Does a strong US Dollar hurt American Manufacturing? I am reading this article about the strengthening of the US Dollar when I came across this paragraph:

"But there are reasons to be cautious. A strong dollar will squeeze American manufacturers, which have otherwise benefited from falling energy prices and rising wages in China. That will weigh on growth in the United States and further suppress inflation, which is already well below the Fed’s target."

Am I understanding it correctly that because the Dollar is getting stronger that it will hurt American Manufacturers?

Source article: http://www.msn.com/en-us/money/markets/the-dollar-keeps-rising-for-good-or-evil/ar-BBoJUq2?li=BBnb7Kz&ocid=iehp

Most manufactured products are sold domestically, but even so a strong dollar will (usually) cause a decline in sales and profitability of US manufacturers. The reason for this is that a strong dollar makes foreign products relatively cheaper, not just manufactured products, but all products. Therefore it becomes cheaper for person to buy, say a foreign-made washing machine compared to an American-made washing machine.

What news articles like this don't mention is that a weak dollar hurts Americans because it makes everything they buy, like gasoline, more expensive, not just manufactured goods.

The exception to the rule is during wartime. For example, as a result of World War II the United States dollar became stronger AND manufacturing profitability increased at the same time. But this was because competitors in Europe had all their factories in ruins, which is not the case today obviously.


What is the reasoning behind the sharp fall of oil prices starting in mid 2014? Things I have considered:

Poor economic conditions around the world could have caused an unpredicted decrease in demand. The resulting surplus has begun driving prices down.
This could be exacerbated by a decade of record-high prices that spurred massive investment that changed supply capacity. I know part of this could also be a result of technological innovation that, over the last few years, has changed supply capacity. Add to this the relatively recent discovery of new pockets of oil/natural gas here that producers have begun exploiting.
Consumer's expect prices to continue falling and so they forgo purchasing fuel if possible. This slowdown in demand can actually help fuel that expected price drop. This could contribute to a steady downward pressure, I think.
Geopolitical relations between America, Saudi Arabia, Russia and Iran. I know that Saudi Arabia and co. could slash production in an attempt to remove the excess supply and drive prices of oil up again.
America is now a (the?) leading oil producer world wide and the USA do not import nearly as much oil as it once did. The fact that the USA are using oil extracted and refined domestically has obvious implications etc. An interesting question is how OPEC's recent announcement to not cut production and instead let prices stay low might affect domestic production where things like horizontal drilling and fracking drive up the cost of extraction.

I would really appreciate a substantiated walkthrough of what has caused this very sharp turn around in oil prices. I know the last decade was a time of record highs...so why now the massive landslide in the value of oil?

I should say I am hoping to hear from economists who perhaps have some specialized knowledge here. I do have an undergrad degree in economics and I have read and am familiar with most of the general arguments.  I am looking for a well substantiated and thorough answer that will deepen my understanding of this issue.

My understanding of the recent drop in oil price is due to recent changes in US drilling. They are now the worlds largest oil producer. This article by the economist does a good job explaining.

My answer (borrowed very heavily from the economist.)

Demand is low because of weak economic activity, increased efficiency, and a growing switch away from oil to other fuels.
America has become the world’s largest oil producer, creating a lot of spare supply.
The Saudis and their Gulf allies have decided not to sacrifice their own market share to restore the price. They could curb production sharply, but the main benefits would go to countries they detest such as Iran and Russia. Saudi Arabia can tolerate lower oil prices quite easily. It has \$900 billion in reserves. Its own oil costs very little (around $5-6 per barrel) to get out of the ground.

For further reading, the NY times has a decent article explaining it a little more.

edit:
I think it is safe to assume that OPEC has market power. They can get oil far cheaper than their competitors (as referenced above).

With that in mind,
The below reference provides a model which explains what we are experiencing here. Cournot competition seems a perfect model to use.

Naoum-Sawaya, J. and Elhedhli, S. (2010). Controlled predatory pricing in a multiperiod Stackelberg game: an MPEC approach. J Glob Optim, 50(2), pp.345-362.

A key quote from the above article: "After reducing or eliminating competition, the predatory firm
can raise its price and compensate the loss by earning monopoly profits in the long run".

This second provides a very brief overview of OPEC and their behaviour.

OPEC reflects on its history. Salisbury, Peter, Middle East Economic Digest.

I couldn't find an empirical study comparing a Stackleberg model to the OPEC cartel but I do not doubt that this has been done to death.


Predicting $y$ when response variable is $\ln(y)$ My estimated model is

$$\hat \ln(y_t)=9.873-0.472\ln(x_{t2})-0.01x_{t3}$$

I'm asked to find a predictive CI at 95% confidence for the mean of $y_0$, when $x_{02}=250$, and $x_{03}=8$. We're to assume that $s^2 x_0(X^TX)^{-1}x_0^T=0.000243952$, where $x_0=(250,8)$.

I have a solution from a previous year, that goes like this:

  I find the CI of the form
  $\text{CI}(E[ln(y_0)|x_0])=\left[\hat\ln(y_t)-t_{\alpha/2}s_E,\hat \ln(y_t)+t_{\alpha/2}s_E\right]$, where $t$ is
  the $\alpha/2$ upper-quantile of distribution $t(n-k)$ and
  $s_E=\sqrt{0.000243952}$. This gives me $[7.1563,7.2175]$.

  Then the author does
  $\text{CI}(E[y_0|x_0])=[e^{7.1563},e^{7.2175}]=[1282.158,1363.077]$.

I disagree with this last step (by Jensen's inequality we'll underestimate). In Wooldridge's Intro to Econometrics, in page 212, he states that if we're sure the error terms are normal, then a consistent estimator is:

$$\hat E[y_0|x_0]=e^{s^2/2}e^{\hat \ln(y_0)}$$

So, I was thinking of doing

$$\text{CI}(E[y_0|x_0])=\left[e^{s^2/2} 1282.158,e^{s^2/2}1363.077 \right] = \left[ 1282.314,1363.243 \right] $$

Is this correct?

Also, the solution to this exercise states that $\text{CI}(E[y_0|x_0])=[624.020,663.519]$, which is far from either solution I've got.

Any help would be appreciated.

P.S: I've also read that the correction should not be used to the CI but only for the point estimation $\hat E[y_0|x_0]$

You do not find the same answer because of what I suspect to be a typographical error, which would thus be the main reason of your problem: $x_{03}$ would be set to $80$, not $8$. Another possibility, if you keep $x_{03}=8$, is an error in the second estimated coefficient, say, $\hat{\beta}_2 = -0.1$ instead of $-0.01$.

Anyway, one of these modifications solves everything and yields the same result as the solution to this exercise.

Considering this change, with $t_{\alpha/2}=1.96476138969835$, one gets

Method 1

$\text{CI}(E[y_0|x_0])=[e^{6.43618291164626},e^{6.49755798189177}]=[624.020307335178,663.519326788772]$
(the given solution to this exercise)

or Method 2
(as stated In Wooldridge's Intro to Econometrics, in page 212) if we're sure the error terms are normal (and one is extremely lucky)

$$\text{CI}(E[y_0|x_0])=\left[e^{s^2/2}624.0203,e^{s^2/2}663.5193 \right] = \left[ 624.0960,663.6002 \right] $$

however

the method 2 is very unlikely to be correct, since as you mention in your question [...] the (underestimation) correction should not be used to the CI but only for the point estimation.

Why ? I would say because of the dependency betweeen the two terms, knowing the expectations of $e^{s^2/2}$ on the one hand and $\hat{y_0}$ on the other hand does not mean one knows the one of $e^{\frac{s^2}{2} + \hat{\ln(y_0)}}$.


How to calculate the risk-free rate of cryptocurrencies? For a conference I need to show the Sharpe ratio's of bitcoin portfolios using different trading strategies. To calculate the Sharpe ratio, I need the Bitcoin's risk-free rate. Risk-free rate for normal stock markets is usually taken from Treasury documents. But cryptocurrencies have no central government and are not affiliated to any country. So how to determine the risk-free rate for, for example, Bitcoin? Is it simply 0?

Instead of looking at bitcoin like a currency, I think you should look at it like a regular stock. The "return" is the return of your fiat money (USD) that's investing in Bitcoin... so the risk free rate should be the risk free rate of your money, i.e. T-bill, etc.


Can $u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4}$ be solved by Kuhn–Tucker conditions? Consider

$\max_{x_1, x_2, x_3, x_4} u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4}$

s.t. $\; p_1x_1 + p_2x_2 + p_3x_3 + p_4x_4 \le w$

I know we can solve the max problem through separately considering case(i): $x_1, x_2 > 0$ and $x_3 = x_4 = 0$; and case (ii) $x_1 = x_2 = 0$ and $x_3, x_4 > 0$.

But is it possible to solve the whole optimization problem through the Kuhn–Tucker method?

We can write down the Lagrangian $L(x,\lambda)=\sqrt{x_1x_2}+\sqrt{x_3x_4}+\lambda(w-p_1x_1-p_2x_2-p_3x_3-p_4x_4)$

with the complementary slackness conditions:

$\frac{\partial L}{\partial x_1}=\frac{1}{2}\sqrt{\frac{x_2}{x_1}}-\lambda p_1 \le 0,\quad x_1 \ge 0, \quad \text{and}\quad  x_1 \frac{\partial L}{\partial x_1}=0$.

$\frac{\partial L}{\partial x_2}=\frac{1}{2}\sqrt{\frac{x_1}{x_2}}-\lambda p_2 \le 0,\quad x_2 \ge 0, \quad \text{and}\quad  x_2 \frac{\partial L}{\partial x_2}=0$.

$\frac{\partial L}{\partial x_3}=\frac{1}{2}\sqrt{\frac{x_4}{x_3}}-\lambda p_3 \le 0,\quad x_3 \ge 0, \quad \text{and}\quad  x_3 \frac{\partial L}{\partial x_3}=0$.

$\frac{\partial L}{\partial x_4}=\frac{1}{2}\sqrt{\frac{x_3}{x_4}}-\lambda p_4 \le 0,\quad x_4 \ge 0, \quad \text{and}\quad  x_4 \frac{\partial L}{\partial x_4}=0$.

However, when guessing say, $x_1 = 0$ and $x_2,x_3,x_4>0$, $\lim_{x_1 \to 0}\frac{\partial L}{\partial x_1} \to \infty$, which does not satisfy the complementary slackness $x_1 \frac{\partial L}{\partial x_1} = 0$.

I do not know whether we can use the Kuhn–Tucker method to solve this optimization problem? And if not, what are the reasons?

Why do you want to guess that some $x$ is zero? What is the problem of having all four goods strictly positive at the solution?

In fact, due to the presence of the square root in the first order conditions, the solution looks straightforward, since the inequality cannot hold (and assuming exhaustion of the budget).

ADDENDUM
Given the f.o.c's provided by the OP, all $x$'s have to be strictly positive at the solution, since otherwise we have division by zero and/or the undetermined form $0/0$.

This in turn implies that $\partial L/\partial x_i = 0$ at the solution, which now becomes easy to compute.


Market order's variables I am not an economist, so my question could be stupid for you.
However, I need to understand how market order works and which variables plays in a trade.
For example: let us suppose I am a trader and I have at the time t=0 a sum of cash and stocks.
How do they change?
Do I need consider intraday and daily trades?
And what about the spread between bids and asks?

I am a financial economist, so I will attempt to answer what I think you are asking.  A market order isn't one concept, it's many.  Each place that accepts trades operationalizes it differently.  It also depends upon whether it is a small order or a large order.

For a small order, the order result will clear at the bid if it is a sell order at the bid and at the ask if it is a buy order.  Only in that case will the outcome be the same everywhere.

For a large order, it depends upon where the security trades at and it can depend upon the internal policies of which broker-dealer you use.  For example, if you place a large market order on a stock that trades on the NYSE then what you are actually doing is instructing your broker to go to the floor of the exchange, to a place called the "post," and continue to bid until you are the high bidder, if buying or the low bidder if selling, until your order is filled.

On the other hand, a large market order on the NASDAQ will be filled up to the stated size limit.  After that, it depends upon a number of things.  For example, if there are multiple market makers then decisions to fill or not fill is made by each maker depending on orders they have, their inventory needs and what risks they will take and for what fee structure.  Because a market order essentially says "I will pay any price," the makers have liberal pricing powers on large market orders.  Also, the processing broker can sometimes cross the order with other orders they have pending from their own customers and so it never really makes it to the market itself, other than for record keeping purposes.

Outside of this, there are order crossing services in what have been nicknamed "dark pools," which are available to the largest financial institutions but not to ordinary traders. Different rules are in use for things other than stocks and for stocks traded in non-US exchanges.

To provide an example, imagine you own $\$1,000$ and also own 100 shares of ABC which is currently trading at 9.90 bid and 10.10 ask.  It trades on the NYSE.  A decision to sell 100 shares at market would increase cash to $\$1,990$ and reduce shares to zero.  Since you may or may not be permitted to short sell the stock depending on your contract with your broker and the availability of shares to borrow, a decision to short sell 100 more shares of ABC would increase cash by the new bid, which for our purposes will be 9.85 per share, for $985 and add one hundred shares on the short side in the margin account.  The cash will also be segregated and held as collateral on the long side of the margin account.

A large market order for a thinly traded stock could take a month or more to fill.  For a "pink sheets" stock it could take years.  For a heavily traded stock, it could take less than a second.

It is important to note that the recording of a trade for customer accounting purposes may not match market records.  Consider a person who sold 100 shares of ABC for 9.65 per share.  They record an increase in cash of $965 and a decrease in shares by one hundred shares.  The "tape" may not record it this way if it is part of a large buy order.  In that case, if the weighted average price was 10.10 then the market would see one large order for 10.10 per share, though it may also be the case that nobody actually received that amount of money.  It is also the case that the time of order completion will not match.


How did the UK become so indebted? In 2011, household, financial, and business debts stood at 420% of GDP in the UK.

This doesn't sound like a very good state of affairs (am I wrong?).

If this is a negative state of affairs how did the UK arrive at such a position? Presumably someone in a position of governance monitors the macroeconomic state at all times.

If so, why was corrective action not taken at 200% (or whatever)?

A non-mainstream answer...

As Steve Keen is fond of pointing out, mainstream economists (incorrectly) think that the level of private debt has no macroeconomic effects so nobody was looking out for any unusual build up.

Keep in mind the following two facts:

Most private debt is in fact loans from banks - in other words
demand deposits - which are money. So when private debt rises,
the money supply grows.
House prices are not properly reflected in standard measures of inflation.

In the years running up to the crash of 2007/8, central banks were monitoring the level of inflation and adjusting interest rates so as to keep inflation low. There was a housing bubble which meant that house prices were rising relative to the price of everything else (i.e. stuff recorded in inflation measures). The housing boom meant that private debt (i.e. the money supply) was rising at around ten percent a year whilst inflation was running at around only two or three percent. Almost no mainstream economists thought that this was dangerous.


Dynamic of 10 year UST given supply shock of the bonds that the Fed will buy into It looks like the US government are gonna issue a lot of bonds in the near future. Basic demand/supply implies that this will lower the price of those bonds i.e higher yields. At the same time it seems that the world is looking desperealty for dollars.

Hence where are all these dollars gonna come from if not the Fed? i.e the Fed buy all the bonds in order to one finance the deficit and two keep yields down.

What would be the long term effect of this kind of behavior?

Who will buys bonds; not including the FED

When a government wants to issue bonds, it will usually do so via a bond auction, where the bond will be bought by large banks or financial institutions.

Those institutions will then sell the bonds on, often to pension funds, other banks, and individual investors.  So other banks and individuals also buys bonds.

https://www.ig.com/en/bonds/what-are-government-bonds

other factors/actors pressuring up prices on these bonds.

If the economy is doing poorly (less economy growth) then investors might step back a bit from riskier investment and instead pile into government-backed Treasury’s, which pushes prices higher and yields lower.

https://www.investopedia.com/ask/answers/111414/what-causes-bonds-price-rise.asp

How does the dynamic of all this work with inflation?

When inflationary pressures emerge, Treasury yields move higher as fixed-income products become less desirable. inflation eats into the purchasing power of every dollar you receive from bond interest in the future.

Additionally, inflationary pressures typically force central banks to raise interest rates to shrink the money supply. In inflationary environments, investors are forced to reach for greater yield to compensate for diminished purchasing power in the future.


What are the current economic theories of product advertising? Are there any well known economic theory references about advertising? It seems you could think of advertising as imposing a negative externality on other producers or on consumers in that it takes up bandwidth, or a positive one instead in that its a way of subsidizing programming or generating public information...

Should we put Pigouvian taxes on advertising or instead subsidize the necessary infrastructure?

This post is about advertising , but does not have any references:

There is a vast literature in both economics and marketing on advertising. Some highlights relevant to your specific question:

A classic paper (Grossman and Shapiro 1984) looks at competitive advertising and indeed finds that advertisers tend to send too many ads. Intuitively, some customers attracted by an ad aren't new demand, but rather simply stolen from a rival firm. Sending the ads these consumers saw wasted resources without creating any genuinely new trade, and are therefore sub-optimal.
More recent work (such as Anderson and de Palma, 2012, and van Zandt, 2004) considers information overload: the problem that ads crowd out other ads when consumers have limited attention. Again, this leads to sellers sending too many ads.

More generally, Bagwell (2007) has a nice survey of the economic literature on advertising.

Incidentally, it is also conceivable that there might be too few ads in equilibrium for some kinds of product. For example, if you and I both sell products that are very similar and the main function of ads is to inform consumers about the characteristics of those products then advertising is a public good. I would prefer to free-ride and let you bear the expense of advertising to inform consumers. I can take the money I save on advertising and use it to offer lower prices or better quality and thereby capture the demand of the consumers you so generously informed. The fact that arrangements such as vertical integration or franchising help to mitigate this free-riding problem is one reason why such arrangements are sometimes viewed more favourably by competition authorities.


What are the assumptions of real business cycle theory and Keynesian theory? What are the differences between the approaches of Keynes and Real Business Cycle theorists? What are the assumptions made by both the theories?
How do they differ in their methodology?
Do they contradict each other??

I wish to get a basic idea of the theories with a  slight bit ofrigour.

The distinction is between "nominal" and "real" recessions and booms.

Real business cycle theory was developed to point out the fact that variations in employment and hours could occur even in an economy where markets were working competitively and there were no pricing frictions. In the RBC world, recessions and booms are driven by "real" factors: variation in technology, variation in the supply of commodities used as input in the production process, etc. A consequence is that in the RBC world while increased government spending on consumption goods indeed raises output and employment (the fiscal multiplier in RBC models is between 0 and 1), following such a policy during a recession is socially suboptimal. (You force people to work more and consume less.) To justify government spending during a recession is no easier and no harder than to justify it during "normal times", and then the argument becomes one about market failure, public finance, etc.

In contrast, Keynesian theory (and its modern cousins) say that while "real recessions" in the above sense may indeed exist, there are also "nominal recessions": these are recessions caused by "less spending" (for instance, if you're working with MV = PY, they are recessions caused by a fall in V). The reason this creates a recession is because there are nominal rigidities in the economy - workers are unwilling to accept nominal wage cuts, producers face "menu costs" which make price changes infrequent, etc. Because of these rigidities, a fall in "aggregate spending" manifests itself not only in the form of lower prices, but also in the form of lower output.

So far, everything I said is also consistent with monetarism, for instance. However, this is not all there is to Keynesian theory: Keynesians go further and claim that the solution to a shortfall in spending is for the government to increase spending and "make up the lost demand". In other words, if you think of the AD-AS model, Keynesians think that government spending can raise AD. This idea has been discredited in academia for decades because it ignores budget constraints - there's only so much money available in the economy, if the government borrows money from you and spends it, that's money someone else did not spend. It's not clear how government spending boosts "money velocity", and in fact there are New Keynesian models where increased government spending is deflationary and makes a nominal recession worse by creating more demand for real money balances.

Keynesian ideas have made a resurgence in the past 10 years thanks to the zero lower bound. The argument above about budget constraints is no longer true when nominal interest rates are stuck at zero, because now people will actually start hoarding cash instead of spending it. Therefore, increasing government spending does not "crowd out" private spending, because households and firms are just sitting on the cash they have anyway. Monetary stimulus is ineffective because any additional money is just held by the public. This is the "liquidity trap" a nutshell. Critics point out that permanent monetary stimulus as opposed to a temporary one can still work in a liquidity trap (as pointed out in Krugman (1998)) and that monetary models (say, with cash-in-advance constraints) are indeterminate at the zero lower bound: without anchoring consumption and prices in the future to some level chosen arbitrarily, it's not possible to pin down a unique equilibrium of the economy today.

There's more to be said on this subject, but this should be enough for an answer.


Is there a specific definition of short run and long run? Like normally how long can be said as long run? And does specific time length of these words matters?

The actual length of time does not matter. Simply, in the short-run capital is fixed and labor is variable. In the long-run both capital and labor are variable (which gives firms enough time to, for example, build a new factory to match an increase in demand). It would be really fortunate if there was a general time frame, but that would vary from industry to industry. The long-run for, let say, Ford is a pretty long-time because they are very capital intensive. However the long-run for, lets say, a Clown Rental Service, is very short because it is entirely labor dependent.

Hopefully this answer helps.


Economics Online Seminars As education moves to the internet, so are research seminars. Some of these seminars are regular and others appear to be temporary due to the covid-19 and the lockdown.

Here are some examples from the American Economic Association

Regular seminar(s)

The Chamberlain Seminar - A regular open online international
inter-institutional econometrics seminar in honor of Gary Chamberlain
(1948–2020)

Temporary Seminars

Virtual Macro Seminar Series
Online Seminar in Gender Economics
Virtual IO seminar
...

And also,

Princeton Webinar Series on COVID Economics

Beyond the AEA list and the Princeton webseminar, I am looking for links to find conferences, workshops, and talks hosted by economic research institutions from all over the world. One requirement is that registration be open to all, as some of the online seminars are reserved for faculty only.

Update

Virtual Economics stores various online seminars with a super useful calendar.

I have two here to add to your list.

Brookings Insitute

https://www.brookings.edu/events/

St. Louis Fed  Economic lowdown
(FREE)

https://www.econlowdown.org/

There is also the National Association of Business Economics (NABE)
But to get access to their webinar resources you have to register on their site.
I know this won't qualify as it is not free but they are a good source of up-to-date information.  I felt that this would be a good share.

www.nabe.com

Others that I just found:
Peterson Institute for international Economics

https://www.piie.com/events

National Bureau of Economic Research (www.nber.org - click on videos)
or

https://www.nber.org/video_archives.html

Organisation for Economic Co-operation and Development (OECD)

http://video.oecd.org/

World Bank
https://www.worldbank.org/en/about/archives/past-events


What branch of Economics does 'e-governance' fall under? I need to work on a project regarding e-governance in a region of India, and, I need to consult professors in education institutes who would have knowledge in this subject. So, for that I need to know what part of Economics does e-governance come under?

Does it come under Development Economics, Public Economics or any other field?

This is Public Economics, under the JEL code H11:

Examples of such papers on e-Governance using the H11 JEL code are:

https://ideas.repec.org/a/ekz/ekonoz/2003311.html
http://www.sobiad.org/ejournals/journal_ijebeg/arhieves/2009/01ajay_kr_singh.pdf
https://ideas.repec.org/p/cpr/ceprdp/11761.html
https://ideas.repec.org/a/eco/journ3/2016-04-38.html
https://ideas.repec.org/p/wiw/wiwrsa/ersa14p905.html

Note that papers usually have multiple JEL codes. That is the case of the last three papers given above. Some also use codes related to Economic Development (Under JEL codes O), if they refer to developing countries. But the common denominator is Public Economics.


Economics and Euclidean geometry I am looking for economics papers which use concepts, techniques and theorems from geometry. I am mainly interested in Euclidean geometry, the kind of material that is taught on high-schools (e.g. proving theorems about triangles, squares, circles, etc.). But, other kinds of geometry are also interesting.

I looked at some papers about land economics, thinking that it geometry can be useful there (after all, the word "geometry" means "measurement of land"). But, the papers I found used mostly advanced measure theory and topology. I am looking for more basic geometric methods.

UPDATE 19-9-2017

I just received word from the author that the book is now freely downloadable in English, at this link.

Got it. I remember browsing the pages of this book. But it was in Greek, and it does not appear to have been published also in English:

Euclidean Economics: A Mathematical Method for Construction and Application of Economics Models

  "The book establishes that economics can be studied and utilised on
  the basis of a minimum of fundamental hypotheses and the general laws
  of mathematics. Starting from 12 major propositions, it proves that
  closed exchange networks are replicated by systems of 2n first-order
  non-homogeneous linear differential equations, which simulate
  household, business, bank and government receipts and payments. Such
  networks are defined in the (R2n, t) vector space, where n is the
  number of sectors or markets and countries or currencies, while t is
  the elapsed time. Uniqueness, stability and controllability of the
  steady state as well as takings and outgoings are functions of
  behaviour coefficients and policy parameters. Annual sales of
  services, products and securities divided by average salaries, prices
  and values yield the man hours, output items and liquidity units
  traded. Demanded quantities do not coincide with available quantities.
  Potential inflation or deflation is proportional to the weighted
  deficit or surplus of market goods. Digital animation of the
  endogenous variables is possible on the basis of historical, projected
  or hypothetical data about the exogenous variables."

Author: Sophocles Michaelides
Language: Greek
Publisher: Mesogios Publications – Ellinika Grammata
ISBN: 9963-9176-0-7
Year: 2006

The summary does not state it clearly, but the "12 major propositions" are Euclidean, as I recall.


Gross value added and worker salary I'm trying to figure out how the Gross value added is calculated. The first question that I have encountered is "Does the Gross value added of an activity includes workers salary?" If not, what is the difference between GVA and an activity profit?

I assume that you're interested in gross value added as a national accounting concept (which is the most frequent use of the term). In that case, it is formally defined by the UN's System of National Accounts as "the value of output less the value of intermediate consumption". Here is a table from the freely available old version of Understanding National Accounts showing this breakdown for the nonfinancial corporate sector of France:

This definition is made on the production side, but gross value added can also be broken down into income. On the income side, it includes worker salaries, as another account excerpted from Understanding National Accounts shows:

As we can see above, gross value added is decomposed into compensation of employees (of which "wages and salaries" is the most important part), other taxes less subsidies on production, and gross operating surplus. Gross operating surplus can further be decomposed into consumption of fixed capital (basically depreciation) and net operating surplus.

Combining Tables 3 and 4, we see how the initial "output" accruing to a firm can be progressively whittled down:

First, we subtract intermediate inputs to obtain gross value added.
Then, we subtract compensation of employees and taxes less subsidies on production to obtain gross operating surplus.
Finally, we subtract consumption of fixed capital to obtain net operating surplus.

Of all these concepts, the final one ("net operating surplus") is closest to our usual concept of profit, since it subtracts payments for intermediates, compensation of employees, production taxes, and depreciation. Nevertheless, there are a number of conceptual and technical differences between this and profit as it is usually defined: for instance, the net earnings of a corporation subtract interest payments, while "net operating surplus" does not. Instead, "net operating surplus" can be viewed as a broader measure of capital income. (Indeed, when Piketty and Zucman (QJE 2014) plot "capital shares" of national income in Table XII, they are actually plotting net operating surplus as a share of national income for each country, taken from the national accounts.)

Finally, note that all these definitions are quite generic and meant to apply to many levels of aggregation: firms, industries, areas, sectors, or entire economies. The tables with gross value added above show the "production" and "generation of income" accounts for the non-financial corporate sector, but all national accounts constructed using the same principles provide an analogous account for other sectors—including households, government, the total economy, etc.


If I have a £25,000 loan, in a balance sheet do I include it in the Cash as well as a liability? I'm new to all this and balance sheets are extremely confusing.

In this example I've received a £25,000 loan from the bank, it has a fixed interest rate of 6% to be paid over 1-5 years.

This is the only cash I have to finance my business at the moment and I don't have any other assets (2000 cash from personal finance)

So what I'm wondering is, in a balance sheet do I include the 25,000 as a Cash asset as well as putting it in the liabilities as I have to pay that back?

If someone could explain this to me or maybe show me what it would look like in a mini balance sheet I would be super grateful!

Yes, you are correct: add the 25k both in cash and in liabilities.

The balance sheet represents what you have (assets) and what you owe (liabilities). So when you get the loan you do have 25,000 in cash under assets, but you also owe it and will need to repay it at some point (which appear as 25,000 in bank loans, under liabilities). As you repay it, the value in liabilities decreases. If you need to learn more there are several free online courses, like this one.


Did Zimbabwe have an inflation of 89.7 sextillion percent? From a Cato Institute article by Steve Hanke1 (emphasis added):

The Economist’s most recent infraction on Zimbabwe’s hyperinflation appeared in the May 2016 issue. The magazine claimed that the hyperinflation peaked at an annual rate of 500 billion percent. Where did this figure originate? You guessed it. That figure is buried in the IMF’s 2009 Article IV Consultation Staff Report on Zimbabwe.
In reality, Zimbabwe’s annual inflation rate in September 2008 was 471 billion percent, not 500 billion percent. More importantly, Zimbabwe’s hyperinflation peaked in November, not September. It was then that Zimbabwe recorded the second-highest hyperinflation in history: a whopping 89.7 sextillion percent. This is 179 billion times greater than the IMF’s figure.

Did Zimbabwe, at one point, record a hyperinflation of 89.7 sextillion percent? Wikipedia cites the IMF figure.

How did Steve Hanke come up with the number 89.7 sextillion?

Is Steve Hanke's methodology accurate? Reasonable? Trustworthy?

Why are the two numbers so different?

Note: Steve Hanke certainly seems to believe that inflation for some countries is higher than actually reported (e.g. the Zimbabwe article I cited, this tweet regarding Sudan from 9 hours ago, and this tweet regarding Argentina from 11 hours ago). Maybe this could be considered in an answer?
1Professor of Applied Economics and Co-Director of the Institute for Applied Economics, Global Health, and the Study of Business Enterprise at The Johns Hopkins University in Baltimore

The figures you question are from Hanke and Kwok (2009).

According to Hanke and Kwok (2009), yes.
A stock (Old Mutual) was listed on both the London Stock Exchange (in GBP) and the Zimbabwe Stock Exchange (in Zimbabwe dollars). Under the assumptions of price arbitrage and purchasing power parity, one can infer Zimbabwe's inflation rate.
I haven't carefully attempted to replicate their work, but I can see no reason to question Hanke and Kwok's general methodology.
The Economist's figure of 500 billion percent is for Sep 2008. (Hanke and Kwok's estimate for Sep 2008 is 471 billion percent.) The higher figure of 89.7 sextillion percent is Hanke and Kwok's estimate for the month to Nov 14, 2008.

Their Table 1:


Simple Sketch of Mirrlees 1971 Mirrlees' 1971 paper (An Exploration in the Theory of Optimum Income Taxation) on optimal taxation can sometimes be hard to follow. Does anybody know of (or could even provide here) a simple sketch of the derivations of the optimal nonlinear income tax schedule in his paper?

You can find a didactic exposition of Mirrlees (1971) -- including derivations of optimal tax schedule formulas for different social welfare and utility function -- in section 4.2 of "The Economics of Taxation" by Bernard Salanié (2003, First Edition).

I bet it is still somewhere in the second edition too, but I do not have a copy of it so I don't know in which section that would be.


Formula for splitting profit and loss for every person I am looking for a formula to calculate even distribution of loss or profit between involved parties. Let's speak with some examples as I feel it will be easier.

Example 1

Person 1

Balance: 2,000,000
Supplies (investment): 70,000

Person 2

Balance: -260,000
Supplies (investment): 260,000

Person 3

Balance: -17,000
Supplies (investment): 84,000

Description

As we can see one person made profit in this example. To distribute everything evenly he should pay every person loss (so 259,000 to Person 2 and 17,000 to Person 3) and divide what's left by 3 and distribute that as well.

Example 2

Person 1

Balance: 2,000,000
Supplies (investment): 80,000

Person 2

Balance: 1,000,000
Supplies (investment): 150,000

Person 3

Balance: -900,000
Supplies (investement): 900,000

Person 4

Balance: -150,000
Supplies (investment): 100,000

Description

As we can see two people here made profit so it gets trickier. We still want to distribute everything evenly. Easiest way I see is to sum all the negative balances (1,050,000 here), subtract that from profit (3,000,000 - 1,050,000 = 2,950,000) so everyone 737,500 / 4 so Person 2 has to give back a little from his balance (profit) and so does Person 1. Easiest would be to cumulate all profit in one account (e.g. Person 1) and make Person 1 split everything but it seems more work.

Example 3

Person 1

Balance: -10,000
Supplies (investment): 50,000

Person 2

Balance: -20,000
Supplies (investment): 20,000

Person 3

Balance: -500
Supplies (investment): 500

Description

As we can see no-one made any profit but Person 1 earned 40,000 as he used 50,000 for supplies and  has only -10,000 in losses. So this 40,000 should be evenly distributed but according to their usage of supplies.

Is that correct way of thinking? Is there a formula for splitting profit and loss?

Either I totally misunderstand the question, or this is just adding up numbers, there are no economic or mathematical principles involved. (In which case this is not the right SE for it.)

Denoting the "balances" by $b_1,b_2,...$ and the "supplies" by $s_1,s_2,...$ total profits are
$$
\Pi_{total} = \sum_i (b_i-s_i)
$$
You want everyone to end up with a proportional share of this, so that in the end they have
$$
\frac{s_i}{\sum_i s_i} \Pi_{total}.
$$
To compensate for their investment, each person should get
$$
x_i = s_i + \frac{s_i}{\sum_i s_i} \Pi_{total}.
$$
One can verify that
$$
\begin{align*}
\sum_i x_i & = \sum_i s_i + \sum_i\frac{s_i}{\sum_i s_i} \Pi_{total} \\
& = \sum_i s_i + \Pi_{total} = \sum_i b_i
\end{align*}
$$
so we made no mistakes, you can indeed give people their values $x_i$.


Sources of historical cross-country government debt to GDP data I am looking for a source containing debt (government debt) to GDP data of different governments. Do you know of any reliable sources with data going back as far as possible (at least 1960s)?

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

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

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

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


How can valuable retail real-estate stay vacant for an extended period of time? Anecdotally, the story often goes like this:

A land owner leases his commercial retail space at an expensive price. The place stays vacant for months or years at a time. Eventually someone decides to lease the place. The rents are very expensive and eventually the leaser goes out of business.

This article goes someway to describing the phenomenon I am looking to explain
This article has the Leichhardt mayor signal an attempt to address the problem.

There are many other families like the Wakils, who are content leaving their property vacant. This example is largely relating to Australia but it does happen elsewhere.

Why would they do that? Surely any rent earned would be better than no rent.

My thoughts are:

There could be some sort of tax concession in place. If a landowner tries to lease for \$5k a month, the tax write-off could make the owner better off than if they actually leased it for \$4k a month. The below suggests this happens to at least some degree.

  Leichhardt mayor is calling for a range of legislative changes to allow rates to be increased and tax concessions reduced for landlords who leave their shop fronts empty unnecessarily... there is currently no allowance to reduce rates for those property owners who keep their properties tenanted or to increase rates for landlords who are using their properties as a tax write-off.

The returns to land-price speculation make leasing a secondary priority.
Structural change in how valuable retail space is. With the increase in grocery deliveries and other forms of online shopping, maybe people don't have as much need to shop. This, coupled with possible stickiness in rental prices will result in a significant drop in quantity demanded.
Some people just don't care. (I find this particularly unsatisfying considering the magnitude of the values involved)

To me, it is clear there is at least some form of regulatory failure present here. If these places were rezoned into residential, they would get filled very quickly as this phenomenon seems primarily restricted to commercial real-estate. The council (and probably the community) would prefer to have this area remain commercial but residential is surely better than vacant.

Before applying irrationality to explain the phenomenon, consider the following simplistic model of a rational owner: assume there is the high rent $R^h$ and the low rent $R^{\ell}$. The owner faces the prospect of earning either

$$V(h) = \sum_{t=1}^{T_1} \beta^{t-1}R^h + \sum_{t=T_1+1}^{T_2} \beta^{t-1}\cdot 0+ \sum_{t=T_2+1}^{T_3} \beta^{t-1}R^h +...$$

or

$$V(\ell) = \sum_{t=1}^{\infty} \beta^{t-1}R^{\ell} = \frac{1}{1-\beta}R^{\ell}$$

Favor the "low-rent" scenario by ignoring all terms in $V(h)$ except the first sum (this reflects that the property may go unleased for "many years", so remote-future income gets fully discounted). Based on these considerations alone, if we observe the "high rent" scenario, it must be the case that

$$V(h) > V(\ell) \implies \frac{1-\beta^{T_1}}{1-\beta}R^{h} > \frac{1}{1-\beta}R^{\ell} \implies R^{h} > \frac{1}{1-\beta^{T_1}} R^{\ell}$$

which can be re-arranged to give

$$\beta < \left(\frac {R^h-R^{\ell}}{R^h}\right)^{1/T_1}$$

The right hand side can be estimated by real world data: obtain average magnitudes for the high and the low rent, as well as the average time a business under the higher rent pays it prior to fold (the $T_1$ parameter). These will lead to an estimation of the upper bound for $\beta$ in order for the above inequality to hold, and justify the "high rent" scenario observed.
Then one can examine this upper bound and contemplate whether it appears "reasonable".
As a numerical example, assume $R^h = 2R^{\ell}$ and $T_1=2$ (say years). Then it must be the case that

$$\beta < (1/2)^{1/2} \approx 0.71$$

"Too low" (i.e. too high discounting) one would tend to say. But don't look at benchmark values of $\beta$ that are used in macro-models. Try to think what the discount factor attempts to capture here.  And in any case, a person with very high discounting, is not "irrational" -this is how he experiences the world.

And then, there are other considerations: accepting low rents tends to drive the asset values down. Also, It may be the case that this is incremental income for land owners, above some comfortable level from other sources, meaning declining utility of wealth may kick in. Further, constant occupation physically wears the asset down faster. Etc.

My point is, "people are just jerks" (i.e. arguing for irrationality) can explain everything - and so it really explains nothing.


Crude oil benchmarks and production places I discovered recently that there are 3 main price indicators for crude oil (used by the IMF): WTI, Dubaï, and UK Brent. If I understand correctly, each place trades some specific kind of oil (with more or less sulfur among other), which is related to the production place.

Is there some stylized facts, or a precise matrix available, which relate the production place and the price index?

My first guess was OPEC production $\Rightarrow$ Dubai and US production $\Rightarrow$ WTI but I'm not sure regarding the UK Brent...

This article states:

  Brent, WTI and Dubai-Oman are the main crude oil benchmarks of
  the current oil pricing system. Nearly all oil traded outside America and the Far East is priced using Brent as a benchmark. WTI is the main benchmark used for pricing oil imports  into  the  USA.  Dubai-Oman  is  used  as  a  benchmark  for Gulf  crudes (Saudi Arabia, Iran, Iraq, the UAE, Qatar and Kuwait) sold in the Asia-Pacific market.

Regarding where the oil is produced, according to Investopedia:

  “Brent” actually refers to oil from four different fields in the North Sea: Brent, Forties, Oseberg and Ekofisk. [...] WTI refers to oil extracted from wells in the U.S. and sent via pipeline to Cushing, Oklahoma. [...] [Dubai-Oman is a] “basket” product consisting of crude from Dubai, Oman or Abu Dhabi.

The above is sometimes visualised in the following map:


Prove that if a good is inferior, it is also a Giffen good This was asked in my online midterm test, and I proved it using the fact that a Giffen good and an inferior good behave in the same manner with respect to increase or decrease in purchasing power. Although I know that there exist inferior goods that are also giffen, I'm not able to find a rigorous proof.
Thank you for your help.
Edit 1 :As pointed out in the comments, I feel its necessary to clarify some aspects of the question Firstly, the proof can be mathematical or verbal with the support of a graph. Secondly, this is the original question, it was not given the other way round. The question was preceded by the statement "A Giffen Good is a highly inferior good" and then the question was given.

As pointed out in one of the comments, a descriptive answer to the question is available here. However, here OP has asked for a rigorous proof. It is not true that if a good is inferior, it is also Giffen. On the contrary, if a good is Giffen, it is inferior. Here's a proof for this. Note that I am using some of the properties directly as including their proofs will make the answer undesirably long.
First some definitions:
Let $h_i(\mathbf p,u)$ and $x_i(\mathbf p, m)$ be the compensated (or Hicksian) demand function and Marshallian demand function for good $i$, respectively. Here, $\mathbf p$ is the price vector, $u: \mathbb R^n \to \mathbb R$ be the utility function meeting all the regularity conditions (quasi-concavity, continuity, etc.), and $m$ is the income.
Formally,
\begin{align}
\mathbf h(\mathbf p,u) = \arg \min\limits_{\mathbf x} \, \mathbf {p \cdot x} \\
\text{such that } u(\mathbf x) \geq u
\end{align}
Further, let $e(\mathbf p, u)$ be the expenditure minimizing function for a given minimum utility level $u$. So, $e(\mathbf p, u) = \mathbf{p\cdot h}(\mathbf p,u)$.
For Marshallian demand function:
\begin{align}
\mathbf x(\mathbf p,m) = \arg \max\limits_{\mathbf x} \, u(\mathbf x) \\
\text{such that } \mathbf {p \cdot x} \leq m
\end{align}
Now, from duality we have:
\begin{align}
h_i(\mathbf p,u) \equiv x_i(\mathbf p,e(\mathbf p, u))  \\
\end{align}
Differentiating this equation w.r.t $p_i$:
\begin{align}
\frac{\partial h_i(\mathbf p,u)}{\partial p_i} & = \frac{\partial x_i(\mathbf p,e(\mathbf p, u))}{\partial p_i} + \frac{\partial x_i(\mathbf p,e(\mathbf p, u))}{\partial e}\frac{\partial e(\mathbf p, u)}{\partial p_i}  \\
\end{align}
In the terms, $ \frac{\partial x_i(\mathbf p,e(\mathbf p, u))}{\partial p_i}, \frac{x_i(\mathbf p,e(\mathbf p, u))}{\partial e}$, $e$ is not really being treated as a function, so we replace with $m$, giving:
\begin{align}
\frac{\partial h_i(\mathbf p,u)}{\partial p_i} & = \frac{\partial x_i(\mathbf p,m)}{\partial p_i} + \frac{\partial x_i(\mathbf p,m)}{\partial m}\frac{\partial e(\mathbf p, u)}{\partial p_i}  \\
\end{align}
Rearranging gives:
\begin{align}
\frac{\partial x_i(\mathbf p,m)}{\partial p_i} & =  \frac{\partial h_i(\mathbf p,u)}{\partial p_i} - \frac{\partial x_i(\mathbf p,m)}{\partial m}\frac{\partial e(\mathbf p, u)}{\partial p_i}  \tag1
\end{align}
Now, note the following properties:
(1) From convexity of preferences (or quasi-concavity of utility function), $h_i(\mathbf p, u)$ is non-increasing in $\mathbf p$. Therefore, we have that:
$$\frac{\partial h_i(\mathbf p,u)}{\partial p_i} \leq 0$$
(2) $e(\mathbf p, u)$ is non-decreasing in $\mathbf p$. So we have:
$$\frac{\partial e(\mathbf p, u)}{\partial p_i} \geq 0$$
Using these in $(1)$, we can say:
$$\frac{\partial x_i(\mathbf p,m)}{\partial p_i} > 0 \text{     only if}\,\, \,\, \frac{\partial x_i(\mathbf p,m)}{\partial m} < 0$$

A side note: it seems that at some places (in some comments and the descriptive answer sited above) that a Giffen good is the one that does not follow Law of demand. This is not strictly speaking true. The law of demand pertains to Hicksian demand not the Marshallian demand. As it can be seen in the proof, $h_i(\mathbf p, u)$ is always non-increasing in $p_i$, but $x_i(\mathbf p, m)$ may not necessarily be. So the law of demand always hold under the regularity conditions on preferences.


Why does slowly decaying ACF indicate that a time series is non-stationary? I am a student studying time series econometric online and looking for help talking around some of the principles. There is one point I am trying to understand better.

I've come across some literature online which talks about how non-stationary data series have slowly decaying ACF. The graph of the ACF of VWAP in this post is a good example: https://coolstatsblog.com/2013/08/07/how-to-use-the-autocorreation-function-acf/

Could someone explain why a slowly decaying ACF is an indication that a series is non stationary? I think hearing an explanation will help me get a better understanding of the material.

Thanks very much,
Adrian

The (simplified) definition of a stationary process is that the mean and variance of the process are constant over time.

If the ACF is slowly decaying, that means future values of the series are correlated / heavily affected by past values. If past values of the series are high, the future values should also be high. If the value goes up, future values will also go up (assuming positive auto-correlation here). This means the mean will change over time, which means that the process is non-stationary.


Price level and purchasing power of currency(PPP) This could be a silly question, but I'm a bit confused with this concept.
Don't we say usually the purchasing power(or value) of currency(or money) is low when the price level is high in one country(i.e. negative relationship)?
However, in international economics, it looks like a country's price level has postive relation to purchasing power of it's own currency.
For example, the prices of United States are higher than that of Korea and at the same time, the purchasing power of dollar is higher than Korean won.
How can I understand this kind of contradiction?

Prices in themselves don't mean much when you want to predict purchasing power.
Imagine a loaf of bread costs 100 of country A's monetary units in country A, while it costs 2 of country B's monetary units in country B. This does not tell you anything about purchasing power because you do not know if you could buy a loaf of bread for 100 of country A's monetary units in country B or vice versa.
You also need to consider the currency A to currency B exchange rate, usually denoted by $E_{B/A}$. Then purchasing power/real exchange rate is calculated by
$$
\frac{P_A}{P_B} \cdot E_{B/A} ,
$$
where $P_A$ and $P_B$ are price levels in countries A and B respectively. If this is larger than 1, then using country A's currency one could buy more goods in country B than in country A, while if it is smaller than 1 then the reverse is true.


Utility Functions: Implying endless consumption? Do utility functions imply that if a consumer's income infinite, his consumption should also be infinite? The reason why I'd think this is the case is based on my basic understanding of utility functions.

Recall your cobb-douglas style utility function:

$$U(x_1...x_n)=\prod_{i=1}^nx_i^{\alpha_i}$$

where $0<\alpha_i<1$ and $\sum_{i=1}^n\alpha_i=1$

If our consumer is utility maximizing he should spend all of his income in a given period or even over multiple periods.

A practical application would be to answer the question of whether or not consumption growth in consumption (C) in the GDP equation can grow holding the number of consumers in an economy fixed as argued on the my answer Can an economy grow without its population growing?.

Thank you to   Kenny LJ for inspiring this question.

When the utility function is strictly increasing, it follows that more consumption provides more utility. So it seems evident to say "more income more consumption". But discussing infinity outside mathematics makes no sense. So we want to examine

$$u'(c) > 0\;\;\; \forall c,\;\;\; I\to \infty \;\;\;?\implies? \;\;\;c\to \infty$$

And the answer is "the question is indeterminate" or at least "it depends on the particulars", since what will matter is the rate at which Income and Consumption "go to infinity". If consumption goes faster, it will eventually deplete the infinite income, and if the consumer has infinite horizon, it will end up with no income. Etc.

If we want to entertain concepts from Non-Standard Analysis, and treat "infinity" not as a limiting concept but as something more concrete, then the answer will be the same, because this will be indeterminate also in Non-Standard Analysis, absent the particulars of the situation.


Continuous function in microeconomics In the following picture two preference relations are defined -

Ist preference relation defines lexicographic relation. Though we know that lexicographic preferences doesn't have utility function. They are defined at a point so we cannot define a utility function - is discontinuous. But how can we show it in terms of upper and lower contour set being closed?

Why second one is continuous?

Note - some terminologies -

A binary relation >~ on the metric space X is continuous if, for all x in X, the upper and lower contour sets, { y in X : y > ~ x} and {y in X : x >~ y}, respectively, are closed.

The upper contour set of x is >~ (x) = {y in X : y >~ x}

The lower contour set of x is >~ (x) = {y in X : x>~ y}

Take $y_1=y_2=1$. As the figure below shows, the lower left segment of the boundary of the upper contour set of the lexicographic preference is open.


What are the differences between hedging with swaps, options or futures? For instance if a bank wants to hedge against interest rate risk, it could use interest rate swaps, or options or futures contract. Or in any other example, when a manager is hedging against risks.

Can somebody show it how these differ from each other in an example?

The scope of this question is quite large. There are a lot of ways of hedging interest rate risk. Note that there is a quantitative finance stack exchange, and this question might fit better there.

All rates instruments have a sensitivity to interest rate changes. That is, their value goes up or down in response to interest rate movements.

If we assume that all interest rates move together in parallel (that is, spreads are unchanged), all you need to do to hedge interest rate risk is find instruments that have a value change that cancels the risk you want to hedge.

To a certain extent, most non-credit rates are correlated, and so one can use a wide variety of instruments to hedge.

However, rate movements are not perfectly correlated. As such, hedges may need to be structured to have a sensitivity closer to the risk to be hedged. How that is done is the full time job of interest rate traders. That is, too large a scope to be ansered in a single question here.


In the Cournot Duopoly Model,why is the Equilibrium achieved at 1/3 Rd of the Market Share? I've been reading it for a while,while I do get the action reaction movements,I can't understand as to how the 1/3rd value was reached. Can anyone intuitively or mathematically explain as to how it's necessarily 1/3rd and not say 1/6 or 3/5?

It is not always necessarily 1/3rd. That just happens to be the outcome in the standard textbook example.


Elasticity when the demand function is given Given the demand function, $ q = kp^{-\epsilon} $, how do I calculate the elasticity? As a result, I do know that the elasticity when the demand function is in this form is $ - \epsilon $. But I'd like to know how. I also found a derivation online that proceeded like this:

(1) Take logarithm on both sides
(2) Differentiate on boths ides
(3) You'll get: $$ \frac {\text{d} \ln(q)}{\text{d} \ln (p)} = - \epsilon $$
(4) The LHS of the above equation is simply elasticity.

How does $$  \frac {\text{d} \ln(q)}{\text{d} \ln (p)} $$ represent elasticity?

The definition of elasticity of demand with respect to price is: $\varepsilon_{q,p} = \frac{dq}{dp} \cdot \frac{p}{q}$. So in your demand function we have:

$$q = kp^{-\epsilon}$$
$$\frac{dq}{dp} = -\epsilon kp^{-\epsilon - 1}$$
$$\varepsilon_{q,p} = \frac{dq}{dp}\cdot \frac{p}{q}  = -\epsilon kp^{-\epsilon - 1} \cdot \frac{p}{kp^{-\epsilon}} = -\epsilon$$

And we have the answer you're looking for.


Why GDP is converted to 2010 $US constant in international studies? GDP is a widely-used macro control variable in finance-related papers, especially for international studies. I am wondering what is the reason why GDP is converted to $US 2010 as noted by WorldBank.
From my understanding, in international studies, they convert every currency-related variable to the US dollar to be comparable by using the exchange rate every year. However, I do not understand why they convert to the US dollar in a fixed year when it comes to GDP, and why the chosen year is 2010 in this case?

Why GDP is converted to 2010 $US constant in international studies?

They do that in order to express GDP in real terms. This is incredibly important because nominal GDP is very deceptive since money constantly changes its value. US dollar in 2005 is completely different dollar from US dollar in 2021 so GDP expressed in 2021 US dollars can't be compared to GDP expressed in 2005 dollars. It would be like trying to compare distances in imperial and metric units without any conversion.
For example, suppose that nominal GDP in year 2020 was 200 and in 2021 nominal GDP was 400. Does that mean that economy now produces twice as many goods and services? Well we do not know. It is entirely possible that the economy produces more or it might produce same amount of goods and services or less. This is because nominal GDP is combination of real GDP  and price deflator:
$$\text{Nominal GDP} = \text{Real GDP} × \text{GDP Deflator}$$
Problem is that if you look at nominal GDP you never know if it increases just because prices (i.e. deflator) changed or because we actually have higher output real output, and consequently nominal GDP is next to useless for comparison of output across time.
However, while nominal GDP is useless we can still make comparison across time by calculating real GDP where we get rid of the price level by dividing the nominal GDP with the deflator.
$$ \frac{\text{Nominal GDP}}{\text{GDP Deflator}} = \text{Real GDP} $$
Real GDP can serve as a basis for comparisons across time because real GDP accounts for the change in prices by being expressed in constant dollars (dictated by the year for which deflator is set 1). You can have a look at Mankiw Macroeconomics pp 25 to learn more.

why the chosen year is 2010 in this case?

You always have to choose some year to be a base year for deflator (year when deflator =1). You can choose any year you want. In this case they choose 2010. There might be some situation where you want to set deflator to some specific year for sake of making informative graphical illustration, but other than that the choice of base year is completely arbitrary. If you run empirical regressions with GDP being expressed in 2010 dollars you will get the same results as when the GDP is expressed always in 2005 dollars.


Data for currency crises Dear StackExchange users,

I am currently studying currency crises and for that I need data from 1980-2018. I have used data from IMF, OECD, BIS, WORLD BANK, etc., but I still have some missing data especially for Real effective exchange rate (REER), Reserves, discount rate for countries such as: Argentina, Peru, Thailand, Australia, Georgia, Ukraine, Russia, Indonesia, Korea, etc.

Does anyone know any good online source or any database from well-known papers where I can find this kind of data.

P.S. I also need some data and any idea how to calculate financial contagion.
A dataset and do file would be really helpful for that.

Thanks in Advance,
Arbnor Gashi

I would begin my search by finding related papers in the Journal of Applied Econometrics that contains currency as a key word.

After a related paper is identified, I would to go to the data archive URL: http://qed.econ.queensu.ca/jae/ to see if the data in the paper were uploaded there.

Two papers I found that are related to financial contagion (and possibly leading to a relevant data set for your study):

Eichengreen, B., Rose, A.K. and Wyplosz, C., 1996. Contagious currency crises (No. w5681). National Bureau of Economic Research.
Dungey, M. and Renault, E., 2018. Identifying contagion. Journal of Applied  Econometrics, 33(2), pp.227-250.

You can also use the references therein to find more related papers. I hope it helps so far.

P.S. If your school has a subscription to Bloomberg Terminal, I believe those currency data can be found in the Terminal.


Term for the phenomenon when an undesirable but competitive strategy dominates For example, in some sports, the use performance enhancing drugs is considered undesirable, but it is difficult or impossible to be competitive unless you use performance enhancing drugs.  So, the use of performance enhancing drugs becomes this sort of undesirable dominant strategy that is a struggle to control.

Other examples abound.  Is there a succinct term in the economics field for such phenomena?

A game outcome that is Pareto optimal or Pareto efficient is one where no one player can be made better off without making at least one player worse off. So a Nash equilibrium can easily be Pareto sub-optimal (or Pareto inefficient), which means that it is possible to one player can be made better off without making at least one player worse off. However, "The interesting thing about the prisoner’s dilemma is that all options are Pareto optimal except for the unique equilibrium, which is for both to defect."


How do you differentiate between a business expense and an investment for the purpose of profit reporting? As I understand it, in a company, profit will be invested, either into capital assets or into projects.
How do you distinguish between an expense, and reinvesting profits back into company projects?
For instance, if Pfizer makes \$100B in revenue, spends \$80B on business expenses doing so, then spends the remaining \$20B on research for a new drug, would they have made \$20B in profit? or \$0?

In economics profit is simply defined as total revenue minus total costs or:
$$\Pi = TR-TC$$
In your case if

Pfizer makes \$100B in revenue, spends \$80B on business expenses doing so, then spends the remaining \$20B on research for a new drug.

from economic perspective the profit would be:
$$\Pi= TR -TC = {\\\$}100B - ({\\\$}80B+{\\\$}20B) = 0B$$
So from economic perspective the profit will be zero. (However, note the economic perspective is not necessary the same as an accounting perspective - I mention that since you reference reporting, but in this case accounting profit would also happen to be zero if $20B$ is on accounts treated as cost).


Basic question on trade based on comparative advantage The following question is taken from Economics: Principles and Applications 6th Edition, by Hall and Lieberman.

This question about applying the theory of comparative advantage between a hypothetical trade situation between US and China. Trade between these two countries involve only two goods - soybeans and T-Shirts. It has been established that the US has CA in soybean production whilst China has CA in T-Shirts. It is further known that, for the US, the opportunity cost of producing 100 bushels of soybeans is 200 T-Shirts. Now consider Qtn 9b in the top image.

My working is in bottom image and my final answer is that the US consumers will gain 70 more T-Shirts for consumption, compared to the situation before trade. However, in  an answer I found online, the US has 270 more T-Shirts available for consumption, compared to the situation before trade.

My answer was 70 more T-Shirts. Consumption experiences a net gain of 70. The raw gain in consumption due to importing from China is 270 but that is AFTER the US incurs the opportunity cost of producing 100 bushels of soybeans (due to specialisation) - which is decreasing production of T-Shirts by 200.

Where did I go wrong?

You did not factor in the 4 Darwinian goals of global trade:

Find foreign markets to absorb excess production, that is, where excess production can be dumped.
Extract foreign resources at low prices.
Deny geopolitical rivals access to these resources.
Open foreign markets to domestic capital and credit so domestic capital can buy up all the productive assets and resources.


Cash and negative interest rates Recently, I read an IMF blog on how the negative interest rate policy can be implemented feasibly here. I don't really understand what they are saying in this paragraph:

  When cash is available, however, cutting rates significantly into negative territory becomes impossible. Cash has the same purchasing power as bank deposits, but at zero nominal interest. Moreover, it can be obtained in unlimited quantities in exchange for bank money. Therefore, instead of paying negative interest, one can simply hold cash at zero interest. Cash is a free option on zero interest, and acts as an interest rate floor.

What I guess they are trying to say is that when cash is available, people need not take up loans and hence, the availability of cash diminishes the effectiveness of the policy. Could someone please help to enlighten me on this?

Actually they're saying that, when cash is available, people need not to deposit their money into the bank, and hence is "guaranteed" (not taking into account risks associated with holding on to cash, like fire or getting stolen) a 0% interest rate.

Having cash, therefore, means that if the deposit rate goes into the negative territory (you're charged to deposit your money), then people could simply stock cash at home. As a result, the interest rate could not go much into the negative territory.


How could the Euro zone be broken up in an ordered way? Let’s assume that the members of Euro zone all agreed that it would end in 18 months time with each country getting its own currency.

What process could be put in place to allow this to happen without causing of lots instability?

No Time To Argue

Most importantly, there cannot be an "18 months period of notice". Tt has to be decided suddenly and there cannot be any period in which individuals could respond to the new plan by withdrawing their money and moving cash from one of the member countries to any of the others.

New Currencies

Each country has to have its own currency. These currencies should be free floating against each other, which on the other hand means that some will value up and some down. That is, Germany's new currency will probably value up against whatever Greece will have.

Capital Controls

Therefore, it will be of higher value to have your Euro exchanged for German money than for Greek money. Any bank account will have to immediately be translated into local currency. Also, no one will be allowed to move cash Euro between the member countries.

One way to immediately establish the new currency would be to simply stamp the old money with country specific stamps.

Citation

Note that Greek's new finance minister implied that their train of thoughts follows exactly these lines of thinking [my own translation]:

  Greece is not going to leave the currency union, as it cannot go back
  to the path of development on which it was on, hadn't it joined the
  union. An exit would lead to chaos in any case: For the moment, there
  is no new Greek currency as a new Drachm. Preparations for the
  introduction of such a currency would take months and would have the
  same effect as announcing a depreciation several months in advance.
  But you can only have a depreciation over night and unexpectedly,
  otherwise there are massive movements of capital flight/export.

From this german article:

  Die Währungsunion verlassen soll Griechenland nach den Worten von
  Varoufakis aber in keinem Fall. Denn damit könne das Land nicht auf
  den Entwicklungspfad zurückkehren, den es ohne Eintritt in den
  Euroraum genommen hätte. Ein Austritt habe auf jeden Fall Chaos zur
  Folge. Denn gegenwärtig gebe es keine griechische Währung wie eine
  neue Drachme. Vorbereitungen für die Einführung einer solchen Währung
  würden Monate dauern und hätten die gleiche Wirkung wie die
  Ankündigung einer Abwertung mehrere Monate im Voraus. Doch eine
  Abwertung könne es immer nur über Nacht und unerwartet geben, sonst
  gebe es riesige Bewegungen zum Kapitalexport, warnt er.


Labor as a commodity Can anyone enlighten me if there are economic theories where labor is considered as a commodity like cloth and wine in the Ricardo theory, so that it can be exported and imported similarly to other commodities? I would be grateful for references.

So in modern English, a commodity is a raw material for production or basic agricultural good that can be exchanged for money. Labor, by this definition, is neither a raw material, no one grinds humans up to build stuff, I hope; an agricultural good, similar reasoning; nor exchangeable for money, as slavery and indentured servitude is illegal and efficient in most places. (Letting people make their own work decisions, or at least not forcing them to work, is good, generally speaking.)

Even with a more generously wide definition of a commodity, commodities are generally seen to be fungible, which means you cannot easily differentiate between the good/service based on region, or that they all of each type of commodity is seen as equivalent. So if you are willing to say that all labor is equivalent...

Basically, labor is generally not seen as a commodity.


How/why does foreign investment get scared by the monetary policy? In an interview with Daron Acemoglu, he says "the hot money which was floating through Turkey has stopped after FED's declaration that we are going to give much more attention on monetary policy".
Basically I know some fundamental things like monetary policy interests with the foreign currency but dont get exactly how does it effect directly. Why or how do foreign investments get scared by monetary policy?

Monetary policy affects the value of a country's currency (e.g. interest rate & money supply changes affect the value of cash).
Foreign investment is made by purchasing that country's currency (via currency exchange), then purchasing financial instruments in that country (stocks, exchange traded funds, bonds, etc.)
If a country decides to lower their currency's value over time (to make their goods cheaper to foreigners, for example), then any foreign investment would be exposed to currency devaluation.
A concrete example…

Turkish commodity market, sells 1 ton of cotton for 230 Lira (~$100USD) on January 1, 2015.

US investor exchanges $100USD into 230 Lira, buys 1 ton cotton on 1/1/2015.

Turkey decides to lower currency value by decreasing interest rate, increasing money supply, reduce reserve requirements. Value of Lira drops from 230 Lira for 100 USD to 270 lira for 100 USD.

US investor sells 1 ton cotton a year later for 250 Lira.  Exchanges Lira to USD. Receives $92.60USD.

What would normally be a modest ~9% gain from price appreciation of the cotton from 230 to 250 turns out to be an ~8% loss due to currency devaluation which occurred from monetary policy changes.
If a foreign investor isn't confident that monetary policy will drive up a country's currency value (in which they will be investing), then they should rightly be scared by monetary policy changes a government plans to make.


Negative consumer externality vs demerit good - what's the difference? The example I was given for each was cigarettes.

What market may have negative consumer externalities but is not a market for a demerit good?
What is a type of demerit good that may not have a negative consumer externality?

Demerit goods are goods where it is agreed by society that consumption is harmful for the consumer yet it is still consumed due to bounded rationality or because you disagree with society while negative consumer externalities occur when actions of a consumer is harmful for society.

Goods that are demerit but may not have negative consumer externality:

Any type of unhealthy food. E.g. cinnabuns.

Carcinogenic stuff, alcohol, etc.

Basically anything you regret having consumed a few hours later.

If consumption of these goods do not harm society, then there are no negative externalities, as long as no one else cares about the consumer :'(

Good that may have negative consumer externality but may not be a demerit good:

Loud music


The United States' position on the Laffer Curve According to a 2012 IGM panel (cf. reference below), most experts believe that a federal income tax cut would lead to a higher GDP in five years, ceteris paribus. Is this effect purely Keynesian, and based on a presumption that the U.S. was still recovering from the recession and that greater fiscal stimulus was called for, or does it truly reflect a belief among the majority of mainstream economists that the U.S. federal tax regime is sitting on the wrong side of the Laffer curve as the title indicates?

Source: http://www.igmchicago.org/igm-economic-experts-panel/poll-results?SurveyID=SV_2irlrss5UC27YXi

Question B in the link answers your question: most participants believe that taxable income would not rise enough to offset the tax cut, indicating that they do not believe we are on the wrong side of the Laffer Curve.


Measuring inequality at the zip code or county level in the United States? I am trying to calculate a statistic for inequality at the zip code or county level in order to merge with another data set. I am using IRS SOI data, but the data given is returns by AGI bin (i.e., 1-25k, 25-50k,..., 200k+)

This does not seem specific enough to calculate a Gini coefficient because there is no microdata available to the general public and percentile shares are not given.

How could I calculate a measure of inequality from the data in the IRS SOI datasets?
Are there better methods to approach this problem?

I'm not sure specifically what data you have but it sounds like you have enough data to calculate a rough gini estimate.

Gini is equal to: (The average variance for incomes) / (2 * the mean)

Since Gini is a standardized indicator and not dependent on the level of income, just the variance, you can construct a rough gini metric using your data.

If you assume 0-25K = 0, 25K-50K = 1, 50K-75K = 2 etc. You can treat the buckets as incomes. You can then calculate the average variance between the incomes weighted by the number of individuals in each bucket and divide it by 2 X the average income (bucket). In doing so you've created a rough gini coefficient for each zipcode.

You should note that this statistic is rough and not perfectly accurate since it ignores any variation in distribution of income within the bucket. It may be that the 25K-50K bucket has most of its individuals at 40K income and few in the 25K income which would negatively bias your gini estimate.

Assuming this is for a research paper this methodology should be discussed and the possible flaws with this estimate should be disclosed. It does however provide the best approximation for inequality given the information you have.


Example of an economy where Equilibria may not be efficient, where one agent is altruistic I'm looking for a theoretic example of an economy where one agent is altruistic, while the others are not, that would make a walrasian equilibrium not efficient.

This is an old question. The first example of inefficiency caused by altruism that I know of is due to Winter, S. (1969). A Simple Remark on the Second Optimality Theorem of Welfare Economics. Journal of Economic Theory, 1, 99–103, but I am sure others were around before that.
Now, the example in Winter(1969) does not answer your question because it features altruism for all agents in the economy. As mentioned by The Almighty Bob you can find another example in Heidhues and Riedel (2007). Another good reference is Dufwenberg, M., Heidhues, P., Kirchsteiger, G., Riedel, F., & Sobel, J. (2011). Other-Regarding Preferences in General Equilibrium. The Review of Economic Studies, 78(2), 613–639, which is a summary paper of Heidhues and Riedel (2007) and contributions on the topics by the other authors.
Without more constraints on the preferences, it is not hard to find an example satisfying the conditions of your question. I am sure you could find it yourself, if you haven't already. But in order to make the answer complete here is one:

$\Omega \equiv \{(1,1),(1,1)\}$ (individual endowements)
$U_1 \equiv \min \{x_1,y_1\}$ (perfect complement, no altruism)
$U_2 \equiv \min \{x_2, y_2\} + 2*U_1$ (perfect complement, with (strong) altruism toward $1$)
Walrasian equilibrium = {(1,1),(1,1)}, together with whatever (finite) relative price you like.

I guess it is clear that the Walrasian equilibrium is not Pareto efficient. Notice that this "result" highly depends on the definition of the consumption space. If you add

Donation of good $x$ from $2$ to $1$, and
Donation of good $y$ from $2$ to $1$,

to the consumption space, then you would recover efficiency (although it might take a little care to define a meaningful notion of Walrasian equilibrium in this case).


Why does a current account deficit contribute to making a country a "sitting duck" for currency speculators? George Soros had this to say about the factors surrounding his famous short of the British pound:

The U.K. had a large current-account deficit…, modest FX reserves and
no capital controls to rebuff the speculators,” he said.“In short, it
was a sitting duck.

I'm thinking maybe the opposite would be true. The fact the UK had a current account deficit would seem to imply a depreciating currency, with cheaper exports and more expensive imports. At this juncture, I would think more investors would buy in to the currency, enticed by the prospect of asset appreciation. So wouldn't it make more sense to view current account deficits as having appreciating pressures (rather than depreciating)?
I doubt my econ is better than a billionaire, so I'm hoping (and anticipating) someone can explain the flaw in my logic.
Question
Why does having a current account deficit contribute to making a country vulnerable to hedge funds shorting the currency?
Note: I did not stipulate assumptions about the currency regime in question. Base case can be for a peg (the system used by the GBP at the time), but if other regimes (floating, currency board) merit a look, I'll leave them as optional.

I do not think this answer is definitive, but want to point out that there are two very different regimes: pegged or floating currencies.
For a pegged currency, the central bank (or similar body) is attempting to keep the currency value pegged to an external currency or gold. (I am assuming this is a traditional peg, and not a currency board.) A current account deficit implies a capital inflow, and implies a drain on central bank reserves if the private sector is not acting to support the peg. Since the central bank cannot create whatever it is pegging at will, it would eventually be forced off the peg or to devalue. (It can absorb inflows indefinitely.) One can look at the history of the Gold Standard/Bretton Woods era to see this, or search for the literature on “rational currency runs.”
For a floating currency, the currency value can go up or down. The currency market is a market, and at least some weak version of the Efficient Markets Hypothesis applies - it is not easy to make money with simple rules based on public information (other than taking on risk premia, like owning equities for the long term). One cannot look at central bank foreign currency reserves and decide that the currency will move one way or another. Presumably, a country that loses export competitiveness will eventually have its currency lose value, but we can look at countries like the United States or Australia and see that they can support current account deficits for long periods without anything too interesting happening to the currency. That said, many people extrapolate the pegged situation to floating currencies in market commentary.
Since there’s not a whole lot of interest in articles that state “we cannot find a relationship between the current account deficit and the currency value,” it would be harder to find literature on the subject.


What are estimates of the elasticity of demand for credit with respect to interest rates? When interest rates go up one percent (not one percentage point), what happens to demand for credit? I've only been able to find two papers in this area:

Gross and Souleles (2001) study credit cards and find -1.3%
Follain and  Dunsky (1997) study mortgages and find as -1.5 to -3.5

There are two margins here of potential interest. First, shocks to one borrowing rate can shift borrowing into other sources, leading to overestimation of total debt elasticities. Second, shocks to borrowing rates can lead to a mixture of lower spending overall and more cash spending. Overall wealth is an interesting example of the other the latter, because wealthy households can choose to spend less or borrow less in response to higher rates while poor households can only spend less.

Are there papers I've missed that study this effect? Of particular interest are studies that additionally explore these effects on different sub-populations.

These papers look relevant, to one degree or the other:

Karlan, D., & Zinman, J. (2009). Observing unobservables: Identifying information asymmetries with a consumer credit field experiment. Econometrica, 77(6), 1993-2008.
The authors write:"We estimate the presence and importance of hidden information and hidden action problems in a consumer credit market using a new field experiment methodology. We randomized 58,000 direct mail offers to former clients of a major South African lender along three dimensions (...) These three randomizations, combined with complete knowledge of the lender's information set, permit identification of specific types of private information problems. (...) We find strong evidence of moral hazard and weaker evidence of hidden information problems."

Mandell, L. (1971). Consumer Perception of Incurred Interest Rates: An Empirical test of the efficacy of the Truth-In-Lending Law. The Journal of Finance, 26(5), 1143-1153. "The purpose of this article is to use national sample survey data to measure
the effect of the Truth-in-Lending Law (enacted in 1969) on the consumer’s knowledge of interest rates that he is actually paying on an installment loan.(...)
Aside from measuring the overall effect of the law on all persons, analysis
of various population subgroups will be made to see whether the law has had
differential effects upon the interest rate perception of persons based upon
personal characteristics such as age, income, amount borrowed, total debt and
education."

Calem, P. S., & Mester, L. J. (1995). Consumer behavior and the stickiness of credit-card interest rates. The American Economic Review, 1327-1336.
The authors present empirical evidence (from a 1989 Survey) that supports the "stickiness" of credit card interest rates, attributing it, as they write, to "(i) consumers facing search costs; (ii) consumers facing switch costs; and (iii) firms facing an adverse-selection problem if they were to unilaterally reduce their interest rates."

Ausubel, L. M. (1991). The failure of competition in the credit card market. The American Economic Review, 50-81. The original paper to which the previous one provided additional support. It contains both theoretical discussion and empirical evidence, as well as counterfactual calculation (what "would" the interest rates be if perfect competition held in this market).


feature of indifference curve The characteristic feature of indifference curve is that it will not touch the X axis or Y axis. But as a special case it will touch the Y axis if the combination is between Money and Commodity. "If money is taken on Y-axis, then IC curve can touch oy-axis" here we have taken 'money' on Y-axis and 'commodity' on X-axis. Here my doubt is could we use indifference curve for one commodity? If so please explain me with an example.

An indifference curve can touch the axes, take for example the case of perfect substitutes, if the consumer his utility is given by
 U=x1+x2
 then obviously he is indifferent between bundle (10,0) and (0,10). So not touching the axes is not a characteristic of indifference curves as such, even though in the case of Cobb-Douglas functions it holds.

As for your other concern, whether an indifference curve can take as input only one good, with the other input being money: this is perfectly possible, it is even a more general case than the indifference curve for two goods. In the case of the inputs x1= a good and m=money held by the consumer we can formalize the utility maximization problem in the following way:
max U=u(x1,m)
Subject to the constraint: b=p1x1+m
As you see the standard form can be used with just one change: the price of a unit money held is of course 1.

And now the more general case, again let x1 be a good the consumtion of which we are interested in and now let y be the MONEY SPENT on all other goods. Now again we can use the modification of the budget constraint above. That is: price of y is 1.
In short: anything can be an input in an utility function, just think about your own preferences: you dont just enjoy goods, you enjoy holding money and giving to charity etc. but also spending time with friends/family, with some modifications all this can be put in the form of a utility maximization problem and thus an indifference curve can be constructed for any two inputs, holding other inputs fixed.


Would Pilots and Air travel be considered complementary? Now, my economics teacher and I have a disagreement. According to theory, as the price of air travel (airline tickets) increases, the demand for pilots will decrease as well because fewer people will be willing and able to buy the same airline ticket with an increased price, this should result in a fall of quantity demanded of airplanes and thus fewer pilots will be required/demanded. Thus, an increase in the price of air travel results in a decrease of demand for pilots. Thus, pilots and air travel are complimentary. My teacher thinks that pilots and air travel are not complimentary. Can anyone confirm my logic and economic claims?

Consumers buy airline tickets but don't hire pilots, so I wouldn't call those two complementary in the usual sense of "complementary goods".


Perfect complement preferences in an exchange economy So I have an exam in a bit, I understand that to find the optimal choice you have to equate tangent of the two indifference curves. However, if the other indifference curve is a perfect complement, what is MRS? I calculated the MRS as infinity/infinity.

Take a look at the question below:

Suppose Jane has an endowment of 2 units of x and 2 units of y, and has preferences given by utility function $u_J(x_J , y_J) = x_J^{2/3} \cdot y_J^{1/3}$ . Suppose Derek has an endowment of 4 units of x and 1 unit of y, and has preferences given by the utility function $u_D(x_D, y_D) = \min(x_D, 2 y_D)$.

On an Edgeworth box diagram, indicate the set of Pareto efficient allocations. Explain how it is determined.
Compute the competitive equilibrium (prices and quantities) for the exchange economy

Was I right about the MRS being infinity over infinity? If yes, then how would I compute the Pareto Efficient outcome when I cannot equate the MRSs? I was thinking that the solution will be on one of the vertexes of Derek's indifference curve but I'm not sure (because kinks are not diff).

Any ideas?

Set of Pareto Efficient Allocations consists of feasible allocations $((x_J, y_J), (x_D, y_D))$ satisfying $y_J=\displaystyle\frac{x_J}{2}$.

Competitive Equilibrium is the price $(p_x, p_y=1)$ satisfying the following conditions:

Budget Requirement: $p_xx_J+ y_J = 2p_x + 2$ and $p_xx_D+ y_D = 4p_x + 1$
Equilibrium Conditions: $\displaystyle\frac{2y_J}{x_J} = p_x$ and $y_D=\displaystyle\frac{x_D}{2}$

Solving the system of equations we get equilibrium price vector as:
$(p_x, p_y) = (1,1)$
and the equilibrium allocation is
$((x_J, y_J), (x_D, y_D)) = \displaystyle \left(\left(\frac{8}{3}, \frac{4}{3}\right), \left(\frac{10}{3}, \frac{5}{3}\right)\right)$


How to compute elasticity of substitution in labor market of blacks and whites using experience-education groups? I'm reading "Competition in the Promised Land – Black Migrants in Northern Cities and Labor Markets", by Leah Boustan, and I'm trying to understand her computation of black and white elasticity of substitution in labor market
She uses a Cobb-Douglas function:
$$Y=AL^{\alpha}K^{1-\alpha}$$
and then defines aggregate labor as:
$$L=\left(\sum_{e=1}^{n} \left(L_{e} \theta_{e}\right)^{\frac{\delta - 1}{\delta}}\right)^{\frac{\delta}{\delta - 1}}$$
aggregate labor by educational group as:
$$L_{e}=\left(\sum_{\substack{1 \leq e \leq n\\1 \leq x \leq m}} \left(L_{ex} \theta_{ex}\right)^{\frac{\eta - 1}{\eta}}\right)^{\frac{\eta}{\eta - 1}}$$
and aggregate labor by experience and educational group by:
$$\left(\left(L_{exb} \theta_{exb}\right)^{\frac{\sigma - 1}{\sigma}} + \left(L_{exw} \theta_{exw}\right)^{\frac{\sigma - 1}{\sigma}}\right)^{\frac{\sigma}{\sigma - 1}}
$$
Then she derivates the production function relative to $L_{exr}$ (where $r=w,b$) and obtains:
$$ln w_{exr}=ln(A^{\frac{1}{\alpha}}k^{\frac{(1-\alpha)}{\alpha}})+\frac{1}{\delta}\cdot ln(L)+ln\theta_{e}-(\frac{1}{\delta}-\frac{1}{\eta})\cdot ln(L_{e})+ln\theta_{ex}-(\frac{1}{\eta}-\frac{1}{\delta})\cdot ln(L_{ex})+ln\theta_{e_{exr}}-\frac{1}{\delta}\cdot ln(L_{exr})$$
I cannot figure out how to reach this expression. I thought what I need is just 1) to substitute the L terms backwardly, 2) take the derivative, and 3) apply log. The substitution gives:
$$A K^{1 - \alpha} \left(\left(\sum_{e=1}^{n} \left(\theta_{e} \left(\sum_{\substack{1 \leq e \leq n\\1 \leq x \leq m}} \left(\theta_{ex} \left(\left(L_{exb} \theta_{exb}\right)^{\frac{\sigma - 1}{\sigma}} + \left(L_{exw} \theta_{exw}\right)^{\frac{\sigma - 1}{\sigma}}\right)^{\frac{\sigma}{\sigma - 1}}\right)^{\frac{\eta - 1}{\eta}}\right)^{\frac{\eta}{\eta - 1}}\right)^{\frac{\delta - 1}{\delta}}\right)^{\frac{\delta}{\delta - 1}}\right)^{\alpha}
$$
But the derivative of this expression relative, for example, to $L_{exb}$ is a equation very different from the expression showed by the author (even after the log).
I must be making a very silly mistake here, but how can I get the desired expression from the equations of L? Is there a textbook where I can find a discusson about elasticity of substitution between demographic groups?
EDIT:  paper version of this part of the book can be found here. In my research I noted that Boustan's work is based on Ottaviano (2006), and Card and Lemieux (2001).
Here is a jupyter notebook with the equations

I dont want to be rude but the only equation you copied correctly is the
productivity augmented Cobb-Douglas production function.
Equation 2 is equation 2 from Ottaviano, Peri (2008) (on page 8) it says:
$$L=\left(\sum_{e=1}^{n} \theta_{e}L_{e}^{\frac{\delta - 1}{\delta}}\right)^{\frac{\delta}{\delta - 1}}$$.
In the remaining equations $\theta$ is not under the exponent as well:
$$L_{e}=\left(\sum_{\substack{1 \leq e \leq n\\1 \leq x \leq m}} \theta_{ex} L_{ex} ^{\frac{\eta - 1}{\eta}}\right)^{\frac{\eta}{\eta - 1}}$$
Is the equivalent of Ottaviano, Peri (2008) equation 3 on page 9 and
$$\left(\theta_{exb} L_{exb}^{\frac{\sigma - 1}{\sigma}} + \theta_{exw} L_{exw} ^{\frac{\sigma - 1}{\sigma}}\right)^{\frac{\sigma}{\sigma - 1}}
$$
Is the equivalent of Ottaviano, Peri (2008) equation 4 on page 9 and
the expression for the logarithm of the wage is equation 2 on page 11 of Boustan(2008):
$$ln w_{exr}=ln(A^{\frac{1}{\alpha}}k^{\frac{(1-\alpha)}{\alpha}})+\frac{1}{\delta}\cdot ln(L)+ln\theta_{e}-(\frac{1}{\delta}-\frac{1}{\eta})\cdot ln(L_{e})+ln\theta_{ex}-(\frac{1}{\eta}-\frac{1}{\sigma})\cdot ln(L_{ex})+ln\theta_{e_{exr}}-\frac{1}{\sigma}\cdot ln(L_{exr})$$
Whith the correct expressions its all boring algebra:
Fn. 29 on page 11 says:

Following Ottaviano and Peri (2006), I first express output as a function of the capital-output ratio (κ = K/Y)

Thus we have:
$Y=AK^{1-\alpha}L^{\alpha} \Leftrightarrow Y=A\big(\frac{K}{Y}\big)^{1-\alpha}L^{\alpha}Y^{1-\alpha} \Leftrightarrow \\Y^{\alpha}=Ak^{1-\alpha}L^{\alpha}\Leftrightarrow Y=A^{\frac{1}{\alpha}}k^{\frac{1-\alpha}{\alpha}}L$
Observe that:
$$W = x^{\frac{\zeta}{\zeta-1}} \Leftrightarrow \frac{\partial W}{\partial L_{exr}} = \frac{\zeta}{\zeta-1}x^{\frac{1}{\zeta-1}}\frac{\partial x}{\partial L_{exr}} =\frac{\zeta}{\zeta-1}W^{\frac{1}{\zeta}}\frac{\partial x}{\partial L_{exr}} (*)$$
$\omega_{exr} = \frac{\partial Y}{\partial L_{exr}} = A^{\frac{1}{\alpha}}k^{\frac{1-\alpha}{\alpha}}\big(\sum_{e=1}^n\theta_eL_e^{\frac{\delta-1}{\delta}}\big)^{\frac{1}{\delta-1}}\theta_eL_e^{\frac{-1}{\delta}}\frac{\partial L_e}{\partial L_{exr}} \overset{(*)}= A^{\frac{1}{\alpha}}k^{\frac{1-\alpha}{\alpha}}\theta_e\frac{\partial L_e}{\partial L_{exr}}L^{\frac{1}{\delta}}L_e^{\frac{-1}{\delta}}(1)$
$\frac{\partial L_e}{\partial L_{exr}} \overset{(*)}= \theta_{ex}\frac{\partial L_{ex}}{\partial L_{exr}}L_e^{\frac{1}{\eta}}L_{ex}^{\frac{-1}{\eta}} (2)$
$\frac{\partial L_{ex}}{\partial L_{exr}} \overset{(*)}= \theta_{exr}L_{ex}^{\frac{1}{\sigma}}L_{exr}^{\frac{-1}{\sigma}} (3)$
Plug back (2) and (3) into (1), take logs and you will obtain the result.
NOTE I dont quite understand why the derivative of $k = \frac{K}{Y}$ wrt L is not taken here.


Why low labour productivity for Govt Services in UK and USA in 2000s? My labour productivity data for USA and UK show that the "Government services" sector for both countries are below their economies' average.

This trend is observed in the 2000s.

Are there any reasons for the low labour productivity in the sector for the 2 countries?

Referring me to some reliable sources will be helpful too.

Thank you

The biggest issue (in the US national accounts, at least) is the fact that government production is recorded on a cost basis rather than a market value of output basis (due to the lack of market values for many government services).

From the NIPA Primer, pages 2-3:

  GDP is composed of goods and services that are produced
  for sale in the “market”—the generic term referring
  to the forum for economic transactions—and of
  nonmarket goods and services—those that are not sold in
  the market, such as the defense services provided by the
  federal government, the education services provided by
  local governments, the emergency housing or health care
  services provided by nonprofit institutions serving
  households (such as the Red Cross), and the housing services
  provided by and for persons who own and live in
  their home (referred to as “owner-occupants”).

  [...]

  In cases where there are no similar market transactions
  available to impute a value of the good or service being
  produced, the output of these services is valued by estimating
  the costs (such as employee compensation and
  purchases of materials and supplies) of producing the
  good or service.

As a result, any direct government production is recorded as though the workers add no value that they do not capture through their salaries. Given the technical difficulties (not to mention the political issues) that arise when one tries to come up with an alternative estimate of the value of government production, this is probably the most neutral approach, and the approach that is most accurate in differences, though it obviously gets the level wrong.