SIR Model and Information/ Innovation Economics The SIR Model from epidemiology is being discussed a lot recently due to the COVID19 scenario. I recently read this article about the Corona virus and what economics can offer-
 https://afinetheorem.wordpress.com/2020/03/13/the-simple-economics-of-social-distancing-and-the-coronavirus/

In the beginning itself, it mentions that "the most straightforward epidemiological model of infection – the SIR model dating back to the 1920s – is actually quite commonly used in economic models of innovation or information diffusion, so it is one we are often quite familiar with."

Which economic model or which class of economic models is likely referred to in this line? Where can I read more and learn about these models of information and innovation?

I'm not familiar with this area, so I can't tell you what are the seminal works, etc., but a quick search finds Gurley & Johnson (2017) "Viral economics: an epidemiological model of knowledge diffusion in economics":

  We model the diffusion of economic knowledge using an epidemiological model of susceptible, exposed, infected/inspired, and recovered populations (SEIR). Treating peer-reviewed journal publications as evidence of a scholar’s infection/inspiration with energy for an idea or theme, we estimate the coefficients of a four-equation simultaneous system for each of 759 sub-fields of economics. Results show that some sub-fields of economics (or viruses, here) grow endogenously much faster than others, and just over half have basic reproduction properties sufficient to ensure survival without the annual addition of new protégé scholars.

Which in some sense is amusing because it's applying the model to economics knowledge/research itself. (The paper looks like it has been in draft out there for a while; there's one dating back to 2011, which is freely available on SSRN.)

I suspect the paper cites some other relevant work(s) in this area.


For a given set of consumption bundles, how do we know there are bundles that the consumer is indifferent between? In my professors lecture notes (it's more like a book), he states four properties of preferences relations:

monotonicity
transitivity
continuity
completeness

He then goes on to discuss utility levels and indifference curves. He describes indifference curves as level sets and that consumption bundles that the consumer is indifferent between lie on the same indifference curve.

My Question:

For a given set of consumption bundles, how do we know there are any bundles that the consumer is indifferent between? I don't see how we can define indifference curves without knowing that.

We can obtain the result that Indiference Sets are not singletons, i.e. that consumption bundles that are equivalent under the preference relation must exist, by using a Consumption Set $X$ defined over $\mathbb R_+^n$, i.e. over real vectors, together with the property of Continuity of preferences (alternative-weaker prerequisites may exist though).

An equivalent way to state the property of Continuity of preferences (see for example Mas-Collel et al, ch 3.C), is that $\forall x \in X$ the upper contour set $UCS$ and the lower contour set $LCS$ are both closed, i.e they include their boundaries. The contour sets are sets that include consumptions bundles "at least as preferred as $x$" (upper) and "at most as preferred as $x$" (lower). In order for them to "include" their boundary", a boundary must exist in the first place. But their boundary is the Indifference Set, the set containing all bundles as preferred as $x$.

So your question essentially boils down to Is it possible that the boundary of the upper or lower contour sets of $x$, sets that are defined over real vectors, is a single point?

I believe that envisioning this in two-dimensions will show that it is impossible, but let's prove it.

Ad absurdum, assume that this holds for some $x \in X$. Then for any other consumption bundle in $X$, say $x'$, we will have either $x'>_{pr} x$ or $x'<_{pr} x$. In other words, any other point in $X$ will belong either in $UCS_x$ or in $LCS_x$, but not in both.

So consider two such points , $x''>_{pr}x>_{pr}x'$. Assume that $x'=\{\mathbf y_{(n-1)}, y_n\}$, $x''=\{\mathbf y_{(n-1)}, y_n+\epsilon(k)\}$, i.e. that they differ in only one of the goods in Goods Space, $\epsilon(k)>0$.

Transform now these two points into two sequences of points, $\{x''_k\}$ and $\{x'_k\}$, indexed by $k= 1,...$ and by constructing the sequence $\{\epsilon_k\}$ such that $\{\epsilon_k\} >0\; \forall k$ but also $\lim_{k\rightarrow \infty} \epsilon_k = 0$. The consumption space as defined permits these constructions.  We note of course that $\{x'_k\}$ is a constant sequence since its value does not change  as $k$ changes, but that's perfectly legal.

Consider now the sequence of pairs, for each $k$, $\{(x''_k, x'_k)\}_{k=1}^{\infty}$, and it holds that

$$ x''_k >_{pr} x'_k\;\;\;\forall k  \tag{1}$$
$$\lim_{k\rightarrow \infty} x''_k = x'$$
$$\lim_{k\rightarrow \infty} x'_k = x'$$

Under Continuity of preferences we should obtain
$$ (1) \implies \lim_{k\rightarrow \infty} x'' >_{pr} \lim_{k\rightarrow \infty} x'$$
but this is obviously not possible since these limits are identical.
So by assuming that there exists an $x$ in the Consumption Set to which no other bundle is equivalent in terms of the preference relation, we have violated the Continuity property.

Alternatively, since the bundles are defined over real vectors, and both $UCS$ and $LCS$ are closed due to the Continuity property, then every Cauchy sequence in each of them that converges has its limit in them. So the sequence $\{x''_k\}$ has its limit in $UCS_x$, while the sequence $\{x'_k\}$ must have its limit in $LCS_x$. But this limit is the same as shown above, and equal to $x'$. But the only common point of these two sets is $x$. So it must be the case that $x'=x$. But this cannot hold since we have started by assuming $x>_{pr} x'$.

An example where indifference sets are singletons is the case of Lexicographic Preferences. And Lexicographic Preferences are not continuous.


Economic interpretation of the concavity of the expenditure function What is the interpretation of the expenditure function's being concave?

The expenditure function is always concave.

Suppose you consume two goods. Suppose the price of one of those goods, say $p1$, increases. Suppose also that, rather than rebalance your demand, you increase consumption of good one enough to maintain some given level of utility (let's say whatever level of utility you had whenever consuming goods 1,2 before the price of good 1 increased). Then your expenditure rises linearly.  Suppose instead that you rebalance your demand. Then your expenditures rise but not as much as whenever you do not rebalance your demand. Thus, concavity.

So, I suppose an interpretation here is that a consumer always has the ability to rebalance demands s.t. he/she maintains some desired level of utility in the cheapest way possible. Worst case, expenditures increase linearly. But linear functions are both concave and convex.

This is a very loose way to discuss this. However, I think it gives intuition, which is what I think you are looking for here.


Does labor mobility create a certain type of market failure? Oxford professor Ewart Keep writes in a paper titled Market Failure in Skills (p. 3) that

  For firms there is the
  problem of investment in
  staff who may leave taking
  their skills with them.

Some of the historical solutions to this problem involve limiting the mobility of the labor force, ranging from slavery, indentured servitude, and more recently some kinds work visas that are only valid for one employer.

So in this sense, some human rights are bad for markets, leading to certain kind of market failure. Is this view uncontroversial among economists? And a complementary question: can measures that limit worker mobility also result in other way in market failure?

Well, from the same paper (p. 5), it's not all that clear that the theory translates to actual market failure:

  There is very little reliable data on either the scale of
  poaching or its impact upon employers’ training
  decisions – despite this being frequently adduced by
  policy makers as the prime cause of market failure in
  training. One of the few recent surveys to touch on the
  issue (4) suggested that poaching was a serious problem
  for no more than about one per cent of the employers in
  the sample, whereas an earlier survey of employers
  suggested that the possibility of poaching had
  discouraged as many as 38% from investing in skill (5).

The references cited for data being:

  (4) J. Kitching and R. Blackburn. 2002. ‘The Nature of
  Training and Motivation to Train in Small Firms’, DfES
  Research Report RR330, Nottingham: DfES.

  (5) Training Agency. 1989. Training in Britain, London:
  HMSO.

I think this constitutes a partial answer, but I'm quite interested in more data, in particular from other countries.

And, yes, as I suspected, labor immobility is also a form (perhaps less controversial) of market failure. But this does in turn raise the interesting question whether you can fix one market failure without causing another (in the labor market).


Understanding the use case of farming crickets in developed countries Currently, farming crickets is quite labor intensive.

No wonder that if you compare prices, in developed countries you get crickets at say \$100/kg, while in Thailand they cost under \$2/pound, in an e-shop \$29/kg which comes close to production cost in a developed country.

Nevertheless, there are quite many cricket farms for human food opening in developed countries.

Why?

I think there are probably a few different answers to your question, all of which likely play some role.

First, in many developed countries, insect use in human food is regarded not as an inferior good, but a normal good. By highlighting things like nutrition content (specifically protein), they're trying to capture a market that includes more affluent, health conscious consumers. These individuals are likely to be a bit less price sensitive, and may even use price as a signalling component. Therefore, products using crickets might be less sensitive to pricing compared to other goods.

Second, companies trying to sell cricket-based products might also feel that their consumers would be more concerned about ingredient sourcing to distant farms. This could be because of perceived fears of quality differences, or because of things like a preference towards local sourcing.

Third, it seems that many of the newer farms opening in the developed world like the one profiled here are addressing the issues of labor intensity in cricket production by increasing efficiencies and utilizing more technology in the production process.

There's also likely some natural home bias in products like this. Much of the grassroots support for increased cricket consumption is driven by the farmers themselves. Because stronger community roots can improve these efforts, and because of the high costs of researching, incorporating, and offshoring production facilities to a distant country, there might just not be that much of an economic incentive to move production overseas. It isn't trivially easy to offshore an entire production facility, and the profitability and long term market potential might not have quite reached a position where that's profitable yet.


Testing the long run phillips curve / Contradicting empirical results? I've been working with some historical macroeconomic data of the Canadian economy and am having difficulty empirically testing the Phillips curve long run and short run versions.

I got the data from FRED, logged the variables and then plotted them.

The results are unsatisfactory; the scatter plot I have is:

A shape which is looking like a bow, going up right and then back.

I tried using fitting the data using a loess curve again yielding unsatisfactory results.

Im probably not doing something right as the data does not seem to fit with either the short run or long run versions of what the Phillips curve represents.

So to offically crown myself as conspiracy theorist of the day on Economics.SE (which is probably a problem for a mod):

Does this analysis disprove both the long run and short run Phillips curve?

*for Canada?
** what is incorrect in this analysis?

You are assuming the PC has not shifted over the period. For example, you can see at the top right some sort of PC. To see this better, you need first to analyse the data in evidence for regime shifts. The first suggestion is to connect the points over time. US example below:

This will let you see possible structural changes in the PC, together with movements between two PCs. This gif shows this more clearly:

Knowing the monetary and economic history of Canada should certainly help you understand the movement and changes of the PC. For example, you cannot expect the PC to hold over the oil crisis period, where the economy was basically in stagflation.

Once you identify sub-periods, estimate the PC for each subperiod.

A paper from the Central Bank of Canada estimating the PC and its regime shifts can be found here. Notice that standard analysis of PC are much more elaborated than a simply bivariate correlation. Strictly speaking, you are assuming there is no other variable involved in the correlation. The example of structural changes might for example be captured with changes in a variable you are omitting.

PS: I gave an answer to a related question here.


Economic concept where turning something down heightens emotional attachment For example, say a person has turned down an offer for a competing position with another company. That person now has an increased sense of attachment to their current position with the logic "I turned down that offer, I must really like my current job".

This sometimes looks a little like sunk cost "I just watched the first 9 out of 10 seasons of this television show. I must really like it, so I'll watch the 10th"

What's the name of this economic concept? Is this maybe a psychology concept instead?

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


Interest rate - Price of Credit vs Price of Money I read somewhere that interest rate as the price of money is wrong but rather it is the price of credit. Can someone elaborate and explain what this means?

Interest rates are not to be directly considered as the price of credit. Instead, they are unequivocally linked to it. This is simply due to how bonds are priced.

$$
P = \sum_{n=1}^N \frac{C + M[{I_{n=N}}]}{(1+i)^n}
$$

Where $i$ is the contractual interest rate, $C$ is the coupon payment, $N$ is the number of payments, $I_{n=N}$ is an indicator function taking the value of $1$ when $n=N$ is $true$ or $0$ otherwise, $P$ is the market price of the bond, $M$ is the value of the bond at maturity.

In a second time, there is a link between money and credit, but indeed, transitively saying that interest rates are "the price of money" is a bit simplistic since it omits a great part of institutional and financial mechanisms.


What prerequisite courses do I need in order to specialize in Mechanism/Market design theory? After seeing some lectures on Youtube, I came to learn about a few, namely, Game Theory and Microeconomics, but I am not sure whether this is all that is needed. Please do add as many courses as possible or refer to the courses that should be taken from the following list: http://www.lse.ac.uk/resources/calendar/programmeRegulations/undergraduate/BScEconomics.htm

The list you posted was for an undergraduate degree in economics. Mechaism design usually won't come up in any serious way until graduate school. Until then, my advice is to take as much as the following as possible:

microeconomic theory,
game theory (often covered within microeconomic theory),
mathematical methods/optimisation.

Mechanism design falls under the rubric of microeconomics theory, which at the advanced (i.e. postgraduate) level is highly technical. So achieving a high degree of mathematical sophistication in addition to a solid grounding in microeconomic theory is probably the best strategy.


List of commercial banks by country in Europe How do I find a list of all operating commercial banks by country?

I am only interested in commercial banks. Not building societies nor community banks.

I expected that that list should be made available on EuroStat
or from consolidated banking data by ECB
but it's not as they don't differentiate between commercial banks and other credit institutions.

For example, for UK at some point in that past, that list would look like this.

I think i have answers for your question.

In "thebanks.eu" you can find banks list by country and there is a filter so you can find commercial banks in Europe.
https://thebanks.eu/banks-by-country

There is an other answer for your question; "stockopedia.com". This time you can find banks list and data. But there is no filter so you can not find only commercial banks and this service isn't free.

https://www.stockopedia.com/sectors/banking-services-551010//


Solution to the Bellman equation is a fixed point I have recently started studying dynamic optimization. I cannot quite wrap my head around the fact that the value function of the Bellman equation is a fixed point of a contraction mapping.
As far my understanding is rather naive: if the problem is finite, say:
$$\sum_{t=0}^T \beta^tu(c_t)$$
we construct the Bellman equation from the end, as if we knew the maximum possible value of the sequence in advance. Starting from the last period $T$, we just repeat the maximization by adding an optimal term reflecting current period utility $u(c_t)$, until we arrive to the period $0$. From here I can clearly see how contraction mapping works.
But the infinite case is not so easy for me to comprehend: I can only suppose, that, by iteration of the Bellman operator $(Bv)(x)$, we perform a "calibration" of the policy function until we find the value function (i.e. the maximum possible utility given our transversality conditions) $(Bv)(x)=v(x)$. Am I, at least, thinking in the right direction, or this idea should be understood in a different way?
Thank you in advance.
(Also, this is my first question on .stackexchange ever, and if there are any issues with presentation of my question, please, let me know)

I am by no means an expert on this, but maybe this helps. Here is a simple example for a bellman equation

$V(y) = \max_x u(x,y) + \beta V(y')$

$s.t. \, y' = f(x,y)$

This is a functional equation in an unknown function V. A solution to this problem is a function V that satisfies the equation above. If you look at the equation, it's pretty clear that the solution has to be a fixed point of the operator on the RHS of the bellman equation: if you take the correct V and an arbitrary y and calculate

$\max_x u(x,y) + \beta V(y')$

$s.t. \, y' = f(x,y)$

you will get $V(y)$. The operator that is the RHS of the Bellman equation operates on functions, and the solution is a fixed point in some space of functions.

It's a different question whether this fixed point exists and how to find it. Here, you appeal to the contraction mapping theorem: under typical assumptions on u and provided $\beta<1$, the maximization step above is a contraction mapping for any guess of V. This means that there exists a unique fixed point V, and you can find it by successive iteration.


Simulating a Hamilton-Jacobi-Bellman Say I have solved an HJB of the form:

$\rho V(k) = \max_c g(c) + V'(k)(z - c)$

I have calibrated $\rho$ to monthly parameters. I would like to simulate the development of $k$. I start with $k(0)$. However, unlike in discrete-time, I'm not sure what happens next.

Is $k(1) = k(0) + (z-c(0))$, with $k(1)$ being the value of $k$ for the next month? Or do I need to somehow integrate along the lines of $k(1) = \int_0^1 (z-c(t))dt + k(0)$? There's many references on solving these things, but I couldn't find any references on simulating it.

Expanding on jmbejara's answer and your question about integration, there are really three steps here:

Solve the HJB equation $\rho V(k) = \max_c g(c)+V'(k)(z-c)$. (You're already done this.)
Obtain the policy function $c(k)=\text{argmax}_c g(c)+V'(k)(z-c)$. (You presumably already did this while solving the HJB.)
Substitute $c(k)$ into the law of motion for $k$ and numerically solve that differential equation for $k(t)$:$$\dot{k}=z-c(k)$$

It sounds like you already had (1) and (2) and were just unsure about what exactly to do in (3). If you're working in a deterministic environment (and from the HJB it looks like you are), no discretization on your part is necessary: you can just use a canned ODE solver from Matlab or any other software package to numerically solve the differential equation above for $k(t)$.

To be a little more specific:

If the HJB is simple and you have an analytical solution for $V(k)$, and thus can easily compute $c(k)$ as well, that's great. You can just plug $c(k)$ into the law of motion for $k$ and tell your software package of choice to solve it and obtain the trajectory of $k(t)$.
If you had to numerically solve the HJB, then that's great because it means that you probably have already used some kind of numerical ODE solution technique and will be familiar with it. On the minus side, it means that when you initially obtain $V(k)$ and $c(k)$, you'll only get it for a grid of $k$, rather than having some kind of formula you can apply everywhere - which is a problem, because you'll need to be able to determine $c(k)$ at any point $k$ in a continuum if you're going to numerically solve the $\dot{k}$ differential equation for $k(t)$. The simplest way around this, to my knowledge, is to fit a spline to (or use some other approximation method on) the discrete grid of $(k_{grid},c(k_{grid}))$ values that you have. Then you can obtain an approximate value of $c(k)$ anywhere that's covered by the spline, and it will be extremely accurate assuming that your ODE is well-behaved and you have a dense grid.

Things get more complicated in a stochastic environment, but your case looks deterministic. (And to be clear, I'm just a dabbler here: numerical methods are not my area of expertise. But this is what I know.)


Looking for the title of a short (~100 page) Herbert Simon book about "Bread-bricks" I'm trying to find a short (~100 page) book by Herbert A. Simon in which he presents a simplified economics in which there is only one item of value and it is called the 'Bread-brick'. One can eat a breadbrick, or sell it, or store it, etc. He uses this simple world to illustrate certain topics in the study of economics. I have been looking for it for ages, and I don't know the title. I've googled endlessly, and perused all Simons books on google reader but I have come to nothing.

It is my impression that it is "bean-bricks" and it is not a book but a paper/essay under the title "The long-range economic effects of automation", which was included in the book

HERBERT, A. S. (1965). The Shape of Automation for Men and Management.

Go to the on-line digital library of Carnegie Mellon University

and enter in the search "The Economic Effects of Automation" (without the "long-range" part). It (freely) downloads what appears to be a first version of the work (20 pages). The file may appear to not be a .pdf one, but I opened it with .pdf software alright.

At the end of page 9 Simon writes:

  "In our hypothetical economy, only a single commodity, which we shall call beanbricks, is produced. Beanbricks serve both as the sole
  consumption good (they are eaten), and as the sole form of capital
  (they are burned as fuel used in producing more beanbricks). The other
  productive resource in the economy, besides beanbricks, is labor".

It does look like it is the first time Simon uses the term (the file is a scanned copy of Simon's manuscript).

P.S: Note that standard economic models of growth essentially assume exactly the same framework, since output is costlessly transformed into capital or becomes consumption.


How to Represent as a Payoff Matrix I'm trying to represent the following as a pay-off matrix.
I have 100 dollars to invest in one agricultural stocks with a choice of apples, pears or grapes. Return on investment relies on whether enough water is available (with scenarios of 'yes there is enough' and 'no there isn't enough' occurring with equal probability) and whether the weather is ideal (again with scenarios of 'yes its ideal' and 'no it isnt ideal' occurring with equal probability). Both the availability of water and weather are independent to each other.

With ideal weather and enough water, I will receive 130 dollars from
apples, 110 dollars from pears and 130 dollars from grapes.
With ideal weather and not enough water, I will receive 120 dollars from
apples, 110 dollars from pears and 120 dollars from grapes.
With unideal weather and enough water, I will receive 110 dollars from
apples, 120 dollars from pears and 105 dollars from grapes.
With unideal weather and not enough water, I will receive 100 dollars from
apples, 105 dollars from pears and 100 dollars from grapes.

I know this is a decision problem under uncertainty, so the states of nature would be one of the 'players' in a normal form game and then the decisions would be another. So would it be appropriate for the table to have three rows corresponding to investing in each fruit and then four columns corresponding to each possible combination of the weather and water outcomes? And if so, how exactly would I bring the probabilities of each occurring into the mix? The four possible outcomes of the weather and water are all equally likely to occur ($p=0.25$), so could I just multiply all the dollar return amounts and put expected returns in the table instead?
Any help would be greatly appreciated.

You have the right idea, make a 4 by 3 payoff matrix with fruit at the top and at the side weather/water yes/no, giving 12 different cells, then put the respective dollar payoffs.
You could also make another table and find the expected payoff by multiplying each payoff by its probability, although since all the probabilities are the same, the table wouldn’t show anything different/useful to the normal payoff matrix with nominal dollar values.
Then add up the values in each fruit column and the highest value will be the optimal strategy.


Utility theory and portfolio optimization: utility of what exactly? In finance, a common problem is selection of an optimal portfolio given some constraints (e.g. budget constraint and perhaps nonnegative allocation constraint). One can define the optimization problem based on maximization of expected utility. For example, if the utility function is $u(x)=x-\frac{A}{2}x^2$, then (in absence of constraints aside from the budget constraint) this yields the well-known mean-variance portfolio optimization.

Questions:

What is $x$? Is it (portfolio) return (in \$), % or logarithmic return, total wealth (initial wealth + portfolio return) or yet something else?
Which choice is typically used in portfolio optimization?
Which choice makes most sense from the perspective of utility theory?

I am interested in this in the context of trying to pick a sensible value of $A$ to represent preferences of a "typical" agent. In my experience, $A=2$ as commonly found in the literature does not seem to align well with $x$ being logarithmic return (yields funny portfolios). Thoughts on this will also be appreciated.

Given the popularity of mean-variance portfolio theory and how basic my questions are, I suppose they have been considered before (perhaps even treated in textbooks). References would be appreciated.

Edit: In addition to the answer I got for Question 2, I am still highly interested in obtaining an answer for Question 3 (as well as alternative answers to Question 2).

In mean-variance optimisation I have typically seen the below quadratic utility function where $[]$ is the expected return (or mean return) of a possible portfolio, $\sigma^{2}$ is the return variance of that portfolio and $A$ is a parameter that the determines the sensitivity to variance.

$$=[]−\frac{1}{2}A\sigma^{2}$$

As an aside, maximising % return, also maximises $ return, log return and total wealth. They might not be equivalent when optimising for mean and variance though.


2010 flash crash: cause and rationale for illegality A British trader has been arrested on accusations of having triggered the 2010 "flash crash" that saw the Dow plummet by 600 points in 20 minutes. This is reported, for example, here (BBC), or here (FT, paywalled). In these reports, it is claimed that the crash was triggered by some sort of irregular trading in a type of futures contracts called eMinis.

Can someone explain

What exactly is it that the trader is alleged to have done, how did this allow him to make irregular profits, and what is the mechanism by which he was able to single-handedly move the entire equities index?
If the trader participated only in legitimate voluntary trades via the normal market mechanism, what exactly is the behaviour that is being considered as potentially illegal here, and what is the rationale for this illegality (i.e. how can the authorities distinguish this seemingly illegal behaviour from normal market trading activity)?

What exactly is it that the trader is alleged to have done, how did this allow him to make irregular profits, and what is the mechanism by which he was able to single-handedly move the entire equities index?

  According to the Complaint, for over five years and continuing as recently as at least April 6, 2015, Defendants have engaged in a massive effort to manipulate the price of the E-mini S&P by utilizing a variety of exceptionally large, aggressive, and persistent spoofing tactics.  In particular, according to the Complaint, in or about June 2009, Defendants modified a commonly used off-the-shelf trading platform to automatically simultaneously “layer” four to six exceptionally large sell orders into the visible E-mini S&P central limit order book (the Layering Algorithm), with each sell order one price level from the other.  As the E-mini S&P futures price moved, the Layering Algorithm allegedly modified the price of the sell orders to ensure that they remained at least three or four price levels from the best asking price; thus, remaining visible to other traders, but staying safely away from the best asking price.
  Eventually, the vast majority of the Layering Algorithm orders were canceled without resulting in any transactions.  According to the Complaint, between April 2010 and April 2015, Defendants utilized the Layering Algorithm on over 400 trading days.
  The Complaint alleges that Defendants often cycled the Layering Algorithm on and off several times during a typical trading day to create large imbalances in the E-mini S&P visible order book to affect the prevailing E-mini S&P price.  Defendants then allegedly traded in a manner designed to profit from this temporary artificial volatility.
  (http://www.cftc.gov/PressRoom/PressReleases/pr7156-15#PrRoWMBL)

The offical verdict has a step-by-step walkthrough

If the trader participated only in legitimate voluntary trades via the normal market mechanism, what exactly is the behaviour that is being considered as potentially illegal here, and what is the rationale for this illegality (i.e. how can the authorities distinguish this seemingly illegal behaviour from normal market trading activity)?

  Sarao was charged in a federal criminal complaint in the Northern District of Illinois on Feb. 11, 2015,  with one count of wire fraud, 10 counts of commodities fraud, 10 counts of commodities manipulation, and one count of “spoofing,” a practice of bidding or offering with the intent to cancel the bid or offer before execution.
  (http://www.justice.gov/opa/pr/futures-trader-charged-illegally-manipulating-stock-market-contributing-may-2010-market-flash)

The relevant articles for spoofing are: Title 7, United States Code, Sections 6c(a)(5)(C) and 13(a)(2)

  (5) Disruptive practices
  It shall be unlawful for any person to engage in any trading, practice, or conduct on or subject to the rules of a registered entity that-
  (A) violates bids or offers;
  (B) demonstrates intentional or reckless disregard for the orderly execution of transactions during the closing period; or
  (C) is, is of the character of, or is commonly known to the trade as, "spoofing" (bidding or offering with the intent to cancel the bid or offer before execution).


How to determine a corner solution? Growth Model I'm working on a paper called "Fertility clubs and economic growth" of Ahituv and MOav (linked below) and arrived at this point:

The paper shows three optimal conditions respect to consumption (ct), intergenerational transfers (st+1), solved in the images and the educational level (et+1).
Following the paper, I shall use the rt+1 equation derived on the images to get the et+1 optimal level, but, there is a note that says the following:

According to the corner solution showed in the note and replacing the value of rt+1 that I get in the first two images I get the result, but is not a good answer, because I need to know how to get that condition.
I tried to solve the general model detailed on Moav (2001), and I get the result showed, but in this case it doesn't includes the intergenerational transfers and the interest rate. In the next image you could see the general model solution respect to et+1

As Moav (2001) says, the extended model is just a case where Teta is =1, but I can't just justify the development of the model with that answer, I need to solve it.
Am I doing something wrong? If I have to compute the corner solution in the note, how should I do it?
THANKS A LOT!!
Ahituv Moav Paper: http://scholar.google.com.ar/scholar_url?url=https://www.cesifo-group.de/dms/ifodoc/docs/Akad_Conf/CFP_CONF/SC_CONF_1999-2006/GRI_2001X2002/PAPERS2/gri02-moav__221461_en.pdf&hl=es&sa=X&scisig=AAGBfm0HqRpnafuT244j5-Exa5QjPYhtbA&nossl=1&oi=scholarr
Moav (2001) Cheap Children an persistence of poverty (sorry, I couldn't find the link)

What the authors seem to be doing in the footnote is imposing a condition stating that if intergenerational transfers tend to infinity (say for the case of children of billionaires) there will be no growth in wealth from human capital investment.
This condition is here to just communicate that the parent views allocation between human capital of the child and physical capital as substitutes.
This is communacated by the fact that we have $w_{t+1}h_{t+1}+r_{t+1}s_{t+1}$ being concidered in the same logarithm together.
Hope this helps


Demand functions in merger simulation models Currently competition authorities usually decide whether to approve a merger or not based on the total revenues or capacities of the merging firms and some rule of thumbs. A reason for this is that they do not always have a stronger mandate because of the legal background.
Merger simulation models promise a more analytical policy approach. For a good survey see Budsinki & Ruhmer (2010).

It is my understanding that the kind of data needed to estimate the demand function of a market, or usually demand functions in the case of differentiated products, is not publicly available. Yet rival companies frequently have similar data which they use to estimate their market share.

How would one go about legally acquiring such data?
Are there any ways with which to estimate cross elasticities without said data?

In your case, you might try to reach the said antitrust authority and ask for the dataset. You also could reach the parties themselves and ask for the shared data. Authorities acquire these datasets through parties BI data and/or third parties that might have some connection to the merger (companies concerned with the operation, clients etc). I believe it is highly improbable that the data is made publicly available anywhere.


Why do rich and poor countries trade in different goods and why do rich countries trade in similar goods with other rich countries? I think that differences in climate is one key factor but I think it could be explained by David Ricardo's theory on international trade differences???

The key is production capabilities, not relative specialization. In words of Hausmann and Rodrik (2006):

  The idea that rich (poor) countries tend to export goods exported by other rich
  (poor) countries is quite obvious and is compatible with many possible theories. For
  example, in conventional trade theory a la Heckscher-Ohlin, countries export products
  that are more intensive in the factors of production that are relatively abundant at home.
  As development takes place, physical, human and institutional capital is accumulated and
  the products countries export become more intensive in these factors. ...

  Labor-abundant countries trade with land- or capital-abundant countries in order to
  acquire more efficiently the goods that are intensive in the factors they don’t have. The
  transition between goods is of little significance: they are the passive consequence of
  changing factor endowments.


Classification of Two-Person Games I'm looking for a classification of all simultaneous, complete information, two-person, two-action games.  By classification, I mean a partition of all payoff matrices into a (finite number) of categories.  Sample categories would be prisoner's dilemma and Stag hunt.

I'm willing to accept substitutes, like a classification of a different set of games.  There is no unique answer to this question, and I'm not looking for an answer in the context of a particular class.

A paper reference is fine, although an online source would be better.

Legal Disclaimer: I apologize in advance for violating any social conventions for this site.

If you look at generic games, that is games where players are not indifferent between any choices such a classification is easy to produce. Let the strategy sets be
$$
S_1 = \left\{a,b\right\}, S_2 = \left\{c,d\right\}
$$
and let the utility/payoff functions be denoted by $U_1$ and $U_2$.
The characterization will be based on the dynamics of the game, that is given a strategy profile $(s_1,s_2)$ will any player wish to alther his strategy. This will also give you all the equilibria. Without loss of generality you can assume
$$
U_1(a,c) > U_1(b,c).
$$
(Should this not hold, switch the labels of the strategies $a$ and $b$.)
 We still need to know if player 1 prefers $(a,d)$ to $(b,d)$ or vice versa, and also if player 2 prefers $(a,c)$ to $(a,d)$ and if he prefers $(b,c)$ to $(b,d)$. This gives eight possible combinations which will characterize the game classes. (But due to symmetry actually there will only be four classes.)

Category 1.
$$
U_1(a,d) > U_1(b,d) \mbox{ and } U_2(a,c) > U_2(a,d) \mbox{ and } U_2(b,c) > U_2(b,d).
$$
In this category $a$ and $c$ are strictly dominant strategies. A game like this will play out like the prisoners dilemma in that it has a single Nash-equilibrium which is also a dominant equilibrium.

Category 2.
$$
U_1(a,d) < U_1(b,d) \mbox{ and } U_2(a,c) < U_2(a,d) \mbox{ and } U_2(b,c) > U_2(b,d).
$$
This game will play out the matching pennies game, in that there are no equilibria.

Category 3.
$$
U_1(a,d) < U_1(b,d) \mbox{ and } U_2(a,c) > U_2(a,d) \mbox{ and } U_2(b,c) < U_2(b,d).
$$
This game will play out like a coordination game, e.g. Battle of the Sexes or Chicken. There are two equilibria, $(a,c)$ and $(b,d)$.

Category 4.
$$
U_1(a,d) > U_1(b,d) \mbox{ and } U_2(a,c) > U_2(a,d) \mbox{ and } U_2(b,c) < U_2(b,d).
$$
In this category $a$ is again strictly dominant. $c$ is not, but a rational player 1 will always play $a$, and $c$ is best response to that. I don't know if this game has a well accepted name, it has one Nash-equilibrium $(a,c)$.

Due to symmetry, all other combinations belong to one of these categories.

If you wish to admit indifference between several outcomes, it is still possible to use this kind of classification, but the number of categories will be much larger.


Horizontal demand curve If it is assumed that every consumer within a particular region has the same 'valuation' for a certain product, and consumers will purchase no more than one unit of the product, is the market demand curve perfectly elastic (horizontal)?

Any insight would be appreciated.

Let $v_i$ be the valuation that the $i$-th consumer has for the product, and $v^*$ the common valuation of the product, where the $v$'s are measured in monetary units, and are assumed continuous.  Consumers are here assumed binary -they either purchase $0$ or $1$ (i.e. the product is indivisible). We assume that if the valuation is equal to the price, they do want to purchase the product.

Write the indicator function $I\{v_i\geq p\}$, that takes the value $1$ if the valuation is greater or equal than the price (and so the consumer will want to buy the one unit of product. Let there be $N$ consumers. Then, demand can be expressed as

$$Q^{d} = \sum_{i=1}^NI\{v_i\geq p\}$$

and since the valuation is assumed common to all,

$$Q^{d} = N\cdot I\{v^*\geq p\}$$

We see that  if $p\leq v^*$, quantity demanded will be equal to $N$, while if $p> v^*$ quantity demanded will be equal to $0$.

Diagrammatically, this gives


Trading in the presence of priorities Suppose there is an airline that wants to sell 200 seats in a flight. It can either sell them as business class or as economy. Ideally it would sell all  as business class, but it is willing to give away seats as economy in case not all can be sold as business class.

Then there is a number of consumer, which all prefer economy seats, but each of them is willing to buy business class in case no economy seat is available.

Is this a well-known problem?
What is it called?

Edit:

I suppose this is roughly a "game of chicken". But I believe in real markets there will some equilibrium, but I don't know what it depends on.

If I understand you correctly, all customers prefer economy class to business class (that is, they only care about the lower price).

First, the way you've specified the problem, the airline will always make every seat a business class seat, because if no economy seats are available, the airline will (a) sell the same number of tickets (since customers buy business class if economy isn't available) and (b) sell all the tickets at a higher price.

But maybe you meant something like, fewer people will buy business class seats because the price is higher, so the airline may wish to make some seats economy class so they fill every seat. That is, the airline may initially wish to offer tickets for business class, wait until they stop getting new orders, then lower the price to economy class in order to fill the rest of the seats. Depending on the underlying model of demand and purchasing you may get different results.

I'll highlight one, the 'Coase conjecture', which argues that the sort of pricing scheme I described above will break down because customers rationally anticipate that the airline will lower prices as soon as they stop getting new orders, so they wait for the price to drop.


Pareto set and Edgeworth box General equilibrium framework; two individuals, two goods represented in an Edgeworth box.

Is it true that if the preference are both strongly monotonic the Pareto set will go from the origin of an individual's axis to the one of the other's axis? By origin, I mean the points of the box where an individual has everything and the other nothing. The reason would be that the allocation of all goods to one of the single individuals is Pareto optimal.

The Pareto optimal set should always pass through the origin because it's one of the point that makes it impossible to better off a consumer without harming the other.


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

I would also welcome suggestions of clear definitions for what we should mean as consensus , specially considering that economics is an area with a lot of methodological divergence. Let me try first, a suggested definition for consensus in this setting would be:

  the existence of a group of experts that would claim that the result
  is certainly true.

The principle of comparative advantage

As Paul Samuelson (1969) put it:

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

Example

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

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

Maximum possible production

          American  Chinese
Soybeans     100      30
Steel         4        3

A layperson could reason:

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

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

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

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

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

Numerical example:

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

1. Consumption without trade

          American  Chinese
Soybeans     75       15
Steel         1       1.5

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

2. Production after specialization but before trade

          American  Chinese
Soybeans     100       0
Steel         0        3

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

3. Consumption after specialization and trade

          American  Chinese
Soybeans     80       20
Steel        1.2      1.8

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

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


Price discrimination- how much is optimal? I am of the understanding that as a general rule, price discrimination does not benefit consumers. Yet I can think of a situation where it does. Look at two countries, Australia and India. The price levels are very different. If there is no price discrimination, prices are identical. Suppose firm profits were higher if they priced out Indians and sold just to Australians.

I am of the impression consumer surplus will be higher if a firm could choose two different prices, one to India and one to Australia.

Under what conditions would partial price discrimination be beneficial?

I am thinking, for simplicity, this firm is a monopolist and there are >2 types of consumers, each with a different valuation of the good.

Varian has a paper on Price Discrimination and Social Welfare in which he gives some necessary and sufficient conditions for (third degree) price discrimination to increase welfare.

A necessary condition is that the total level of output (i.e. the total number of consumers served) increases as a result of the discrimination.

A sufficient condition is that the profitability of the new output (i.e. after discrimination) exceeds the profitability of the old output (before discrimination) evaluated at the new prices.


If South America were to unite as one country would they become an economic superpower? Often borders can hold back different parts of the world and if they consolidated together they could succeed so much more. What would be the pros and cons If South America were to break down their borders and develop together as one country?

Would this make Soth America a superpower and a leading country in GDP?

In answer to the narrower question of how significant an economy South America would be, here's a rough comparison of current (2016) GDP:

The Caribbean is included in Latin America for good measure (and because that's the way the World Bank cut up the data).  The US is 3.5 times the size, the EU 3.1 times, and China 2.1 times.  The economic area would be almost 3 times the size of the Brazilian economy.

In terms of pros and cons, there are probably larger political than economic issues involved.

Source


Is real income the same as present value of income? For example, if I know in time period 2 I will get paid £x in real terms

Where the real interest rate of borrowing and lending is r% between period 1 and 2

Is this the same as being paid £x/(1+r) in period 1?

Or is this the same as being paid £x in period 1?

Real income refers to the income of an individual or group after taking into consideration the effects of inflation on purchasing power. For example, if you receive a 2% salary increase over the previous year and inflation for the year is 1%, then your real income only increases by 1%. Conversely, if you receive a 2% raise in salary and inflation is at 3%, then your real income shrinks by 1%.

Net present value is the value today of a stream of income over time - it is influenced primarily by interest rates.

There is some relationship between the terms - because they both discuss the value of money in relationship to to time, but real income discusses the difference of buying power over time due to inflation and NPV focusses on the theoretical equivalence of money today versus a stream of money over a period of time - largely influenced by the risk of receiving that income and the available alternatives of investment during the time period.

Investopedia definition of Real Income


Road to equilibrium in a basic economic model I am reading a (macro)economics book which introduces a model of a small, closed economy. Two relations are presented. The IS relation (savings equals investments, or demand equals production) and the LM relation (money supply equals money demand).

The book then goes on about what happens in an economy given by this model .... but is the model's equilibrium one that occurs naturally? Is real-life money supply equal to money demand? Is real-life investment equal to savings?

My question in short: why does the economy converge to these equilibriums?

If you want to focus on the real world, we need to realise that the savings equal investment (S=I) is an accounting identity. That is, it always holds, no matter what.

Importantly, it holds on any time frame, which means that every single transaction will obey it. (You would need to imagine an extremely short-term national accounts that reflects just one transaction.) Therefore, there is no conceivable set of transactions that break the accounting identity, assuming that the accounting is done correctly.

The supply/demand relationships in the real world are trickier. Production of goods could exceed "demand", as the excess ends up in inventories. However, we could pretend that the increase in inventories was planned, and so once again production equals demand. The money supply/demand relationship just tells us that the private sector allocates between "money" and "bonds", but that appears to be another accounting identity. (I am unsure about that statement, and it may take a few steps to get to that point. Since all financial instruments end up being held by some entity, presumably supply and demand have to match.)

In other words, accounting identies always hold, and that is independent of what any particular model says.

If we return the model, "equilibrium" is an assumption/solution technique to find a solution to the systems of equations. That is, within the IS/LM model, the market balance conditions determine the solution. If we change the model, we might get difference conditions to determine the solution.

Since a mathematical model is not the same thing as the real world, we should not say that real world behaviour is directly related to the mathematics. That is, it is unclear if it makes sense to ask whether the real world reaches "equilibrium", without defining what real-world phenemona define "equilibrium." Instead, the test is whether the mathematical model (whose solution is defined by "equilibrium") offers useful insight to real world behaviour.


How is population growth predicted? I follow some Japanese based websites, and I've read that "Japan population is going to reduce by half in 50 years". The estimates in this article are more optimistic, according to the graph it seems to estimate around 30 millions lose in population in the same period of time.

Then, I looked into this chart in Wikipedia about countries population growths. Some European countries like Spain and Portugal seems to have much worse population growth than Japan. Japan -0.12 , Spain -0.21 , Portugal -0.45 . Then I read this article, and they say Spain will lose 5.6 millions inhabitants in the following 50 years. This is proportionally a much lower figure than Japan, in spite of it is stated by that Wikipedia article Spain decreased much more than Japan in the period of 2010-2015 . I suppose many factors are taken into account for calculating population growth aside births and deaths such as immigration, emigration, etc.

Are there mathematical equations to calculate population growth? How are they predicted?

It's possible that the stories about drastic drops in Japan refer to working-age population, not the population itself.

This is a link to the U.S. Census methodology.

I have only casually looked at these data over the years, but I would summarise the general idea as follows.

We already have the current population distribution. We work with the data based on the number of people in each age cohort.
We have estimates of life expectancy based on age, and actuaries spend a lot of time working on developing projections. (The defined benefit pension and life insurance industry depend upon such actuarial projections.)
We usually have a good idea of the birth rate, based on the characteristics of under-30 population. Even if we miss, it takes a long time for the errors to really add up. (People have to reach puberty before the prediction error compounds.)
This covers the existing population; what remains to do is estimate the effect of net migration.

For the developed countries, the big unknown is typically net immigration. In the euro area, the collapse of economies has often caused a considerable amount of emigration.

Outside of net immigration, the only thing that could cause the projections to off is a massive change in the death rate (or birth mortality). Birth rates tend to be slow-moving; the baby boom after World War II was a response to highly unusual earlier conditions (Great Depression, WWII). Life expectancy is another wild card, but it is unclear how much it will change.


Relevance of change in Inventory in calculation of Free Cash Flow Free cash flow (FCF) can be obtained by
$$
\text{FCF}=(\text{Revenues}-\text{Cost}-\text{Depreciation})(1-\tau)+\text{Depreciation}-\text{Capital Expenditures}-\Delta(\text{Net Working Capital})
$$
where $\tau$ is the corporate tax rate and
$$
\Delta(\text{Net Working Capital})=\Delta(\text{Cash}+\text{Inventory}+\text{Receivables}-\text{Payables})
$$
is the increase in net working capital over the period of interest. Besides inventory, all of these items appear to be monetary, except for depreciation which only affects the FCF through taxation, and so that contribution is also monetary.

But what about inventory? A change in inventory does not generate any monetary gains or losses, or does it? If it does not, how come a change in inventory is included in the calculation of the FCF?

When you manufacture a product, you incur some production cost. However, you do not account for this production cost in the $\text{Cost}$ line of the income statement until you actually sell the product. While the product is sitting in your inventory waiting to be sold, you have already incurred some (actual, monetary) cost that is not visible in the $\text{Cost}$ line. That is why you have to adjust the reported $\text{Cost}$ by $\Delta\text{Inventory}$ to obtain the actual, monetary cost for the period.

This is why $\Delta\text{Inventory}$ belongs in the FCF calculation.


Who created the concept of "present value"? I cannot find anything on this online. The wikipedia article is purely technical, except by a mention that such system was used in England in early 16th century.

Do you know who was the first to come up with this idea and technique?

It has been argued that the concept of present value was implicit in Liber Abaci (1202) by Leonardo of Pisa (also known as Fibonacci).  This paper by Goetzmann makes this claim in its abstract and introduction, and presents (pp 26-7) an example from Liber Abaci of what appears to be present value analysis.


Do assets without rental income streams appreciate relative to assets with rental income streams? In his book "The Armchair Economist", economist Steve Landsburg critiques an op-ed concerning the relative value of stocks and real estate:

  James K. Glassman wrote a piece in The New Republic to prove that stocks are better investments than real estate. He calculates that "if you bought a 200,000 dollar home in Foggy Bottom [a neighborhood in Washington, D.C.] in 1979, it would have been worth 316,000 dollars [ten years later]. But if you bought 200,000 dollars worth of stock in 1979, it would be worth 556,000 dollars [ten years later]—and you'd have another 68,000 dollars in dividend income."
  Well, yes, but if you'd bought the house you would have had a place to live for those ten years, whereas if you'd bought the stock you'd have been making rental payments to a landlord. This renders Glassman's comparison meaningless. All he shows is that if you compare all of the benefits of owning stock to some of the benefits of owning real estate, then the stock comes out ahead. Big deal.

  Glassman's piece has a place of honor in my Sound and Fury File because his conclusion is so exactly the opposite of the truth. He explains that "stocks appreciate faster than real estate; they always have and they always will. The reason is that a share of stock is a piece of a company in which minds are producing value. Real estate just sits there." The truth is that stocks appreciate faster than houses precisely because a house does not just sit there; it provides shelter, warmth, and closet space every single day that you own it. Stocks need to appreciate faster to compensate for the fact that they don't provide any comparable stream of services. If stocks and real estate appreciated at the same rate, nobody would own stocks.

My question is, what are the mathematical details of Landsburg's claim in bold?  If A is an asset that produces a stream of rental income, and B is an asset that does not produce a stream of rental income, then must the relative price of B with respect to A be constantly increasing?  Is there a model that shows this?  And what exactly causes this relative price change?

I believe he assumes that there is no arbitrage and also that there are no pricing bubbles. So two assets that have the same price today would have the same net present value.

Let $P_t$ denote the price of an asset in year $t$, $d_t$ the dividend (or rental income or cashflow) you get from said asset in year $t$ and let $r$ denote the interest rate (which I assume to be constant for simplicity's sake). Then the price of the asset today is
$$
P_1 = \frac{d_1}{1+r} + \frac{P_2}{1+r}.
$$
Using iteration
$$
P_1 = \sum_{t=1}^{n - 1} \frac{d_t}{(1+r)^t} + \frac{P_n}{(1+r)^{n-1}}.
$$
If you compare two assets with
$$
P_1^A = P_1^B
$$
where
$$
\forall t: \ d_t^A > 0, \ d_t^B = 0,
$$
then or all $t>1$ you will get:
$$
P_t^B > P_t^A.
$$
This is somewhat paradoxical, as a there is no clear reason why $P_t^B$ should be positive if it never pays dividends. You could assume that it has not yet payed any dividends but will start doing so soon.

However I think Landsburg's main argument is that $d_t>0$ holds for the house
as well, not just the stock.


Protectionism and smaller countries If I understand correctly, for a small country, whose supply chains needs to be transnational, protectionism introduces market inefficiency such that even unilaterally removing tariffs would be preferable.

But are there any circumstances where a small country would benefit economically from a protectionist tax policy?

If for example the whole world placed high tariffs on all goods and services from a country, would this make a protectionist policy desireable?

There are sometimes cases where protectionist trade policies are a good thing. (note this is a big debate, so a bit of bias here).
Lets look at an example to make it clear...
Suppose I'm country A and you are country B.
I'm a small country, you are a large one.
My country is 100% agriculture based. Your country is completely diverse and strong in all sectors.
My country realizes it is time to diversify and become more integrated into the global economy/market. Instead of just agriculture based products, my country wants to also sell computer monitors.
Here is where the problem occurs, if my country just starts producing computer monitors and try's to sell them, people will just continue to buy your countries computer monitors because they are better quality and probably cheaper in price due to comparative advantage. So now what? What must my country do to compete with yours, and grow? Well if my country makes your products more expensive, (aka a tariff) less people will buy your monitors and more people will buy mine (only in my country). This would allow my computer monitor(tech) sector to grow on it's own, without a big bully competitor(your country in this scenario) forcing me out before I even get started.
Over time once my tech sector has grown enough to compete with yours, I would lower/get rid of the tariffs and be better off.

Hope this helps you understand.


Who originated the term "deadweight loss" and when? I am looking for the first use of the term "deadweight loss."  Any suggestions either as to who it was who first used it or how to search for it?

So far as the "when" is concerned, Google Ngram can be helpful for this sort of question.  It suggests (see here) that use of the term was nil or close to nil until 1960, since when its use has grown fairly steadily.


Real exchange rate of India and United State? According to OECD the price level of India is 29, and that of united states is 113, and nominal exchange rate is 64-1(INR-$). So what is the real exchange rate?

Is it $$RER = NER\times\frac{US_{PriceLevel}}{INR_{PriceLevel}}=273 \\ or \\RER = NER\times\frac{INR_{PriceLevel}}{US_{PriceLevel}}=16$$

I believe it should be the second one, because the price level in India is less than that in US so buying power of dollar should be less. Is this reasoning correct?

Presumably one bundle of goods and services which costs about USD 113 in the United States would cost about USD 29 in India

so the bundle which costs about USD 113 in the United States would cost about INR 18546 in India at a market exchange rate of 64:1

suggesting a purchasing power parity of about INR 16.4 : USD 1

The OECD calculations of PPPs suggest about 17:1 recently for India so this is the correct order of magnitude


If a weak preference relation is complete and transitive, why is the strict preference relation negatively transitive? My textbook says that "if a weak preference relation is complete and transitive, the strict preference relation MUST be asymmetric and negatively transitive". Now, I think I understand why it must be asymmetric - all strict preference relations are asymmetric, correct? However, I don't understand why it is negatively transitive. If the weak preference is transitive, couldn't the strict preference also be transitive?

I think your confusion here stems from misinterpreting negative transitivity to mean "not transitive". But that's not what it means. It is perfectly possible for a binary relation to be both transitive and negatively transitive, as is the case here with the strict preference relation.

Definition 1. A binary relation $\mathcal{R}$ is transitive if: $$x \mathcal{R} y \text{ and } y \mathcal{R} z \implies x \mathcal{R} z.$$

Definition 2. A binary relation $\mathcal{R}$ is negatively transitive if: $$x \not\mathcal{R} y \text{ and } y \not\mathcal{R} z \implies x \not\mathcal{R} z.$$

(Those are forward slashes over the $\mathcal{R}$'s meaning "not". The LaTeX "not" here isn't quite working as well as I'd like.)

The strict preference relation $\succ$ is both transitive and negatively transitive.

It is transitive because $(x \succ y \text{ and } y \succ z)$ implies $x \succ z.$
It is negatively transitive because $(x \not\succ y \text{ and } y \not\succ z)$  is equivalent to $(y \succsim x \text{ and } z \succsim y)$, which, by the transitivity of $\succsim$, implies $z \succsim x$ or $x \not\succ z$.


Real option effect of uncertainty - irreversiblity vs fixed cost There is a growing literature (e.g. Bloom, 2009) studying negative macroeconomic impacts of heightened uncertainty. One channel through which uncertainty can discourage economic activity, and investment in particular, is via real option effect, where if firms face irreversibility or fixed cost in investment, higher uncertainty will encourage them to postpone investment, or exercise their "option to wait".

My question is: which of the two forms of nonconvex adjustment costs (fixed cost vs. irreversibility) is more important for this mechanism, and how do they differ in their effects? Is there any good reference explaining the issue, preferably in discrete-time setting? (I'm aware there's large literature on real options in continuous time, but so far I'm more familiar with discrete-time macroeconomic models).

There exists a post on capital adjustment costs, which gives a good overview of the different types of capital adjustment costs.

http://economictheoryblog.com/2015/08/20/capital-adjustment-costs

However, ultimately the post summarizes Cooper, R. W., & Haltiwanger, J. C. (2006). On the nature of capital adjustment costs. The Review of Economic Studies, 73(3), 611-633.

Regarding your question, I guess as long as there are any sunk costs associated to investment you destroy future option, regardless the nature of these costs. Consequently the nature of capital adjustment cost should not really change the way uncertainty affect investment through real option effects.


Why does the IMF push for austerity? Are there any countries that applied austerity measures and had a positive outcome that was attributed to it? Why do institutions like the IMF often encourage or require it?

Why do so many people die in hospitals? Aren't doctors there supoosed to save lives?

The IMF is the trauma surgeon of government finances. When a country asks the IMF for help, it is because its finances are in very bad shape. They no longer have enough money to pay for public services, infrastructure, pensions, salaries. Without some kind of external help, the government has to fix the problem by some combination of reduced spending, increased taxes, or by printing money (which will increase inflation).

What this shows is that austerity is not imposed by the IMF. Austerity is "imposed" by the inability of the government to finance its own spending.

The IMF, by providing loans when no one else will, actually helps to soften the adjustment. With the extra funding, the government is able to cut spending and raise taxes less than they otherwise would.

Of course, one thing to keep in mind is that the IMF is not a charity. It expects its money back. If the IMF provided grants instead of loans, there would be no need for austerity. But then the IMF wouldn't exist, because it would have run out of money long ago.


Revenue maximization same as increase contribution margins? Under which condition, will it be the same whether you choose to use revenue maximization or to increase contribution margins? In what industry is this possible?

In my thought process, I was thinking that before above condition can be true, the industry/company will need to have no variable costs, only fixed costs - but I am unsure.

Can anyone help me answer above since I can't seem to wrap my head around it.

If "contribution margin" is price minus variable cost per unit, and "revenue" is price times units sold then, even with zero variable costs, optimising

maximum contribution margin
maximum revenue

will typically be at different points

Assuming the demand curve of quantity and price is downward sloping, the contribution margin will fall as quantity increases, so the maximum contribution margin will at the maximum price, typically for minimal quantities.  If instead the demand curve is upward sloping initially and then downward sloping, then without variable costs the contribution margin will be maximised at the highest possible price

Meanwhile total revenue is usually not maximised for minimal quantities as at that point revenue will also be minimal. Instead it will be maximised when marginal revenue is zero (when the increasing revenue for marginal additional quantities exactly offsets reducing revenue from reduced prices), which with a smooth demand curve will typically be at a higher quantity and lower price than the maximum price point


If someone goes for a haircut, does it increase GDP? If I go for a haircut, am I causing the GDP to rise because consumption is rising?

Existing answers are correct, yes, you are increasing GDP.
GDP is a crude measure of how much is spent during a year. This is used as a proxy for living standards (the thinking goes: if an economy is spending more, there's more economic activity and it's probably doing better).
But the logic doesn't always hold, for example:
Consider a scenario where you break my window and I break yours, and we both pay the glazier \$100 each to fix our windows. Our living standards are unchanged, despite the fact that our actions increased GDP by \$200!


Corner solution of the maximization problem Answer

Hello, I upload the actual question with my 8-pages answer. Please can you check it. Is there a corner dissolution for $c=\gamma$. Please share your ideas. Thanks.

Here is the formulation of the problem :
\begin{eqnarray*} \max_{c, h, l} \  & \ln (c - \gamma) + \beta l + \theta h \\ \text{s.t.} &  l + h = 1, \\ & c \leq \omega h + \rho, \\ \text{and} & l, h \geq 0, c \geq \gamma \end{eqnarray*}

Substituting $l = 1 - h$, we can rewrite the above problem as :
\begin{eqnarray*} \max_{c, h} \  & \ln (c - \gamma) + \beta + (\theta -\beta)h \\ \text{s.t.} & 0 \leq h \leq 1 \\ \text{and} & \gamma \leq c \leq \omega h + \rho\end{eqnarray*}

Since utility is increasing in $c$, $c = \omega h + \rho$ will hold in optimum. So we can further reduce the problem to :

\begin{eqnarray*} \max_{h} \  & \ln (\omega h + \rho - \gamma) + \beta + (\theta -\beta)h \\ \text{s.t.} & 0 \leq h \leq 1 \\ \text{and} & \gamma \leq \omega h + \rho\end{eqnarray*}

Please note that we'll assume $\omega + \rho \geq \gamma$. This is because when $\omega + \rho < \gamma$, there is no feasible solution. In other words, there does not exist any $h$ satisfying the constraints.

To solve this problem, we'll consider two cases :

Case 1: $\rho \geq \gamma$

In this case problem can be written as :

\begin{eqnarray*} \max_{h} \  & \ln (\omega h + \rho - \gamma) + \beta + (\theta -\beta)h \\ \text{s.t.} & 0 \leq h \leq 1 \end{eqnarray*}

Derivative of the objective with respect to $h$ is
$\frac{\omega}{\omega h + \rho - \gamma} + (\theta -\beta)$ which yields the following solution :

\begin{eqnarray*} h = \begin{cases} 1 & \text{if } \frac{\omega}{\omega + \rho - \gamma} + (\theta -\beta) \geq 0  \\  0 & \text{if } \frac{\omega}{\rho - \gamma} + (\theta -\beta) \leq 0  \\ \frac{1}{\beta -\theta} - \frac{\rho - \gamma}{\omega} & \text{otherwise} \end{cases} \end{eqnarray*}

Case 2: $\rho < \gamma$

In this case problem can be written as :

\begin{eqnarray*} \max_{h}  \ & \ln (\omega h + \rho - \gamma) + \beta + (\theta -\beta)h \\ \text{s.t.} & \frac{\gamma - \rho}{\omega} \leq h \leq 1 \end{eqnarray*}

Derivative of the objective with respect to $h$ is
$\frac{\omega}{\omega h + \rho - \gamma} + (\theta -\beta)$ which yields the following solution :

\begin{eqnarray*} h = \begin{cases} 1 & \text{if } \frac{\omega}{\omega + \rho - \gamma} + (\theta -\beta) \geq 0   \\ \frac{1}{\beta -\theta} - \frac{\rho - \gamma}{\omega} & \text{otherwise} \end{cases} \end{eqnarray*}

Combining the two cases, we can write the solution as :

\begin{eqnarray*} h = \begin{cases} 1 & \text{if } \frac{\omega}{\omega + \rho - \gamma} + (\theta -\beta) \geq 0  \\  0 & \text{if } \frac{\omega}{\rho - \gamma} + (\theta -\beta) \leq 0 \text{ and } \rho \geq \gamma \\ \frac{1}{\beta -\theta} - \frac{\rho - \gamma}{\omega} & \text{otherwise} \end{cases} \end{eqnarray*}

Using $c = \omega h + \rho$ and $l = 1 -h$ we can get optimal values of $c$ and $l$ in each of the cases.


How can an economy pay for all the products it produces? How can the totality of an economy pay for all the products it produces, if the initial amount of money in the system (before the profits on all of the products is realized) is less than the amount of money after all of the products are sold (at a profit)? The arithmetic does not seem to make sense. Any suggestion out of this riddle?

This is not really a riddle.
First, amount of money in economy is not constant. The amount of money economy has access to is typically growing thanks to policy of central bank/government. For example, you can see from Fred data that amount of money in the US measured by $M2$ increases over time (you can check similar statistics for almost any other country you want save for few that don’t publish it).
However, even if amount of money would be fixed that wouldn’t cause any issue. A price level in an economy is determined by the output and other factors so economy can’t really run out of money.
For example, following Mankiw Macroeconomics 8th Ed money market equilibrium can be described by:
$$MV=PY$$
Where $M$ is money stock, $V$ velocity of money (how often one banknote is used), $P$ is price level (aggregate prices) and $Y$ real output (this is only most simple representation of money market, in more complex models expectations of these quantities matter as well but for this explanation this simplified version will more than suffice).
Hence, if the amount of goods and services increases in the economy ($Y$ goes up), even if $M$ is fixed either $P$ can drop or $V$ can increase (or some combination of those two) to offset $Y$ and make sure that the amount of money in economy is sufficient to purchase or goods and services.
Consequently, economy will always be able to pay for what it produces. Heck, money is strictly speaking not even necessary - people could just barter with each other - money just helps transactions to run smoother.


What are the economic ramifications of rent control? What effect do they have on renters?  Landlords? Are there examples of rent control working, improving living conditions for renters?

I.e. What are the main arguments for/against rent control (purely economic, not emotional or moral).

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

$\textbf{Pros:}$

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

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

$\textbf{Cons:}$

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

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

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

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

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

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

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


Take-it-or-leave-it PBE I've found an interesting question looking at perfect-bayesian-equilibrium. I haven't seen a question where beliefs are not discrete.

There is a single potential buyer of an object which has zero value to
the seller. This buyer’s valuation v is uniformly distributed on [0, 1] and is
private information. The seller names a price $p_1$ which the buyer accepts or
rejects.

If he accepts, the object is traded at the agreed price and the buyer’s
payoff is $v − p_1$ and the seller’s is $p_1$.

If he rejects then the seller makes another
price offer, p2. If the buyer accepts this, his payoff is $\delta_(v − p_2)$ and the seller’s
is $\delta p_2$, where $\delta = 0.5$.

If he rejects, both players get zero (there are no further
￼￼￼offers).

Find a Perfect Bayesian Equilibrium.

My usual approach is to fix beliefs, but I don't quite know how to do this with continuous beliefs. Any advice?

After posting a bad solution yesterday I believe I got a better one:

The strategy of the buyer consists of two functions, $(f_1(v,p_1),f_2(v,p_1,p_2))$ where both functions map to $\left\{A,R\right\}$ (where $A$ stands for Accept, $R$ for Reject).
The strategy of the seller is $(p_1,p_2(f_1(v,p_1)))$. You get the solution via backward induction. In PBE $f_2(v,p_1,p_2)$ maps to $A$ if and only if $v \geq p_2$. (There is inconsequential leeway at equality.) In PBE the seller believes that there is a set $H$ of types for which the buyer refused her offer $p_1$. Then
$$
p_2^* = \arg\max_{p_2} p_2 \cdot Prob(f_2(v,p_1,p_2) = A | f_1(v,p_1) = R).
$$
The buyer will accept offer $p_1$ if and only if
$$
v - p_1 \geq \delta \cdot (v - p_2).
$$
From this you get
$$
v \cdot (1 - \delta) \geq p_1 - \delta \cdot p_2.
$$
The left hand side of this equation is increasing in $v$, so types with high valuation will Accept. This means that in PBE the set $H$ is such that
$$
H = [0, \bar{v}).
$$
From this we get the optimal $p_2$ given $\bar{v}$:
$$
p_2^* = \arg\max_{p_2} p_2 \cdot Prob(v \geq p_2 | v \in [0, \bar{v})) = \frac{\bar{v}}{2}.
$$
In PBE $\bar{v}$ is a function of $p_1$:
$$
\bar{v} \cdot (1 - \delta) = p_1 - \delta \cdot \frac{\bar{v}}{2},
$$
so
$$
\bar{v} = \frac{p_1}{1 - \frac{\delta}{2}}.
$$
We have determined all the PBE strategies but $p_1$.
The expected payoff of the seller is
$$
p_1 \cdot \left( 1 - \frac{p_1 - \delta \cdot p_2(\bar{v}(p_1))}{1 - \delta} \right) + \frac{1}{2} \cdot p_2(\bar{v}(p_1)) \cdot \left( \frac{p_1 - \delta \cdot p_2(\bar{v}(p_1))}{1 - \delta} - p_2(\bar{v}(p_1)) \right),
$$
where
$$
p_2(\bar{v}(p_1)) = \frac{\bar{v}(p_1)}{2} = \frac{\frac{p_1}{1 - \frac{\delta}{2}}}{2} = \frac{p_1}{2 - \delta}.
$$
Substituting this we get
$$
p_1 \cdot \left( 1 - \frac{p_1 - \delta \cdot \frac{p_1}{2 - \delta}}{1 - \delta} \right) + \frac{1}{2} \cdot \frac{p_1}{2 - \delta} \cdot \left( \frac{p_1 - \delta \cdot \frac{p_1}{2 - \delta}}{1 - \delta} - \frac{p_1}{2 - \delta} \right),
$$

You have to maximize this w.r.t. $p_1$. With $\delta = 0.5$ I got
$$
p_1^* = \frac{9}{20}, \hskip 20pt \bar{v} = \frac{3}{5}, \hskip 20pt p_2^* = \frac{3}{10}.
$$


Impact of election outcomes on individual's mood? Behavioral Finance I am currently working on my thesis in behavioral finance. My topic is about short term stock returns after the elections. One paper ("Sport Sentiments and Stock Returns")  proves that the losing country in a sports game exhibits much lower short term stock returns because of the sport event's impact on the mood of individuals. I would like to make a similar argument about the elections in two party systems where close to half the voters will feel like they have lost the elections. My hypothesis is that this could lead to a downbeat mood for everyone who 'lost' the election and consequently lead to lower short term returns. My question now is if anyone knows about a study which has investigated if the outcomes of an election influence the mood of individuals?

TL/DR:

Does anyone know papers investigating the impact of election outcomes on individual's mood?

Thanks for your help in advance!

I can only provide an australian perspective, but we have a variety of consumer confidence sources tracking weekly results. Somewhere in

Here is one analysing elections. It shows a very sharp drop in the lead up but it is short lived. There is evidence that this impacts the stock market.

Shane Oliver wrote about the 2013 australian election, the 2016 Australian election and the Italian election. The most interesting is probably the one published around the 2013 Australian election as it looks at the impact on stock markets. Those sources should be a good starting point. There's a good amount of research going around. The basic gist is that mood is impacted for sure but how important this mood swing is is unclear.


Sample used in calculating the sample regression function Does the OLS (ordinary least squares) method of regression consider only one sample value in calculating the sample regression function (SRF)? If not, then how is the SRF created when there is more than one observation per $X_{i}$?

It is not very clear what you're asking, but if the model is of the form

$$
y_i = \beta_0 + \beta_1 x_i + \epsilon_i \tag{1}
$$

Then the sample regression function (SRF)

$$
\hat{y}_i = \beta_0 + \beta_1 x_i \tag{2}
$$

indeed only considers one value of $x_i$ at the time. If you have a situation in which several observations $y$ are associated with the same value $x_i$, then a linear model is perhaps not appropriate for describing your data


Is this proof correct? i'm new at this, so i´m really sorry sorry if i do something wrong.
The problem is this:
A choice function satisﬁes condition α if whenever $x = C(A)$ and $x ∈ B ⊂ A$, it follows that $x = C(B)$ as well.
Axiom 1: If $x ≠ C(A)$ then C(A) = C(A\{x})
And i need to show if condition α implies Axiom 1.

C(A) is choice function. Here is a definition of choice function (just in case you need it): "Let X be a ﬁnite set of alternatives. Let P(X) be the set of all nonempty subsets of X. We call the elements of P(X) as menus. A choice function is a map C : P(X) → X such that C(A) ∈ A, for all A ∈ P(X). It selects a single element from each menu. A choice correspondence is a map C : P(X) →P(X) such that C(A) ⊆ A, for all A ∈P(X). From each menu, at least one alternative is chosen"

And i found that Axiom 1 does not implies Condition α. Here is a counter example: We have X = {x, y, z}. Take A = {x, y, z} and y∈C({x, y, z})
y∈C({x, y}), z∈C({x, z}) and {y, z}∈C({ y, z}). Here we have a contradiction because C({x, y, z})≠C({ y, z}).
Thank you.

Your "counterexample" also violates condition $\alpha$: $y=C(\{x,y,z\})$ but $y\ne C(\{y,z\})$. So it's not really a counterexample.


Partial differential equations in economics Where, in economics, are partial differential equations used?

I'm particularly interested in micro theory applications, but would also be keen to know of other applications.

Here are a couple of suggestions. There are some PDEs in some recent continuous-time models, for instance in:

A Continuous-Time Version of the Principal-Agent Problem, by Sannikov, Review of Economic Studies (2008)
Persistent private information, by Williams, Econometrica (2011)

I would not be surprised if Yuliy Sannikov used PDEs in some of his other papers (although I have nothing precise in mind).

You can refer to the review by Achdou et al. (Partial differential equation models in macroeconomics, Philosophical Transactions of the Royal Society, 2014) for other references.


Best book to self-study microeconomics What textbook(s) (and other resources) would you recommend to someone who wants to self-study microeconomics to an advanced (graduate) level starting from 0 (i.e. no formal background in economics)?
I have an undergraduate double major in a humanity and natural science. So there is a base of mathematical ability and knowledge of calc. I plan on improving in this area as well, so it isn't essential that all the requisite math is covered, but accessibility without a lack of rigor is of course preferred.

A good balance of intuition and rigour is given by a text called Chicago Price Theory and an accompanying YouTube series from Chicago Economics Dept.
https://home.uchicago.edu/cbm4/cpt/index.html
My only criticism of the YouTube series would be that the ordering of the videos is very poor. It would therefore require simultaneously consulting the text.


Is poverty a mathematical necessity? I recently saw a meme, and the content was something like:

  In the near future, a meteor will 'hit' the Earth, and there will be
  gold rain, and hence everyone will be rich

The ridiculous thing with this is that if everyone has tons of gold, then gold becomes worthless, so in terms of poverty, nothing would change.

This got me thinking!

It is clear that you cannot solve poverty by giving poor people money because than the money would loses its value, and prices go up (since also you would need to print heck a lot of money). However, one thing that might work is if everyone had a job with decent salary. Then, everyone would earn enough money to have decent life.

However, this got me thinking even more!

This solution implicitly assumes that in such a case, everything would be the same except now everyone has enough money to support themselves, but if everyone has a job with a 'decent' salary, say a job with at least paying \$1000 per month, then the values of the money would (or could) drop because everyone has that \$1000, so then \$1000 wouldn't become a 'decent' pay, and not everyone would be able to support themselves with that much money now.

(same thing ...) even more!

Question: Is not having and poor people mathematically possible ?

If you think about it, the very fact that something is valuable, such as gold, depends heavily one the fact that not everyone has that item. Moreover, if all the wealth was distributed equally, and not allowed any imbalances, then we wouldn't be event survive as human species, but any imbalance would results in someone getting richer and some other getting poorer; and this means with some extreme exceptions, the existence of poverty is ensured mathematically.

Edit:

Guys, you are obscuring the core problem in here by dealing with specific details; forget money, thing in terms of wealth. There is some total wealth in the economy, and assume that there is some poverty threshold of in terms of wealth (it does not matter how this wealth is distributed or kept in practice i.e in terms of some money, gold, or silver; it does not matter.) What is this threshold.? we don't know, and we don't have to know for the time being. The analysis will show in what conditions, such a threshold can exists, and there can be no poor with respect to that threshold (of course, we then have to check, when we interpret our results in terms of real money whether that threshold corresponds to a "decent" one).

American economic theorist Henry George wrote about precisely this issue in his famous work Progress and Poverty published in the late 1800s, and based on his observations on the economic development of San Francisco during the gold rush.  His argument was that increasing economic development primarily benefitted landowners, at the expense of both capital and labor.  (However, since landowners were often also holders of large amounts of capital, it was primarily labor that ended up losing out.)  In a nutshell, the leverage that landowners held over the workers allowed them to push wages ever lower, creating poverty as a result of economic progress.  He theorized that taxing economic rent (at/near 100%) would eliminate speculation and thus stop the boom/bust cycle endemic to market economies, as well as providing ample revenue to the government to fund social welfare programs and to develop infrastructure.


Consumption function with negative intercept? I am doing an assignment where I calculate the consumption function of a certain country from empirical data and I am getting a negative intercept. How can this be interpreted because usually, isn't the intercept always positive?

I assume that you ran a linear regression to find the $C(Y)$ function and by negative intercept you mean $C(0)<0$. This does not contradict anything because what you have is an estimate of the $C(Y)$ function based on empirical data that was probably centered around some non-zero value of $Y$. So it is quite possible that the function's estimate is incorrect far from the observed range of $Y$, especially if you were using a linear regression which is a very basic functional form.

If the actual $C(Y)$ consumption function, not the estimate, were such that $C(0) < 0$ then indeed we would have a contradiction. But as long as you are clear that what you have is an estimate for $C(Y)$ this problem does not arise.


Solving an OLG model, value function iteration vs. projection (chebyshev polynomial) I can't decide between using value function iteration or projection on chebyshev polynomials.

I'm inclined to use projection, however I need to compute (for welfare analysis) the value of the value function at some specific age.

Using the decision rules computed by projection and derived from FOCS is it possible to compute the expected lifetime discounted utility?

You could solve for the value function ex-post from the Bellman equation. For simplicity, consider a deterministic dynamic programming problem (in OLG model, you'd have age as another state variable, but I'll abstract from that). If $x$ is state and its next-period value $x'$ is control, $U(x,x')$ is one-period utility and you have somehow obtained decision rule $x' = g(x)$, it must be the case that the value function satisfies

$$
V(x) = U(x,g(x)) + \beta V(g(x))
$$

This is a functional equation in $V()$ that could also be solved by projection method. Alternatively, you could iterate on the Bellman equation (on some grid over state space) just like in VFI, but skipping the optimization step (since you already know the optimal choice), and eventually the value function should converge.


Plotting money market equilibrium for 2020 I am trying to roughly sketch up supply / demand curves by parameterizing the major happenings in the money market in 2020. I intend to use this chart as the template:

Below, I'll outline my thought process for each curve:
Money supply

Interest rate targeted at zero
Fed balance sheet expands (a lot)

Graph implication: money demand curve(straight line) shifts to the right
This is the tricky part, as money demand is not something we can directly observe in practice, though I tried my best to be objective/conservative.
Money demand

Unemployment spikes in April, then slowly stabilizes around 6% in 3Q20

Total income probably drops off a cliff for a few months and slowly revives with industries streamlining / automating / outsourcing, setting a lower total income floor than pre-pandemic times

Stimulus / helicopter money offsets deflationary forces

Risk-off sentiment during March's downturn drives defensive portfolio positioning, increasing demand for cash

BofA September poll: fund manager consensus that it's a new bull market, investors rotate out of cash/equivalents and into higher yielding assets, reducing demand for cash

Graph implication: Money demand undergoes a short-term shift to the right, but trends to a shift to the left from a likely permanent contraction in total income and the onset of a new bull market (admittedly not a slow bull)
Conclusion: I realize there are multiple factors at play here, but I think it's reasonable to assert that, on balance, the demand curve shifts left and the supply curve shifts right.
And thus I present my rough sketch of the money market:

Question
Is this parameterization consistent with mainstream economic analysis on the money market in 2020?

The graph is almost correct given the assumptions about what is happening but not quite. The proper graph should look more like this picture I made in LaTex using tikz:

Where $^*$ denote the new state of things given your assumptions.
You are right that money demand shifts to the left and money supply to the right, but your graph missed an important fact that money demand at zero lower bound (ZLB) becomes flat. This is one of the reasons why monetary policy looses its potency around ZLB (see Blanchard et al. Macroeconomics a Eurpean Perspective pp. 96).
Correction of some misconceptions:
In your post you also have some misconceptions let me correct them:

This is the tricky part, as money demand is not something we can directly observe in practice, though I tried my best to be objective/conservative.

We actually can observe money demand at a given point in time (only the whole demand function is not directly observable). Furthermore, we actually even can, using econometric methods, properly estimate the money demand function.  See Jawadi & Sousa (2013) or Narayan, Narayan,  & Mishra (2009), for examples of that. However, of course this cannot be done in real time but only retroactively as we collect enough data about given time period, so to do that for period covering entire COVID19 crisis this won't be possible until few years down the road.

helicopter money offsets deflationary forces

central banks are definitely trying to expand money supply right now but not via helicopter money. Helicopter money means central bank is directly sending money to households. This has not yet happen to my best knowledge (at least not in US, EU or UK), although there are economists calling for central banks to do so (like Gali 2020 in his VOX$^{EU}$CEPR post).


Prove that if a bond trades at a discount, its yield to maturity will exceed its coupon rate Can someone give me a mathematical proof of this statement?

  If a bond trades at a discount, its yield to maturity will exceed its
  coupon rate.

If a bond trades at a discount, $P<FV$.

$\displaystyle\implies CPN\times\frac{1}{YTM_n}\left(1-\frac{1}{(1+YTM_n)^n}\right)+\frac{FV}{(1+YTM_n)^n}<FV$

$\displaystyle\implies CPN\times\frac{1}{YTM_n}\left(1-\frac{1}{(1+YTM_n)^n}\right)<FV-\frac{FV}{(1+YTM_n)^n}$

$\displaystyle\implies CPN\times\frac{1}{YTM_n}\left(1-\frac{1}{(1+YTM_n)^n}\right)<FV\left(1-\frac{1}{(1+YTM_n)^n}\right)$ --------------(1)

$\displaystyle YTM_n>0\implies 1+YTM_n>1\implies(1+YTM_n)^n>1\implies\frac{1}{(1+YTM_n)^n}<1\implies 1-\frac{1}{(1+YTM_n)^n}>0$

So, we divide both sides of (1) by $\displaystyle 1-\frac{1}{(1+YTM_n)^n}$ to get

$\displaystyle CPN\times\frac{1}{YTM_n}<FV$

$\displaystyle\implies\frac{CPN}{FV}<YTM_n$

$\displaystyle\implies r<YTM_n$

$\displaystyle\implies YTM_n>r$

QED