texts:
I'm studying for a test I have this week and a practice question asks whether or not the price elasticity of demand for the demand function $\ q = Ap^{-x} $, where A and x are positive constants depends on the price p.

I've attempted to use the equation, $ \frac{dQ}{dP}*\frac{P}{Q} $ in order to solve the problem and I am getting the result,

$ \epsilon = \frac{-xA}{p^{x+1}}*\frac{p}{q} = \frac{-xA}{p^{x}q}$

Which would mean that the elasticity does  depend on p, however the answer in my practice exam says that it does not depend on p. Why is that the case/where did I go wrong?


texts:
I recently investigated a bit about the Iranian economy and did not get an interesting result:

Iran's currency dropped to worst low in four decades
(Since the Islamic Revolution in Iran).
Transferring money in Iran is very difficult and sometimes impossible.
Most countries of the world have declined from banking transactions with Iran.

Catastrophic!، right!?

What is the economic situation in Iran?


texts: J Curve and DD Schedule in the Short Run (International Finance)

texts:
Assume that the J-curve is true. What would the DD curve look like during the early period of the J-curve (where the value effect dominates)?  What would the effect of temporary changes in monetary and fiscal policy look like with this DD curve?

I assume that the DD curve might be downward sloping because of the value effect, but I'm unsure how temporary changes in government spending and temporary changes in the money supply will affect the AA and DD schedules in this scenario.  Would somebody please explain?


texts: Is it possible to quantify & cost the ideological obstruction to climate change?

texts:
Paul Rogers in an article on Open Democracy, writes:

It is also significant that the term 'hothouse earth' has caught on, and that the idea of runaway climate disruption is covered in the media in some depth - even by newspapers that have long been impregnable citadels of climate denial
The weekly economist has for many years given ample space to climate sceptics, but recently it's coverage has changed markedly. The cover story of its latest is about the failure to tackle climate change.

Is it possible to quantify and cost the ideological obstruction on tackling climate change given that the earlier climate change is tackled the more effective it would be?
One example of a global effort to limit environmental damage was the Montreal protocol on limiting substances that damage the ozone layer that came into force in 1987 with climate projections showing that ozone layer will return to 1980 levels around 2050-70. Of course, the CFC industry is valued in the billions whereas the fossil fuel industry is valued in the trillions so there is likely to be a much larger push-back from the industry. It's this that I want to have numbers on.
In view of the comment below in the top rated answer, I'd suggest that such an exercise would useful in informing class action suits in the future in the same way that we have had class action suits against big tobacco firms. (In the latter, they are polluting peoples lungs and in the former, the planet lungs).


texts: What does 'Health spending as a share of GDP' mean?

texts:
I am watching a video essay talking about healthcare spending in different countries and one of the first graphs shown was titled: 'Health spending as a share of GDP'. After doing some reading, I think I understand now. It is saying the graph shows money spent on health as a percentage of GDP, but what is GDP. GDP is gross domestic product, which is the total value of goods or services produced and provided in a country in a year. So in my understanding, the phrase means: health spending as a percentage of the value of the entire nations economy. Is this correct? Also does this mean money spent on healthcare by citizens or by governments?

Here is the video. The graph is around 0:16.


texts: Find equilibrium price using excess demand function

texts:
Consider an economy with two agents. There are two goods, x and y. Agents' preferences are Leontif ones as follows:
$u_1(x,y)=\min(x,4y)$ and $u_2(x,y)=\min(x,y)$.
Initial endowment for 1 is (2,4), for 2 is (4,2)
The problem asks me to use the excess demand function to find the equilibrium price and show that there are infinitely many equilibria with that price. The problem also asks what is the cause of such multiplicity of equilibria.
I tried this many times, but I always get that the equilibirum price is (1,-1/2), which is impossible.
Any help is appreciated.


texts: Shape of Isoprofit Curves for Strategic Complements

texts:
Two goods are strategic complements if:
$$\frac{\partial \pi_1}{\partial q_2}>0\;\text{and}\;\frac{\partial \pi_2}{\partial q_1}>0$$
The image below is a picture of best response functions and isoprofit curves for strategic complements

I understand why the BR curves are upward sloping, but I am struggling to understand why the isoprofit curves are shaped the way they are. Can anyone give me the intuition behind the shape of these isoprofit curves?


texts: Assumptions for the existence of a Walrasian equilibrium

texts:
I have a problem set stating that a competitive equilibrium does exist under a series of assumptions on the economy.

The question is "Show that the following six assumptions are needed for existence by constructing counterexamples to it where 5 of them are satisfied and one not".

The assumptions are continuity, convexity and local nonsatiation of preferences and closedness, convexity and inaction of the production set.

From what I got from the question and the TA explanations, it seems that if one of this properties fails, then there should be no competitive equilibrium. But I have actually found cases in which these properties are violated but an equilibrium exists. For example, in an Edgeworth box with bliss point preferences (which are not locally nonsatiated) we can find an equilibirum; the same happens when we have for example lexicographic (which are not continuous) and perfect substitutes.

SO my question is are these assumptions necessary for the existence of an equilibirum or not? And if not, what would be the purpose of the exercise?


texts:
According to this video:

Opportunity Cost of a choice is what you gave up to get it.

Now, let us read the following question:

You are going to a football match next Saturday evening, you have already bought the tickets and cannot resell it. You have just learned that on this Saturday evening, there is also a rock concert that you are interested in. The ticket for the concert costs 40\$ but you value this concert as much as 50\$.
What is the opportunity cost of going to a football match?
a) price of football match’s ticket
b) 40\$
c) 50\$
d) 10\$

My answer was (c). Coz, I gave up the concert which costs 50\$.
However, my teacher says that the correct answer is (d).  Why?


texts: What's the term for the debt you have to pay today?

texts:
Say that a company has a debt of 10 million $US

But from that debt, the company has to pay 2 million $US today. The rest of the debt has to be payed next year and later.

Is there a term for the debt that has to be paid today?


texts: If rent control "doesn't work" and supply induces demand, how can cities improve affordability?

texts:
Suppose we aim that moderately poor people (let's say 1.5× minimum wage) can afford the rent for an apartment meeting minimum quality standards and located within city limits.  This may be a political aim.

What economic policies are effective to achieve this?

Rent control.  Popular, but economics appears to tell us it creates more problems than it solves.  See also the questions Why did Berlin freeze the rent prices as opposed to letting the market set the price? and What is the likely result of rent control in Berlin?.
Increase supply?  In cities, it appears supply may create demand (the more people in a city, the more services, the more people want to live there) so this may not always work either, or only under limited circumstances (perhaps unless building huge amounts, but developers hate vacancies, so I doubt that limit would be surpassed in a free market).
Social housing, owned by the government?  I don't know what economic theory says about this.
Reduce demand?  Not sure how that would work without harming the city.
Impossible?  Should we give up on the idea that poor people can live in alpha world cities such as London, New York, Tokyo, Paris, Singapore, Amsterdam, Seoul, Berlin, Hong Kong, or Sydney?
Something else?

I'm aware that most economists say that rent control "doesn't work" — what are the alternatives that economists may prefer?


texts:
In one of my marketing slides it says: The diagnostic potential of micro test market is low because no survey of panel possible; the diagnostic potential of simulated test market is high.

I think the diagnostic potential is in regard to product positioning.

What does "survey of panel" mean here?


texts:
We've had ultralow interest rates for a very long time now (I think unprecedented in history). Is it possible that this extremely loose monetary policy is creating bubbles? Bill Gross has put out a warning: http://www.marketwatch.com/story/bill-gross-negative-yields-will-lead-to-supernova-like-market-implosion-2016-06-10

Is it possible he is right? What would be the impact on the economy? What will the FED do if this happens, do they have other policy-tools besides QE and lowering interest rates?

thanks in advance


texts: conditional factor demand functions for capital and labor

texts: I don't how to put maths in here so using an image:


texts: Need help with Wakker (2010) on arbitrage

texts:
In Prospect Theory (2010; Cambridge UP), Peter P. Wakker has an exercise assignment 3.3.6 without solution in the book and I'm really unsure about this one. The exercise states on pages 76-77:

Assignment 3.3.6. This assignment demonstrates that risk aversion implies arbitrage. More generally, it shows that every deviation from risk neutrality implies arbitrage. You may assume that risk neutrality for all 50-50 prospects implies complete risk neutrality. Show that arbitrage is possible whenever there is no risk neutrality, for instance as soon as there is strict risk aversion. A difficulty in this assignment is that we have defined risk neutrality for decision under risk, and arbitrage has been defined for decision under uncertainty. You, therefore, have to understand §2.1-2.3 to be able to do this assignment.

This is in the context of classical expected utility theory (not prospect theory or RDU).
I can set up a scenario in which there are consecutive prospects with the same expected value that the decision maker is willing to swap. For example, assume that the decision maker is risk-averse and the utility function is $U(x)=\sqrt{x}$. Consider only 50-50 prospects and write only the respective gains. Let $x_1$=(\$90, \$10), $x_2$=(\$80, \$20), $x_3$=(\$70, \$30), $x_4$=(\$60, \$40), $x_5$=(\$50, \$50). The expected value is \$50 for each, but we get $EU(x_1)\approx 6.32$, $EU(x_2)\approx 6.71$, $EU(x_3)\approx 6.92$, $EU(x_4)\approx 7.04$, ...
That doesn't show arbitrage, though, it merely reflects the decision maker's willingness to swap  prospects with higher risks for those in which the risk is spread more evenly.
How do I show arbitrage?
What puzzles me about this exercise is that there seem to be many no-arbitrage theorems for expected utility and that expected utility is generally accepted as a rationality principle (as opposed to only allowing expected value). But, if I understand correctly, arbitrage in finance is the same as Dutch books, and these are generally taken as arguments for the irrationality of some decision making (e.g. when preferences are cyclic). The bottomline is that I really don't understand this exercise.
N.B.: This is not homework and I'm not an economist. I'm a philosopher who wants to understand Wakker's book.


texts: In finance, the variance of the returns of a security are used as a proxy for the associated risk of the security. I've seen some books include sentences like "if you take variance as a measure of risk...". In what way might variance be an incomplete measure of risk? What alternatives do we have?


texts: Notation: is it correct to write $x \succsim y \succsim z$ before using transitivity?

texts:
Let $\succsim$ complete and $x, y, z \in X$. Suppose $x \succsim y$ and $y \succsim z$. Is it OK to write $x \succsim y \succsim z$ just knowing this?

Or, on the contrary, such expression automatically implies $x \succsim z$?


texts: How to convert an historic value denoted in foreign currency to a modern value in local currency?

texts:
I want to convert GBP in 1968 to USD in 2018, in order to "translate" an amount paid by an individual in Britain fifty years ago. My intention is that an American reader today will be able to better understand the value of the money if it is given in inflation-adjusted USD.

In 1968, £1 exchanged to \$2.38. \$1 in 1968 adjusts to \$7.22 in 2018. £1 in 1968 adjusts to £17.02 in 2018. Finally, £1 exchanges to \$1.34 in 2018.[1]

If we do the exchange first, then £1 (1968) is equivalent to \$17.18 (2018). If we adjust for inflation first, then £1 (1968) is equivalent to \$22.81 (2018). Which is the correct way to do this? Why?

Addendum:

An answer to a similar question suggests that the exchange rate, in some form, should be commutative with inflation adjustment:

  Also, it does not matter which transformation you do first, as its purely multiplicative.

I am not sure whether the author is referring to calculations using the formula that he defines as the "real exchange rate" as "purely multiplicative", or whether he/she meant that the exchange rate and inflation are ideally always going to be commutative (and therefore this case deviates from the ideal by a degree). The answer does not go into very much detail and it is beyond my understanding of economics to determine what the "respective price level" between Britain and the US is in 1968 or 2018.

[1]
I am getting my inflation data from officialdata.org. While I have found on other websites slightly different conversion factors for inflation since 1968 in both currencies, they are only a few cents different from the figures I used here. The nominal exchange rate is, by contrast, an historical fact.


texts: Two ways of calculating real GDP: do they produce the same result?

texts:
My professor gave us two formulas for GDP for 2012 in 2010 dollars:

y = P1 (2010) * Q1 (2012) + P2 (2010) * Q2 (2012) ...

And:

y = x1 / (1 + inflation rate 2010 to 2012)

Where x1 is the nominal GDP for 2012. Do those formula produce the same result? If not, under what assumptions are they close to one another? Which one is used by governments to calculate GDP figures?


texts:
This might be a very basic question, but I am a beginner in macro models. I would appreciate help with my doubt.

In different papers I have read about the elasticity of labor supply or the inverse of the Frisch elasticity of labor supply. However, Thoenissen & Benigno (2008) talk about the elasticity of substitution in leisure, displaying the following utility function:

$
\begin{gather}
U_t = E_t \sum_{s=t}^\infty \beta ^{s-t}\bigg[ \frac{1}{1-\rho}C_s^{1-\rho} (1-L_s)^\eta\bigg]
\end{gather}
$

where $\eta$ is the inverse of the intertemporal elasticity of substitution in leisure.

My question is, is there a difference between the elasticity of labor supply and the elasticity of substitution in leisure? If yes, is it possible to go from the elasticity of labor supply to the (inverse) of the intertemporal elasticty of substitution in leisure?

Thank you very much for your help.


texts: References on foreign ownership of domestic assets

texts:
In Piketty's Capital in the 21st Century, he occasionally analyzes the ownership of domestic assets by foreign countries. On p. 192, he writes:

Japan and Germany have accumulated quite significant quantities of net foreign assets over the past few decades... these amounts are still substantially lower than the net foreign assets of Britain and France on the eve of World War I... it is natural to ask whether this will continue. To what extent will some countries find themselves owned by other countries over the course of the twenty-first century?

A few years ago, there was panic in Vancouver, Canada over increasing real estate prices and it was hypothesized that it was due to increased investment from Chinese buyers. The National Bank of Canada wrote:

From this, we hypothesize that, in 2015, homebuyers from China invested ~US 9.9
billion / Cdn 12.7 billion in Vancouver residential real estate (on a total 2015
residential real estate purchase volume in greater Vancouver of Cdn 38.5 billion,
according to the Real Estate Board of Greater Vancouver); this amounts to 33% of
total purchase volume... The estimated share of purchase volume seems high and we stress this
methodology is truly a back-of-the-envelope attempt at gauging the significance of
capital inflows from mainland China on the local residential real estate markets in
Toronto and Vancouver.

I am looking for references to more material on this phenomenon of foreign ownership of domestic assets. Some topics in which I am interested are:

Historical or present cases of a significant percentage of one country's assets being owned by foreigners, or (in the other direction) a significant percentage of a country's holdings or national income being derived from ownership of foreign assets.
Past or present laws in countries enacted to restrict the degree to which foreigners can own domestic capital.
Occurrences of reneging on the promise of property rights by governments taking away what foreigners owned.


texts: How does the use of a logistic (or probit) regression help address the endogeneity concerns: explanatory variable is correlated with error term?


texts:
Imagine following tiny nation.

It consist only of 100 people running a car manufacturing plant.

The nation imports every resource it needs for manufacturing those cars. It also imports all energy, gas for transportation, food for people, clothing etc from outside.

Because of high competition, the nation ends up selling all cars it produced in a particular year, at a much lower price than resources/energy/gas etc cost them. Hence, the manufacturing cost is greater than the total income from selling the cars.

Let's say the total income from all cars sold is 2 billions for a given year. The total cost for imported goods to run the manufacturing plant and feed/cloth the people was 3 billions.

They also have to pay 200 millions total in debt rates for that year from loans taken at some point.

a) What would be the GDP of such a nation for this particular year?

b) I have been told that the GDP cannot be negative so i assumed that expenses for the imports/debt rates are not included in computing the GDP, or can the GDP actually become negative?

c) Given you knew the GDP and the dept to GDP ratio of such a fictive nation. But you did not know the expenses for imports and also did not know the average interest rate this nation has to pay on it's debt, then would just knowing GDP and debt to GDP ratio of this nation allow you to make any estimates on the health of it's economy?

Ignore salaries of the workers. They just work for food and do not pay taxes. The car manufacturing plant is owned by the state


texts: Do points inside the PPF curve always mean productive inefficiency?

texts:
If a firm produces combinations of goods along the PPF curve, it has achieved its productive efficiency. And when a firm reaches productive efficiency, it means that all factors of production have been fully utilized. And another way of measuring productive efficiency is to look at its average cost. If a firm has reached productive efficiency, it means that the firm is producing at the lowest average cost.
But what about the points that fall inside the PPF?
Let’s say A (15,10) is on the PPF curve, and B (15,5) lies beneath it. Assume that a firm is producing at point B, and the reason why it isn’t producing at a higher level is that there’s still some cash deposit in its business account that hasn’t been withdrawn yet.

Since cash deposit is NOT a factor of production, even the firm is producing at points beneath the PPF, it doesn’t necessarily imply that the firm has not utilized all factors of production. Where did I go run?


texts:
If I always spend a total of exactly $\\\$10$ per week on coffee, then does my demand function have unit elasticity?
According to me, the change in income doesn't affect my coffee consumption, so it does not seem like unit elasticity. Can someone help me understand this?


texts: Remittance: Migrant workers sending money to their families

texts:
I wonder about the role of migrant workers in a general economic context.

Migrant working appears all over the world and on many time and space scales:

around cities (e.g. commuters)
inside countries (more and better paid work in the North than in the South (e.g. Italy) or in the West than in the East (e.g. Germany))
continent wide (e.g. Europe: West-East, North-South)
world wide (e.g. Europe-Africa, North America-South America)

Overall, migrant workers who send some money back to their families seem to make use of arbitrage, i.e. taking "riskless advantage of price and loan differences". (This doesn't mean that the advantage is effortless: The workers and their families pay the heavy price of being torn.)

But this is not the issue of my question. My question is more general and concerns national economics in general and sustainability.

For the (richer) "host countries" (where the money is earned) the economical effect of sending money out (deflation) may be negligible, but for the (poorer) "home countries" (where the money is sent to) the effect may be significant:

inflation (more money than goods)
social conflicts (envy-driven)
accelerated emigration (of workers and experts)
in sum: an economical downward spiral

There's just one positive effect that I can imagine:

compensation of otherwise economic injustice (by historical or actual reasons)

Is there a general opinion about migrant working seen economically from the perspective of the "home countries" (where the money is sent to)? To which extent and how long does this way of economic exchange work? I'd like to learn more about this.


texts: Luce Choice Axiom, Quantal Response Equilibrium

texts: How is the Quantal response equilibrium model influenced by the Luce choice axiom since Quantal Response equilibrium takes into account the rationality parameter ß and I dont see the mention of rationality perturbation in Luce Choice Axiom? And it would be of great help if anyone could post an example application of the Luce Choice Axiom. Thank You.


texts: GNP v. GDP as a true measure of national vibrancy

texts: Is the GNP a more realistic number or measure of national economic vitality regarding its citizenry/residents of the nation in question versus the GDP?


texts: Correlation between salary level and housing prices in a town

texts:
Is there a measurable correlation in a town between salary level and housing prices?

Or, to put it differently: is it politically meaningful to drive up salaries by new investments if the result is unaffordable housing?

UPDATE: I do not want to edit the original question as others wrote their reply with that in mind, but it is right to suggest that it would have been better to ask about causality, not correlation.


texts: Interest rates in Quantitative Easing of 2008

texts: When the US govt printed money in 2008 and lend it to the banks, how much the banks had to pay in interest?


texts: When a land lords sells to an owner occupiers does it push up rents?

texts:
In the article Landlords who own one property ‘left without relief’ under new Victorian Government package posted on 15 April 2020 on the domain website. Barry Plant chief executive Mike McCarthy Makes the claim that landlords selling to owner-occupiers will push up the price of rent by reducing the available pool of rental properties as below.

  “We are going to have landlords that are going to have to sell their
  property and while that’s great for first-home buyers what it does is
  reduce the pool of properties for tenants and over time that will push
  up rents,” Mr Webb said.

There is a similar claim which was made by PETER VERWER chief executive of the Australian property council in this 2013 discussion about a Grattan institute report (Check the transcript for full details.

  They create 1.8 million homes available for rent. They’re not new homes, but they are 1.8million homes that would not exist unless a
  private investor is satisfied with the high compliance costs, the
  quite moderate rent and the maintenance costs to create all of this
  rented space

Does this claim add up, my understanding is that its a zero sum game. e.g. A landlord sells the property and a owner occupier moves in. Then there is one less property available for rent however one less person (or group of people) looking for somewhere to rent.

OR am I missing something?

Notes this is based on content in Australia.

https://www.domain.com.au/news/landlords-left-without-relief-under-new-victorian-government-package-949032/


texts: Can data from discrete choice experiments be used to predict models be used to predict willingnes to pay by specific individuals?

texts:
I am not an econometrician, but noticed that discrete choice experiments are often used to determine willingness to pay for products with specific characteristics and prices. However, these average prices seem to be reported for the average person in that sample, not being specific to specific groups of individuals. For example, by looking at the results I can't tell how that willingness to pay for a given product/price combination varies across individuals with a different socio-economic background, gender, education, etc.

Getting more specific: what would prevent one from taking a reasonably large dataset with a discrete choice experiment and develop a machine lerning model to predict willingness to pay for individuals with specific characteristics?


texts: What is the "gross national saving" for?

texts:
I don't understand what the term Gross National Saving is for. According to the world factbook, it represents the following:

  Gross national saving is derived by deducting final consumption expenditure from Gross national disposable income, and consists of personal saving, plus business saving, plus government saving, but excludes foreign saving. The figures are presented as a percent of GDP. A negative number indicates that the economy as a whole is spending more income than it produces, thus drawing down national wealth (dissaving).

This represents the sum of savings by person, company, and government. But what is this beneficial to? Is a country that has high GNS more stable in finance? When should one look at this statistics to gauge what? In financial stability, is this a better indication than national debt as a percent of GDP, the dependency rate on government bond, or something others?


texts:
What does an increase in the real effective exchange rate signify? I read from a news report that (localized for India):

  Furthermore, REER is calculated in such a way that an increase in its
  value signifies appreciation of the rupee. If we assume that the rupee
  was “fairly" priced in the base year (when the index was set to 100,
  currently 2004-05), REER of more than 100 indicates that the rupee is
  overvalued. Since the current value of the trade-weighted REER index
  is around 115, we see several experts claiming that the rupee is 15%
  overvalued.

Link to article: https://www.livemint.com/Opinion/6nlCPOcpAw2l0MKUZfv8AN/Is-the-rupee-overvalued-or-undervalued.html

I understand that the REER is calculated using:

Bilateral real exchange rate with various trading partners
Weights assigned to these rates according to trade activity

But, I still can't understand what exactly an increase in REER means. If it increases by 10% (say), what exactly does it mean on the ground? And why is it overvalued if it's above 100 -- does that mean a currency is never rightly valued if it's not constant at 100? That'd mean that the REER shouldn't change at all from the base year --- otherwise a currency is never rightly valued. How can that happen?


texts: Why doesn't the concept of employee engagement work in practice?

texts: The concept of employee engagement looks like an overwhelming obvious way of improving business performance, yet since the mid-nineties, and after spending billions on engagement improvement systems, employee engagement is almost exactly where it started at 30%/70% (Gallup). Why?


texts: Suppose I sell bread loaf for 20 dollars, the cost of raw material like oil,flour,electricity.... is 13 dollar, I pay 2 dollars to my workers, 1 dollar to transportation company to transport it to someplace , finally I make 4 dollar profit. Whats things will be considered for the GDP calculations through value added approach.


texts: What is William Nordhaus' contribution to the economics of climate change?

texts:
I'm trying to understand more about the economic repercussions of climate change. I'm unfamiliar with the specifics of the work of William Nordhaus, but it's been predicted in several instances that he will very likely win the economics Nobel prize in the near future* (forbes, nytimes, wsj, npr, marginal revolution). He is most famous for his work on the economics of climate change (which include some estimates of the social cost of carbon).
To clarify with question, what are the merits of William Nordhaus' work that have won him this attention? Was he merely the first to devote serious attention towards a rigorous estimate of the social cost of carbon? Or is there more?
*Update: Nordhaus was awarded the prize in 2018, along with Paul Romer.


texts:
Is there a difference between the meanings of the terms "economies of scale" and "learning curve"?

The term "learning curve" is being used by cost estimators and refers (more or less) to the idea that businesses will have a higher cost per item if they make relatively few products but will have a lower cost per item if they make more products.

I thought this concept sounded similar to decreasing marginal cost within the economies of scale.  Unfortunately, I haven't been able to find information to prove that they mean the same thing.

Can anyone confirm?


texts: How to solve model with a final good (in a perfect competition), and intermediate goods (monopolistic competition)?

texts:
Let's imagine there's only one final good produced by one firm, in a perfect competition market. In the intermediate market, we have $N$ goods which are produced and used as factor inputs for the production function of the final good. The intermediate market is characterized by being monopolistically competitive, where firms only use labour as a factor input. Households consume the final good only, and supply labour.

I'm interested in references for models in this setting, because I'm reading Michael Wickens Macro book, and in page 228 (2nd edition), does the following:

I understand the math behind the equation. What I don't understand is how the author can state that there is an efficiency loss? (The final good production function is a discrete version of a CES function)


texts: Why is the Australian dollar, often viewed by traders as a proxy for the Chinese economy?

texts:
The Australian dollar, often viewed by traders as a proxy for the
  Chinese economy, gained 0.3 per cent against its US counterpart.

From: S&P 500 hits one-month high on renewed trade hopes (September 5, 2019)


texts: Would PPP adjustments between countries be irrelevant if all countries had the same relative prices?

texts: I'm trying to understand the relationship, if any, between the fact that countries have different relative prices (e.g. different 'food price-to-general consumer prices' ratios) impacts the need for purchasing power parity adjustments between countries.


texts: How does 'building land' fit into economic modeling?

texts:
According to the ONS National Accounts 2018 & RICS land valuations and ...

Land that is built on has a value that makes it half of the UK's wealth.
The rest of the land has a value less than 3% of UK wealth.
Building land is created when planning permission is granted.

Another question asked "Why is Land not considered as a fixed capital?".

The top answer said ....

  Physical capital is reproducible, and does have a finite lifetime.

  Hence, almost all land is not physical capital.

  There are corner cases, where land is reproducible, and may appear and
  then disappear again in less than a handful of human lifetimes: in
  those very rare cases, that particular land behaves more like physical
  capital rather than how land generally behaves, and so could be
  classed as such.

Building land can appear and disappear(e.g. post war prefab sites which have reverted to open space) and planning schemes can change building land into something else.

How would this very large asset, building land, fit into economic models?

I can't see how it would fit into a Cobb_Douglas function.


texts:
I have been doing some reading on general equilibrium theory and it has made me highly confused regarding the logic behind NK models. If I have understood correctly, NK models are based on Walrasian or Arrow-Debreu auctions where there is no role for money, banking or credit (since there is perfect barter in this world).

However, in the NK framework the most commonly used methods for introducing money in to the model, is money-in-utility and cash in advance, but this seems very counter intuitive.

In a world with perfect barter, clearly money provides no utility because it cannot be consumed.

And since CIA imposes an additional restriction on consumers that was not present in the Arrow-Debreu world, are we not imposing a welfare reducing constraint?

I understand that in the real world money has many beneficial functions (store of value, removing double coincidence of wants etc etc). But in the Arrow-Debreu/Walrasian world it has no function. And since modern macro models are built around this, including money does not seem logical.

How can we use models to study the price level/inflation when the underlying theory has no logically consistent way of including money? I mean, I have nothing against the fact that money can provide direct utility or that CIA is a real life constraint. My question is on the theory side rather than the empirical side.


texts: Distribution of loans by types of interest

texts:
Im looking for some kind of report that would inculde data on the distribution of loans by types of interest(fixed/floating), spesificaly global not just for one country(developed, undeveloped, developing world). If any of you have known to stumble upon such reports would be grand

Loans between corporations, that is what im looking for.


texts:
I was looking at the deficit for different countries
http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=gov_10q_ggnfa&lang=en

How shall they be read?

For instance Greece had a -15% in Q4 of 2015 and +0.5% in Q2 of 2016.
Does this datum refer only in that specific period? I mean in Q4 of 2015 Greece had a 15% unbalance, but this is not on annual basis.
If we want the yearly data we shall sum up the 4 quarters?
Following this path in the entire 2015 Greece had a total annual deficit of 30%? Isn't it too high?


texts: Instrumental variables vs control function: Which approach and why to handle endogeneity?

texts:
I'm curious if anyone here can summarize the differences between the I.V. and control function approach to handling endogeneity. I think endogeneity is usually addressed using the 2SLS or IV approach and, having briefly studied the control function approach, am unsure what the CF approach offers that 2SLS and IV approaches do not offer.

Can anyone help me clarify here? When would I use a CF approach rather than 2SLS, what does this approach offer that the other two do not etc.

I am a newbie with metrics so any and all input is appreciated.


texts: Pareto allocations and Competitive equilibrium

texts:
Consider the one-consumer one-firm economy.
The consumer has preferences over leisure $l\in(0,L)$ and consumption good $x ≥ 0$ represented by utility function $u(x, l) = ax + l$, where $a > 0$ is a parameter. Moreover, the consumer is endowed with $(0, L)$, that is, has zero units of the consumption good and $L > 0$ units of leisure as an endowment.
The firm uses the production function $f: R_{\geq0}\rightarrow R$ to produce the consumption good out of labor. If the firm uses $z ≥ 0$ units of labor it produces $f(z)$ units of the consumption good, where:
$$f(z)=\begin{cases}
0 &\text{if } z=0\\
z+1 &\text{if } z\in(0,L)\\
L &\text{if } z\geq L
\end{cases}$$
The price of the consumption good is p and the price of labor is $w$. The
consumer owns the firm.
The question asks for the Pareto efficient allocations in the case where $a=1$
I guess we need to solve for $$\text{max}\ u(x,l)\ \text{s.t}\ x\leq f(L-l) $$
and we should consider 3 cases.
When $l=L$ we have $f(L-l)=0$  and $u(0, L) = L$
When $l = 0$ we have $f(L − l) = L$ and $u(L, 0) = L$
When $l \in (0, L)$ we have $f(L − l) = L − l + 1$ and $(L − l + 1, l) = L + 1$
But based on these how can we state the PO allocations? and if we had that $a\neq1$ what would be the competitive equilibria in this case?
Because when again $a=1$ profit allocations would be stated as :
when $z=0$ $\pi=p*0-w*0=0$
when $z\in(0,L)$ $\pi=p*(z+1)-wz=z(p-w)+p$
when $z\geq$ $\pi=L(p-w)$ only in the case when $z=L$ otherwise it won't be optimal.
and we need to solve the consumer’s utility maximization problem as well in order to find CE
But I'm stuck with the other case when $a\neq1$


texts:
I use the systemfit package to evaluate Simultaneous Equations Models (for example 2SLS). But I do not understand how to predict endogenous variables using the new values of exogenous variables using this package.

Therefore, I would like to know how to make prediction (including prediction intervals) using models of simultaneous equations in the "systemfit" package or in some other way (maybe someone knows other packages for this).

I am also interested in how I can calculate the elastic coefficients of models.

I will be grateful to the literature on the topic of modeling simultaneous equations in R.


texts: Can inflation occur in a positive-sum game currency system such as the Stack Exchange reputation system?

texts: As most active users of this site know, the way the reputation system works is that everyone starts out with 1 reputation and a user can earn more reputation by asking good questions and writing exceptional answers (as well as other methods), and a user can lose reputation by writing bad questions and answers.  This way, users can make a profit or take a loss without taking/giving currency from/to another user.  Can inflation happen with a system like this?  As more reputation is gained, does it mean less?


texts: Quickest way to learn about yield management and revenue maximization?

texts:
I have been asked to determine the optimal ticket prices for live-events. Strictly speaking, I'm working as a data scientist for this company, so this question is a outside my field of expertise. I have a PhD in physics, and I've been trying to learn Micro-econ by watching MIT/Coursera videos.

Separately, from reading articles online, I know that given the inventory (which is similar to airline tickets or hotel rooms) I don't want to find the optimal prices by solving a revenue maximization type problem but rather through yield management. Is this correct?

There are already questions on SE (Where to start learning economics as a mathematician?, Introductory or Primer text on Economics?), about resources for learning intro economics.

But what I would like is a set of books, or online tools that would take someone like me with NO formal training in economics from zero to a firm grasp with the concepts of yield management and revenue maximization.


texts:
Consider the game below played by three players. Player 1 chooses one of the rows (T vs B). Player 2 chooses one of the columns (L vs R). Player 3 chooses one of the three tables (A vs B vs C). Each payoffs cell gives payoffs to players 1, 2 and 3, respectively.
Why are the strategy profiles are (T, R, A), (B, L, A), (B, L, C) and (T, R, C)?
I am stuck in the fact that how do we start at choosing the equilibrium. So for example at A do I choose an equilibrium there and again at B and C. Or do you consider all three players simultaneously? For example, if Player 2 chooses L what's the player's 1 and 3 move?


texts: Why isn't the "annihilator" matrix a zero matrix?

texts:
I am struggling to understand why M is not null since:
$$\mathbf M=I−X(X′X){^-}^1X′=I−XX{^-}^1X'{^-}^1X′=I-I=[0] $$
What's wrong with that reasonning?


texts:
Take a cont. diff, convex and increasing cost function $c(X)$. Say you start with a stock $K$, and want to (dis)invest $I$. Many adjustment cost functions (for example, the first example on page 2 here) then are of the type

$$ K c\left(\frac{I}{K}\right)$$

What is the purpose of scaling investment costs with $K$ here? Marginal cost of investment is

$$ c'\left(\frac{I}{K}\right)$$

It seems that this gives the property that marginal cost of investment decreases in existing capital stock. Is this observed in the real world, or does it rather simplify computations? Are there (popular) alternative formulations of adjustment costs?


texts:
I recently rediscovered Rothschild and Stiglitz's classic paper, "Equilibrium in Competitive Insurance Markets".

In footnote 7, they refer to an earlier version of their paper for details on the robustness of their results to their assumptions. Does anyone know how to track that version down? Many different Google search queries haven't worked.

The complete citation for the working paper is

  Rothschild, M., and J. E. Stiglitz, "Equilibrium in Competitive Insurance Markets," Technical Report No. 170, IMSSS Stanford University, 1975.

On a separate note, the published version of their paper is beautifully written. You would be remiss to not have read it.


texts: How can you profit from junk bonds and selling treasuries, if the junk bond doesn't default?

texts:
Junk Bond/Treasury convergence
Typically junk bonds, given their speculative grade, are undervalued as people avoid them. Therefore the spread over treasuries is more than the risk of default, by buying junk bonds and selling treasuries, to hedge interest rate risk. Often profits can be achieved by buying junk bonds and selling treasuries, unless the junk bond defaults.

Wikipedia doesn't detail this interest rate hedge. Assume that a junk bond never defaults and the semistrong-form of the EMH:
Zvi Bodie, Alex Kane, Alan J. Marcus. Investments (2018 11 edn). p 338.

      The semistrong-form hypothesis states that all publicly available information regarding
the prospects of a firm must be reflected already in the stock price. Such information
includes, in addition to past prices, fundamental data on the firm’s product line, quality
of management, balance sheet composition, patents held, earnings forecasts, and accounting
practices. Again, if investors have access to such information from publicly available
sources, one would expect it to be reflected in stock prices.

Correct me if I'm wrong, but Treasury bonds' interest usually $<$ junk bonds' interest. So

why would anyone rational sell you junk bonds and buy T-bonds from you (so that you can long junk bonds and short T-bonds)?

wouldn't this spread over treasuries always be forthwith arbitraged?


texts: What determines whether slavery is economically efficient in industrialized/modern era economies?

texts:
Various forms of slavery were nearly universal before the industrial revolution. After industrialization, it would naively seem forced labor would continue to be widespread, as there is no way to compete against it. But it only remained or became entrenched in a few locations and market sectors. Even current non-industrialized economies rarely involve slavery. I can't find a convincing explanation of why.
The coincidence with industrialization suggests slave profits are disproportionately vulnerable to automation, but slavery was largely agricultural and declined before much agricultural automation, while wage labor specifically coincided with industry. Why are profits higher from agricultural/automatable work, but not those from factory work and non-automatable services, when using slaves rather than wage labor?
I find it impossible to believe it was because of lofty values for human rights. But imagining US/English history without a labor movement, for example, seems like it was resulting in the kind of sweathouse economy I would have expected to be typical. Do the data show that labor movements decisively shifted the equilibrium world-wide?
I also find it impossible to believe that most work requires education incompatible with being indentured, or that maintaining discipline and motivation would be prohibitive. Do the data say otherwise?
Maybe workers create so much more profit when they are themselves maximal consumers that capital creates political pressure to inflate wages above subsistence, to create (investment) markets? I think this would be capitalists' explanation, but coordination among capital would be susceptible to being undercut, prisoner's-dilemma style, by competitors willing to use slaves. I think the only thing that prevents that in an international context are trade agreements, but again, it is hard to believe those have been so dramatically effective.
I haven't been able to find this question addressed with data, it is always completely overwhelmed with ideology.
Some common explanations claim slaves cost more to maintain than they produce (under most circumstances). That can't be right -- workers make enough to eat, profit their employers, and buy comforts unavailable to slaves (including time off, medical care, and retirement), considering redistribution of course. So why hasn't capital driven those comforts to zero?
The first answer here contains an insight I find plausible: you can fire/exchange a wage worker, but you can't sell an unproductive slave. So capital is willing to pay to insure against sinking costs into future labor of uncertain value. Another way to emphasize the mechanism is to focus on the cost of management necessary to utilize workers' full capacity -- workers can do this more efficiently than an employer. I find this line quite persuasive, are there data? @1muflon1 cites Anderson & Gallman (1977) -- is this the best reference in this vein?
Are there respected/consensus analyses of historical data that shed light on this question?


texts:
Will Both Consumer and Producer Surplus decrease as a result of a decrease in demand? Or is this not possible?

Assuming there is a decrease in demand for travel, I'd like to know how this affects both types of surplus.

Thank you!


texts: symmetry of equilibria with heterogeneous players

texts:
I have a question about game theory terminology. I am working on a model in which players are heterogeneous in two dimensions, and there are four types of players. For example one type of players receive some reward and have some cost of playing, while the other type differs in this reward and cost.
I am interested in the equilibria of the game in which the strategies of users who face the same reward and costs (i.e. same type) are the same.
I think symmetric equilibrium in this case is misleading since not all players are expected to have the same strategies, but it is something more like a separating equilibrium across types. However, there is perfect information so I'm unsure whether separating/pooling equilibria concepts can also be applied here.
Any thoughts/references would be helpful!


texts: Why are the Fed's goals often described as the "dual mandate" and not the "triple mandate"?

texts:
The Federal Reserve Act Section 2A states:

  The Board of Governors of the Federal Reserve System and the Federal Open Market Committee shall maintain long run growth of the monetary and credit aggregates commensurate with the economy's long run potential to increase production, so as to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates.

Three goals are given, namely:

Maximum employment;
Stable prices; and
Moderate long-term interest rates.

So why is it that many (or even most) writings* usually refer only to the dual mandate, i.e. the first two goals of maximum employment and stable prices? Why do they seem to ignore the third goal of moderate long-term interest rates?

Is it because the third goal is less important? Or perhaps because the third goal somehow follows automatically if the first two are fulfilled?

*Examples: Chicago Fed, Richmond Fed, St. Louis Fed. Indeed, the last says the following but gives no explanation:

  But wait a minute: None of this sounds like a dual mandate. Rather, it sounds as if Congress has given the Fed three mandates—if not four. Over the years, the mandates were boiled down to two: maximum employment and price stability. And now, some say the central bank can focus on price stability.


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

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


texts: What is the difference between a transitory and a permanent shock?

texts: In my study of time series regression models in econometrics, we are discussing basic time series regressions and interpreting the effects of shocks in finite distributed lag models. I was wondering what the difference is, in intuitive terms, between a transitory and a permanent shock. According to my understanding at the moment, every shock would be permanent because you cannot undo the past. Wouldn't saying that an effect is transitory be like completely erasing its effect from existence and never accounting for it? I think I am wrong, but I don't know why.


texts: The Frisch-Waugh-Lovell Theorem: an exercise

texts:
I have an equation of the form(all vectors): $y=X_1\beta_1+X_2\beta_2+u$.

I'm interested in knowing if the beta OLS estimators and respective residual for this equation are the same as for when we apply OLS to the following equations:

$P_{X_1}y=P_{X_1}X_2\beta_2+v$
$P_Xy=X_1\beta_1+X_2\beta_2+v$,

where the $P_Z$ are the usual definition of projection matrices, using $Z$.

So, I've tried using the FWL theorem, and I've got respectively:

$\hat\beta_2 = (X_2' P_{X_1}X_2)^{-1}X_2'P_{X_1}y$, and $\hat v = (I- P_{X_1}X_2(X_2'P_{X_1}X_2)^{-1}X_2'P_{X_1})P_{X_1}y$. I was wondering if I miscalculated $\hat u$ since looking at equation 1, since both $y$ and $X_2\beta_2$ are projected in to the space spanned by columns of $X_1$, the residuals would be zero.
$\hat\beta_2 = (X_2' M_{X_1}X_2)^{-1}X_2'M_{X_1}P_X y$, and $\hat v = (I- M_{X_1}X_2(X_2'M_{X_1}X_2)^{-1}X_2'M_{X_1})P_{X}y$.  However, I do not see how the estimate for $\beta_2$ is equal in both cases, since if you notice that applying OLS to equation 2, we get $\hat \beta=(X'X)^{-1}X'P_X y=(X'X)^{-1}X'y$.

Any help would be appreciated.

Edit1: well, I found out how to do the 2nd point. We have to notice that $M_{X_1}P_X=(I-P_{X_1})P_X=P_X-P_{X_1}=P_X'-P_{X_1}'=(M_{X_1}P_X)'=P_X'M_{X_1}'=P_X M_{X_1}$ and that $ X_2'P_X=(P_X X_2)=X_2'$.
As to the 1st point I have no idea...


texts: Is technical analysis somehow a valid method for investment?

texts:
I personally think technical analysis (TA) is not useful at all but I still see lot of courses about technical analysis, and even people using it.  They have the advantage of being easy to learn and they claim themselves as following the "behavioral economics" theory.

Is the traditional & simple TA somehow valid?  I'm asking about the one that uses moving averages, graphs, momentum lines to try to predict market moves.

The behavioral economics theory is valid and 2 people won Nobel prizes because of that, so I'm not arguing its validity, but its consequences or usefulness as an investment method.

Please take into account not only a highly efficient market (eg, the US), but other smaller and less efficient markets (I'm from Argentina).


texts:
First, I am a French student, so forgive me for my English which can be not clear at all.

I have to analyze a financial series. I have some difficulties to make the second part of the work which focuses on ARMA model. I can't read (interpret?) my Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) correlogramm.

To my mind, here we have a MA(0) but I don't know if it's possible. In this case, what does it mean ?

And I don't know also with the PACF graph, if we are in a AR(3) or AR(6). And why the first stick is not over the "confidence level" ?

It is possible that my interpretations are false, please tell me.


texts: Max Likelihood Estimators of a stable Gaussian VAR$(p)$ process. Are the Lutkepohl formulas correct?

texts:
In «New Introduction to Multiple Time Series», page 90, we have the following formulas for the ML estimators of a stable Gaussian VAR$(p)$ process:

where $\tilde \alpha = vec(\tilde A_1,...,\tilde A_p)$.

And here is exactly where my doubt resides. If for $\tilde \alpha$ estimator, I need $\tilde \mu$ estimator, but then for $\tilde \mu$ I'm going to need also $\tilde \alpha$. So, how is this dependence broken, or is this solved by an iterative algorithm that will reach a fixed point?

I've also posted this question in CV, but I didn't get any answer.

Any help would be appreciated.


texts:
How does positive monotonic transformation of production function effect the resulting profit function?
For example if we had production function $f(x) $ and that gave profit function $\pi(p,w)$. Now if we transform the production function as let's say $f(x)^{\mu}$ where $\mu>0$, how would that effect the profit function?


texts: How much does one percent of unemployment 'cost'? (Unemployment elasticity)

texts:
There is always debate that increasing minimum salary will pour in more money into the budget as those who get minimum salary will spend them immediately.

The counter argument is that increasing minimum salary will increase unemployment and it will bring all the downsides (sitting on benefits, less spending, crime,...)

I was wondering is there established 'elasticity' between unemployment to GDP e.g 1% raise in unemployment would reduce GDP growth by X%? I am sure it will differ from country to country and also change from 10% to 9% and from 2% to one will not be the same, still there should be some ratio or formula with wide margin?

How much does rise of one percent in unemployment affect GBP?


texts: How to make deliberate devaluation or depreciation of a currency?

texts:
It is said in Wikipedia, that devaluation can be done as monetary policy act.

But HOW this can be done if there is no fixed rate?

What are actual tools Central Bank can use?

One thing I can imagine -- currency intervention.

What are others?


texts:
I was wondering whether anyone might be able to help me or at least push me in the right direction with this New Keynesian Model. I apparently have that the household function is as follows:

Furthermore, for final and intermediate goods producers, I have that:

As for market clearing and as for monetary and fiscal policy, I further have that:

What I am having issues with is:

(1) Finding the relevant F.O.C. for the households and the firms (assume that sigma does not equal 1) for the utility function.

(2) Showing that the set of log-linear equations can be expressed as:

I hope there will be some generous and helpful souls out there who can give me a helping hand! I greatly appreciate any type of help!


texts: Why are complementary goods defined as when a good's demand is inversely correlated with the price of another?

texts:
Take a standard example: hamburger patties and hamburger buns. It is understandable that if the supply of hamburger patties increases (for whatever reason), the price of these patties will decrease, thus causing an increase in the demand for hamburger buns.

Now, let's say the price of hamburger patties decreases due to a decrease in demand (maybe doctors come out saying beef causes cancer). Why would the demand of hamburger buns increase when the demand of hamburger patties decreased? Standard definition of complementary goods (that I've seen so far) implies that the price decrease of hamburger patties would cause the demand for hamburger buns to increase, but that defies common sense.

Wouldn't a more sensible definition be that goods are complementary when the demand of one good is correlated with the quantity demanded of the other?


texts: Why does a decrease in interest rate reduces the velocity of money circulation?

texts:
I have seen sources that claim high interest rates increase the velocity of money circulation, but haven't really seen any concrete explanation for this. This is how I think it works: High interest rates -> high opportunity cost of holding money -> Demand for money decreases -> people dont want to hold money and will spend it -> higher velocity of income.

On the other hand,wouldn't a high interest rate make saving more attractive and thus reducing the velocity of income circulation?

EDIT: Sources that apparently claim this are referred to below:

This source does not explicitly state the relationship but somewhat explains the causes: http://thismatter.com/money/banking/money-demand-money-velocity.htm

A wikipedia page that seems reasonably credible states this relationship, but I am unable to fully understand their explanation:
https://en.wikipedia.org/wiki/Velocity_of_money

This exam question from Cambridge International Examinations that explicitly states the relationship (the correct answer is D)


texts: Relationship between Growth in Purchasing Power and Real Interest Rate equations

texts:
My textbook gives these two equations including the real interest rate and says that the second equation (b) can be arrived at from the first (a), but doesn't explain how.

rr = Real Interest Rate, r = Nominal Interest Rate, i = Inflation

Equation (a):
$$Growth\ in\ Purchasing\ Power=1+r_r = \displaystyle\frac{1+r}{1+i}$$

Equation (b):

$$Real\ Interest\ Rate = r_r = \displaystyle\frac{r-i}{1+i}$$

I'm feeling slightly obtuse but I've been away from math quite a while, and can't figure out how to rearrange the first formula into the second one.

What are the exact equation steps necessary to get from: $ r_r = \displaystyle\frac{1+r}{1+i}-1$ ⇒ $r_r = \displaystyle\frac{r-i}{1+i}$ ?


texts: question regarding econometric testing of the natural rate hypothesis

texts:
Hi All: I have the Lucas, 1972b paper "Econometric Testing Of the Natural Rate Hypothesis" but unfortunately not as a pdf. ( it's from a book that contains a lot of Lucas' papers called "studies in business cycle theory").  Assuming that someone reading this question has read that paper and understood it, could you explain how equations 11) and 12) come about. Thank you very much for your help.

ADDENDUM TO ORIGINAL QUESTION:

I am going to write the equations that lead up to the two equations
that I don't follow the derivation of. My hope is that not many people have
the pdf of the file so  the equations will obviously help.

1) $y_t = a(P_{t} - P^{*}_{t})$  (aggregate supply function ).

7) $y_{t} + P_{t} = x_{t}$ ( aggregate demand schedule )

8) $x_{t} =\rho_{1} x_{t-1} + \rho_{2} x_{t-2} + \epsilon_{t}$ ( AR(2) for $x_{t}$ ).

9)  $ P_{t}^{*} = E(P_{t+1}| x_{t}, x_{t-1}, \eta_{t}) + \eta_{t} $
( Definition of agent's expectation of the price at time $t+1$. )

10) $ (1+a) P_{t} - a P^{*} _{t} = x_{t} $
(obtained by straightforward algebraic manipulation of  (1) and (7). )

Meanings of variables:

1) $P_{t}$ is the price level at time t.

2) $P^{*}_{t}$ is the expected price level at time t+1 where the expectation is taken at time t. ( the agent's expectation of price level ). Essentially, $P_{t+1}$ is the next period's price level, the variable of which, $P^{*}_{t}$, is a forecast.

3) $y_{t}$ is the output at time t.

4) $x_{t}$ is the log of the money supply and is a shift parameter. It is part of a policy rule which gives the current value of $x_{t}$ as a function of the state of the system.

After these equations are explained,
the author then says:

"We shall seek linear solutions $P_{t}$ and $P^{*}_{t}$ to equations 9 and 10: "

11) $P_{t} = \pi_{1} x_{t} + \pi_{2} x_{t-1} + \pi_{3} \eta_{t} $

12)  $ P^{*}_{t} = \pi_{4} x_{t} + \pi_{5} x_{t-1} + \pi_{6} \eta_{t} $

Equations 11) and 12) are the equations whose derivation escapes me totally. Thanks a lot for your help.
                                               Mark

                                                     Mark

P.S: For any newbies wrestling with the theory behind RE, this paper is the clearest and simplest that I have found, aside from the derivation of 11) and 12). I highly recommend it. I only found the book recently and have decided that out of all the top RE people, Lucas really stands out as far as the clarity of his writings.


texts: Why do all apartment complexes in Albuquerque have pools?

texts:
Apartment builders have a constrained optimization problem whereby they balance building different amenities to attract tenants with varying preferences. Recently when searching for apartments I noticed that every single apartment seemed to have a pool. I feel like many people would prefer a small decrease in rent and open space, more parking, a larger fitness center, ect to a pool. Apartments have many other variances in terms of parking, landscaping, price, ect, yet the pool seemed to be a universal. Does this simply reflect that the apartment market cannot be perfectly competitive or that preferences for pools is near universal? Is there an economic explanation or cognitive bias that would explain this kind of convergence?

PS: I will not be offended if this is closed. I'm not sure if this type of question is not on topic for this site.


texts:
After posting this question, I realized that there was quite a bit of controversy surrounding the use of Hotelling's Rule to estimate the price of oil.  Participants on this site seemed to be evenly split on the issue.

From an Economics standpoint, How helpful is Hotelling's Rule in determining the price of oil?

From my analysis, it doesn't make sense that the price of oil should depend on Hotelling's rule instead of the traditional supply and demand models.

For example, when fracking was "new," its use was limited, making the impact on the oil industry negligible.  Because the amount of oil produced was small, supply (for the most part) remained constant; businesses would also be incentivized to raise prices to market levels, increasing their profit margins.
However, as fracking became more widely used, the oil entering the market increased, affecting the price of oil (and, originally, causing concern for OPEC).
Years from now, when the Middle East is out of oil, companies will shift to drilling less accessible and more expensive oil, increasing the prices of oil for the consumer.  Eventually, the last barrel of the oil will either cost an enormous amount of money or will be worthless because of the rise in substitutes (solar, hydro, and wind power; electric cars).

Thoughts or other analysis?


texts: Looking for data about collateral and safe asset

texts:
I'm supposed to report the evolution of the use of collateral on financial markets. I found some substantial data concerning the amount of collateral available (i.e. the amount of safe assets in the economy), but I can't get hold of numbers about the effective amount of collateral used and exchanged on the markets. Ideally, I'm looking for quarterly statistics.

I read a lot of research articles, but this is most of the time pages and pages of text and formulas, with no concrete numbers.

Any of you has an idea of where I could search what I need?


texts: Walk through for calculating impulse response function, given VAR equation & coefficients

texts:
Can someone walk me through how to manually calculate the IRF values that Eviews outputs for the effect of a nonfactorized one unit innovation.

I have my VAR equation and coefficients:

VAR Model - Substituted Coefficients:
===============================
MARKET_A = 1.38531644845*MARKET_A(-1) - 0.456533910287*MARKET_A(-2) + 0.0908884378218*MARKET_B(-1) - 0.0116001711851*MARKET_B(-2) - 0.0458678142475

MARKET_B = 0.0934164283416*MARKET_A(-1) - 0.0678660464848*MARKET_A(-2) + 1.34042022538*MARKET_B(-1) - 0.372260999882*MARKET_B(-2) + 0.0341759469926

The Eviews output for the effect of a nonfactorized one unit innovation from MARKET_A.

 Period MARKET_B    MARKET_A

 1   0.000000    1.000000
 2   0.093416    1.385316
 3   0.186763    1.471058
 4   0.258970    1.421328
 5   0.310545    1.318772
 6   0.346591    1.203253
 7   0.371878    1.092721
 8   0.389868    0.994217
 9   0.402869    0.909562
 10  0.412376    0.838231

Nonfactorized One Unit

To calculate period 2, I have tried plugging in the values in the equation i.e

0 for MARKET_B(-1),
0 for MARKET_B(-2)
1 for MARKET_A(-1)
0 for MARKET_A(-2)

but the output is not the same for the first period.
Obviously, I'm missing something. Could someone point me in the right direction?


texts:
Do you know of a package allowing to create objects representing agents with (strict) preferences over (a finite set of) discrete objects $A,B,C,…$, and profiles thereof.

A minimal requirement would be to have  a method like compare defined on any instance agent of the class, with agent.compare(X,Y) returning True if the agent likes $X$ more than $Y$, and False otherwise.

The only related package I have found so far is svvamp. Do you know of any other?


texts: Keynesian consumption law not applicable in USA ?

texts: I was looking at some numbers and saw that in USA in 2010 consumption was at 70% but savings were close to zero and that even places were there is high income savings are still low while the keynesian law says that when the salary rises savings also tend to rise, how come in USA even the people who have a high income tend to consume it all and not save ? Is there a main cause for this ?


texts: How did the Federal Reserve determine 3.5T USD in assets?

texts:
The financial media have reported that...

  In general, Fed officials appear to have converged to a minimum
  balance sheet of roughly $3.5 trillion, which means the runoff would
  end in the second half of the year
  Link

and it was also reported to come specifically from Chair Powell...

  the chairman has said that the reduction in its bond holdings will end
  soon, with a balance sheet probably no lower than around $3.5 trillion Link

The level of 3.5 T USD will be arrived at, at the rate of 50 B USD per month as described here at this link.

How was the target level of 3.5 T USD determined?


texts: How can Factor Income paid to abroad be negative?

texts:
There was a question in my book in which the factor income paid to abroad was given as negative .

I guess here negative means that we are not paying but receiving from them but how can it happen that we are receiving income from normal residents of other countries ?

Is it true that factor income paid to abroad can be negative or is it only in theory ?


texts: New Keynesian Phillips Curve (NKPC) derivation in Clarida, Gali & Gertler (2002) using Rotemberg

texts:
I have some issues in deriving the NKPC in Clarida, Gali & Gertler (2002) that you can find here.
I'm asked to derive the NKPC by combining the log-linearized optimal price setting rule (22) with the
price index (24), but I don't get the same result (equation 46).
Besides, I'd also make the same applying Rotemberg rather than Calvo, with the following two formulas:

I assume equation 24 to be of this kind given that in Rotemberg every firm changes its prices every period. However, the result I get after having log linearized these two equations is weird. In fact, I don't get anything similiar to what is written in the paper. Specifically, I can't cancel out the price  and I don't get inflation expectations.
Please, let me know what you get in computing the NKPC in this case.
Thank you in advance.

P.S. Maybe I forgot a  in the second term in 1, but I'm not sure about that.


texts: Visual Representation of mixed strategy profile using a simplex in $R^3$

texts:
I am looking for a reference to learn how to plot mixed strategy profile in a two player game with three pure strategies.

Looking forward to any advice or suggestion.

(Here is the question regarding simplex I posted in mathematics.stackexchange)


texts: Is there always a pure Nash equilibrium in a resource selection game?

texts:
Denote $[r]\triangleq\{1,2,\ldots,r\}$.
Consider a game with $n$ players, $[n]$, each has $m$ strategies, $[m]$.
Each player $i$ has an associated payoff function, which considers only his selected strategy, and the number of players selected the same strategy:
$$U_i:[m]\times[n]\to[0,1]$$
Furthermore, the utility function is monotonically decreasing in the number of players which picked the same strategy, i.e.
$$\forall i\in[n],j\in[m],k\in[n-1]:U_i(j,k)\geq U_i(j,k+1)$$

Does this game always have a pure Nash equilibrium?
Can we (computationally) find it efficiently?

Notice that the special case, where all players are symmetric ($\forall i,j\in[n]: U_i\equiv U_j\equiv U$), the game reduces to an exact potential game and therefore is guaranteed to have a pure Nash equilibrium.
The potential function for the symmetric case would be, given a strategy profile $s$:
$$\phi(s) = \sum_{j\in[m]}\sum_{k=1}^{\#_j(s)} U(j,k)$$
Where $\#_j(s)$ is the number of players in $s$ playing strategy $j$.


texts: Why are my 2SLS estimates much larger than my OLS estimates?

texts:
When performing IV regression, it is often taken as a sign of unbiasedness if the IV estimates are similar to the OLS estimates of the same model.  My question is:  If the estimates are very different, what possible explanations are there for the difference?

Say for example, with a strong instrument, that one finds that the IV estimates of some coefficient are 10 times larger than the OLS estimates.  Is this most likely a sign of severe bias in the OLS estimates?  Or is it just as likely that the exclusion restriction is not satisfied, and so the IV estimator is possibly even more biased than OLS?

I understand that this is an open question, but if anyone could just give me the basic range of possible explanations, and perhaps point me towards some literature on interpreting IV results when they are significantly different from OLS, that would be much appreciated?

Best regards,


texts:
The Socialist candidate for the upcoming presidential elections Benoit Hamon says he wants to roll out the Universal Basic Income in France, to be paid by "taxing the wealth created by robots" (for example, news here).

How do you tax the wealth created by robots? What is so special about this policy? Is it not just a higher tax on capital?

(The answer I am looking for is like someone providing a briefing to Hamon on how to implement this policy. I am expecting concrete ideas. Some analysis of why the implementation would work or not are valuable.)


texts: How do we explain the difference in average leverage between banks and non-financial firms?

texts:
I've been reading a little about the capital structure of banks. For example, in this working paper, "Financing as a Supply Chain: The Capital Structure of Banks and Borrowers" by Gornall and Strebulaev (accessed 2014), it mentions this:

There is disagreement on the causes and effects of high bank leverage; however, there is no disagreement that banks and other financial institutions are indeed highly indebted. The average leverage of U.S. banks, measured as the ratio of debt to assets, has been in the range of 87%-95% over the past 80 years. At the same time, the average leverage of public U.S. non-financials, measured in the same way, has been in the range of 20%-30% over a long period, below the predictions of many models. This dramatic difference in financial structure is puzzling at first glance.
In this paper, we explain this gap by modeling the interaction between a bank's debt decisions and the debt decisions of that bank's borrowers....

I am unfamiliar with this literature. I'm wondering, what other explanation exist in the literature to explain the difference in the average leverage between banks and non-financials?


texts:
There are N agents living in an economy with two goods, $X$ and $Y$. Their preferences are described by the following utility function $u(X,Y) = 2 \sqrt{XY}$. Each agent is endowed with 1 unit of $X$ and $y_{i}$ units of $Y$. Each unit of $Y$ is sells for $p$ units of $X$.

The question is to show that each agent gets a utility of $\frac{1 + py_{i}}{\sqrt p}$.

Here is what I have tried:

The agent chooses $X,Y$ in order to maximise $2\sqrt{XY}$ subject to $X + pY = 1 + p y_{i}$ So I have expressed the resource constraint in units of good $X$. The LHS is what the agent can buy and the RHS is the endowment, also expressed in units of $X$.

I then re-arrange the constraint in terms of $Y$, i.e, $Y = \frac{1}{p} + y_{i} - \frac{X}{p}$ and substitute this in to the utility function, with the FOC with respect to $X$ and then substitute the optimal value of $X$ back in to the utility function to get an expression in terms of $y_{i}$. However, the expression is not what I am supposed to get.

If anyone wants to check my algebra, here it is:

The utility function becomes $2\sqrt {(X/p) + Xy_{i} - X^2/p}$ Differentiating this w.r.t $X$ I find that $X^* = (1/2)(1 + y_{i}p)$. I substitute this in the utility function, $2\sqrt{X^*y_{i}}$ but this does not equal $\frac{1 + py_{i}}{\sqrt p}$.

Any ideas on where I am going wrong?


texts: How are the price signals of stocks in the stock market centralized?

texts:
We can look up the price of a stock, like that of Google, and it gives a particular figure. I would like to know how the price signal is "centralized". What I mean is: if the trades happen between individuals holding the stocks, then how is the overall trading price arrived at? Surely, the individuals who are on the buy side and the sell side would have to "register" the sale with the SEC or something? That's the way it happens with other tangible items, like houses and cars, etc.

The stock price on the market acts as a global signal, which efficiently moves financial capital around. Without it, we would be left to our best guesses, which might take too long to converge on a single number, if it ever did at all.


texts: Does investment directly influence demand?

texts:
I quote from the first page of India's Economic Survey 2019 (an official document) -

  Investment, especially private investment, is the “key driver” that
  drives demand, creates capacity, increases labour productivity, introduces new
  technology, allows creative destruction, and generates jobs.

Does investment directly drive demand? If so, how? I can only see investment leading to higher productivity which increases supply and displaces jobs.If not, is the increase in demand a ripple effect of investment? If yes, what's the connection?


texts: Minimizing the error: Transforming dependent variable

texts:
As given in the picture, question ask us to transform dependent variable, by premultiplying with a weighting matrix W, (which will change the regression coefficient into C'β) such that the expression (given in question) has a minimum mean squared error.

So, I solved part a) by solving for the brackets of E[(w′y−c′β)(w′y−c′β)′] and differentiating with respect to w, I obtain the expression as

$w′y=[c′ββ′x′(xββ′x′+σ^2.I)^{−1}]y$

My question is What does this espression signify or simply put what did we do/ what are we trying to achieve and why it is not practical to use above estimator? Any help or suggestion will be helpful.

PS: Is it impractical because $σ^2$ is unknown?

Expression can be rewritten as -

$w′y=[c′ββ′x′(E(yy') )^{−1}]y$

Because Xβ = E(Y|X) and Var(y) =$σ^2$I, By the formula

Var(Y) = E(YY') + E(Y|X)E(Y|X)'

Edit: Expressions for estimated β is given by (X'X)$^{-1}$X'Y where, define A= (X'X)$^{-1}$X'. This gives estimated β = AY. So, the expression W'Y be also denoting another expression for estimated β, an expression computed such that the discrepancy between the stylised expression for est_β ie W'Y and the weighted β ie C'β is minimum? Am I thinking on correct lines?


texts: What is the importance of moving seasonality in seasonal adjustment?

texts:
Both Stable and Moving Seasonality are computed in Sliding span test (or D8 F-Stat test) and M7 statistics. But what is the purpose of finding out the presence of moving seasonality in seasonal adjustment test statistics? Does greater moving seasonality result in lower identifiable seasonality?
Intuitively, a greater moving seasonality also imply that the series is seasonal, so why should it lower identifiable seasonality?
Also what is the effect on the seasonally-adjusted series if it has a greater moving seasonality?
Thank you


texts: What accounts for the high GDP of the United States?

texts:
Wikipedia defines GDP as:

  Measure of the market value of all final goods and services produced in a period (quarterly or yearly) of time.

So, I take it that the total value of all goods (and services, whatever "Services" means) manufactured within the country per year is the country's GDP. This YouTube video does a nice job of explaining it too:

What is Gross Domestic Product (GDP)?

The United States GDP, also from Wikipedia, is around $19 trillion!

According to the definition, US should manufacture USD 19 trillion worth of goods (finished products) and services within the US, but again, according to this Wikipedia article, US manufacturing industry outputs only about $2.2 trillion worth of goods.

So, what accounts for the remaining $17 trillion? Is it the "Services"? If so, what are these services and how are they measured?


texts: Monopolistic and Bertrand (Nash) Competition

texts:
Can we view the monopolistic competition equilibrium (a la Dixit-Stigliz) as the limit case of a Bertrand competition with an infinite number of firms providing differentiated products, where the resulting equilibrium is a Nash equilibrium in prices?

I am looking for references on this topic. Thanks.


texts:
During Recession, banks loans decrease which leads to financial constraints and ultimately Investment suffers and declines.

my question is - "Are loans lower because of demand or supply?"

My thoughts are - We know that money can/is generated by banks at will so it doesn't seem like it is money supply problem but then my reading from newspapers tells me that it is the banks which stops lending perhaps due to realization that business firms will have a hard time so probability of low profits and therefore stops credit and as a result investment suffers. or Is it the other way round that Investment stops in recession due to meagre growth which result in low profitability and firms default on their loans leading to build of Non performing assets (NPA) and then banks responds to that?

If it is the former then why banks don't lend when it could help offset the slowdown/recession as Investments could potentially offset it and If it is the latter then does it not aggravate the problem because until investments picks up again, you can't have growth which means no profits and further adds to NPA problem?


texts: Relation between linear utility function and U=max{x,y}

texts:
I'm studying general equilibrium theory, and in the study guide I came across a utility function of the type $U=\max\{x,y\}$, which I'm not that familiar with. I study mainly from two books: Intermediate microeconomics by Varian and Nicholson's Microeconomic Theory and couldn't find any details about the nature of this kind of utility function in either.

My teachers over the semesters have mentioned some details about it as a curious fact, so I know the choice of the consumer is driven by the relative price of the goods, in this case x and y, so he'll choose to consume the cheaper good, and if the relative prices are equal he'll be indifferent towards both. Also I know the indifference curves have the shape of an inverted L.

What is not clear to me is how is it related to the Perfect Substitutes utility function since both seem extremely similar to me, but the indifference curves are very different.

Is the utility function $U=\max\{x,y\}$ a more general case?
More importantly, when the relative prices are the same, how can we illustrate consumer's choice in that inverted L indifference curve, doesn't it turn linear?


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

texts:
A definition in my book states

  $ \sigma^* \in \Delta$ is a Nash equilibrium for $\Gamma$ if for all $i \in I$ and all $\mu_i \in \Delta_i, \; U_i (\sigma^*) \geq U_i(\sigma^* \backslash \mu_i)$.  The set of Nash equilibria for $\Gamma$ is denoted $Eq(\Gamma)$

What does the $\backslash$ here represent, divide or element not included?


texts: Equilibrium with Externalities: Solving without FOC

texts:
I have a general equilibrium problem, where households given objective function $U(c,n)$ solve for working hours and consumption $n, c$, and firms use labor to produce a consumption good - their objective function is $V(n)$. There are potentially profits, which is paid out to the workers through wages $w$. Households spend all their labor income on the production good.

There is the externality that working more leads to higher income on the household side, and spending higher income onto the consumption good yields higher profits for the firm - in turn leads to higher wages for the household. These things just happen in my environment, take my word for it - I'm trying to simplify as much as possible.

Usual Equilibrium Household optimality, firm-side optimality and market clearing means that all FOC have to hold. Usually, I would solve this taking the first-order conditions for $U(c,n)$, taking firm's demand $Y$ as exogenous, and replace - after taking the FOC - $Y = nw$.

Here, instead I want to rather find my equilibrium without FOC. It is $w, n, c$ such that

Firms behave optimally: $V(n) \geq V(n')$ for all $n'$
Households behave optimally: $U(c,n) \geq U(c',n')$ for all $c', n'$
$wn = Y$

This makes much more sense for me since it is in this environment much easier to find the stationary state in the objective functions rather than the roots of the first-order conditions.

However, I'm worried that without two steps, I cannot "first solve FOC, then replace $Y=wn$. How do I ensure that household's are neglecting the externality of their labor/consumption choice?


texts: Why marginal benefit is decreasing as more and more pizzas are being produced?

texts:
I'm taking one of my initial courses in Economics on my own and currently reading Economics by McConnel, Brue and Flynn. On the page 13, the book is trying to explain about Optimal Allocation. They are giving example of production of pizzas and robots, here is the table:

A, B, C, D, E are the possible alternatives of production when resources are allocated accordingly. Now, the book asks "of all the attainable combinations of pizzas and industrial robots, which is optimal (best)?" Then they go on to explain a little bit about marginal benefit and marginal cost and the optimal amount of the activity occurs when MB = MC.
In the next paragraph they write, "Consider pizzas. We already know from the law of increasing opportunity costs that the marginal costs of additional unit of pizza will rise as more units are produced. At the same time, we need to recognize that the extra or marginal benefits that come from producing and consuming pizza decline with each successive unit of pizza. Consequently, each successive unit of pizza brings with it both increasing marginal costs and decreasing benefits."
How marginal benefit is declining as more and more pizzas are produced? Increase of marginal cost is understandable as more and more robots are being sacrificed for successive units of pizza, but won't more and more pizza gonna fulfill more and more satisfaction of people? Why marginal benefit is decreasing? Does it have to do with supply and demand (more pizzas means lesser will be its price)?


texts: How does demand-supply equilibrium interact with profit maximisation?

texts:
My understanding of supply and demand is that at higher prices sellers are more willing to supply and buyers will demand less, and the total transaction volume will be supply or demand, whichever is less. At some finite price the two are equal, given an equilibrium; and whereas at a higher price demand and hence transaction volume would fall, at a lower one supply and hence transaction volume would fall. Thus the equilibrium price should also maximize transaction volume.

But here's where I get confused. Excuse my inventing notation. Suppose at selling price $P$ there is a transaction volume $V(P)$, maximised at equilibrium price $P=P_E$ so $V'(P_E)=0$. If the unit cost to the seller is $c$, their profit is $\Pi=(P-c)V(P)$. Hence $$\dfrac{d\Pi}{dP}=V(P)+(P-c)V'(P),$$ which at $P=P_E$ is $V(P_E)>0$. Thus the profit-maximising price exceeds $P_E$. This logic seems to imply profit maximization won't occur at the equilibrium price.

So what does microeconomics actually predict happens in a market?


texts:
I have three goods:

beer
carp (fish)
museum ticket

Is it possible to tell anything about market structure if I have annual price data of the industries? Here's the time-series plot on a single graph:

I would like to give advice whether a firm should entry the market or not. Is is it possible to decode price data like "the incumbent firms must have been playing a Bertrand's price competition game at the carp market"? Or do I need further details to say anything about the market structure?

Is it possible to apply IO theory if I have only price data of an industry? I really need some clues, please.


texts: Splittet Value Function and Hamilton-Jacobi-Bellman equation

texts:
General Problem

Let $k\in\mathbb{R}_+$ be the state variable, $k=k^*$ a fixed point (saddle) and $v(k)$ a value function. The problem is, that the value function has two distinct functional forms, where the switch is at the fixed point.

Do you have any reference for theses kind of problems?
Do you think a solution to the model below can be approximated?
What about a kink in the control/policy function?

Model

Let $t\in[0,\infty)$ and $k\in[0,2]$ is the state. There are two players $i=1,2$ with controls $\tau_i\in[0,1]$. Production is given by $f:[0,2]\to\mathbb{R}_+$. The wages and interests are given by $w_1=f(k)-f'(k)k$, $w_2=f(2-k)-f'(2-k)(2-k)$ and $r_1=f'(k)-\tau_1$, $r_2=f'(2-k)-\tau_2$ respectively. The law of motion for the state is given by
\begin{align}
\dot{k}=r_1-r_2.
\end{align}
There is a saddle at
\begin{align}
k^*=1,~ \tau^*_1=\tau^*_2
\end{align}
where $\tau_i^*$ depens on some parameters. Utility is given by the function
\begin{align}
u(g_i,c_i)=h(g_i)+c_i
\end{align}
where $u_g>0<u_c$. Public good is with $g_i=\tau_i k$ and consumption
\begin{align}
c_1=\begin{cases}
w_1+r_1k+\int^1_k{[r_2-a(\theta)]d\theta},\quad & k\in[0,1)\\
w_1+r_1,& k\in[1,2]
\end{cases}
\end{align}
and
\begin{align}
c_2=\begin{cases}
w_2+r_2,\quad & k\in[0,1)\\
w_2+r_2(2-k)+\int^k_1{[r_1-b(\theta)]d\theta},& k\in[1,2]
\end{cases}
\end{align}
with $a:[0,1]\to\mathbb{R}_+,~b:[1,2]\to\mathbb{R}_+$ representing some cost for $\theta\in[0,2]$.
The payoff functionals are then given by
\begin{align}
j_i(\tau_i,\tau_j)=\int^\infty_0{e^{-\rho t}(h(g_i)+c_i)dt}
\end{align}
with $\rho>0$ time preference rate. And the value functions are
\begin{align}
v_i(k)=\sup_{\tau_i} j_i.
\end{align}
Setting up the Hamilton-Jacobi-Bellman (HJB) equations for each player yields
\begin{align}
\rho v_i(k)=\max_{\tau_i} h(g_i)+c_i + v'_i(k)\dot{k}.
\end{align}
Firstly, I will fix $\tau_2$ at the equilibrium level $\tau^*$. Then the HJB for player 1 reads

\begin{align}
\rho v_1(k) &=\max_{\tau_1} h(g_1)+c_1 + v'_1(k)\dot{k}\\
  &=\begin{cases}\max_{\tau_1} h(g_1) + w_1+r_1k+\int^1_k{[r_2-a(\theta)]d\theta} + v'_1(k)\dot{k},\quad & k\in[0,1)\\
    \max_{\tau_1} h(g_1) + w_1 + r_1 + v'_1(k)\dot{k},& k\in[1,2]
    \end{cases}
\end{align}

The FOCs are
\begin{align}
\tau_1=
\begin{cases}
(v_1'(k)+k)^{-1},\quad & k\in[0,1)\\
(v_1'(k)+1)^{-1},\quad & k\in[1,2]
\end{cases}
\end{align}

First pass implementation

I used the algorithm provided by Benjamin Moll.  For reference: in his optimum growth model the value function converged within 8441 iteration and it took 0.825062 seconds.

I used a CB Production function $f(k)=k^\alpha$ with $Ak$-Technology, that is $f(k)=k$ (for $\alpha<1$ I have a problem) and log preferences a la $u(g,c)=\ln g +c$. A linear cost function with $a:\theta\mapsto (1-\theta)$.
I stopped after 200 iterations which already lasted for 21mins. In the first panel is the guess of the 1st and 200th value function. The second panel shows the difference for between the value function (convergence tendency). And the last panel ist the actual policy function, say, $\tau_1(k)$ (note the kink at $k=1=k^*$). It seems to be right from an intuitive perspective. That is, a country lowers its tax rate on capital if the capital stock is realitively small and vive versa. I'm not quite sure why the procedure is so time consuming.

Update

I was able to increase the speed. Then I increased the range of the grid to the respective endpoints of the state, as well as the number of grid points and ran the VFI (40000 Iterations) until I was out of memory. First panel contains first and final value function. The algorithms is converging with $|v^{40000}-v^{39999}|=0.0077$. The kink in the policy function still remains, but the shape slightly differs now.


texts: How does a cash deposit change the M1 measure of the money supply?

texts:
The question asks what is the immediate effect of the cash deposit on the M1 measure of money supply. The official answer is "There is no change in the M1 measure of the money supply. (Demand deposits increase by the same amount that cash holdings fall.)." However, I think the some of the money deposited into the bank will be lend out and deposit into other banks and so on. So the multiplier also applies here, so the money supply should increase by the multiplier times the cash deposited minus the cash deposited(minus because cash holding has decreased). Why is that not true?

Please suggests if anything is not clear.

My guess: maybe it is because the question asks "immediate" effect and hence does not include the process of money being lend out again etc.?


texts: Why do stock exchanges not operate at a fixed frequency?

texts:
Would this not be more fair towards traders who don't trade at high frequency?

And would it not be possible to distribute this fixed frequency to other exchanges, modulo relativity?

The reason I'm asking is because I recently learned that high-frequency traders are beating inter-market sweep orders.


texts: Is there a theoretical basis for any popular income- or wealth-distribution model?

texts: When modelling income or wealth, we probably want a continuous distribution with a lower bound; statisticians have named many, but Pareto and log-normal distributions have been among the most historically popular. Many studies have tested how well these fit the data, and (when they seemed to) estimated the parameters. But is there a theoretical basis for either of these, or for any other model? I found this motivation for a Gamma distribution, but I suspect it's far from being mainstream in economics.


texts: Why, in general, do product or service prices rise in time?

texts:
My question is simple:
Why is it, in general, that the prices of products or services (regardless of demand and supply) are always on the rise in western society? For example, the rent we pay increases every year. The ticket prices for public transport are getting higher every year. The costs of living: higher every year. On the other hand, money income from labor also rises. Why can't they stay stable? Is this inherent in the western economical model?
Or is it because of the constant battle between employees and employers? Which leads to a spiral of ever-increasing prices. Employers ask higher prices, employees higher wages, after which the employers increase the prices, etc.
Government policies can intervene, of which communism is the ultimate example, but that's based on a non-capitalistic economic model, though in the former USSR the number of products increased just as well, although they were state possessed. The visible material world in the former USSR, for example, how the cities and infrastructure looked like didn't differ, that much from how our cities look like. Economic growth and activity took place there too. Hospitals improved, technology in general (the space program among it) made progress, there was a separation between people who lived in bigger state-possessed houses (these were the people who had the power in the state: the employers) and cars different from the Lada, obliged to buy for the employees in the state. It was more uniform though and those who diverted from the norm were put away (as is the case in western societies, calling themselves somewhat arrogant, part of the first world, and communist countries the second one; in current times the borderline between the two has blurred or has vanished altogether). The system, although totally state-controlled, did provide for everyone (as long as you conformed, but that's the case in western societies too, where in fact it provides for everyone too, and also with huge differences between the employees or the employers). And it's a fact that the gap between the people who have a huge amount of private possession and those with a small amount is ever-increasing. Which was also the case in the former USSR but not on such a big scale as in the western world in which we now live. And who cares if you live in a privately owned house or a state possessed house? Only the rich people here, I guess. The more they possess, in general, the more they long to possess, like an addiction. Let it be clear though that communism, as well as capitalism (just look at the national debt of the U.S.A.: 14 000 000 000 000$!), is not my cup of tea!
All of this as an aside though.


texts:
As I understand it, tariffs are used to generate revenue for governments and also punish suppliers or influence their respective governments.  Usually the end user pays the tariff.

Is there a metric that is used to measure which stakeholder is impacted?


texts:
I am looking for any recent estimates of the global STEM workforce (STEM = Science Technology Engineering Mathematics, and ideally includes software engineers).

Time series data would be even better, but I understand how unlikely it is to find such data.


texts:
If every person in America was given a million dollars what fundamentally changes that causes prices to rise? Intuitively I was thinking that this is simply a production problem. With more money there is more effective demand but without a rise in productivity prices will simply shift to a new equilibrium.

I had this thought and I was wondering if it's a good way to understand inflation.


texts: Why would investors from other countries want to invest in a country with a large CA deficit?

texts:
According to my textbook, the current account and financial account must balance; therefore, a country w/ at large CA deficit will need to fund this by a financial account surplus (i.e. they need to receive FDI funds, encourage foreign investors to buy their bonds etc.)

But why would a country want to invest in another country that has a structural CA deficit (as a structural CA deficit implies the country is uncompetitive and therefore it is a risky investment).


texts: What is it about the money market safeguards that increase volatility?

texts:
In recent coverage of the Fed's repo operation, I was struck by this line:

  It also indicated Wall Street is struggling to absorb record sales of
  Treasury debt to fund a swelling U.S. budget deficit. What’s more,
  many dealers have curtailed trading because of safeguards implemented
  after the 2008 crisis, making these markets more prone to volatility.

I do not find this so intuitive, because increasing volatility seems to be an unlikely policy objective in the context of other initiatives at the time (TARP et all.)

Question

I hope I did not over-simplify the matter, and I would like to understand what is the regulation the article refers to and what is the logic behind the perceived "more prone to volatility?"


texts:
I have been trying to work this out for quite a while now, but I can't seem to understand how to solve these kind of questions. Any help (or hint) would be highly appreciated.

Professor Goodheart's colleague Dr. Kremepu gives 3 midterm exams. He drops the lowest and gives each student her average score on the other two exams. Polly Sigh is taking his course and has a 60 on her first exam. Let $x_2$ be her score on the second exam and $x_3$ be her score on the third exam. If we draw her indifference curves for scores on the second and third exams with $x_2$ represented by the horizontal axis and $x_3$ represented by the vertical axis, then her indifference
curve through the point ($x_2; x_3$) = (50; 70) is:

L-shaped with a kink where $x_2 = x_3$.
three line segments, one vertical, one horizontal, and one running from (70; 60) to (60; 70).
a straight line, running from (0; 120) to (120; 0).
three line segments, one vertical, one horizontal, and one running from (70; 50) to (50; 70).
a V-shaped curve with its point at (50; 70).


texts: Question regarding preferences in Gale and Shapley (1962)

texts:
Is it correct to say that preferences in the classic Gale and Shapley College Admissions problem are quasi-linear?
Or is this something thats introduced later in the literature, vis a vis Shapley and Shubik (1971), Kelso and Crawford (1982), etc?
Thanks