If I shred a $20 bill, is society poorer? What is the effect on the real economy? If the answer is yes, society is poorer, then the converse must hold true: that the government could make us all wealthier by simply printing money.
However, a collapse in the money supply must have an effect on the real economy. One less Chipotle burrito gets sold. More formally, Milton Friedman's entire thesis was that a collapse in the money supply caused the Great Depression.
Which is it, yes or no? And what are its reverberations throughout the "real" economy?

You have to make distinction between short-run and long-run.
Short-run: In short-run money is not neutral, meaning that in short-run money and other nominal variables can affect real output. A one example why this is true are sticky wages. In presence of sticky wages wages (for example due to nominal contracts that take time to renegotiate) a fall in money supply and deflation would lead to increase in real wages above the equilibrium level. This would cause excess unemployment and loss of output until wages would finally adjust.
So in short-run amount of money and nominal variables in general have a real effect on economy although this effect is not as simple and clear cut as saying that shredding one bill will lower output and printing one more will increase it as the effect of changes in money supply depend on macroeconomic conditions (for example at zero lower bound increases in money supply will be mostly offset by drop in velocity of money  see Krugman; 1998). However, discussing fully the reverberations money have in the short run is beyond the scope of SE answer. I recommend having look at Blanchard et al. Macroeconomics: an European Perspective chapters 3-10, 20-22 and 24 with emphasis on chapters 3-10 which have the core.
Long-run: In the long-run you get the classical dichotomy and money are neutral. This is almost definitional since long-run is in macroeconomics defined as a long period of time where among other things prices have time to adjust and are flexible.
This can be best seen from the AS-AD diagram below that I took from Mankiw's Principles of Economics:

As you can see short-run aggregate supply is increasing in aggregate price level so money are not neutral and can affect the level of production. However, the long-run aggregate supply is orthogonal on price level. No matter what the aggregate price level is the production will be always same and determined by the production possibilities of an economy (i.e. determined by real factors that affect the production possibilities of an economy).
This is intuitive as economy ultimately cannot produce more than it is possible given its production function and resource constraints. If an economy faces following production function $F(L) = 5\sqrt(L)$ and we have $100$ units of labor then we cannot produce more than $50$ units of output no matter how much money we print or destroy. Volume of money in circulation in the long-run does not make factors of production more productive nor it increases the stocks of factors production so by itself it can’t change how much economy can produce in the long-run.


how is a trade imbalance related to domestic savings? I was confused by a statement in an article from Paul Krugman in the NY Times:

  The reason America runs persistent trade deficits isn’t that we’ve
  given away too much in trade deals, it’s that we have low savings
  compared with other countries.

Source: NYT

Intuitively I thought a trade imbalance was simply exports minus imports, and had nothing to do with savings.  I saw some referenced equation demonstrating its "truth", but I still don't understand it.

My questions:

Is he talking about personal savings, as in how much is in people's bank accounts?  Or is it about government savings, as in taxes minus expenditures?
Any hints to help intuitively shed light on how savings would affect a trade imbalance, which seems unrelated to me?

When Krugman talks about savings, he is presumably talking about the difference between production and consumption (personal consumption and government consumption) in a country as a whole. Although measured in monetary terms, this is really about stuff, i.e. goods and services. It is not about personal savings of money in a bank.

Some of the difference will be used to make things producing stuff for the future, i.e. as investment. In a closed economy, in this sense savings must equal investment, since building up stocks of stuff for future use would also count as investment, while simply wasting the excess stuff would make it not count as valuable production.

In an open economy, it is possible for production and use (consumption and investment) to differ, and so it is possible for savings and investment to differ.   If use exceeds production, i.e. investment exceeds saving, the extra stuff has to come from somewhere, namely as net imports of stuff.  If production exceeds use, i.e. saving exceeds investment, then the extra stuff has to go somewhere, namely as net exports.

So what Krugman is saying is that having a trade deficit is associated with production being less than use, and so with savings in this sense being less than investment.  So he is suggesting that the US trade deficit is associated with low savings.  Using his definitions, that is almost tautologically true as a matter of arithmetic. It is also more coherent than Trump's simple exports good, imports bad, which is little more than saying send stuff abroad but do not get stuff back.

Krugman's next step is to say that the US trade deficit is a consequence of low savings. That is putting a suggestion of causality into the relationships, something much less obvious. It also raises the question of how to change the position; elsewhere it appears that Krugman would not support efforts to reduce consumption or investment. He would welcome increased production; so too would Trump.


Inflation, cause or result of monetary emission? The argentine economist Fernanda Vallejos, while trying to protect the government because of the inflation, the following:

  Inflation is not the result but the cause of monetary emission. As
  there's inflation (because of other reasons not important here),
  people need more money and the central bank needs to print more money.

How can you argue against that?  As it seems to be the opposite of modern theory on inflation.

Context: This is in Argentina, where it has an important deficit, monetary emission and inflation are around 40%.

The problematic part of the statement, is the "because of other reasons not important here" part . In other words: "ignore general equilibrium" -which is an unacceptable statement to make when discussing government policy and actions.

Consider the naive quantity theory of money:

$$PQ = VM \tag{1}$$
$P$ is the price level, $Q$ is output produced (measured in quantity), $M$ is money supply, and $V$ is "velocity of money", an indicator of the "transactions technology" in the economy, how fast money circulates around to settle transactions.

Assume now that we are talking for a "small" country that needs to import basic factors of production like raw materials or energy. "Small" here means "with no market power". Such a country is a price-taker in the international market. More over, substitution possibilities for these factors are usually small to non-existent.

Competitive markets or not, the economy's output will be distributed to factors of production and for our purposes, it doesn't matter whether there will be "capital rents" and "profits", or only capital rents. Use for convenience three factors of production and write

$$PQ = rK + wL + p_fE \tag {2}$$

where $r$ and $w$ are nominal, and $p_fE$ is the nominal cost of imported factors. Denote $s_f$ the foreign exchange rate (units of local currency per one unit of foreign currency), $c_f$ the price of the imported factors in foreign currency, so $p_f = c_fs_f$.
Use this and substitute $(2)$ in $(1)$

$$rK + wL +c_fs_fE= VM \tag{3}$$

If something happens to the international market and $c_f$ goes up to $c_f' > c_f$, this will tend to increase the left hand side. This "something" in the international production factors market does not relate to the level of domestic output $Q$, or to domestic money transactions technology, $V$. More over, at least in the short run, factor substitutions will not happen, wages do not move that easily, and firms will maintain their output level while increasing selling prices, to cover the increased production costs. And since the reasons for the increase affect more-or less the whole economy, it is not that likely that competition will stop firms from doing so: they all want to cover their increased costs, they all know that the cost-rise is general and comes from abroad, so they don't need to actually collude in order to sustain a price increase. "Common knowledge" suffices.

So in order to preserve the equality in $(3)$ it appears that we must have

$$rK + wL +c_f's_fE = VM',  \;\; M' > M\tag{3}$$

You see? This is the phenomenon called "imported inflation". Whatever the reasons were for the price increase (the "not important" reasons), inflation was not caused by the expansion of the money supply (that's indeed true), and what else the government could do than raise the money supply to service the higher nominal level of output?

Of course what the story above does not say, is that foreign factors of production will want a "money" that they accept, and most likely this won't be the local currency of this small country. And by increasing the money supply the exchange rate $s_f$ will suffer (increase), because $s_f = h(M), \;\; h' >0$, increasing in this way further the costs of imported factors in terms of local currency, and making the increase in the money supply equivalent to "shoot oneself in the foot". And this is only one more step towards the road to general equilibrium.

The essence here is that
a) it is trivial that there are many other factors that may tend to affect prices upwardly, except money supply expansion

b) in the presence of these other influences, increasing the money supply is not necessarily the appropriate government response.


Quasi-concavity of profit function I'm doing a simple exercise from my textbook: suppose the revenue function is $R(p)=p^{1-\epsilon}$ with $\epsilon > 0$. Suppose the cost function is convex. Show that the profit function is quasi-concave if $\epsilon > 1$.

My attempt: Let the demand function then be $q(p)=p^{-\epsilon}$ and the cost function some $c(q(p))$.

The first-order condition is
$(1-\epsilon)p^{-\epsilon}-c'(q(p))q'(p)$ and the second order condition $-\epsilon(1-\epsilon)p^{-\epsilon-1}-c''(q(p))q'(p)^2-c'(q(p))q''(p)$.

The second term $-c''(q(p))q'(p)^2$ and third terms $-c'(q(p))q''(p)$ are negative under convexity of the cost function. Hence the second order condition is unambiguously negative if the first term is negative. But that happens for $\epsilon<1$, the opposite as conjectured.

Your attempt is almost correct.

Let the demand function be $D(p) = p^{-\epsilon}$ and the cost function some $C(D(p))$ so that $R(p) = D(p)p = p^{1-\epsilon}$, right?

Then, I'd rewrite your first and second order conditions - as you only provided the expressions but it would be great to write them in a form of equations (or inequalities). So that:

First order condition: $R'(p) - C'(D(p))D'(p) =0$

And the second order: $R''(p) - C''\left(D(p)\right)\cdot D'(p)^2 - C'(D(p))D''(p) < 0$

This is the moment when we kind of split our approaches. I also do agree that the second term in second order condition is negative. However, it is not necessarily $R''(p)$ that is negative - rather the whole relation $$R''(p) - C'(D(p))D''(p)<0 \;(*)$$ Now, we want the second order condition to hold for every $p$ that satisfies the first order condition. Thus, I would substitute the $C'(D(p))$ from the first condition to the $(*)$ and hence, I end up with: $$R''(p) - \frac{R'(p)D''(p)}{D'(p)} <0 \;(**)$$

Now it's time for the brute force. Calculate all derivatives in $(**)$.

$$ -\epsilon(1-\epsilon)p^{-1-\epsilon} - \frac{(1-\epsilon)p^{-\epsilon} \cdot -\epsilon(-1-\epsilon)p^{-2-\epsilon}}{-\epsilon p^{-1-\epsilon}} <0 \implies \epsilon > 1$$ for both, $p$ and $\epsilon$ positive.

P.S. If you think about it, letting $\epsilon<1$ would imply that $R'(p)>0$ and thus, the first order condition would have no solutions. Why?

P.P.S. I believe a similar exercise is in Industrial Organization: Markets and Strategies by Belleflamme and Peitz in their chapter about "monopoly pricing strategies" but with the inverse demands $P(q)$.


More direct way to derive indirect utility function from expenditure function I have this general form for a expenditure function $e(p,u)=f(u)\cdot g(p)$ where $f(u)$ is increasing monotonic. How can I derive a functional form for an indirect utility function from this expenditure function?

Make e (p, V (p, r))=r, hence f (V (p, r)) g (p)=r. Then use the inverse function theorem:
V (p, r)=h (r/g (p))
Where h is the inverse of f.


Does immiserizing growth exist outside of theory? For a course in international trade, our professor touched on the idea of immiserizering growth.  He emphasized that immiserizing growth was a theoretical outcome from specialization of trade and did not provide the class with examples on the global market.
What are some real world examples of immizerizing growth?

The concept of immiserizing growth describes a situation where a mainly exporter country that grows, finds itself worse-off because the terms of trade (relative prices) change too much against it.

Immiserizing growth has generated some theoretical interest in the past, and various situations have been determined under which such a phenomenon may arise, enhancing the original contributions by
Johnson, Harry G. 1955. "Economic Expansion and International Trade," Manchester School 23, pp. 95-112
and
Bhagwati, Jagdish. 1958. "Immiserizing Growth: A Geometrical Note," Review of Economic Studies 25, (June), pp. 201-205.

I do not know of any real-world example though. On the contrary some studies have been conducted which have estimated the critical values for the variables of a real-world economy, in order for it to face the possibility of immiserizing growth-and these thresholds are not observed in practice.

As an example, Ramon Lopez (1991), in "Microeconomic Distortions: Static Losses and their Effect on the Efficiency of Investment", studying the economy of Chile for the period 1974-1989, estimated that, under full employment, the critical tariff rate for the prospect of immiserizing growth to arise would be $185$%, while with unemployment, it would be $260$%, which are too high compared to observed tariff rates.

The real concern about International Trade is its distributional effects inside each country, i.e. whether it creates "misery" for part of the population, while benefiting some other part. This is also "immiserizing growth" (for some of the citizens) but not in the sense meant by the scholars that originally coined the term.


What does the seasonal adjustment curve for major macroeconomic metrics look like? All the explanations of seasonal adjustment that I found from a quick search either don't give any quantitative examples, or give an example with a time series that is either made up or represents an extremely specific microeconomic data set.

I'm curious, what does the seasonal adjustment curve look like for major macroeconomic variables like GDP or the unemployment rate? I don't need precise numerical values; I'm just curious about what the curve looks like visually - what are the busier and slower times of year, and what is the order of magnitude of the deviations from the annual mean.

(I know there are different methods for seasonal adjustment, e.g. additive vs. multiplicative models - either one will do.)

Quarterly GDP seasonally adjusted

source:  https://aneconomicsense.org/category/econ-data/gdp-productivity/
AnEconomicSense.org by Frank Lysy

Monthly unemployment rate seasonally adjusted

Source: https://www.researchgate.net/figure/Seasonal-adjustment-of-US-unemployment-using-the-defaults-of-seasonal-The-result-is_fig2_329822239
by  Christoph Sax and Dirk Eddelbuettel

These are just some examples.

To manually do it in excel this link  from Catherine Hood shows an example

http://www.catherinechhood.net/SeasAdjShortTimeSeriesExcel.pdf

simplest case- – A Quarterly Series with a Flat Trend

Steps to calculate the seasonal adjustment:

Calculate the average for the series. This will be use as the trend.
Calculate the difference between the original series and the trend. Label this as "residual"
Calculate the seasonal factors (SF), which are the average of the residuals for a given quarter.

For example, the seasonal factors for all the Quarter 1 values will be (111+87+145) / 3 = 114.3333 and so on.

Subtract the seasonal factor from the original series to get the seasonally adjusted series. For example, for Quarter 1, 1991, we have 864 – 114.333 = 749.6667.


Could debt cause inflation instead of deflation? It is well known that debt can cause deflation, especially during crisis: to repay their debts agents sell their goods which causes a fall in prices.

But if there is no crisis and agents "have the time" to repay their debt, would it be possible to have the opposite mechanism, inflation: to repay their debts (and make their investments profitable) agents would sell their products for an higher price causing a raise in prices?

In the general case it seems difficult because this could destroy market shares if there is competition.

But in some cases I wonder if it could:

monopolys (especially state monopolys, and this would be a kind of hidden tax),
competition but with all competitors in debt so that all have to sell at higher prices to survive,
...

Yes it can.

If debt originates from the banking system, then it potentially has a side effect of money creation. Whether or not money is actually created when a bank loan is made depends on the banking system's regulatory framework, and the lending policies of its banks, and these can vary widely.

However if there is net excess of bank lending over bank loan repayment and loan default, then money creation is occurring, and the additional money can and indeed usually does, result in inflation.


Deriving Simple Tax Multiplier with Calculus (Macro Ugrad) It looks like I am making a calculus mistake here, and I am really banging my head against the wall.

Here is my work:

[img]http://i.imgur.com/e19Fmrx.jpg[/img]

I know I should be getting $dY/dT=-(MPC)/(1-MPC)$, where $MPC=dC/dY$
If this is at all helpful here is a picture of page 295 in 7th edition of Macroeconomics By Mankiw that briefly describes the process.

[img]http://i.imgur.com/VKPbZbz.jpg[/img]

It is confusing to me that he uses $C'$ for both terms on right-hand side when $C$ is composed of two arguments, so I decided to use Leibniz notation to see what is going on.

Thanks for help!
Chris

So here $C$ is a function with the argument $Y-T$, like $C=f(Y-T)$

So differentiate the equation: $dY=C' * (dY-dT)$

The result immediately follows like in the book.

The reason you don't do the partial derivative is that C has only one argument - while Y and T are in there, it only takes in 1 input.


Pushing taxes - economic etymology Frequently a description that is clear in the mind of its author is not as clear to a reader. It is even worse when the reader finds the description clear but actually misunderstands the intention of the writer.

There are many such descriptions in economics. As social animals, economists learn from each other and copy each others phraseology - if I understood it, it is probably clear. However not all widespread phraseology is clear. A good example is in cooperative game theory, where Lloyd Shapley wrote a note titled 'Let's Block "Block"'. (If you read it be sure to read the footnote as well.) Shapley was among the originators of the phrase 'block' as used in cooperative game theory. But 'blocking' was actually a precisely defined mathematical concept in the science and as events unfolded it became clear that in some cases the popular meaning of the word conflicts with mathematical definition, resulting in Shapley's note.

After this introduction I will state my questions.

Is it correct and/or useful to say that in a market where a per unit tax (or quantity tax) is levied on the good the suppliers push part of the tax onto the consumers?
Is it correct and/or useful to say that in the same situation consumers and suppliers share the tax burden?

I do have an opinion in these matters:

Without further information about the market structure this phraseology is unclear and therefore its use is incorrect. An example:
Suppose the supply side of this market is provided by a state run company. The company does not care about profit but does care about social optimum, hence they operate at the level where marginal cost is equal to the market price. Of course the government needs funds for other projects. (For public goods where the free market would not reach an optimal allocation.) Thus it levies a tax on other goods, also on the one in our example. This shifts the supply curve upward. Is the welfare maximizing state company really 'pushing the tax onto the consumers'? I would say no. The market mechanism was changed and the new equilibrium allocation is different. Yes, consumer prices are higher in the taxed equilibrium if we compare the two.
Perhaps you find this example contrived. Another objection I would raise against the phrase is that in case of perfect competition companies have no price setting power at all, they are price takers. How is it then possible for them to push taxes? Again, I think the market mechanism is changed, and this changes the equilibrium price and quantity.
In almost all cases this phraseology is unclear and therefore its use is incorrect.

In the UK in May 2016 the Alcohol Duty payed on alcoholic beverages was 852 million pounds. I would argue that this tax is levied on the suppliers of the beverages. Of course consumers are made aware of the tax and suppliers use the money payed by consumers to transfer to the treasury but consumers transfer exactly 0 million pounds to the treasury under the heading Alcohol Duty. The other approach where we estimate a demand and supply curve and calculate the equilibrium price without the Alcohol Duty and compare this to the price consumers pay and the price suppliers get with the duty would yield a different outcome. But this obfuscates matters greatly. Again, what happens is that the market mechanism is changed. The duty raises the equilibrium price payed by the consumers and lowers the equilibrium price received by suppliers. Sometimes this phraseology also talks in welfare terms and mentions the tax burden. I find this somewhat better as both consumer and supplier welfare is decreased in this case. Usually however this burden is equated with the tax received by the state. This is generally incorrect as it does not take into account the deadweight loss caused by the tax. So while the tax does burden both consumers and suppliers just by comparing these burdens one does not get anything akin to who is paying what share of the tax. The market mechanism is changed by the tax. Comparitive statistics may be preformed to examine welfare changes. These concepts exist and are clear.


Quantitative easing and interest rate parity Suppose a country initiates quantitative easing by printing money and buying government debt. This will put a downward pressure on interest rates. Will this action tend to depreciate the country's currency against USD because money supply has increased decreasing the value of money? Suppose, further, that the final interest rate after quantitative easing is less than the USD interest rate. From interest rate parity, I believe it would follow that the currency would appreciate against the dollar. If yes, there are two opposing influences on the currency. Which one will prevail?

Will this action [QE] tend to depreciate the country's currency against USD because money supply has increased decreasing the value of money?

There is considerable market folklore about this topic. However, from a fundamental basis, all QE represents is a change in the maturity structure of government liabilities. Long-term liabilities (bonds) are swapped for short-term liabilities (money). There is no good explanation as to why that would directly affect exchange rates (ignoring the interest rate effect, discussed next).

From interest rate parity, I believe it would follow that the currency would appreciate against the dollar. If yes, there are two opposing influences on the currency. Which one will prevail?

Interest rate parity is best thought of as an arbitrage condition: interest rate differentials plus the currency basis (which is a traded spread) determines forward rates. This is “covered interest parity”, and it holds (except perhaps in extremely stressed markets).
If interest rates fall due to QE - which is itself debatable - this implies strengthening forwards (assuming the basis does not move). This is necessary to equalise returns.
However, you are asking whether the spot exchange rate will strengthen. From a practical perspective, this is unlikely to even detectable.

The belief that the spot exchange rate will follow forwards is a variant of the Efficient Market Hypothesis, and from what I have seen, this effect is either weak or non-existent. Feel free to search for “uncovered interest rate parity,” it is a large area of research.
The strengthening of forwards is at the tenors associated with bonds. If a 10-year bond yield falls by 20 basis points due to QE, can we really tell whether the currency strengthened by 20 basis points per year over the next 10 years relative to its previous trajectory?


Why do companies launch products at much higher prices, only to reduce the price drastically after a few months? I see this to be a prevalent trend - companies too often launch products at much higher prices than they know is gonna lead to good sales numbers, only to reduce the price drastically after a few months. And by the time they do so, they lose any competitive advantage they might have had, and thus can't "recover" any more as far as product sales are concerned.

Let's take a concrete example - the Razer Phone 2. They knew people didn't know much about the brand when it was launched, as Razer is new into making phones. Thus, it only made sense to have launched it for something more reasonable, like $600 perhaps. But no, they launched it for \$800-850. And of course, it didn't sell well. And now after 2-3 months, its price is \$500. But it lost traction - all the excitement that was there when it was first launched about its gaming capabilities is not so fresh in people's minds anymore. Moreover, there are other products at competitive prices that are more value for money. Why couldn't they have launched it for \$600 in the first place?

Another example - Blackberry. They were all but practically dead after a few years of not catching on the Android train. Then they decided to adopt Android a couple years back, and launched a phone (I can't remember its name). It was a good product, but again, they priced it ridiculously high for a company coming back from dead, and making a first product with a new technology for them. Of course it didn't sell well. But had they launched for half the price, I strongly think the phone would have sold well. I know I for one would have bought that phone, but for around \$400 - not for \$750.

Is the reason greed or over-optimism? Surely that can't be right? Don't they want to sell more products, and thus get more profits?

P.S. I am not a finance student or economics student. Just a layman trying to understand why so many companies go for seemingly stupid product pricing.

Two very general reasons are:

1) High prices at the beginning target "early adopters" - people that have a higher "willingness to pay" for a new product just to have it first. Early adopters know that they pay more, and they 're ok with it.

2) As regards consumer reaction, it is much better to reduce prices than to increase prices. So sometimes prices are set high to "feel" the market response and then adjust accordingly.

Note: these are very general and "universal" reasons for the phenomenon. The degree to which are qualified in each special case, market, country, etc its a matter of examination. Also, in some circumstances other strategic considerations may lead to the opposite action: start very low to "sweep the market" (price self-subsidy) in order to drive competitors out/increase market share, and then start increasing prices when market has become "captive" to a degree.


Is the shareholder-creditor conflict the same as debt-equity conflict? I am having some problems understanding the difference between shareholder-creditor conflict and debt-equity conflict.

I understand what the shareholder-creditor conflict is about, but when I try to understand debt-equity conflict I get to the conclusion that it is the same since

-> A shareholder owns a piece of the company in the form of stock (equity).

-> A creditor lends money to the company (debt)

I am asking because I am reading two articles where the main conflict of interest in the first article is shareholder-creditor conflict, but in the second article the main conflict is debt-equity..

article: "The leverage ratchet effect" by Admati et. al. (2015)
article: "A theory of LBO activity based on repeated debt-equity conflicts" by Andrey Malenko and Nadya Malenko (2015)

No. Creditor and debt holders are not necessarily the same. The firm owes money to both. You can have debt holder vs other creditor conflict, who has priority and who has what charge to which asset.


Arch Model and $\sigma$ In my problem set about ARCH models I'm given that
$\epsilon^2_{t}=\alpha\epsilon^2_{t-1}+v_{t}$
But then I'm asked to calculate
$E(\sigma^2_{t+n}|I_{t-1})$.
So is the same to calculate $E(\epsilon^2_{t+n}|I_{t-1})$, isn't it?
Thanks in advance

It is the same in practice, they are both variances some people will write it as $\sigma^2$ some as $\epsilon^2$. Variance in error tells you what is the variance in the variable you predict.


Why would Switzerland, with its export-driven economy, worry about weakening against the dollar? I was reading about the SNB's decision to abandon the peg in 2015, and among the various articles I read, one from CNBC quoted the SNB president saying the following

  "The euro has depreciated considerably against the US dollar and this, in turn, has caused the Swiss franc to weaken against the U.S. dollar. In these circumstances, the SNB concluded that enforcing and maintaining the minimum exchange rate for the Swiss franc against the euro is no longer justified," the statement said.

My takeaway from this statement is that part of their justification for removing the peg came from the effect it was having on the franc's value against the dollar.

I know they wanted this peg in the first place to lower the franc's value against the euro as Switzerland's economy was largely reliant on exports to euro zone countries, so having a weaker currency than the euro would help exporters.

But I don't understand why the franc's performance with the dollar would be a concern? Wouldn't that just help Swiss exporters sell to US importers as well as Europeans? Or does falling below the dollar have other consequences?

Its not totally clear, but it seems that what they are saying is that, as long as the euro was a strong currency, they did not want to have the frank much stronger than the euro. Later, on, when the euro lost value, they no longer wanted to insure that the franc wasn't much stronger than the euro.

In other words they don't want a very strong currency, but they are ok with having a stronger currency than their neighbors.

The question includes just one of the concerns for central bankers. It says that the Swiss export to their neighbors, so they don't want their products to be uncompetitive with those of other Europeans. That would mean less purchases, lower GDP etc. This was the logic used when they imposed the cap on the franc price relative to euros.

However, the central bank has another main concern, which is that it wants to make sure the currency remains a good asset for investors. It has to make sure the currency doesn't lose value, otherwise, it hurts all those investors that trusted in it. So, for the world wide capital markets to demand the Swiss franc, the central banker needs to maintain a reasonably high value for it. This is the core concern when they are allowing the franc to increase in value relative to a (falling) euro.


How to determine which triangle is DWL? On a graph where there is a shift in either the demand or supply curve, there is often a deadweight loss, but which triangle is correct? For instance in this image the DWL is the green triangle, but what about the white triangle beneath it? They have the same area, so are both of them equally valid? If not, how can I determine which triangle is DWL? Thanks!

Here's a quick and dirty trick:

  DWL is the triangle that points (horizontally) towards the efficient quantity.

If equilibrium quantity is lower than the efficient quantity, DWL should point rightward, and it represents the amount of unrealized gains from trade.

If equilibrium quantity is higher than the efficient quantity, DWL should point leftward, and it represents the amount of social loss due to over-production/consumption (when social marginal cost is greater than social marginal benefit).


Categorisation of Harmonised System codes for economic analysis I work a lot with Harmonised System Codes (https://en.wikipedia.org/wiki/Harmonized_System). In a nutshell, the Harmonised System (HS) provides a way to record all goods based trade in and out of a country. Countries also impose tariffs (taxes) and other conditions on goods based off the HS system.

The problem with the HS system is that some of the groupings are not "free standing", meaning that they have words such as "not elsewhere specified", or "includes goods other than those under this HS code."

As a consequence, some analyst will introduce a grouping system on top of the HS. For example, they say that this chunk of HS codes will be summarised as "beef and veal", these codes as "cars" etc. However, many analyst also don't declare what the groupings mean when they publish their research.

There is a Standard International Trade Classification (SITC)(https://en.wikipedia.org/wiki/Standard_International_Trade_Classification) but this does not match well with the HS codes.  This means I can't group HS codes by SITC, report the trade values and tariffs in a database.

My question whether the community has come across any grouping system that works with the HS coding system? From my research, I noticed that DG Agri has this system but it is only for agricultural products.
https://ec.europa.eu/agriculture/sites/agriculture/files/trade-analysis/statistics/outside-eu/2015/product-classes-details_en.pdf

Also on agriculture, the World Trade Organization has a single grouping for "Agriculture" (using Annex 1 of the Agreement on Agriculture) but doesn't split the groupings any further.

If you are looking for classification like Agri-food trade presentation that covers products other than agricultural, you should check out the Combined Nomenclature (CN) of the European Union and its Explanatory Notes.

It is established on the basis of the Harmonized System and it covers all the products that can be subject to customs and tariffs in the EU. Seek Annex I to the the basic CN Regulation (Council Regulation (EEC) No 2658/87 on the tariff and statistical nomenclature and on the Common Customs Tariff). Be sure to use the latest version, though, as it is updated on a yearly basis. Here's a link to 2018 version, but if you want to be accurate, you should also include amendments (there were five of those since publication of 2018 verion). Perhaps the most readable is of course Explanatory Notes to the CN (so something like this).

If you are interested in jurisdictions other than EU, please find links to cusoms nomenclature under Harmonized System's wikipedia page, you've posted. I'm sure all of them will have the same problems as Harmonized System. It is simply impossible to explicitly list all the products in the World and such listings will always be half open with use of phrases like 'not elsewhere specified'.

Hope that helps.


When using consumables consider the purchase or market price? Say I use two fuels to heat my home (space heating): oil and wood. I purchase both in bulk, at a price decided at the time of purchase.

Wood is cheaper per kWh, but I purchase both because oil has other uses (heating water for example, plus it's sometimes useful to have redundancy). So I purchase, say, three tonnes of logs for £300, and 1800 litres of oil for £1100.

When a given fuel has been used, I must purchase some more at the market price.

Now, the price of oil has collapsed and it is now may be cheaper per kWh to use it for space heating.

So, one any one night, how do I decide which fuel to use? Should I be using the market price at the time of use, or the purchase price?

Assuming you plan to keep both oil and wood in stock, and they both give you the same quality of heating, presumably you should burn whichever will cost less for you to replace. That would be the fuel that will cost less to buy in the future when you buy it.

If you don't have any special knowledge about what prices will do in the future, I think the most neutral position would be to assume they will stay where they are now, so you should burn whichever currently has the lowest market price - oil in your scenario.

Having done that you could if you wanted to sell the wood that you didn't burn, which you say is worth more than the oil, buy the exact quantity of oil that you did burn, and have money left over. That must be better than burning the wood.

I've assumed for simplicity that there are no transaction costs incurred in the act of buying and selling.


Is it valid to assume that the international price of consumer durables is constant? While studying tariffs in International Trade, we often come across a Demand Supply diagram along with a world supply curve that is perfectly elastic. Here we assume that the international or the world price of that good is constant and based on this assumption we carry on with our analysis.

Considering commodities or goods such as wheat, it is safe to assume that the world price will remain the same as it is produced in huge quantities all over the world and no one country/producer can cause a shift in the supply curve.

However, consumer durable such as LCD or Plasma televisions are not produced in such abundance and are often produced by certain countries, say for instance Japan or China.

This reasoning has led me to question the assumption made while drawing the world supply curve in the tariff diagram. I would like to know whether this reasoning is valid or not and if not, then why?

The assumption almost never holds. Not for televisions, nor pretty much any other consumer durable (nor wheat, but that's not a consumer durable anyway).

It's a simplifying assumption that's used to make a particular problem easier to solve.

But in reality, the market changes continuously; furthermore there are often oligopolistic forces at play.

The least that should be done, when making the assumption, is to include a discussion about the possible implications on ones results, when the assumption does not hold. One could also do a sensitivity test with and without the assumption; and/or cite other studies that have gone deeper into the implications of using the assumption.

Classical economics has a long, disreputable history of making big claims on the basis of invalid assumptions. It's down to us to change these bad habits.


Conjecture Steady State from limit properties The question is related to this thread. I'd like to derive a unique steady state for an optimal control problem.

Consider the following programm
\begin{align}
&V(x_0) := \max_u \int^\infty_0 e^{-\rho t}F(x(t),u(t))dt\\
s.t.~&\dot x(t)=f(x(t),u(t))\\
&x(0) = x_0
\end{align}
where $\rho > 0$ denotes time preference, $V(\cdot)$ is the value and $F(\cdot)$ an objective function. $x\in X$ is the state variable and $u\in U=[0,1]$ the control. The state is governed by $f(\cdot)$. The Hamilton-Jacobi-Bellman equation reads
\begin{align}
\rho V(x)=\max_u [F(x,u) + V'(x)f(x,u)],\quad \forall t\in[0,\infty)
\end{align}

Now presume that the feedback control is given by
\begin{align}
u(x) = \frac{1}{1+V'(x)} = \arg\max_u [F(x,u) + V'(x)f(x,u)],\quad \forall x\in X.
\end{align}

Suppose there is a fixed point at $x = \tilde x$ and we can derive an alternative representation for the optimal control in the fixed point with
\begin{align}
u(\tilde x) = \frac{\rho + u'(\tilde x)}{\rho + u'(\tilde x) + 1}.
\end{align}

Suppose additionaly the HJB in the fixed point is given by
\begin{align}
\rho V(x)=\ln\left(\frac{1}{1+V'(x)}\right) + 1 - \frac{1}{1+V'(x)}.
\end{align}

If $\rho\to 0$ approches zero we must have $V'(\tilde x) = 0 \Rightarrow u(\tilde x) = 1 \Rightarrow u'(\tilde x) = \infty$. On the other hand if  $\rho\to\infty$ approches infinity we must have $V(\tilde x) = 0$ by the definition of the value function and thus again $V'(\tilde x) = 0 \Rightarrow u(\tilde x) = 1$. Summarizing we have the following properties in equilibrium
\begin{align}
\lim_{\rho\to 0} u(\tilde x)=\lim_{\rho\to\infty} u(\tilde x) = 1.
\end{align}

Well, that's at odds with
 \begin{align}
\frac{\partial u(\tilde x)}{\partial \rho}=\frac{1}{(\rho + u'(\tilde x) + 1)^2} > 0
\end{align}

being a strictly monoton increasing function, contradicting our previous result. Note, however, that we may resolve the issue by observing
\begin{align}
\lim_{u'(\tilde x)\to\infty}\frac{\partial u(\tilde x)}{\partial \rho}= 0
\end{align}

So, can we finally conjecture that we must have in the fixed point $u'(\tilde x) = \infty \Rightarrow u(\tilde x) = 1$ such that
\begin{align}
\rho V(\tilde x)=\ln(1) + 1 - 1 \Leftrightarrow V(\tilde x) = 0.
\end{align}

Upgrading an exchange of comments, a critical point in the question is the expression
\begin{align}
\frac{\partial u(\tilde x)}{\partial \rho}=\frac{1}{(\rho + u'(\tilde x) + 1)^2}
\end{align}

which is mistaken , because from

\begin{align}
u(\tilde x) = \frac{\rho + u'(\tilde x)}{\rho + u'(\tilde x) + 1}.
\end{align}

we obtain

\begin{align}
\frac{\partial u(\tilde x)}{\partial \rho}=\frac{1+\partial u'(\tilde x)/\partial \rho}{(\rho + u'(\tilde x) + 1)^2}
\end{align}

The OP notes that the sign of $\partial u'(\tilde x)/\partial \rho$ is indeterinate, and so $\partial u(\tilde x)/\partial \rho$ cannot be said to be monotonically increasing, which was what drove the pinning-down of the steady state.


Change in Welfare from an Incentive based Supply Restriction My question is related to the following graph:

The supporting example is given with regard to a policy of an acreage limitation program to provide incentive for farmers to leave fields fallow.

Why does the cost to the government include all of $D$, and not just the portion of $D$ to the left of  $Q_0$?

My textbook (p. 327, Pindyck & Rubenfeld, Microeconomics, 7th Ed.) says:

  Incentive Programs In U.S. agricultural policy, output is reduced by incentives rather than by outright quotas.  Acreage limitation programs give farmers financial incentives to leave some of their acreage idle. [The figure above] also shows the welfare effects of reducing supply in this way.  Note that because farmers agree to limit planted acreage, the supply curve again becomes completely inelastic at the quantity $Q_1$, and the market price is increased from $P_0$ to $P_s$.

  As with direct production quotas, the change in consumer surplus is $$\Delta CS=-A-B$$ Farmers now receive a higher price for the production $Q_1$, which corresponds to a gain in surplus of rectangle $A$.  But because production is reduced from $Q_0$ to $Q_1$, there is a loss of producer surplus corresponding to triangle $C$.  Finally, farmers receive money from the government as an incentive to reduce production.  Thus the total change in producer surplus is now $$\Delta PS=A-C + \text{Payments for  not  producing}$$

  The cost to the government is a payment sufficient to give farmers and incentive to reduce output to $Q_1$.  That incentive must be at least as large as $B+C+D$ because that area represents the additional profit that could be made by planting, given the higher price $P_s$. (Remember that the higher price $P_s$ gives farmers and incentive to produce more even though the government is trying to get them to produce less.)  Thus the cost to the government is at least $B+C+D$, and the total change in producer surplus is $$\Delta PS=A-C+B+D=A+B+D$$

(This ended up being a long post, but I find the approach of the textbook a bit outdated).

It is interesting to examine the issue from a (simplistic) game-theoretic point of view.

Assume a fixed (no entry) large number $N$ of small identical producers, meaning that the actions of each one individually does not affect the market. The market demand curve and the market supply curve are common knowledge. For next period, the government wants to restrict production below the current market clearing. The government announces that it will pay an amount $T$ to any producer that respects the deal and restrict his production, on top of the revenue he will earn in the market.

We assume that each producer has to evaluate the following options: either he conforms with the government plan  or he doesn't. In combination with either "all others conform", or "all others do not" (here lies one aspect of simplification).

So each individual producer faces four possible future states:
1) All conform
2) He conforms while the rest don't
3) He doesn't conform while all others do
4) Nobody conforms.

The motive to not conform comes from the fact that if he alone does not conform, the market price won't be affected, because he is "small".

First, a diagram:

$P_c$ is the price that will prevail if all producers conform to the government plan and produce in total $Q_c$. Correspondingly, $P_d$ is the price that will prevail in the market if each producer attempts to exploit for his own benefit the price hike (each assuming that the others will conform to the government plan). Then the quantity supplied will end up being $Q_d$. Finally $P_L$ is the price which producers would normally want to produce $Q_c$, absent government interference. Note carefully that the long-term market clearing point is out of the picture. Nobody "cares" about it, now that the government jumped in and essentially, reshaped the market structure in terms of the market's prospects.

We now assume that the individual long-term supply curve is a zero-pure-profit, best-response function, so the payoffs for each possible state are expressed as deviation from this best-response function. This is a critical assumption.

Then, the game in normal form as experienced by each individual supplier is ($q$ is just $Q/N$)

\begin{array}{| r | r |r |}
  \hline
\hline
   &  \text{All others conform} & \text{All others deviate} \\
  \hline
\text {I conform}   & (P_c-P_L)q_c+T & (P_d-P_L)q_c+T\\
  \hline
\text{I deviate}   & 0 & (P_d-P_c)q_d \\
  \hline
\end{array}

Note the reason why the lower left corner has a payoff of $0$: if the producers produces $q_d$ and receives a unit price $q_c$, he is on his zero-pure-profit, best-response function -nothing is gained on top (so we do not ascribe any benefit to "be larger" in terms of revenues).

It should be clear from the above payoff matrix that "I conform" is already a pure dominant strategy without the need for any strictly positive government incentive $T$.

What I am (momentarily) saying, is that the Government needs only to announce the program, with a "token" incentive $T$, and everyone will conform to it. Essentially the government functions here as a "cartel creator", bringing all suppliers to cooperate in a decentralized manner in order to restrict quantity and increase price.

Well, it doesn't sound as a very convincing description of reality, does it?  "Token incentive programs" do not appear to work in the real world. So something must be critically mistaken in our assumptions.

And it most probably is: the assumption that a producer does not care about his scale of production. This neglects the fact that especially with small producers "costs" include their reward for their own labor and use of their own equipment. So a higher scale of operations does increase the income of the producer, even though it may not bring "pure profits" over and above the remuneration of the production factors.

So let's approach the construction of the payoff matrix in a different way. Assume that "all other costs of production" except the producer's own income (like materials, third-party services, additional laborers, etc) are constant per unit of output, denote it $b$. Then the producer income is $I = (p-b)q$.

The payoff matrix in terms of income becomes now

\begin{array}{| r | r |r |}
  \hline
\hline
   &  \text{All others conform} & \text{All others deviate} \\
  \hline
\text {I conform}   & (P_c-b)q_c+T & (P_d-b)q_c+T\\
  \hline
\text{I deviate}   & (P_c-b)q_d & (P_d-b)q_d \\
  \hline
\end{array}

We can reasonably argue that $P_d<b$ and so without the government incentive, Income in the right column will be negative. Note that here "I conform" is already dominant if all others deviate, because losses are smaller.

Here in order for "I conform" to become a dominant strategy we must have that

$$T > (P_c-b)(q_d-q_c)$$

This is essentially "the cost of avoiding treason". In order to deal with loss-aversion we could also argue that the government will guarantee "no-loss". Then the government incentive should be

$$ T > \max \{ (P_c-b)(q_d-q_c),\; (b-P_d)q_c\}$$


Why doesn't stock market help to boost the economic growth directly? For example, during the recession, the central bank often goes to buy financial instruments that are riskier than government bonds (such as corporate bonds)- which is called "quantitative easing" that increases the price and lower the interest yield of these riskier assets.
So, by the action, the central bank indirectly encourages people to invest in the real sector (and not in the stock as returns/interest yields are low) directly which will help boost the economy. This could be an investment in buying a house, land, factory, etc. Even pure consumption could put pressure to produce more commodities.
Therefore, I'm wondering why stocks trading couldn't help to boost economic growth. For example, if the interest yields are high, people will invest in these stocks and earn higher returns thus having extra income that they are willing to spend more on goods and products. Or what is the role of the stock market in economic growth?

First there are some inaccuracies in your question.

The central bank often goes to buy financial instruments that are riskier than government bonds (such as corporate bonds)- which is called "quantitative easing".

This is simply not true large part of QE program consists of buying government bonds (treasury securities). Private bonds or other long term fixed income securities can be part of QE as well but QE does not focuses on them (see Fed QE explainer).
Now to your question:

what is the role of the stock market in economic growth?

Stock markets or capital markets in general have first order impact on economic growth and development (e.g. see Demirgüç-Kunt, & Levine, 1996; Bekaert & Harvey 1998; Akenten, Boateng, & Kiros, 2020; Freixas  & Rochet (2008) Microeconomics of Banking,  second edition and sources cited therein).
This is because stock markets help to ensure that capital is allocated to its most valued uses by transferring funds that can be used to purchase capital from people who have excess funds  to people who have ability to put that capital to the most efficient uses. Capital accumulation and investment plays an important role in economic growth as you can learn from any textbook on economic growth (e.g. see Sala-i-Martin & Barro (2003) Economic Growth, Second Edition).
However, the above cannot be simply reduced to saying that growth of stock market will translate into economic growth. Rather the relationship is more complex. Stock market helps economy grow by helping to efficiently allocate capital, and when economy grows stock market will generally grow as well because as companies get more productive (or as old companies are replaced by new more productive ones) their valuation increases. Consequently growth of a stock market is rather a consequence of growth of real economy rather than cause of it (even if stock market function itself - not its growth - helps economy grow). In addition to the above it is also important to mention that in order for stock market to fulfill its functions it also needs some appropriate amount of regulation. Poorly designed capital markets might not have the same beneficial effects.
Furthermore, stock market can grow due to number of reasons unrelated to real economy. For example, if there is high amount of savings but low number of viable investment projects then asset prices can increase because of demand caused by people who want to save. If there is high demand for assets such as stocks but at the same time if firms do not have any viable ways of efficiently investing the money, then people might bid the stock prices up without really affecting investment. In addition, you need to distinguish between nominal growth and real growth. In a presence of inflation stock market can grow in nominal terms but not real ones because firms are getting nominally more profitable but not more profitable in real terms.


What are examples of inversely (negatively) correlated stock prices in economics? I’m looking for example of two goods/wealth that demonstrate inverse/negative correlation. For example if price of A rises then price of B falls. May be it is oil or gold prices along with some other wealth. Or may be some share prices (stocks) of some two companies. I can’t find example of such negatively correlated prices data.

Have you tried Google? By copying a part of your question into Google I was able to find several examples. The best one may be this site which lists 20 positively and negatively correlated stocks for any stock you pick:
http://www.market-topology.com/correlation/


Is there a book or notes that explain all about inflation? Is there a book or notes or papers (but for easy understanding please) that explain all about inflation?
Not at a research level but student level.
From what is previously needed to define and understand inflation,  to calculate inflation, to models to analyze inflation, how does inflation impacts economic agents (firms, families, etc), and other things that should be known about inflation too.
So far I haven't find a book nor PDF notes that mentions all these. I've encountered helpful youtube videos but most of them don't say where is that information from, nor is rigorous, yet are helpful because they gave you an idea of what's going on.
Thank you in advance

If you are looking something for student level the best place to start are textbooks. You will not generally find these just for single topic such as inflation (for that you would have to look at research papers but you explicitly state you are not looking for that) but they offer rigorous treatment with references to the literature.
Mankiw Macroeconomics Chapter 5 gives nice undergraduate introduction to  inflation, for more full undergraduate treatment you can have look at Lewis and  Mizen Monetary Economics.
Walsch Monetary Theory and Policy offers graduate level treatment of many models including inflation. In fact virtually all models there involve inflation in one way or another.
You could supplement Walsch also with Romer Advanced Macroeconomics or with Woodford Interest and Prices.


How do we estimate production functions? In a standard economics education we learn about production functions, indicating an output as a function of a given input of capital and labour.

An average model looks like this:

(1)    $F(L,K)=L^{a}K^b$

When dealing with real data however, we are first exposed to regression models which are additive in nature which look like this:

(2)      $y_i={\beta}_0+{\beta}_1x_1+{\beta}_2x_2+...+{\beta}_nx_n$

How do we get a production function that looks like (1) when dealing with real data?

The following is the basic idea if we are to estimate the parameters by linear regression.

Take the natural log of the production function $F(L,K)=L^aK^b$, you will then get $$\ln(F)=a\ln(L)+b\ln(K).$$
For each entity (e.g., firm) $i$, collect data on the production level $F_i$, the amount of labour $L_i$, and the amount of capital $K_i$. Note that measurement issues may arise and that it is important to be explicit about how one is to interpret 'production', 'labour' and 'capital', and how to measure them.
Apply the transformation $X_i\mapsto \ln(X_i)$ for each variable $X_i$ for each entity $i$ in your dataset. (If there is any $X_i$ such that $X_i\leq 0$ then this will not work. You may delete those observations $X_i$ for which $X_i\leq 0$. If it is real data, think about the following question. "Why is $X_i\leq 0$? Has the dataset been wrongly registered?") Economists also apply the transformation $X_i\mapsto\ln(X_i+\epsilon)$ as an approximation when $X_i\geq0$ and $X_i=0$ for some $i$, where $\epsilon>0$ is some small number.
Now, regress $\ln(F)$ on $\ln(L)$ and $\ln(K)$ using your converted dataset (cf. 3) under the assumption that the intercept term is equal to $0$. This gives you estimated values $\hat{a}$ and $\hat{b}$ of $a$ and $b$. Hence, your estimated production function, which is supposed to capture some general tendency regarding production, is $$\hat{F}(L,K)=L^\hat{a}K^\hat{b}.$$
(If the production function is written as $F(K,L)=AL^aK^b$, where $A$ captures technology for example, you will get an intercept term $\ln(A)$.)

If we are using nonlinear regression, then we take the nonlinear least squares (NLLS) estimate of $a$ and $b$ by solving $$\min_{a,\, b}\sum_i\big(F_i-L_i^aK_i^b)^2.$$ Numerical computing softwares (which uses algorithms such as the Gauss-Newton algorithm) may assist you when finding the NLLS estimate.


Effect of a good's inputs on elasticity of supply I am trying the answer the question:

  If a good is produced using inputs for which there are no substitutes, the good's

  A. Elasticity of supply is likely to be small
  B. Elasticity of supply is likely to be large
  C. Elasticity for demand will be small
  D. Elasticity of demand will be large

I am unsure of the correct answer. I don't think it would be (C) or (D) as the question notes that what goes into the good is likely substitutes, not the good itself. That leaves (A) and (B) I don't however see how these would effect the elasticity of supply. Elasticity of supply is defined as % change in quantity supplied divided by % change in price. I am failing to see how the price of a substitute would affect what is in the numerator or denominator. How is the quantity supplied of a product and the price at which it is sold dependent on the fact the substitutes are unavailable? Producers could adjust either quantity or price in order to make up for the substitute-less good. I would greatly appreciate some insight.

Consider the extreme case: all available quantity of the no-substitute input is already employed.

To trace the supply function, let's assume that we are already at some price level, and let's increase the price of the final good: will quantity supplied increase? No, because it cannot do so -there is no available additional input to use for this increase. In this extreme case the price elasticity of supply of the final good is zero, due to the situation in the inputs market.

Assume now that a little quantity of the no-substitute input is still unemployed. Being unique, we expect that it will command a high price if it is demanded for employment. So increasing quantity supplied of the final good, bears a high cost in terms of steeply increasing production costs. In this case, the price elasticity of supply of the final good is not zero, but "small"...

...compared to the case where the inputs needed for production are generally available and so the cost to employ them is smaller than in the previous case. Here we expect that under the same as before final-good price increase, final-good suppliers will find it profitable to increase their quantity supplied more than in the former case -so here the price elasticity of supply of the final good will be "large"(er).


How to utilize the projection matrix in econometrics? When consider the following DGP : $y=X\beta^{*}+\epsilon$ where $\beta^{*}$ is a $\tilde k\times1\ $ vector.

Define the projection matrices: $P_{X}=X(X^{T}X)^{-1}X^{T}$ and $M_{X}=I-X(X^{T}X)^{-1}$.

first problem is prove that $X^{T}P_{X}=X^{T}$ and $ X^{T}M_{X}=0$

I thought this problem is too simple to think because P is just I. So, I think that there is an intention for given problem considering second problem.

Second problem is Prove thath if $X_{(i)}$ is the $i^{th}$ column of $X$, then, $M_{X}X_{(i)}=0$

My question is

What is the point of first problem?
Can I solve these problem by considering $X_{(i)}=XA\ $ where A has a vector consisting of just 1 and the other columns are all zero? or Should I utilize first problem's solution?

This kind of projections in econometrics are usually employed for partialling out some covariates from a linear regression.

Observe that in general $P_X\neq I$. Consider $X=\begin{bmatrix}1&5\\1&0\\1&1\end{bmatrix}$. Then $X'X=\begin{bmatrix}3&6\\6&26\end{bmatrix}$ and $(X'X)^{-1}=\begin{bmatrix}26/42&-6/42\\-6/42&3/42\end{bmatrix}$ then $X(X'X)^{-1}X^T=\frac{1}{42}\begin{bmatrix}41&-4&5\\-4&26&20\\5&20&17\end{bmatrix}\neq I$.

First problem: $X^TP_X=X^TX(X'X)^{-1}X^T=(X^TX)(X'X)^{-1}X^T=I_{(\tilde k\times\tilde k)}X^T=X^T$

Similarly: $X^TM_X=X^T[I_{(\tilde k\times\tilde k)}-P_X]=X^TI_{(\tilde k\times\tilde k)}-X^TP_X=X^T-X^T=0$

The second problem is a direct consequence of $X^TM_X=0$, simply now you can post-multiply for $X_{(i)}$ since you are considering just one single column. The approach of $X_{(i)}=XA$ where $A$ is a vector $\tilde k\times 1$ of 0 apart from the $i$-th element which is 1. Then it should be straightforward to see: $0=(XA)^TM_X=M_XX_{(i)}$


Which economical consequences could happen to a country if it forbiddes importing cars? My country has major economical headaches each 10 years or so, like hyperinflation or defaults or things like that. It's been 17 years since the last major crisis (a larger crisis than the 1930's crisis) but it looks like we are aiming again towards the same. Usually we have trade imbalances or fiscal deficits which causes my country being unable to sustain the current money exchange rate, the goverment devaluates the currency and that leads people to increase the price of the goods in the same rate "just in case other prices increase the same rate", that usually is the cause of a snowball inflation.
I was taking a look at our current imports. Usually I can't get a detailed list but we have a trade imbalance deficit record of 8,47 billions last year (2017) and the car imports increased in 2 billions in one year, being 6,3 billion total the amount of imported cars. My question is, being the trade imbalance a major cause in the inflation we have, why we just can't stop importing cars, at least in the proportion it creates imbalances? Why we can't live with new cars or imported (non national) cars? Could there be any serious consequences to this or we are just paying the consequences of some people wanting to live with goods/cars which signals their high social status?

1- Some basic macroeconomic fundamentals

I highly doubt a trade imbalance is causing high inflation. The trade deficit is likely happening because of economists call "Twin Deficits". I'll spare you the accounting that leads to this equation and present you a setorial balances identity. Let $S$ be private savings, $I$ be capital formation, $G$ be government spending, $T$ be government revenue (in taxes), $X$ be exports and $M$, imports. We have:

$$(S-I) + (T-G) = (X-M)$$

In intuitive terms, the private sector balance plus the public sector balance, which is basically the domestic balance, must equal the trade balance. This happens due to sheer accounting, it's not a "theory". This is the same in the US, Venezuela, China and in a tribe of herdsman.

When $(T-G)$ is negative, we have a budget deficit - your country's case. Assuming people are saving the same amount, investment must fall or imports must go up. The more realistic scenario is that both things happen.

And we also have the Long-Run Fiscal Equilibrium condition. Let $M^s$ be money supply, $B$ be government debt, $P$ the price level, $r$ be the real interest rate and $t$ be time, we have:

$$ \frac{M^s + B}{P} = \sum_{t=0}^{\infty} \frac{(T_t - G_t)}{(1+r)^t}$$

This basically means that real government passive must equal the liquid present value of expected government savings. If people expect the government to continue to have budget deficits, either interest rates or the price level must go up. That's what's causing inflation. This also means that if the government increases the money supply without credibly signalling it will save more in the future, it will also implicate an increase in the price level, inflation.

2- Some basic microeconomic fundamentals

If importing cars gets prohibited, the supply of cars will go down. The supply curve shifts to the left. This means less cars available and more expensive ones.

Higher car prices signal domestic producers to make more cars. Supply goes up again and prices tend to converge to a new equilibrium. The problem is making cars domesctically might no be very efficient. Your country employs more capital and labor in other activities because it is more productive to do so. If it weren't and there was an easy opportunity to make money by producing cars, people would just do it.

Restricting imports is basically making your country poorer by forcing it to have less goods and services available and allocating precious capital and labor to activities that aren't as productive. It's a very bad idea.


Macroeconomics: Aggregate Demand, Equilibrium Dynamics and Expenditure Multipliers I am having a hard time with the following economic questions (See attached). Here is my approach:

Note about the curves: The graph below depicts an economy where a decline in aggregate demand has caused a recession. Assume the government decides to increase government purchases as fiscal policy to reduce the burden of this recession.

How much does aggregate demand need to increase to reach long-run equilibrium?

A: 100 billion
Because that's the AD1-AS equilibrium to AD1-LRAS line
MPC =.75 (and thus MPS = .25)

How much do government purchases need to increase to shift aggregate demand by the amount you found in part 1)?

My logic:
The expenditure multiplier = 1/MPS = 1/(.25) =4

Delta Y from 1) is 100 billion

Therefore, 4X= 100 (x = government purchases) leading to x = 25
Suppose the MPC is 0.6. To restore the economy to its long-run equilibrium, aggregate demand must be increased by i) ___________ and government purchases must be increased by ii) ________________

Delta Y is the same as 1), so it's 100 billion for i)

MPS changes to .6, so the multiplier is 1/.4 = 2.5, 100/2.5 = 40 billion in government purchases to restore long-run equilibrium.

So then, how are my answers wrong according to the program?

In shifting the$\ AD_1 \rightarrow AD$ curves to achieve long run equilibrium, Real GDP will have to increase by 200 billion. Refer to the diagram below, (in purple).

$\ MPC = 0.75 \rightarrow MPS = 0.25$

In this 3 sector closed-economy model, the multiplier can be calculated using :

$$\ K = \frac{1}{MPS+MPT} $$

Assuming MPT (Marginal Propensity to Tax) = 0, then $\ K = \frac{1}{MPS} = \frac{1}{0.25} = 4 $

$\ \Delta Y=K\Delta (AE) $, considering only government expenditure, then
$\ \Delta Y=K\Delta G $

Substituting the values, $\ 200B = 4G \rightarrow G = 50 $

If currently, the $\ AD $ component is $\ AD = 400B $ at $\ MPC = 0.75 $, then we can calculate the original income, $\ Y = (0.75)^{-1} \times AD = (0.75)^{-1} \times 400Bil = 533.33Bil $

Now using this value of $\ Y $, we can calculate the new $\ AD $ component at $\ MPC = 0.6 $, which is $\ AD_{new} = 0.6 \times 533.33Bil = 320Bil $

Hence, using the same approach as in Part 1, the lime-green line is $\ AD_{new} $, the purple section represents $\Delta AD, $ which, as in Part 2, with a new multiplier of $\ K $ calculated using the new $\ MPS = 0.4 $, and substituting those values into $\ \Delta Y=K\Delta G $ will result in your new government expenditure.


How will asteroid mining impact the economy? Just a side note, I'm not sure if this goes here, or in a science exchange...

Asteroids are expensive, and can easily be worth billions of dollars. They contain many types of precious metals, like gold, and platinum.

In the future, asteroid mining will be a huge business. With new advancements  in technology, and cheaper launches, we can ship asteroid material to Earth, with a huge ROI.

But how will bringing back all these metals impact the economy?

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

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

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

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


Proving that Marshallian demand is of the form: $x_i^*(p,I) = \hat{x}_i^*(p)I$ with certain conditions Can I please have some feedback/help proving the following. My proof is below but I am quite uncertain as to whether my solution is efficient. Thank you.
If $u(x)$ is a homothetic utility, then show that Marshallian demand is of the form: $x_i^*(p,I) = \hat{x}_i^*(p)I.$
$\textit{Proof.}$ If $u(x)$ is homothetic then
$$
\forall \alpha \in \mathbb{R}_{+}, \forall x : \hskip 6pt
\frac{\partial u(x)}{\partial x} =
\frac{\partial u(\alpha \cdot x)}{\partial x}.
$$
Now suppose $$
x_i^*(p,I) = \hat{x}_i^*(p)I
$$
does not hold, which is equivalent to
$$
u(x_i^*(p,I)) \ne u(\hat{x}_i^*(p)I).
$$
Precisely, $x_i^*(p,I)$ and $\hat{x}_i^*(p)I$ may be set valued. In this case we refer to two elements, with at least one of which is not included in both sets.
Case 1.
$$
u(x_i^*(p,I)) > u(\hat{x}_i^*(p)I)
$$
As $u$ is homothetic
$$
u(x_i^*(p,I)) =  u(I \cdot \frac{1}{I}\cdot x_i^*(p,I)) = I \cdot u(\frac{1}{I}\cdot \hat{x}_i^*(p)I).
$$
Using this we have
$$
I \cdot u(\frac{1}{I}\cdot x_i^*(p,I)) = u(x_i^*(p,I)) > u(I\cdot \hat{x}_i^*(p)I) = I\cdot u(x_i^*(p,I))
$$
thus we have
$$
u(\frac{1}{I}\cdot x_i^*(p,I)) > \hat{x}_i^*(p)I)
$$
However as $\frac{1}{I} \cdot x_i^*(p,I)$ is clearly an element of $B(p)I$ this is impossible as $\hat{x}_i^*(p)I$ gives maximal utility in that budget set.
Case 2.
$$
u(x_i^*(p,I)) < u(\hat{x}_i^*(p)I)
$$
As $\hat{x}_i^*(p)I$ is clearly an element of $B(p,I)$ this is impossible as $x_i^*(p,I)$ gives maximal utility in that budget set.
Thus we have proven that
$$
u(x_i^*(p,I)) = u(\hat{x}_i^*(p)I)
$$
which is equivalent with
$$
x_i^*(p,I) = \hat{x}_i^*(p)I.
$$

You have exactly the right idea. For a clearer and more efficient proof, I would suggest the following:

I am not entirely sure what the index $i$ is referring to. A specific good of the bundle? I don't think you need this.
$\hat x (p) $ denotes an optimal bundle for an income equal to $1$, right? It is clearer to write $\hat x (p, 1)$  in order to be consistent with your notation.
The claim which you want to prove is "If $\hat x (p, 1)$  is optimal at an income of 1, then $I \hat x (p, 1)$ is optimal at an income of $I$" . By the way, it is not generally true that every optimal bundle at $I$ is given by $I \hat x (p, 1)$.
To prove the above claim, you only need to note that $I \hat x (p, 1)$ is feasible at $I$ and then argue that it is weakly preferred to every other $y$ that's feasible at $I$. You basically did this in your answer when you noted that the bundle $y / I$ is feasible at an income of 1, and then used optimality of $\hat x (p, 1)$.
As a final remark: Homotheticity is really a property of preferences, not derivatives of utility representations. Indeed, all you need for your argument is that scaling any two bundles by the same positive scalar does not change the preference between then.


Given a rational $\succsim$ over a finite set $X$, show that there exists $x \in X$ such that $x \succsim y, \forall y \in X$ I have been able to show this constructively, but would like to prove it by induction. However, I am stuck with the induction step:

Consider $\succsim$ defined over $X=\{x_1,...,x_n\}$ and where without loss of generality $x_1$ is the element such that $x_1 \succsim x, \forall x \in X$. Now, consider adding element $x_{n+1}$ to the set. My reasoning is that since $\succsim$ is defined over the original $X$, there is nothing telling us that $x_{n+1}$ should be in a complete relation with the elements in $X$ (i.e. $\succsim$ is not defined over a bigger set).

Is this reasoning correct? In that case, I don't see how you could prove this by induction.

You are almost there, but I think you are starting in the wrong place. I think the key is as follows: we want to prove the claim for set $X=\{x_1,\ldots,x_n\}$.

Start with some $X'\subseteq{X}$ for which the claim is true. Such an $X'$ exists because the claim is true for the set $\{x_1\}$ (by completeness and reflexivity).

If $X'=X$ then we're done. If $X'\neq X$ then we proceed with induction:

Denote by $\bar{x}$ an $x\in X'$ such that $\bar{x}\succsim y, \forall\ y\in X'$.

Now construct a new set $X''=X'\cup\{x_i\}$, where $x_i\in X\backslash X'$. Because $\succsim$ is rational (preferences are complete) over $X$, we either have $x_i\succsim \bar{x}$ or $\bar{x}\succsim x_i$ or both. Thus, if the claim holds for $X'$ it also holds for $X''$.

We can repeat this inductive step until $X''=X$, which must happen after finitely many iterations because $X$ is finite.


Can people lack a comparative advantage and a comparative disadvantage? Source: Question 9b, p 61, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw
= Question 8b in Principles of Microeconomics, 4 Ed, 2008

  9. Are the following statements true or false? Explain in
  each case.
  b. “Certain very talented people have a comparative
  advantage in everything they do.”

  Answer: b. False; it is not true that some people have a comparative advantage in everything they
  do. In fact, no one can have a comparative advantage in everything. Comparative
  advantage reflects the opportunity cost of one good or activity in terms of another. If you
  have a comparative advantage in one thing, you must have a comparative disadvantage
  in the other thing.

Abbreviate comparative advantage as CA. Mankiw's question above motivates the titled one.

E.g., suppose in a 3-person economy: person A's CA is cooking and person B's foraging, yet person C does nothing.

Comparative advantage doesn't work like that.

If person A's CA is cooking, person C has a comparative advantage in foraging. With B, C has a comparative advantage in cooking.

It's not possible to have a comparative advantage or comparative disadvantage in everything: If you were better at everything than someone else, you would have an absolute advantage. As soon as two people have different skills for anything, they have a comparative advantage of some kind.

It is possible for two people to have no comparative advantage/disadvantages whatsoever: If both people are exactly equal at everything they can do, then there is no comparative advantage or disadvantage between them at all.


Bayesian incentive compatibility for a general distribution Suppose there are $n$ bidders and a seller. Bidder $i$ observes a private signal $v_i$ from $[a,b]$. Let $\mathcal{X} = \times_{i=1}^n[a,b]$ Each bidder is represented by a random variable, that has a joint distribution $F(\textbf{v})$, where $\textbf{v} = (v_1,v_2,...,v_n)$. Let $(\textbf{Q}(\textbf{v}),\textbf{M}(\textbf{v}))$ be the direct mechanism, where $\textbf{Q}(\textbf{v})$ is the allocation rule and $\textbf{M}(\textbf{v})$ is the payment rule, where $\textbf{Q}(\textbf{v}) = (Q_1(\textbf{v}),Q_2(\textbf{v}),...,Q_n(\textbf{v}))$ and $\textbf{M}(\textbf{v}) = (M_1(\textbf{v}),M_2(\textbf{v}),...,M_n(\textbf{v}))$

The ex-post utility for bidder $i$ is given as $U_i(v_i) = v_iQ_i(v_i,v_{-i}) - M_i(v_i,v_{-i})$. From this, we can find out the expected utility function as $$u_i(v_i) = \int_{\mathcal{X}_{-i}}(v_iQ_i(v_i,v_{-i}) - M_i(v_i,v_{-i}))\,f(v_{-i}|v_i)dv_{-i}$$ Writing $\int_{\mathcal{X}_{-i}}Q_i(v_i,v_{-i})f(v_{-i}|v_i)dv_{-i} = q_i(v_i)$ and $\int_{\mathcal{X}_{-i}}M_i(v_i,v_{-i})f(v_{-i}|v_i)dv_{-i} = m_i(v_i)$, the expected utility function can be re-written as $u_i(v_i) = v_iq(v_i)-m_i(v_i)$. $F(\textbf{v})$ can be any joint distribution,i.e, it is not necessary that the joint distribution can be written as the product of marginal distributions.

Incentive compatibility now dictates that $u_i(v_i) \equiv v_iq(v_i)-m_i(v_i) \geq u_i(v_i^{'}) \equiv v_iq(v_i^{'})-m_i(v_i^{'})$. From here, we get that

\begin{equation}
\begin{split}
u_i(v_i) & \geq v_iq(v_i^{'})-m_i(v_i^{'})\\ &=v_iq(v_i^{'})-m_i(v_i^{'}) + v_i^{'}q(v_i^{'}) - v_i^{'}q(v_i^{'}) \\ &= (v_i - v_i^{'})q(v_i^{'}) + (v_i^{'}q(v_i^{'})-m_i(v_i^{'}))\\ &= (v_i - v_i^{'})q(v_i^{'}) + u_i(v_i^{'}), \,\,\, or, \\ u_i(v_i)-u_i(v_i^{'}) & \geq (v_i - v_i^{'})q(v_i^{'})\,\,\,\,\,\,\,\, -(1)
\end{split}
\end{equation}
Similarly, we can get $$u_i(v_i^{'})-u_i(v_i)  \geq (v_i^{'} - v_i)q(v_i)\,\,\,\,\,\,\,\, -(2)$$
From $(1)$ and $(2)$, we get that $$(v_i - v_i^{'})q(v_i^{'}) \leq u_i(v_i)-u_i(v_i^{'}) \leq (v_i - v_i^{'})q(v_i)$$

Given the above expression, is it possible to write the expected utility function as $$u_i(v_i) = u_i(a) + \int_a^{v_i}q_i(t)\, dt,$$ for any distribution. Specifically, I know that this holds true for the IPV case. So, my question is that is it possible to write the utility function as the integral of $q_i(.)$ without the assumption of independence?

Your reformulation is certainly correct for independent values.

However, if value $v_i$ carries information about $v_{-i}$, you cannot write the incentive compatibility like that.
For independent value draws, the probability of winning and the expected payment in the direct mechanism depends only on your reported type $v'_i$, not on the true type $v_i$. That is the reason why you can write
$$u_i(v_i) \geq u_i(v_i^{'}) = v_iq(v_i^{'})-m_i(v_i^{'})$$
instead of $\widetilde u_i (v_i^{'},v_i) = v_iq(v_i^{'},v_i)-m_i(v_i^{'},v_i)$. That is, you cannot formulate your expected utility like this. If this was the expected utility, you could also formulate the expected transfer in a similar fashion and derive a revenue-equivalence result, but revenue equivalence requires independent values.


What would be the disadvantages of a TTIP? Well the question kind of says it all, what I would like to know is,if a TTIP between America and EU is put in place even though not only Europe and America will benefit from it but also other countries who export to Europe and America because of the augmentation of demand, would there be any drawbacks for consumers? I know that some companies will find it hard to compete with others but then again what could that cause for us consumers ?
Sorry for my bad English its been a long time.

TTIP is a combination of trade agreements and property rights / legal changes.

Trade Liberalization

Most of the current debate in European countries is not so much about trade - we all know trade liberalization yields welfare gains. In the first-order, these are split between consumers and firms: Consumer get a larger variety / cheaper goods, and (surviving) firms can reach more customers.

These are efficiency gains, and could be split up anyhow between these two groups. To the extent that surviving firms get some of these welfare gains, workers of these firms might get some of the benefits. I'm trying to be very cautious here, because on this last bit, I don't think we have sufficient empirical evidence - and theory will support different results based on the wage setting mechanism.

Of course, there will be firms that lose, and workers that will be fired - which is why the US has set up (I think under WIA) Trade Adjustments Assistance for workers who lost their jobs due to trade. This is one way of sharing the welfare gains of trade with those who lose.

Copyright and Regulation

The issue with TTIP is mostly the legal power that firms get. US american firms could sue France for french regulation at US courts. This downside is off topic here. However, the angst here is that is not welfare gains for each single country. Countries with stronger regulations will lose. Even for the world as a whole, it is unclear whether this yields efficiency gains, or whether firms just reap surplus from countries/governments.


Prove all cost functions are concave in input prices and demand for inputs is downward I've seen proofs that cost functions are concave of the form

$C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$

although this neither feels convincing nor does it seem like a path towards also proving that input demands are downward sloping.

To be more concise in my question, it is two parts.

First, prove that all cost functions, regardless of the production function, are concave.

Second, using the first step, also show that input demands are downward sloping.

Let $x(w, q)$ denote the solution to the cost minimization problem :

\begin{eqnarray*} \min_{x} & \ w\cdot x \\ \text{s.t.} & \ \ f(x) \geq q \end{eqnarray*}
where $f$ is the production function.
Since $x(w, q)$ minimizes cost at $(w, q)$, following holds for all $w$ and for all $q$ :
\begin{eqnarray*} w\cdot x(w, q) \leq w\cdot x(w', q) \ \ \  \forall w' \end{eqnarray*}

Also we know that cost function is cost of cost minimizing input choice :
\begin{eqnarray*} C(w, q) = w\cdot x(w, q) \end{eqnarray*}

First, we'll show that $C$ is concave in $w$. Consider any arbitrary $w'$, $w''$ and an arbitrary $\lambda \in [0, 1]$.
\begin{eqnarray*} C(\lambda w' + (1-\lambda) w'', q) & = & (\lambda w' + (1-\lambda) w'')\cdot x(\lambda w' + (1-\lambda) w'', q) \\  & = & \lambda w' \cdot x(\lambda w' + (1-\lambda) w'', q) + (1-\lambda) w''\cdot x(\lambda w' + (1-\lambda) w'', q) \\  & \geq & \lambda w' \cdot x(w', q) + (1-\lambda) w''\cdot x(w'', q)  \\  & = & \lambda C(w' , q) + (1-\lambda) C(w'', q) \end{eqnarray*}
Therefore, $C$ is concave in $w$.

To show that input demand is downward sloping, consider any arbitrary $w'$, and $w''$,
\begin{eqnarray*} w'\cdot x(w', q) & \leq & w'\cdot x(w'', q) \\ w''\cdot x(w'', q) & \leq & w''\cdot x(w', q) \end{eqnarray*}
Adding them we get
\begin{eqnarray*} (w'-w'')\cdot (x(w', q) - x(w'', q)) & \leq & 0 \end{eqnarray*}
We now consider a special case where $w'$ and $w''$ differ only in the $j$th input's price. Consequently,
\begin{eqnarray*} (w'-w'')\cdot (x(w', q) - x(w'', q)) = (w_j'-w_j'') (x_j(w', q) - x_j(w'', q)) & \leq & 0 \end{eqnarray*}
Therefore, demand for $j$th input is inversely related to its price.


What is the relationship between the disciplines of Economics and Economic Geography? Given the importance of natural resources in both Economic Geography and Ecological Economics I also wondered what the relationship was between these two in particular.

I see both Economic Geography and Ecological Economics as different.
Economic Geography is the study of the determinants and effects of the spatial distribution of economic activity. Economic Geography is considered as a sub-field of economics, so it's applying standard economic thinking to the geography. In particular, Paul Krugman studied the location of economic activity across space, using agglomeration economies to explain why industries cluster within particular countries and regions.
According to Robert Costanza, Ecological Economics is a transdisciplinary field. It studies the interdependence and coevolution of human economies and natural ecosystems. It's true that this coevolution is studied both intertemporally and ... spatially, but not as a sub-field of economics. It's an attempt to look at humans embedded in their ecological life-support system, not separate from the environment.


why is market clearing price assumed in cournot model with homogenous products In the cornout model two firms choose the amount of a product they wish to produce. It is assumed that the price that results is the market clearing price for the total supply. Is there a justification for this?

[...]
   One way to interpret this result is to see our two-stage game as a mechanism to generate Cournot-like outcomes that dispenses with the mythical auctioneer.

A justification is given in Kreps-Scheinkmann (1983). They argue that this is the outcome if price competition follows production. For details see the linked article.


Does the linear probability model require the regressand to be zero/one-valued? Typically, the dependent variable in a linear probability model (LPM) is a 0/1-valued binary variable. What if the dependent variable $y_i$ is still binary but take on general values $a$ and $b$ rather than 0 and 1? Technically, the resulting predictor still retains its nice properties, e.g., it is the minimum mean squared error (MMSE) linear predictor. Again, we may also transform $y_i$ into a 0/1 variable; but sometimes we want to keep the original values, say, for interpretation.

My question is: Can we still call the estimator the LPM estimator? If not, what should we call it?

The "LPM" label refers to the structure of the equation, not to the estimator. LPM models can be estimated not only by least-squares methods but also by maximum-likelihood for example.

As regards the nature  of the dependent variable, we are talking about an affine transformation here.  Let a model be with a binary dependent variable and a single regressor for simplicity,

$$y_i = \beta_0 +\beta_1x_i +e_i$$

with $y_i \in \{0,1\}$. We are then told that the original variable was

$$z_i = a+(b-a)y_i$$

so $y_i=0\implies z_i =a$ and  $y_i=1 \implies z_i =b$.

Then the model for $z_i$ is

$$z_i = a+(b-a)[\beta_0 +\beta_1x_i +e_i]$$

or

$$z_i = \gamma_0 +\gamma_1x_i + u_i$$

$$\gamma_0 = a+(b-a)\beta_0,\;\;\; \gamma_1 = (b-a)\beta_1,\;\;\; u_i = (b-a)e_i$$

The structure of the model remains the same, an equation linear in parameters, so it is an LPM model still.

Since $(a,b)$ are presumably known values, after estimating the $z$-model, and obtaining estimates for the gammas, we can recover the estimates for the betas also, if they are of interest.


Why is the production possibility set convex? I'm studying International Trade and came across this question: Suppose a specific factor model where the global production of something is given by $Q_{w}=Q_{1}(.) + Q_{2}(.)$, with $Q_{1}, Q_{2}$ strictly increasing on all arguments and also strictly concave. So $Q_{w}$ will also be concave. As so, the superior sets of the level curves should be convex. But what I see is that the inferior set in this case is convex.

What am I not understanding here?

Perhaps you are confusing two things.

If $Q_1$ and $Q_2$ denote the production of goods 1 and 2 in a single country and you are in the space defined by them given $L_1 + L_2 = L$ then it is indeed the inferior set (the production possiblity set defined by the feasible $(Q_1,Q_2)$ pairs) that is convex. Formally this means that for all feasible $L_1,L_2,L_1',L_2'$ labor allocations you have
\begin{eqnarray*}
\mu \cdot Q_1(L_1) + (1-\mu) \cdot Q_1(L_1') & \leq &
Q_1(\mu \cdot L_1 + (1- \mu) \cdot L_1') \\
\\
\mu \cdot Q_2(L_2) + (1-\mu) \cdot Q_2(L_2') & \leq &
Q_2(\mu \cdot L_2 + (1- \mu) \cdot L_2').
\end{eqnarray*}
As this is equivalent to saying $Q_1$ and $Q_2$ are concave this is true given the condition that you describe. In this situation the function $Q_1 + Q_2$ has no meaning at all. What are we adding up? Ducks and cars? What will be the unit of measurement here?

But if $Q_1$ and $Q_2$ represent the production of a single good in countries 1 and 2 given the  amount of labor allocated and the space is $L_1, L_2$, the curves being levels of $Q_w$, then it is the upper level curves that are convex. You can see this straight away because the marginal products of $L_1$ and $L_2$ are decreasing hence their rate of teachnical substitution is 'decreasing' as well. Formally:

By definition the function $Q_w(L_1,L_2)$ is concave if for all $L_1,L_2,L_1',L_2'$ and for all $\mu \in [0,1]:$
\begin{eqnarray*}
\mu \cdot Q_w(L_1,L_2) + (1-\mu) \cdot Q_w(L_1',L_2') & \leq &
Q_w(\mu \cdot L_1 + (1- \mu) \cdot L_1',\mu \cdot L_2 + (1- \mu) \cdot L_2').
\end{eqnarray*}
We know that the functions $Q_1$ and $Q_2$ are concave, meaning
\begin{eqnarray*}
\mu \cdot Q_1(L_1) + (1-\mu) \cdot Q_1(L_1') & \leq &
Q_1(\mu \cdot L_1 + (1- \mu) \cdot L_1') \\
\\
\mu \cdot Q_2(L_2) + (1-\mu) \cdot Q_2(L_2') & \leq &
Q_2(\mu \cdot L_2 + (1- \mu) \cdot L_2').
\end{eqnarray*}
Adding these up we get
\begin{eqnarray*}
\mu \cdot \left(Q_1(L_1) + Q_2(L_2)\right) + (1-\mu) \cdot \left(Q_1(L_1') + Q_2(L_2')\right) \leq \\
\leq
Q_1(\mu \cdot L_1 + (1- \mu) \cdot L_1') + Q_2(\mu \cdot L_2 + (1- \mu) \cdot L_2').
\end{eqnarray*}
And since
$$
Q_w(L_1,L_2) = Q_1(L_1) + Q_2(L_2)
$$
we have
\begin{eqnarray*}
\mu \cdot \left(Q_1(L_1) + Q_2(L_2)\right) + (1-\mu) \cdot \left(Q_1(L_1') + Q_2(L_2')\right) \leq \\
\leq
Q_1(\mu \cdot L_1 + (1- \mu) \cdot L_1') + Q_2(\mu \cdot L_2 + (1- \mu) \cdot L_2') \\
\\
\mu \cdot \left(Q_w(L_1,L_2)\right) + (1-\mu) \cdot \left(Q_w(L_1',L_2')\right) \leq \\
\leq
Q_w(\mu \cdot L_1 + (1- \mu) \cdot L_1',\mu \cdot L_2 + (1- \mu) \cdot L_2').
\end{eqnarray*}
which is what we set out to prove.


General question about IV Suppose we want to estimate
\begin{equation} y = \alpha_0 + x_1 \beta + c'\gamma + \varepsilon
\end{equation}
where $\beta$ is the variable of interest and $c$ is a vector of controls. We suspect $E[x\varepsilon]\neq0$ but we have an instrument $z$ such that $E[z\varepsilon]=0.$ My question is - as long as IV is valid - should we care that there could be an endogenous control $c_1$ such that $E[c_1\varepsilon]\neq0$? Why or why not?

My hunch is that it doesn't because as long as IV is valid (it satisfies inclusion-exclusion principle) the correlation between controls and unobservables should not lead to the inconsistency of the estimate of $\beta$.

In general, if $c_1$ is endogenous, you need instruments for $c_1$ as well.

Example: Even when $x_1$ is exogenous, if $c_1$ is endogenous and $x_1$ and $c_1$ are correlated, then OLS (which is the IV estimator using $x_1$ as IV for $x_1$) is generally inconsistent.

Exceptions exist. For example, when exactly identified, if $(Ezc') (Ecc')^{-1} (Ecu)=0$, then your IV estimator is consistent, I guess. (Can derive this using standard technique involving the law of large numbers.)


In Mankiw's Macreoconomics, how come capital is assumed to be fixed while investment is assumed to be variable? I'm looking at Greg Mankiw's Macroeconomics (7th edition), at the model presented in chapter 3:

$Y = C + I + G,$

where $Y$ is total output, $C = C(Y-T)$ is consumption, $T$ are net taxes (fixed by policy), $I = I(r)$ is investment, $r$ is the interest rate, and $G$ are government purchases (fixed by policy). The model further makes the assumption that

$Y = F(K,L),$

where $K,L$ are the factors of production, capital and labor, and are assumed to be fixed, so that $Y$ is therefore fixed as well. Using the fact that $Y,T,G$ are fixed, it follows that $C$ is also fixed and thus saving,

$S = Y-C-G,$

is fixed. But the model entails that $S = I(r)$ and therefore any movement in saving translates into a movement in investment (and thus the interest rate). How is it possible that investment is considered variable, if investment is the purchase of new capital goods and capital is taken as fixed? If investment increases, then so should capital.

It seems that Mankiw has implicitly assumed that all the investment is used to replace the depreciated capital. See the second sentence in the Investment section of Chapter 3-3:"Firms buy investment goods to add to their stock of capital and to replace existing capital as it wears out. "

Usually, the law of motion of capital is written as
\begin{equation}
K_{t+1}=I_{t+1}+(1-\delta)K_{t}
\end{equation}
where $\delta$ is the depreciation rate of capital. By assuming capital to remain at a fixed level $\overline{K}$, I believe that Mankiw is trying to only discuss the steady state in which capital is remained at a constant level, while avoiding introducing any more details. Since this is just the beginning part of textbook, everything is made as simple as possible. There is even no time subscripts for variables!


What's the difference between loans, notes, bonds and mortgages? Long-Term Investments

Multi-year investments in:

Debt securities: loans, notes, bonds, mortgages
Equity securities: shares of other companies

These assets are normally not intended to be sold (and converted to cash) within one year

Can anyone explain what's the difference between loans, notes, bonds and mortgages?

Loan is an umbrella term for individual(s)/organization(s)/government(s) borrowing from another individual(s)/organization(s)/government(s).

Mortgage is a type of loan for the purpose of obtaining funds for real estate which also puts lien on the property (meaning if you don’t pay the loan you will loose the property).

Note is a contract for loan with specific repayment date and interest. However, I am surprised that they are listed as long term finance as these are usually payable within 1 year (although there can be exceptions).

Bonds are very similar to notes except they have usually higher term to maturity and interest payments on bonds are usually called coupons.

These are by the way not even all possible long term debt instruments, you could for example have debentures and many more. Hence, the text probably just wanted to give you some examples of these.


Behavioral Game Theory Reference Request I am interested in studying behavioral game theory, particularly in incomplete information games. However, I am having trouble finding a current "textbook" like source to learn from. I've been reading over Colin Camerer's book Behavioral Game Theory: Experiments in Strategic Interaction, however, I was curious whether there was something more recent/updated (as it's from 2003, if I recall correctly). I've found various articles on JSTOR and similar databases, but it hasn't been as fruitful an endeavor as I had hoped. Any recent text suggestions/places to look would be sincerely appreciated. (If the text I brought up is considered the "gold standard" for the field, pardon my ignorance; I've only recently started looking into the topic.)

I know a bunch of people who teach behavioral economics using Erik Angner's book.
I love Rani Spiegler's book on behavioral economics in IO called "Bounded Rationality and Industrial Organization." Both books will introduce models that can be applied to poker.
Perhaps a little lighter but still scientific readings would be Kahneman's "Thinking, Fast and Slow" or Ariely's "Predictably Irrational."
As already suggested, a "handbook" is always a good place to start: Handbook of Behavioral Economics - Foundations and Applications.


National income referred as GDP? National Income is the total value of all services and goods that are produced within a country and the income that comes from abroad for a particular period, normally one year.

Gross Domestic Product is defined as the value of the goods and services generated within a country.

By definitions,
National income= Income from within the country and from abroad.
GDP=Income within the country.

Here my doubt is I have seen in some textbooks why national income is referred as GDP and vice versa in measuring methods of national income?

The degree of precision with which the various terms for these economic aggregates are used may vary with the context.

But if one is trying to be strictly correct, three distinctions should be borne in mind:

Gross v Net: net meaning net of a deduction for depreciation of capital.
Domestic v National: national being inclusive of net property income from abroad (ie income earned by nationals from assets located abroad, less income earned by foreigners from domestically located assets) and also, as Kenny LJ points out, similar net international flows relating to employment income and taxes and subsidies.
At factor cost v At market prices: the latter being inclusive of indirect taxes.

In terms of these distinctions: GDP is clearly gross and domestic.  National income, without further clarification, could be either gross or net, but it is clearly not domestic.  So GDP and national income are conceptually distinct, although they could be numerically the same if national income is measured gross and the property income and other flows as above from and to abroad happen to net to zero.