$

For growth rate per capita capital to be constant, y/k = Y/K must also be constant. (Characteristic of the Harrod Neutral)

We Need To Define The Balanced Growth Path With Technological Progress
Taking the original production equation:
$Y = K^\alpha (AL)^{1 - \alpha}$

and dividing by AL (number of effective labor units) we are given our production function representing effective labor.
$$ \tilde{y} \equiv \tilde{k}^\alpha$$

Doing The Same For Capital Accumulation
Follow steps below:
$$\frac{\tilde{\dot{k}}}{k} = \frac{dln(k/AL)}{dt}$$

$$ \frac{dlnK}{dt} - \frac{dlnA}{dt} - \frac{dlnL}{dt} $$

$$\frac{\dot{K}}{K} - \frac{\dot{A}}{A} - \frac{\dot{L}}{L} = \frac{\dot{K}}{K} - g - n$$

then using this to finding our Capital Accumulation equation below:

$$\frac{\dot{K}}{K} = S \frac{{Y}}{K} - d$$
$$\frac{\tilde{\dot{k}}}{\tilde{k}} = s\frac{Y}{K} - d - g - n$$
And, $$\frac{Y}{K} = \frac{Y}{AL} \frac{AL}{K} = \frac{\tilde{y}}{\tilde{k}}$$

Then,
$$\frac{\tilde{\dot{k}}}{\tilde{k}} = s\frac{\tilde{y}}{\tilde{k}} - d - g - n$$

$$\tilde{\dot{k}} = s \tilde{y} - (d+g+n)\tilde{k}$$

Finally, combining our production function with capital accumulation we get an equation (6) that represents the Solow model with tech changes.
$$\tilde{\dot{k}} = s \tilde{k^\alpha} - (d+g+n)\tilde{k}$$

So our steady state is when (7) is true.
$$\tilde{\dot{k}^*} = 0$$

If we set this to be true for our steady state (denoted by *) levels of capital and output per effective labor. (8 and 9)
8: $$\tilde{k^*} = [\frac{s}{d+n+g}]^\frac{1}{1-\alpha}$$
9: $$\tilde{y^*} = [\frac{s}{d+n+g}]^\frac{\alpha}{1-\alpha}$$

In the steady state: (10)
Capital (and income) per capita grow at the rate of exogenous technological growth.

$$\tilde{k} = K/AL$$
$$k = K/L$$
$$k = A\tilde{k}$$

$$\tilde{k} = \tilde{k}^* = [\frac{s}{d+n+g}]^\frac{1}{1-\alpha}$$
$$k(t) = A(t)\tilde{k}^*$$
$$lnk(t) = lnA(t) + ln\tilde{k}^*$$
$$\frac{\dot{k}}{k} = \frac{\dot{A}}{A}$$

If you graph out
$$\tilde{\dot{k}} = s \tilde{k^\alpha} - (d+g+n)\tilde{k}$$

Any savings rate changes, s, change the savings curve and therefore change $$\tilde{k^*}$$
Population or depreciation changes, n and d respectively, rotates the straight line, (d+g+n)k.
Changes in these affect the growth rate of per capita capital and per capita income only outside the steady-state.
exo-tech growth changes the graph sort of like n and d by changing the level of $$\tilde{k^*}$$

This exo-tech growth changes the growth rate of per capita capital and per capita income in the steady state (along balanced growth paths).


How are shell companies used for tax evasion? The recent release of leaked documents on Mossack Fonseca has information on corporations and individuals using the firm's services for, among other things, tax evasion:

The massive security breach shows how a global industry of law firms and big banks sells financial secrecy to politicians, fraudsters and drug traffickers as well as billionaires, celebrities and sports stars. [...]
Using complex shell company structures and trust accounts Mossack Fonseca services allow its clients to operate behind an often impenetrable wall of secrecy. Mossack Fonseca's success relies on a global network of accountants and prestigious banks that hire the law firm to manage the finances of their wealthy clients.
Panama Papers and Mossack Fonseca explained, Australian Broadcasting Corporation

What are "shell companies" and how can they be used to hide money or avoid paying taxes?

Another key feature of those shell companies is that they hide the ultimate beneficiary of the transactions. Banks, insurance companies and most financial services firm must make enquiries as part of the "Know Your Customer" (KYC) regulations: they should be able to find out who will benefit ultimately from the transactions, or in the name of whom they are carried out. THeoretically (ate least in the EU), if they fail to identify an ultimate beneficiary, they should refuse to carry out the transaction AND warn the responsible authority (typically the local equivalent or representative of the FATF - Financial Action Task Force)

But a succession of shell companies in different countries, in particular in countries which apply a strict confidentiality of the investors of a company, make it very hard to be sure that the beneficiary identified is indeed the ultimate beneficiary.

Thus, those shell companies also serve the purpose to hide their owner to their counterparts. This feature is most appreciated for tax evasion and money laundering (obvisouly).


Games with perfect but incomplete information in real life It is hard to imagine such a game. Here is an example from wikipedia:

  Suppose you are playing a game of chess against an opponent who will be paid some substantial amount of money if a particular event happens (an arrangement of pieces, for instance), but you do not know what the event is. In this case you have perfect information, since you know what each move of the opponent is. However, since you do not know the payoff function of the other player (which will affect its behavior even if it does not alter your own victory conditions), it is a game of incomplete information.

Do such game situations exist in real life?

What kind of equilibria can we observe?

Is there a dominant strategy that could be adopted in such a game? Is there a way to maximize your gain even though you don't know all the details?

Still in the chess example, you might start forming some beliefs after a few moves, if you notice for instance that the opponent is always sacrificing his pawns for nothing, maybe in his desired position he needs to have a certain amount of pawns... Or if given the opportunity to exchange queens and in a classical game of chess it would have been advantageous, but he doesn't do it, assuming he takes rational decisions, perhaps it is absolutely necessary for him to keep the queen in order to win with the altered rules.

You might assign certain probabilities to the different possible goals of your opponent and update them with every move he makes.

A classical example of a game with perfect but incomplete information is an English auction. We know what all the bids have been up to this point but we don't know everyone's valuation of the good being auctioned.

In general, formulating a strategy in this case involves some beliefs about your opponents' payoffs. Typically these are exogenous to the game but I guess you could have some revealed preference throughout an extensive game.


How do economies grow? These days, we hear again and again about the so-called "need" for economic growth. But how do countries actually grow economically? That is, why/how does their GDP increase over time?
Related, what are policies that are believed by economists to interact the most with growth? And what are these channels of interaction? I'm not looking for dogmatic answers on this part, make sure that you state the causal chain as neutral as possible and link references when possible.
See also

What is the relevance of economic growth?
What is the Gross Domestic Product (GDP)?

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

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

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

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

Labor

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

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

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

Capital

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

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

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

Technology

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

So then, what are good policies/channels?

Increase investment

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

Increase effective labor

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

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

better education
training on the job
couching of unemployed

Increase technology

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

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


Venezuela Petro Cryptocurrency As I understand it, a primary feature / requirement of cryptocurrency is that it is not controlled by a government actor: it is decentralized.  If this is true and the Petro is controlled by a government (i.e. it can 'mint' more coins):

What is the reason to implement cryptocurrency in a manner that allows for greater ease of 'printing money'?

Cryptocurrency is never a good medium of trade exchange compare to printed notes.

Anyone follows the history and trend of cryptocurrency can tell you that, cryptocurrency has become speculative medium than a currency itself. The best scenario to describe the speculation is various Initial coin offering(ICO) that went boom and bust.

A cryptocurrency such as Petro coins does not fair better than others, even Venezuela government say it is "backing" with something like oil. Because the logistics are too complicated and costly. Thus, Petro coin is anything but just yet another ICO to attract speculators to pay it in dollars(or any foreign currency that Venezuela needs).

In short, something like Petro is not going to replace the currency, but as a tool or "virtual commodity honeypot" used by Venezuela to get foreign currency without any sound production.


Compute yield to maturity for a bond with coupons when price is different from face value Given the formula  $P = \sum_{t=1}^n \frac{CF_t}{(1+i)^t} $
 we can apply it to the case of a bond with constant coupons so that :

$\displaystyle P =\sum_{t=1}^n \frac{C}{(1+i)^t} + \frac{FV}{(1+i)^n}  \implies P = C(\frac{1-(1+i)^{-n}}{i})+\frac{FV}{(1+i)^n}$

with  $P$ = price , $C$ = coupon at the time $t$ , $FV$ = face value , $i$ = yield to maturity

My problem : How is it estimated $i$ when $P\neq FV$ and $P, C,FV$ are known ?

I think that it's not possible to obtain an exact result , because it doesn't seem possible to separate the $i$ from the rest . I tried to use Taylor formulas somehow to get an approximation but I haven't come to anything.

EDIT :

Is bisection method the only possible way to proceed ? Is something about polynomial approximation possible?

Following the suggestion by Brian Romanchuk of the 'quick and dirty' bisection method in the comments, I wrote this python program to estimate the yield to maturity :

def find_i(P, C, FV, n, epsilon):

    if P > FV : i_min, i_max = 0 , C / FV
    elif P < FV : i_min, i_max = C / FV , 10
    else : return C / FV

    while True :

        i_mid = ( i_max + i_min ) / 2 # mid point of the current intervall
        point = C*(1-(1+i_mid)**(-n))/i_mid + FV/(1+i_mid)**n - P # it should converge to 0

        if abs(point) < epsilon  : return i_mid # if point is close enough to 0 then finish

        if point > 0 : i_min = i_mid # [i_mid,i_max] : new intervall
        elif point < 0 : i_max = i_mid # [i_min,i_mid] : new intervall

P, C, FV, n = 1100, 100, 1000, 10
epsilon = 10**-5
i = find_i(P, C, FV, n, epsilon)

The choice of $i_{min}$ and $i_{max}$ is important to estimate $i$ in edge cases.
Dealing with negative interest is harder.

I'm going to update the method to improve the computation , for now I list the relavant facts used :

1) When $P = FV $ then $i = C / FV$

2) $P$ and $i$ are negative correlated when $i>0$


Do the number of days in a month affect monthly return? (seasonality) When I see data like monthly return on news or tv, I always find the concept a bit strange, because obviously if you calculate monthly return for February and March, all things being equal, the monthly return of March would be slightly larger than February due to the fact March has more days than February. Is this the case in real life?

Let's make a fake example.

Compound interest of 0.1% over 30 days gives

$$1.001^{30} = 1.030439088$$

Compound interest of 0.1% over 31 days is

$$1.001^{31} = 1.031469527$$

And the percentage change is 1.000970497. That is, you would over estimate the growth rate of a stock by 0.009% if you would compare 30days and 31days without adjusting for it.


Utility maximization problem : free product vs priced product? Here is the original question :

  The ESPN cable TV network runs a major sports information site at www.espn.com. Most of the content is free, but ESPN has a premium membership (see its "Insider") available for a monthly or an annual fee. Similar, but fee-free, sports content can be found at the Web sites of CNN Sports Illustrated, sportsillustrated.cnn.com, and CBS Sports Line,www.cbssports.com. Since ESPN has put a price tag on some of its sports content, it implies that the utility of a premium membership cannot be found at a no-fee site and is therefore worth the price. Is this the case? Use the utility-maximization rule to justify your subscribing or not subscribing to the premium membership.

Which product will yield maximum utility?
Let say if one content is available for free and the other is priced but a utility of that cannot be found anywhere else.
Applying the law of Utility-maximization I get this
( Marginal utility of fee-free content)/(price of fee-free content)   ≠ ( Marginal utility of premium content)/(price of premium content )

So , I am thinking regardless of the price of a premium content the fee-free content’s marginal utility over price will never equal the marginal utility of premium content over the price of premium membership. So, why will one buy a premium product?
Am I correct on this?

I think there are some problems with the framing of your question. Some points...

There are some assumptions that need to be added for a meaningful answer.

Diminishing returns, budget constraint, free disposal etc.
In terms of utility maximization, there needs to be a budget constraint. if you add one and seek to maximize utility, the consumer will hold $x_2=\frac{w}{p}$ (spend all their money on good 2, and then hold an infinite amount of good 1.

If you are thinking of something like an app, consider non monetary costs. They operate in the same way. Like the time value of playing a worse app. or movies, if you are given a choice to watch a terrible movie for free or pay to see a good movie, you may elect to pay. In which case time is a factor. You can't consume an infinite amount of terrible movies at time $t$.

In summary, you need to add more to the question. If a good is free, marginal utility has to diminish and $\frac{du}{dx}$ needs to equal $0$ at some point or supply has to be finite. Until at least that is satisfied, the consumer will spend all money on on $x_2$ and hold an infinite amount of $x_1$


What is the reason of devaluation in Turkish Lira? I guess there is a some fundamental issues in the economy but I wonder the apparent reason of the recent devaluation in Turkish Lira?

Does Turkey need to pay debt in very short term? How much is it? What is the reason of the debt?

The recent shift was likely two major interrelated reasons:

First, there was already relatively high uncertainty regarding the future viability and value of the currency (as @zeta-band noted, they're already incurring high deficits).

Second, Erdogan has made statements suggesting that, if re-elected, he'll take more direct control over the central bank. Given that he'd likely institute policies that would lead to higher inflation (or force haircuts on foreign debt holders), investors see that as a worrying potential future outcome.

Though at the same time, the rising interest rates (which, while lower than rates in Turkey, are higher than they were previously) in other Western countries has made investment in places other than Turkey more alluring, which also can devalue the Lira.

EDIT 2:

Perhaps clarifying that sentence a bit would be helpful (I left off an implied phrase, which is bolded below, which might have led to confusion)

  rising interest rates in other Western countries has made investment in places other than Turkey more alluring than they comparatively used to be.

I'm saying investors consider a variety of different factors when deciding where to invest. If everything about two countries was absolutely equal (both currently and into the future) then we would expect the investor to put more money in the country who has comparatively higher interest rates. However, this all else being equal assumption clearly never holds in the real world- countries have different political risks, economic risks, exchange rate risks, etc. that investors consider.

At the same time, even if every investor evaluates all of these risks identically (meaning everyone looks at the risks in both countries and agrees how likely each event is to occur, and how each one would affect any given investment) we'd still expect to see some variation in investment patterns. Why? Because every investor is optimizing over an entire portfolio, and is considering different specific investments. Additionally, every investor has their own risk preference, a more risk averse investor might be willing to forgo a higher expected return in one country for the comparative "safety" of another.

Which takes us back to the case of Turkey. It's true that the interest rates set by the Turkish government are quite high compared to other countries. However, if you're a US-based long term investor (meaning here the projects you'd be investing in wouldn't allow you to get a return on your investment for a long time) you might be worried about other perceived risks (like future inflation) that would make the high interest rate not enough to overcome the potential risks.

So what do we see? We see that there are some international investors who choose to invest in the US (or Europe, China, India, etc.- just not Turkey), some who choose to invest in Turkey, and some who split their resources between them. Furthermore, we can ask a hypothetical question: for investors in group 1 (non-Turkey investors), all else equal, how high would the interest rate have to be to induce you to invest? Clearly the answer is higher than the current rate, but at the same time, we'd expect at least some of them to shift investment if the Turkish interest rates were 75%. Clearly, as the Turkish interest rate goes up, more and more of those investors would shift resources into Turkey.

What we can then do, however, is consider that second and third group of investors (those who invest at least some of their resources in Turkey) and as them "how would your portfolios change if the US interest rate wasn't 1 or 2%, but 50%?" Obviously, we'd expect those investors to shift at least some of their investments from Turkey to the US.

The critical thing, however, is that there isn't a discontinuity. That means that as one country raises their interest rates a bit, some investors would likely shift some of their resources into that country. What we care about is the marginal investment in each country- the investment that was only just barely worth it given the conditions. These are the investments that we expect to shift.

So in conclusion, what's driving the devaluation is two fold. On one hand, there's a perception of increasing risks inside Turkey. On the other, the return for investing in places like the US are increasing from what it was previously. These two forces (one pushing down the attractiveness of investment in Turkey; one pushing up the attractiveness of investment in the US) are working in the same direction- to push investment out of Turkey, devalue the currency, and push them into other countries.


Microeconomics: first fundamental theorem of welfare Can somebody tell me why part (2) of this proof is of any relevance?
(1) Assume that $x$ is Pareto-dominated by $y$. Since $x_i$ is optimal for consumer $i$:
if $y_i\succ x_i$ then $p\cdot y_i > p\cdot x_i$
(2) Local non-satiation even implies
if $y_i\succeq x_i$ then $p\cdot y_i\geq p\cdot x_i$
(3) Adding up: $p\cdot\sum y_i > p\cdot\sum x_i= p\cdot w$, in violation of feasibility. ($w$= initial endowment)

The most common version of Pareto dominance says that an allocation is Pareto-dominated if there is another feasible allocation in which at least one agent is better off and everyone else is at least as well off. In particular, the latter allocation can include consumers that are just as well off as before.
It follows from the very definition of a competitive equilibrium that (1) holds. That a consumer chooses the best bundle they can afford means that every better bundle must be unaffordable and, therefore, more expensive.
Now, the sum in (3) is not just over those agents that are strictly better off, it is also over those who are equally well off. For those, one only gets the weak inequality (2) using local-nonsation.
Here is an example where local-nonsation is violated and in which a competitive equilibrium is not Pareto-efficient, showing the importance of the assumption of local non-satiation for the first welfare theorem:

There are two goods and two consumers. Both consumers have the initial
endowment $\omega_1=\omega_2=(1,1)$. For consumer 1, both goods are
perfect substitutes; consumer 1 wants the sum of the amounts of both
commodities they consume as large as possible. Consumer 2, does not
care what they get, they are indifferent among all consumption
bundles. You can check that there is a competitive equilibrium in
which both consumers simply receive their endowment and both goods
have the same price, $p_1=p_2>0$. But the unique Pareto-efficient
allocation gives everything to consumer 1, they receive the bundle
$(2,2)$ and consumer 2 the bundle $(0,0)$. Every allocation that
Pareto-dominates the proposed equilibrium allocation has consumer 1
being better off and therefore receiving a more expensive bundle (for
the equilibrium prices), but consumer 2 receiving a cheaper bundle
that is still as good as before.

There is also a weak notion of Pareto-efficiency: An allocation is weakly Pareto-efficient if there is no feasible allocation in which everyone is strictly better off. One can prove that every competitive equilibrium is weakly Preto-efficient even without local non-satiation: If everyone is better off, (1) implies that everyone receives a more expensive bundle and then we can directly go to (3).


GDP simple question got me confused: the sale of a capital asset a) Delta Air Lines buys a new jet from Boeing for 200 million dollars.

b) Delta Air Lines sells **one of its jets to Kim Kardashian for 100 million dollars.

So..

a) $200 million investment, purchase of the final good, so GDP increased by 200 M

b) No change, but why? Even if the had bought the plane for 50 million and made profit by selling it to Kim? Here's my in length answer I am not too certain of:

Does not change. Why? This good was already included in GDP. It was produced and sold. It has not been modified by Delta Air Lines, thus absolutely no value added to this plane.  It is simply the ownership transfer of a good that was bought. However...Wasn't that a service? I mean, Delta made it EASIER for Kim to buy a plane. They provided a service, so a profit would be added to GDP...NO?

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.


Externalities from motor vehicles - more recent estimates? I am looking for estimates for the externalities from motor vehicles.

There's an excellent paper "Automobile Externalities and Policies" (2007) on this exact issue, but it's a bit old now.

I was wondering if there was more recent/updated study that does something similar?

Handbook on the External Costs of Transport – Version 2019

Commissioned by the European Commission and produced by the research firm CE Delft. I think it was first published in 2008 and had a 2014 update. This is the latest 2019 update.


Cobb Douglas relation with uncompensated law of demand Does a Cobb Douglas or homothetic function satisfy the uncompensated law of demand?

Cobb-Douglas
Short answer
The Cobb-Douglass utility function is additively separable (take logs). Additively separable utility functions have normal goods (i.e. demand increases with income). Normal goods have negative own price effects, so they satisfy the law of demand.
Long answer
Consider the Cobb-Douglas utility function $u(x_1, \ldots x_n) = \prod_{i = 1}^n (x_i)^{\alpha_i}$ with $\alpha_i \ge 0$ and assume wlog that $\sum_i \alpha_i = 1$.
Then demand for good $i$ is given by:
$$
x_i = \frac{\alpha_i y}{p_i}
$$
Take two price vectors $p_1 = \begin{bmatrix} p_{1,i}\\ \vdots \\ p_{1,n} \end{bmatrix}$ and $p_2 = \begin{bmatrix} p_{2,i} \\ \vdots \\ p_{2,n}\end{bmatrix}$ with demands $x_1$ and $x_2$. We want to show that $(p_1 - p_2)' (x_1 - x_2) \le 0$.
We have:
$$
\begin{align*}
(p_1 - p_2)'(x_1 - x_2) &= p_1' x_1 - p_1' x_2 - p_2' x_1 + p_2' x_2,\\
&= y - \sum\frac{p_{1,i}}{p_{2,i}}\alpha_i y - \sum \frac{p_{2,i}}{p_{1,i}} \alpha_i y + y,\\
&= 2 y - y \sum_i \alpha_i\left(\frac{p_{1,i}}{p_{2,i}} + \frac{p_{2,i}}{p_{1,i}}\right),\\
&= 2 y - y \sum_i \alpha_i \frac{(p_{1,i})^2 + (p_{2,i})^2}{p_{1,i}p_{2,i}},\\
&= 2 y - y \sum_i \alpha_i \frac{(p_{1,i} - p_{2,i})^2 + 2 p_{1,i}p_{2,i}}{p_{1,i}p_{2,i}},\\
&= 2 y - y \sum_i \alpha_i \left(\frac{(p_{1,i} - p_{2,i})^2}{p_{1,i}p_{2,i}} + 2\right),\\
&= 2 y - 2 y - y \sum_i \alpha_i \frac{(p_{1,i} - p_{2,i})^2}{p_{1,i}p_{2,i}} \le 0
\end{align*}
$$
Homothetic preferences
Demand functions from homothetic preferences are linear in income:
$$
x(p,m) = \alpha(p) m.
$$
where $\alpha(p)$ is the unit income demand. i.e.:
$$
x(p,1) = \alpha(p) \ge 0.
$$
Then:
$$
\frac{\partial x(p,m)}{\partial m} = \alpha(p) \ge 0,
$$
so homothetic preferences generate normal demands. This means that their won price effect is negative, so they also satisfy the law of demand.


Hep with total differentiation of an AD function Is there anyone who can help me with a total differentiation exercize. I am starting with the following formula for AD:

$$x=\mu ^{-1}(g+i+e)$$

Where $\mu$ is the Keynesian multiplier.

And have to obtain the following result (which is obtained by total differentiating and diving through by x):

$$\dot{x}=-\dot\mu+\frac{\mu ^{-1}g}{x}\cdot \dot g+\frac{\mu ^{-1}i}{x}\cdot \dot i+\frac{\mu ^{-1}e}{x}\cdot \dot e$$

Thank you very much to anyone who wants to help me with every step.

For a variable $X$, let $dX$ denote its total differential. Let $k$ be a constant, and $X$ and $Y$ variables. You'll need the following rules:

$$dk = 0$$

(constant rule),

$$d(X + Y) = dX + dY$$

(sum rule),

$$d(XY) = Y \cdot dX + X \cdot dY$$

(product rule) and

$$d\left(\frac{X}{Y}\right) = \frac{ Y \cdot dX - X \cdot dY }{ Y^2 }$$

(quotient rule). These rules follow immediately from the definition of the total differential. (For more on total differentials, see e. g. chapter 8 of Chiang and Wainwright, Fundamental Methods of Mathematical Economics, 4th ed., McGraw-Hill 2005.)

Now let's start with your equation. By the product rule we have:

$$\begin{align}
dx & = d\left( \mu^{-1} (g + i + e) \right) \\
& = d\left(\mu^{-1}\right) (g + i + e) + \mu^{-1} d(g + i + e)
\end{align}$$

What is $d(\mu^{-1})$? Because $\mu^{-1} = \frac1\mu$, by the quotient rule,

$$\begin{align}
d\left(\mu^{-1}\right) & = d\left(\frac1\mu\right) \\[4pt]
& = \frac{ \mu \cdot d1 - 1 \cdot d\mu }{ \mu^2 } \\
& = -\frac{ d\mu }{ \mu^2 }
\end{align}$$

where we also made use of the fact that by the constant rule, $d1 = 0$. Plug this into the above intermediate result and also apply the sum rule:

$$\begin{align}
dx & = d\left(\mu^{-1}\right) (g + i + e) + \mu^{-1} d(g + i + e) \\
& = -\frac{ d\mu }{ \mu^2 } (g + i + e) + \mu^{-1} \left( dg + di + de \right) \\
& = -\frac{ d\mu }{ \mu } \cdot \mu^{-1} (g + i + e) + \mu^{-1} \left( dg + di + de \right) \\
& = -\dot\mu \cdot x + \mu^{-1} \left( dg + di + de \right)
\end{align}$$

where use was made of the definition of $x$, and the fact that $\frac{ d\mu }\mu = \dot\mu$.

Now we're almost there. Note that since $\frac{ dX }X = \dot{X}$ for any variable $X$, we also have $dX = X \cdot \dot X$; applying this to $g$, $i$ and $e$ and dividing the entire equation by $x$ then yields

$$\begin{align}
\dot x = \frac{ dx }x & = -\dot\mu + \mu^{-1} \cdot \frac{ dg + di + de } x \\
& = -\dot\mu + \mu^{-1} \cdot \frac{ dg }x + \mu^{-1} \cdot \frac{ di }x + \mu^{-1} \cdot \frac{ de }x \\
& = -\dot\mu + \frac{ \mu^{-1} g }x \cdot \dot g + \frac{ \mu^{-1} i }x \cdot \dot i + \frac{ \mu^{-1} e }x \cdot \dot e
\end{align}$$

which is the desired result.


Directed technical change, Acemoglu (2002) framework - trying to understand how an equation is derived You may have read Acemoglu (2002) on the topic of directed technical change. I am reading a similar research paper, and I could not understand how the author derived the final equation using integration. Below are details:

Equation A:

$Y_L=\frac{1}{1-\beta}\left [\displaystyle\int_0^{N_L}x_L(j)^{1-\beta}\,dj\right ]L^{\beta }$

Equation B:

$x_L=\left [\frac{p_L}{\chi_L(j)}\right ]^{1/\beta}L$

Equation C:

$Y_L=\frac{1}{1-\beta}p_L^{\frac{1-\beta}{\beta}}N_LL$

where,

$N_L$ is the number of varieties of machines
$x_L$ is the range of machines, so $x_L(j)$ is a machine type $(j)$
$\chi_L(j)$ is the price of machine type $(j)$

The rest are the usual macro variables.

The author uses the equation B in equation A and derives the equation C after integration. I was wondering if anyone could please help understand how this could be done?

The price $χ_L(j)$ is 1!

You only need to integrate a constant. That's why you have that equation.

(See p. 789, second paragraph, when he normalizes it to 1)


Why hasn't the huge increase in supply provided by Airbnb decreased prices? Simple supply and demand economics would suggest that the huge increase in the supply of rooms to rent by Airbnb should have reduced the price of rental significantly in those cities where Airbnb is most popular. However, this appears not to have happened. Why is that?

There are, for example, ~80,000 airbnb listings in London alone and only ~1500 hotels with ~146,000 hotel rooms.

In fact, it is argued that Airbnb increases prices!

  Our empirical results show that the overall causal impact of Airbnb on
  property values can be large. For example, in areas within 5km of Los
  Angeles’s central business district the price increase has been 14%.
  Within 2.5km of beaches, the price increase due to Airbnb has been
  almost 10%.

How can this be?

To summarize what's detailed below:

Most research finds some small hotel price decreases following Airbnb entry. But the substitution effect between hotels and Airbnb is hardly 1:1.
Furthermore, some research even found increases in hotel revenues in some areas where Airbnb appeared; this is hypothesized to be due to more discriminatory prices that the hotels can practice because Airbnb customers are generally thought to be more  price sensitive and once they largely leave the hotel market, the hotels are left with less price-sensitive customers, on average.
You are further confusing the substitution/competition of Airbnb with hotels with the effect of Airbnb on long-term rents and/or (residential) property prices. The effect of Airbnb on the latter is indeed generally found to be contrary to that on the hotel market, i.e. because Airbnb offers more (and higher-profit) options to residence owners, an increase in long-term rent prices and property prices is observed in some (but not all) areas where Airbnb operates.

Your research (on hotels) is probably not sensitive enough to small effects:

  There is evidence that Airbnb increases the supply of short-term travel accommodations and slightly lowers prices.  [...]

  Airbnb is essentially a positive supply shock to short-term accommodations. Like all positive supply shocks, it should be expected to lower prices. There is some accumulating evidence that Airbnb does exactly this. Zervas, Proserpio, and Byers (2017) examine the effect of Airbnb expansion across cities in Texas. They find that each 10 percent increase in the size of the Airbnb market results in a 0.4 percent decrease in hotel room revenue. They find that most of this revenue decline is driven by price declines. Evidence of the positive supply shock is particularly evident in the 10 American cities where Airbnb’s presence is largest. Dogru, Mody, and Suess (2019) find a negative correlation between Airbnb expansion and hotels’ average daily rates in the 10 U.S. cities with the largest Airbnb presence.

Also, Airbnb and hotels are not necessarily perfect substitutes:

  Further, it is possible that by substituting more strongly for a less-expensive slice of the traditional hotel market—leisure travel as opposed to business travel, for example—that Airbnb introduction might actually be associated with raising measured short-term travel accommodation prices, through a composition effect.

See elasticity of substitution for the theoretical notion.

Also, an MA thesis/study in Norway (not cited in that review) seems to support this idea of hardly perfect substitutability of hotels and Airbnb:

  I find that a 10 % increase in Airbnb supply decreases hotel
  revenue by 0.3 %. This effect is around 20 times smaller than the effect on hotel revenue of an increase in hotel supply.

As for your last claim "In fact, it is argued that Airbnb increases prices!" that source seems to be talking about property prices:

  Our empirical results show that the overall causal impact of Airbnb on property values can be large. For example, in areas within 5km of Los Angeles’s central business district the price increase has been 14%. Within 2.5km of beaches, the price increase due to Airbnb has been almost 10%. This shows that in areas that are attractive to tourists, increases in property values are substantial, while in areas without much tourist demand (e.g. Pasadena), effects are small.

I don't see any contradiction with the findings about hotels.

Also (long-term) rental prices being increased by Airbnb by offering another (short-term) use for the same (residential) resources is consistent with this increase in property prices. Going back to my first (EPI) link:

  The single biggest potential cost imposed by Airbnb comes in the form of higher housing costs for city residents if enough properties are converted from long-term housing to short-term accommodations. If property owners take dwellings that were available for long-term leases and convert them to short-term Airbnb listings, this increases the supply of short-term rentals (hence driving down their price) but decreases the supply of long-term housing, increasing housing costs for city residents.  [...]

  The mirror image of Airbnb’s positive supply shock to short-term travel accommodations is its negative supply shock to long-term housing options.  [...]

  Airbnb—though relatively new—is already having a measurable effect on long-term housing supply and prices in some of the major cities where it operates. For example, Merante and Horn (2016) examine the impact of Airbnb on rental prices in Boston. The authors construct a rich data set by combining data on weekly rental listings from online sources and data from Airbnb listings scraped from web pages. They find that each 12 Airbnb listings per census tract leads to an increase in asking rents of 0.4 percent. It is important to note that this is a finding of causation, not just correlation. [...]

  Barron, Kung, and Proserpio (2018) undertake a similar exercise with different data. They create a data set that combines Airbnb listings, home prices and rents from the online real estate firm Zillow, and time-varying ZIP code characteristics (like median household income and population) from the American Community Survey (ACS). To account for the fact that rents and Airbnb listings might move together even if there is no causal relationship (for example, if both are driven by the rising popularity of a given city), they construct an instrumental variable to identify the causal effect of rising Airbnb listings on rents. Using this instrument, they find that a 10 percent increase in Airbnb listings in a ZIP code leads to a 0.42 percent increase in ZIP code rental prices and a 0.76 percent increase in house prices. They also find that the increase in rents is larger in ZIP codes with a larger share of nonowner-occupied housing. Finally, like Merante and Horn, they find evidence that Airbnb listings are correlated with a rise in landlords shifting away from long-term and toward short-term rental operations.

If you want results that appear more genuinely paradoxical, there is a 2016 paper with those:

  This paper gives an overview of the activities of Airbnb in 14 European cities. Since
  Airbnb provides an online accommodation platform linking property owners and
  visitors, it could potentially affect both the hotel market and the domestic rental market
  in the localities in which it operates. We discuss the structure and the segmentation of
  the accommodation market, and then present some descriptive statistics on Airbnb
  activities in the 14 cities. Finally, we present some estimates of the impact of Airbnb on
  hotels and on rents, among the first estimates for European markets. We find Airbnb’s
  presence in a market has a negative effect on hotel occupancy rates, but a positive
  effect on total hotel revenue and the average daily rate they charge.  In the two cities we
  consider, the platform’s impact on the rental market is ambiguous, suggesting local
  market conditions are important. [...]

  We find that a rise in the number of Airbnb listings in a city was associated over this
  period with a fall in the average hotel occupancy rate, but an increase in the average
  daily rate received by hotels. The combined effect on total hotel revenues was
  ambiguous to slightly positive. On the other hand, the arrival of Airbnb is positively
  correlated with the rental price index in London, but not in Berlin.

However even the seemingly paradoxical divergence between hotel occupancy and their revenues (observed in Europe) has an (elasticity-based) explanation:

  Business travellers are much more able or
  willing to pay for convenience and reliability. For example, Airbnb hosts can cancel
  reservations at short notice and the platform does not penalize the hosts who renege on
  their promises, or compensate the users who find themselves nowhere to stay at short
  notice. The informality of the sharing economy does not (yet) sustain service norms. On
  the other hand, we always expect hotels to observe their promises. By screening out
  budget travellers, hotels may be better able to identify customers with less price-elastic
  demand and thus possibly even raise prices and obtain higher revenue thanks to the
  greater scope for price discrimination. Thus the entry of flexible low cost supply could in
  effect push up the prices and revenues of some hoteliers, though low-cost hotels may
  suffer.

Relevant theoretical notions for this last para: price elasticity of demand (PED); price discrimination.

Unfortunately, empirically testing this latter hypothesis that customers with lower PED go to hotels, wasn't done in that study. This requires more data on the customers than supply-side statistics convey.

There is however some corroborating independent research that confirms that Airbnb customers in the UK have the same age profile as low-cost/economy hotel customers.

  people
  aged 25–34 years are the largest group of users of
  Airbnb.  [...]

  Economy hotels are the most popular among
  people aged 25–34 years.

(Of course, age is not a perfect proxy for income or elasticity of demand.)


How to close the gap between non-Econ background and Macroeconomics I'm a first year PhD student with mathematical finance background, and am not quite familiar with all the assumptions/setup for macroeconomics. During study I found the math relatively easy but I'm having hard time to grasp the often critical relation between variables. For example capital market clearing implies that the total capital that firms have equal to the total assets that households have. First of all, I didn't even know there's a market clearing until I ask my TA, secondly, there are too many such assumptions I don't know. My professor would probably think it's too dumb to tell students about these because most of my classmates have an Econ background, but I don't and it's really killing me. Is there any good reference I can read, open courses I can watch that could help me with this? Given limited amount of time, I hope it won't take as much time as a full course. Thanks in advance.

Sorry if this sounds harsh, but:

You need to start asking more. You're not stupid for asking questions - you're stupid for not asking questions. Be upfront about your different background and ask away.

Of course you should try to research things by yourself, but a lot of assumptions are next to impossible to know or find out in a reasonable amount of time. I've got a 5 years of university economics - primarily in macro and I still struggle with assumptions. So, if you can't find it - ask! And ask your professor about some relevant books / articles.


Relation of Engel-curve to income elasticity of demand; is the slope of the Engel-curve equal to the elasticity of income? I learnt that $\frac{\Delta x}{\Delta m} \gt 0$ for normal goods, $\frac{\Delta x}{\Delta m} \lt 0$ for inferior goods, $\frac{\Delta x}{\Delta m} \gt 1$ for luxury goods and $0 \lt \frac{\Delta x}{\Delta m} \lt 1$ for necessary goods (where x is the amount of units of some good and m is the income).
Now, looking at the Engel-curve for homothetic preferences (i.e. Cobb-Douglas, perfect substitutes/perfect complements), I understand $\frac{\Delta x}{\Delta m} = 1$ for homothetic goods (btw is that a term, "homothetic goods"?).
Since the slope of the Engel-curve is $\frac{\Delta m}{\Delta x_1}$, I'm wondering if $\left(\frac{\Delta m}{\Delta x_1}\right)^{-1}$ is a way to determine the elasticity of demand, which, from my understanding, deals with the exact same values to categorise goods.
So I'm wondering if $\left(\frac{\Delta m}{\Delta x_1}\right)^{-1}$ is equal to the elasticity of income or if there's a way to determine the elasticity of income from the Engel-curve.

Income elasticity of demand
Let $q(y)$ be the Engel curve for a good, i.e. it gives the demanded quantity for a given level of income $y$ (keeping prices fixed). The income elasticity of demand is then given by:
$$
\varepsilon^y_q = \frac{\partial q}{\partial y} \frac{y}{q}
$$
It measures the percentage point change in demand $q(y)$, due to a 1$\%$ increase in income, $y$.
If $\varepsilon^y_q \ge 0$ the good is normal, if $\varepsilon^y_q < 0$, it is inferior. If $\varepsilon^y_q > 1$ it is a luxury good, while if $\varepsilon^y_q < 1$ the good is called a necessity.  The demand for luxury goods increases more than proportionally compared to income. Necessary goods increase less than proportionally.
The advantage of using the elasticity $\varepsilon^y_q$,  instead of the slop $\frac{\Delta q}{\Delta y}$ is that it is unit-independent
We can see this as follows:
$$
\varepsilon^y_q = \underbrace{\dfrac{\partial q}{\partial y}}_{\dfrac{kilos}{Euros}} \underbrace{\dfrac{1}{q}}_{\dfrac{1}{kilos}} \underbrace{y}_{\dfrac{Euros}{1}}
$$
This means that $\varepsilon^y_q$ does not change if we express the goods or the income in different units. For example the elasticity $\varepsilon^y_q$ does not change whether you express income in Euros or Dollars. Also, the elasticity does not change whether you express demand in kilos or pounds. As such, elasticities can easily be compared across countries and over different time periods. The slope $\frac{\Delta q}{\Delta y}$ does not have this advantage.
Homothetic preferences
If preferences are homothetic, the demand function is linear in income:
$$
q(y) = c y,
$$
where $c$ is a constant. In fact, substituting $y = 1$ into this equation gives:
$$
q(1) = c,
$$
so $c$ is the unit income demand (the amount that you would buy if you would have 1 Euro). This means that we can also write:
$$
q(y) = q(1) y.
$$
Engel curves are straight lines through the origin and with slope $q(1)$:
$$
\frac{\partial q(y)}{\partial y} = q(1).
$$
As such:
$$
\varepsilon^y_q = \frac{\partial q}{\partial y}\frac{y}{q(y)} = \frac{q(1)y}{q(y)} = \frac{q(y)}{q(y)} = 1.
$$
So demand curves arising from homothetic preferences have unit income elasticity.


Quantity theory of money Suppose the velocity of circulation (V) is constant. Annual growth rate of real GDP is 5%. The money
supply grows by 14% per year. Use the quantity theory of money to calculate the inflation rate.

My solution:
Given M: 14%, V: Constant, Y: 5%, P: ?
M * V = P * Y
14 * V = P * 5
P = 14/5, am I right?

If not, could you please lead me to the right answer..thanks

M * V = P * Y is not in a form of growth rate, so it needs to be changed into

ΔM + ΔV = ΔP + ΔY
Because V is constant, then

14 + 0 = ΔP + 5

ΔP = 9%

ΔP = Change in price = inflation


Why is sovereign rate a reference? I would like to know why we always focus on 10 years sovereign rates when we talk about interest rates ?
Let me clarify. I'm reading a paper from the Bank of England that emphasizes the fact that since the 80's the natural interest rate is falling. And to illustrate it they show us that 10 years sovereign rates are falling in USA and Europe. But why did they choose these sovereign bond as a proxy for the natural rate ? I mean, the natural rate is influenced by structural forces (demographic, productivity and so on..) while sovereign rate depends on other things (central bank policies, risk etc..).

Sovereign rates in developed countries represent the credit risk-free curve. What maturity on the curve you want to choose is an analytical choice.
The natural rate is in reference to a risk-free curve, and so should align with the sovereign curve. Also,  “Natural rate” is somewhat dated at this point, the preference is to use a more neutral term like r*.


Dummy Variables in Panel data I am building a regression model on some panel data of sales and I am rather new to econometrics. I was thinking of introducing some indipendent variables built as Dummy1*Dummy2 . Is this new interplay variable acceptable or is it going to lead to some estimation errors in the model?

Yes, it is acceptable. Consider a Mincer wage equation. Let's define a dummy variable Female taking on the value one for females and the value zero for males and a dummy variable Married to equal one if a person is married and zero if otherwise. Then, you can estimate a model that allows for wage differences among four groups: married men, married women, single men, and single women. For this you need to interact the dummy variables, for instance Female*Married. But be cautious, you must select a base group to avoid the dummy trap.
A good reference is the chapter "Multiple Regression Analysis with Qualitative Information: Binary (or Dummy) Variables" (Chapter 7) in Wooldridge Introductory Econometrics.


Age effect when controling for individual fixed effects and time fixed effects I have a individual-by-year panel. Although age is varying within an individual, its variation is fully absorbed when I include individual fixed effects and time fixed effects. This is because each individual has a unique birth year. My question is, when I run
$$
Y_{i,t} = \beta X_{i,t} + \alpha_i + \delta_t+\epsilon_{i,t},
$$
does "age effect" play a role in the estimates?

If I understand your question correctly, then in the current set up you describe, the answer is "maybe"--meaning, age might be effecting your estimate as an omitted variable, but you are currently not accounting for it if is doing so in anycase.
To clarify, individual fixed effects are simply controlling for omitted variables that vary among individuals, but not across time. These omitted variables could include such things as age, gender, religion, or whatever, but until they are explicitly accounted for in your model, they are just omitted. In your specification, what the fixed effects model is really doing is just splitting up your estimation of the regression line into multiple lines with their own intercept term, $\alpha_i$. An illustration to make it more clear:

In this image, you have OLS, which is trying to fit a regression line to all the data points. The coefficient you are trying to estimate, $\beta$ is the slope of this line.

Here are those exact same data points, but with a fixed effects model. What the fixed effects model is essentially doing is grouping the different entitities (or in your case, individuals) in the data together, and estimating a separate regression line for each of them. The $\alpha_i$ term is the intercept for each of those entitites/invididuals. The invididual fixed effects assumes that the omitted variables could take on different values for one individual compared to the other, but their effect on that individual themselves will be negligeable or only changing at a constant rate over time. In your model, you can see that the $\beta$ you are trying to estimate does not have the $i$ subscript, which means that you are trying to estimate a single, similar slope, for all these different regression lines, which in theory, should be moving in parallel (as can be seen in the image).
If you believe that one of the omitted variables in your model is actually having an effect on your estimates, such as age, these lines would no longer be parallel, and you would need to account for the omitted variable explicitly as you would do in OLS. So for example, assuming in your model $X$ is your regressor of interest, if you wanted to control for the "age effect", your specification could be something like:
$$
Y_{it} = \beta_1 X_{it} + \beta_2 \text{Age}_{it} + \alpha_i + \gamma_t + \epsilon_{it}
$$
Until you add this control for age to your model, your $\beta$ estimate is not accounting for systematic differences in the different age groups in your data, which, assuming there are differences by age groups, would mean your data is biased.
(*Note: images taken from this helpful document)


Interpretation of a differenced regression I'm experimenting with some data in R and I've found that though there is statistical significance between two variables, however their changes are not statistically significant.

I first ran a standard regression of revenue on price, adding a quadratic term to account for diminishing returns from increase in price. Giving us the formula:

$$y_{Revenue}=\beta_0+\beta_1Price+\beta_2Price^2$$

The results which were produced are:

> summary(lm(Wage~Price+I(Price^2)))

Call:
lm(formula = Wage ~ Price+ I(Price^2))

Residuals:
Min      1Q  Median      3Q     Max
-131.87  -87.77  -27.60   44.15  244.66

Coefficients:
           Estimate Std. Error t value Pr(>|t|)
(Intercept)  -1.650e+03  2.645e+02  -6.238 5.44e-06 ***
Price         3.640e-01  3.640e-02   9.999 5.28e-09 ***
I(Price^2)   -1.026e-05  1.129e-06  -9.086 2.41e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 116.9 on 19 degrees of freedom
  (7 observations deleted due to missingness)
Multiple R-squared:  0.8816,    Adjusted R-squared:  0.8691
F-statistic: 70.72 on 2 and 19 DF,  p-value: 1.577e-09

The second regression I ran was a regression of the change in revenue on change in price. Giving the formula:
$$\Delta y_{Revenue}=\alpha_0+\alpha_1 \Delta Price+\alpha_2 \Delta Price^2$$

Call:
lm(formula = diff(Revenue) ~ diff(Price) + diff(I(Price^2)))

Residuals:
   Min     1Q Median     3Q    Max
-82.52 -42.55 -11.98  19.20 142.36

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)
(Intercept)         5.093e+01  2.649e+01   1.923  0.07046 .
diff(Price)         1.343e-01  7.165e-02   1.874  0.07727 .
diff(I(Price^2))   -4.987e-06  1.691e-06  -2.950  0.00857 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 62.29 on 18 degrees of freedom
  (7 observations deleted due to missingness)
Multiple R-squared:  0.4521,    Adjusted R-squared:  0.3912
F-statistic: 7.426 on 2 and 18 DF,  p-value: 0.004449

Why do these variables lose their degree of  statistical significance while in the regular regression they are significant on the 1% level and how do you interpret such results economically?

If the levels specification is deemed acceptable,

$$y_t = \beta_0 + \beta_1 x_t + \beta_2 x_t^2$$

then it follows that the first-difference specification should not include a constant term in order to be methodologically consistent,

$$\Delta y_t = \beta_1\Delta x_t + \beta_2\Delta x_t^2$$

since $\Delta \beta_0 = \beta_0 -\beta_0 = 0$.

I suggest you run the specification of first-differences without intercept and see what happens.

Note: the slope coefficient estimates you should obtain in the first-difference specification without intercept should be close to the corresponding estimates you obtained in the levels-estimation. Otherwise, the maintained hypothesis of constant slope coefficients becomes questionable, or the model has other misspecification issues.

(this is not to be confused with the case where we run a regression without constant term but with the dependent variable and the regressors centered on their sample means -there we would obtain the exact same slope estimates with the levels specification that includes a constant term, as a matter of algebraic property of least-squares estimation).


Labor theory of value examples and exercises I'm looking for a working book of Marx's Labor Theory of Value. It would be nice if the book would explain his theory with calculated examples and some exercises with solutions that one can do. Since I'm a German I could read The Capital for myself, but I find it too complicated. Any good books on this?

Check these slides, which includes a fairly introductory analysis to the LTV, including some trivial examples and calculations.

Another introduction can be found here (part one) and here (part two).

Yet, this is the best I am aware of. It is an attempt to explain the theory to "undergraduates" using a simple example. Worth reading!