When does the law of diminishing returns apply? Law of diminishing returns does not always apply:

The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant, will at some point yield lower incremental per-unit returns.

I interpret "productive process" as a process that creates a product other than money.

Many productive processes can be done in parallel.

I see how it is true for any process with a central control, because that is limited by the interaction with the instances, so at some point adding a new instance requires additional changes.

But A productive process does not need to be centrally controlled.

If I run a snowball factory, I can add more workers, invest in required infrastructure like gloves, and send them out to build snowballs autonomously.

The central work does not only scale linearly, it even scales constant! The total effort summed up over all instances scales  linearly.

To be strict, it scales exactly linearly because adding a later instance can not add less productivity than an earlier, because the earlier instances are not in communication with the central point at the time. The first instance does not differ from any other, because their creation does not differ.

If I would insist to earn money, the money transport is limited in  bandwidth. We have freight trains, that's good enough. But there is also a limit in snowball to money conversion by market interaction, as a market is finite.

So, producing money is limited final market size, there can be a snowball I can not sell. Adding instances does not increase production of money.

But the production of snowballs seems to be limited only by the availability of snow and homo sapiens - by climate change.

What's wrong with that?

Of course, "law" does not mean it strictly applies always. Is it that I just constructed an example outside its validity? Where is it valid, if that is well defined? Or is the argument above wrong?

Law of diminishing returns refers to profits or benefit per unit of output. This will inevitably decline, profits are defined as total revenue minus costs $\pi=TR-TC$ are thought to be increasing with production but at declining rate, this can be both due to the revenue and cost part.

Costs can in principle be increasing, constant or decreasing with scale. In the first case one source of diminishing returns would be already increasing costs. In the latter case we need to examine the revenue part, but note that most economists think that even if some businesses have constant or decreasing costs along a large part of cost curve these should eventually start increasing as eventually the demand of firm for inputs would be so great to lead to higher and higher increases in the price of those inputs. If you already hired all snow collectors you need to start hiring doctors, programmers etc. to pick snow. So at some point every cost curve should be increasing due to scarcity of inputs.

Now when it comes to the total revenue part that will also be increasing in quantity but at declining rate. The reason for this is that the market price of your good is not set in stone. Increase supply and the price will drop. All people have declining marginal utility of consumption so at some point if you supply too many units to the market the price will drop. Even if you would have constant costs or decreasing costs over the whole cost curve eventually the negative change of price due to larger quantity will be larger than any cost reduction due to decreasing costs.

So in short the law of diminishing returns for firms works both because the more you consume of something the less you desire it so demand is downward sloping and because costs should increase with production at some point along the cost curve.


Is it possible to give, in economics, an example of a relation ( set of ordered pairs) that is not a function? In mathematics, some relations ( sets of ordered pairs) are not functions.

I know economists make use of functions.

But do they also consider relations that are not functions.

In which branch of economics could "non-functional" relations be useful?

I feel that your question might be a little broad, but there are certainly many areas of economics where non-functional relations are used. Two simple examples (there are many others):

One of the most fundamental models of behavior in economics relies on the idea that choices can be represented by "preferences" which mathematically are binary relations that do not have to be functions (they very often are not, e.g., $A \succ B \succ C$ is not a function, since $\succ = \{ (A,B), (A,C), (B,C)\}$.
Economics also relies on correspondences, or ``multivalued" functions (which, depending on the definition, can be just another way to view binary relations). Correspondences are used in a lot of subfields of economics but perhaps most notably in consumer theory, where the choice set of consumer with preference $\succeq$ and budget set $B$ can be a whole subset of the consumption space $C(\succ,B) \subseteq X$ (where $X$ denotes the consumption space).


Why is LIFO allowed in accounting? I was reading about inventory valuation and of course there is first-in - first-out, last-in - first-out and weighted average. I realized at some point that LIFO would cause the highest Cost Of Goods Sold and therefore the lowest profit, in situations where the cost of purchased inventory was rising, so I figured that was a stupid method. But the book I was reading said that LIFO is commonly used in the US as part of Generally Accepted Accounting Practices (bingo!) and not allowed by international standards (IFRS).

So I wondered why a company would want to under-report profit? Well, because it lowers taxes. Is that really such a powerful reason? Wouldn't the increased profit be higher than the increased taxation in normal cases? Is this just an attempt to spite the government or something?

Also, I read that occasionally, the old inventory that has been "on the books" for a long time at a very undervalued cost can be "sold off" and generate a profit spike (just in case you did want to earn some money). These kind of machinations are unintuitive, to me.

My question is, why was this crazy method allowed at all? Historical reasons? Because it took a while for government to wise up? Why has it not been killed off because it is manipulating tax revenue and corporate reporting?

well, LIFO also lowers the value of held inventory too...IF one special thing is occurring:  Inflation.

When there is inflation, LIFO makes things look, well, a little bit better.  During deflation (or flat) FIFO makes more sense.


Increasing returns, implications? If a firm has increasing returns to scale (i.e., doubling inputs more than doubles output) would that firm logically end up being the sole firm in its sector in the long run?
If not, what is the advantage of displaying IRTS?

Provided that increasing returns to scale apply over the whole production function of the company it is likely that it would become natural monopoly. For example, Mankiw in Principles of Economics (pp 292) in some passages even defines monopolies in relation to their cost  function:

When a firm’s average-total-cost curve continually declines, the
firm has what is called a natural monopoly.

Generally the average-total-cost curve will continually decline when firm has increasing returns to scale.
However, there are models with increased returns to scale where monopolies are not inevitable. For example, Wang (2016) presents a model of banking competition where firms face increasing returns to scale, and even though the model predicts increase in market concentration it does not necessary predict that a single bank will become monopoly.


Why does lowering the value of yuan against the USD disadvantage the US and benefit China In this article : https://www.epi.org/blog/trumps-china-tariff-confusion-it-wont-solve-chronic-trade-deficits/ they claim that depreciating the value of the yuan to the USD bolstered China’s economy. The key excerpt is:

For a long time, the fundamental cause of this growing trade chasm
with China was Beijing’s deliberate currency undervaluation. Between
2000 and 2013, China invested more than $4 trillion—nearly 40 percent
of its current GDP—in foreign currency assets, primarily U.S. Treasury
securities.
And it paid off, since it drove down the value of the Chinese yuan
relative to the U.S. dollar. This served as a massive subsidy for
Chinese exports and a tax on U.S. products shipped to China.

My questions are:
(1) How does investing in US assets drive down the value of the yuan?
(2) If the value of the yuan to the USD diminishes, doesn’t that increase the purchasing power of US entities* for products in China e.g. A US citizen can purchase a house in China for less USD. So why is this deleterious for the US and beneficial for China?
*not sure if that’s the correct word to use here. Please feel free to reword q

The article reflects a consensus view of the trade situation between US and China.  Personally I see it differently :  China has been willing to make and ship trillions of dollars’ worth of goods to US in return for entries in a computer (Treasury bonds).  This is undoubtedly good for US consumers, as you say.


Economics Masters Courses? I want to do an economics masters course (not a PHD) in the UK or US preferably with a focus on game theory, auction theory, mechanism design and contract theory though I understand I'll probably have to take at least one macro and metrics course.

I found that NYU has an MA in econ and has good game theory (by Ariel Rubinstein) but are there any others?

This website will be helpful.
Ask that in here.
http://www.urch.com/forums/phd-economics


Gold and loss of faith in central banking In this article here, http://www.telegraph.co.uk/investing/gold/gold-resurgence-whos-buying-gold-and-why/ , it states that "gold tends to do....best when markets lose faith in central banking".

I understand that gold does well when other assets do badly as it acts as a store of wealth, but I cannot understand why it does well when markets lose faith in central banking. I can see that if central banking isnt working markets are probably doing badly, but the quote seems to imply a deeper and more direct connection.

Also can someone think of a historical example when this happened.

I think @DornerA gave a good answer for reasoning behind the mechanism.

For a historical example, look no further than the fiscal crisis and the rapid increase in gold price from 2008-2011.

Of course a lot happened during those years with house prices collapsing in the U.S. Faith in central banking is closely associated with the value of money and the belief of whether a central bank can keep the economy steady or not and in a situation where this belief is low, people gravitate towards widely accepted stores of wealth.


Why does an increase in money cause a proportionate increase in price level according to classical/neoclassical economists? First I am not sure what classical economists say but doesn't increase in Money supply decreases interest rate and cause investment to expand and thus GDP rises.
Therefore the aggregate demand increase, causing price level to rise. But what does proportional mean in this case?

It's a bit hard to answer without a precise model structure, but normally an increase in money will propagate into an increase in nominal demand. For the sake of simplicity, suppose money is equivalent to nominal gdp $M$, whereas real gdp by definition is given by $Y=M/P$. In classical economics, real gdp is pinned down completely by fundamentals of the economy, so that accordingly $P\propto M$ (namely by a factor $1/Y$).


Why are future expenses considered less costly than expenses in the present? I understand that future income is less valuable than income in the present because of the concept of present value, where money available today can be invested to earn interest or can be spent to avoid paying interest, whereas money that is not collected until the future cannot generate interest income or pay interest expenses.

However, if I want to explain why future expenses are considered less costly than expenses in the present, can I use the concept of present value to explain? I know it is linked somehow, but I don't know how to put it into words.

I would appreciate any help or hints. Thank you.

Let's simplify this with an example. If I gave you $100 right now, at the very worst, you could collect interest rate on it (let's assume 5%).

Let's compare two cases:

A) I gave you $100 a year ago.

B) I give you $100 now.

In the first case, you'd have collected interest and now be at $105.

In the second case you'd only have $100.

Note this same logic applies to expenses. You can pay me $100 now.

Or you can pay me $100 next year (and keep the interest for yourself).


What does 'one dollar, one vote' mean? Can you tell/ describe me what the phrase 'one dollar, one vote' means? But you have to use basic English or kid's English. :-)

I found the phrase in one economics book (Introduction to Economics by Stephen L. Slavin, page 4, 1989) and I do not know what it means. I am from eastern Europe.

Thanks for help.

It appears to suggest applying the way shareholders vote in a company to the political setting of democracy: each citizen will have as many votes as his/her monetized wealth. So the rich will have officially "more say" in what gets decided or who gets elected in public office.

Certainly, the general consensus is that economic power does play a role in affecting political outcomes anyway. This approach would make that an official, institutional rule.


Quadratic utility: monotonicity and risk aversion I am taking macro class this fall. One of the problems asks whether decreasing absolute risk-aversion and ever-increasing consumption are two unattractive implications of the quadractic utility function. Could anyone please help with this?

Quadratic utility is given by
$$u(w) = w - b w^2$$
which has derivative
$$u'(w) = 1- 2b w$$
such that for high levels of $w, u'(w)<0$. That is, the utility is not everywhere increasing. This may be weird because even people with high wealth should prefer more to less.
The second derivative is
$$u'(w) = -2b$$
such that absolute risk aversion is
$$\frac{- u''(w)}{u'(w)} = \frac{ 2b}{1- 2b w},$$
which is increasing in wealth. This contradicts evidence that wealthier people take more financial risks instead of less.


The ability of markets and prices to direct resources to higher valued uses: Is this a short run or a long run attribute? I came across the following quote in a lecture:

"In economics, we often talk about the power of markets and prices to
direct resources to higher valued uses." - Mike Munger

Is this ability of the markets to direct resources to higher valued uses considered to come into effect in the long run or the short run?

Everything below this point has been edited keeping the comment of user:Giskard in mind.

I suspect it is a long-run attribute of markets for the following reason:
Imagine that two firms A and B are bidding for raw materials. Society values the good of firm A more highly than that of firm B, and therefore is willing to pay more for the former than for the latter. In the short run, there may be discrepancies in their respective efficiencies, such that A is less productive and therefore less profitable than B. In the long run, A can adjust its methods of production and "catch up" with B in terms of profitability, thereby ensuring that it is able to outbid B (remember that society is willing to pay more for A's output). To me, it looks as if only in the long run can the resources be seen to be allocated according to its highest value to society, due to the above reasoning. Is this argument a sensible one?

No its not necessary long run phenomenon it can hold in short run as well. Rather what matters is how competitive markets are and whether there are any market failures such as externalities etc.
To be even more specific under the first theorem of welfare economics if markets are competitive, complete, information is symmetric, there are no externalities and there are no transaction costs or in general there is an absence of any market failure, then any general equilibrium in competitive markets will be Pareto-efficient.
Pareto-efficiency requires that all resources are allocated to their highest valued uses as if there would be any unexhausted potential gain from trade (i.e. a situation where two individuals each have something they do not value more than what other individual has) two individuals could increase their utility further by actually doing the trade and so the outcome would not be Pareto-efficient.
However, in real life of course the first welfare theorem fails due to market failures and other reasons. In that case market might fail to allocate resources to its most valued uses. Some of the problems might have an effect mainly in the short run and in long run they might still be efficient, but in other cases they wont. In the case you describe the two firms are actually not perfectly competitive but engaged in some monopolistic competition. In monopolistic competition market indeed wont allocate resources to their most efficient uses always in the short-run as firms will have some excess capacity (see Mankiw Principles of Economcis for example) which may imply that not all resources are employed to their most valued uses. But even here I would have to add caveats on that the result would change depending on whether we assume competition occurs on price or quantity and so on.


How can there be an electronic bank run? I read that at 2008 there was an electronic bank run.

From what I undestand bank runs occur due to the fractional reserve banking system. The actual real money you can hold on your hand are a fraction of the total money in banks. So if everyone goes to ATM and gets the money in their hand, it means that the bank runs out of the "real money" and people can't withdraw these "real money".

So if the same number of people, instead of withdrawing from the ATMs, do electronic transactions that eg get their money from a bank to another bank (or any other institution) how can there be a bank run? It just doesn't make sense to me.

What you describe is the "traditional" bank-run.

The 2008 incident you refer to, was called an "electronic bank run", because the problem was not caused by people trying to get tangible paper money in their hands in excess of the actual paper money available to the banks.

The problem was that through electronic banking and electronic wire-transfer orders "funds were redirected out of the U.S. money markets" as one account of the incident puts it.

So why is this a problem?

Because under "fractional banking", electronic money functions exactly as paper money. You work, and your employer pays your salary through a wire transfer. You go buy something and you pay with your debit card, where you transfer electronic money from your account to the shop's account.

In other words, electronic money, once created, is as much actual purchasing power as paper money is. It is wealth.

But this means that this "electronic bank run" was impoverishing the US banking system. But since the transfers were electronic, by necessity they went out of the US economy also -to some bank accounts in other countries.  It was wealth going out of the US economy, not just paper money going out of the banks but still in the economy -and at a speed and volume unimaginable in the old days, due to the wonders of the internet and digital technology.

So essentially, it is a totally different kind of problem (and more serious) than the "traditional" bank run, so it should perhaps have been characterized by using another term.


Obvious Dominance and Milipede Games (Question to Pycia and Troyan (2019) I stumbled over Millipede Games and obvious Dominance in the paper "A Theory of Simplicity in Games and Mechanism Design" by Pycia and Troyan.

On page 12 the authors define millipede Games.

They explain point 3 verbally in the text: "the last condition ensures that passing will be obviously dominant, since if x becomes impossible, then the agent will at least be able to return to any payoﬀ she was previously oﬀered to clinch."

Then they write that Figure 1 shows an example of a milipede Game. But in my understanding of their definition it is not a milipede Game, because Point 3 of the definition does not hold:

Player j could clinch x in her second move, then player i could not return to that payoff although it was previously offered to her.

What is my misunderstanding here? Looking for help! :)

It is a convoluted definition because condition 3:

"At all $h$, if there exists a previously unclinchable payoff x that becomes impossible for agent $i_h$ at $h$, then $C_i^\subset (h) \subseteq C_i^h (h)$."

means that at every history if there is a payoff that player $i_h$ could not have secured (or clinched), but was feasible at every previous history where some other player was taking decisions and now is not feasible, then the set of clinchable payoffs cannot decrease.

That is, the set of clinchable payoffs is not allowed to decrease, except when some special condition is met.

Figure 1 is an example of a millipede game because the set of clinchable payoffs never decreases for players $j$ and $k$. It only decreases for player $i$ when (it goes from $\{x,y,z\}$ to $\{x,y\}$ (from the second to the third move), but this is fine because in player $i$'s third move the only payoff that was previously unclinchable is $w$, but it has not become impossible at that history (since the only impossible payoff is $z$ that was taken by player $j$).

Hope this helps.


Can you recursively forecast one variable using two variables? My question is probably very elementary but I haven't been able to find an explanation of recursive forecasting that I fully understand.

I've read a journal article that seemed to recursively forecast unemployment with an AR(2) process augmented by a variable for depth of recession lagged by one period. It seems to me like that wouldn't be possible if the model doesn't produce forecasts for the other variable to include in the forecast for the subsequent period as well.

So does recursive forecasting use actual values for each subsequent forecast or forecasted ones? And does it just do that for the auto-regressed variable or both? Is it a standard practice to use forecasted values for one variable and actual ones for another?

I have quarterly data on unemployment (U) and change in total lending (DL) in an economy. I want to estimate an AR(2) for U plus DL at t-1. How can I make out of sample forecasts with this model? Is my only option to use predicted values for DL that are forecasted by a separate model?

If it is possible to have actual values of the other variables for example let’s say variable $y$ is always provided by statistical bureau with 5 year lag but for second variable $x$ the values are always up to date you can use them.

However, if you have data for both $y$ and $x$ up to date and you want to make forecasts for next year and further in the future you will have to do auxiliary forecasts for $x$ as well.

When you are doing some out of sample evaluation and you want to make a thought experiment of how the model forecasts $y$ conditional on knowing what was the $x$ then you can do that, but such evaluation won’t be indicative of actual performance when in real life both future $y$ and $x$ is unknown. This is the biggest downside of multivariate forecasting.

However, you can always make an auxiliary forecast for the $x$. Let’s say with an auxiliary AR model for the $x$ variable.


Why don't most of the highly educated people in poorer part of Europe migrate to the Western part? There are a lot of people working in universities in countries like Ukraine, Belarus, Romania, Bulgaria, Poland, and so on with low salaries. Those people have high skills and education.

I saw some students pursuing PhDs in those countries with low salaries when they can just cross the border to earn much more.

Why don't most of them migrate to Western Europe?

What factors bind them in their countries?

There are numerous reasons why one would want to stay in a particular country even though earning power is lower.  These are usually summarized as "frictions" in the labor market.

Culture, familiarity with an area, language, family are all non-negligible "frictions".

I note that while there will be a tendency to vote this closed as not economic, I think the reminder that there are meaningful human incentives other than money and tangible goods may be worth remembering.


Labour Saving vs. Labour Augmenting - what is the difference? It seems reasonable to say that technology generally increases output per unit of labour.  Therefore in any factory which has installed new technology one can reasonably expect that for the same output one is likely to need less employees than before (or perhaps the firm will retain the same number of employees but output will increase).  Therefore, in either case, the output per employee has increased.  Therefore one could say that labour has been saved by the new technology.  One could also say that labour has been augmented by the new technology as each worker is supported by the new technology and is now more productive.

My question is: do we have clear definitions of these two terms and what is the difference?

Consider a Leontief production function:

$$ Y = \text{min}(aL,bK) $$

Optimal capital-labour ratio is:

$$ \frac{K^*}{L^*}=\frac{a}{b} $$

Labour-saving technical change is such that $a$ increases. The optimal capital-labour ratio increases, this is, firms use less labour per unit of capital. This is also called Capital-augmenting technical change (see reference [2]).

Labour-augmenting technical change is such that $b$ increases. The optimal capital-labour ratio falls, this is, firms use more labour per unit of capital.

Notice that how output per worker changes depend on how $Y$ changes. For example, assume that the above adjustment is such that $Y$ is unchanged after the technical change. Then, output per worker increases in the labour-saving case but falls in the labour-augmenting change. A complete analysis would require a general equilibrium approach, where factor prices are endogenous. All I am showing here is that it is not necessarily the case that either type of technical change increases output per worker.

Some references: [1], [2].

PS: I use the Leontief for simplicity. In a Cobb-Douglas, any technical change is Hicks-neutral, as it does not affect the K/L ratio (assuming fixed factor prices). In a CES, the nature of technical change depends on the elasticity of substitution.


Cryptocurrencies: Is it possible to estimate price from market cap? I'm looking at a website that figures out the potential price of a coin if it had a certain market cap.
I'm not sure I understand the underlying calculations though.
It's well established that: Market cap = Circulating Supply * Price
So, if you plug in a market cap value, you'd still need to know the coin's circulating supply to determine its price:  how is it possible to determine the circulating supply of a coin at any given point in time?

The standard definition of market capitalisation is:
Market capitalisation = (number of units in existence)*(price).
Update: VARulle gave a link to the definition they use for “circulating supply”: “The best approximation of the number of coins that are circulating in the market and in the general public’s hands.” They need to eliminate “burned” (destroyed?) coins as well as those that might be lost or sent to unrecoverable addresses.
This is an estimate, and so different sources might get different values. Adjusting market cap in this fashion is not normally done in other asset classes, as people generally want to avoid the use of estimates in discussions.


What's the name for this type of non zero sum game? Many times you hear Economics is a "non zero sum game" implying that anything that is earnt by one person or group isnt lost by other. This might not be the definition of non zero sum game, but that's how it is used many times. What I believe it happens it's part of what is earnt by a person or group is lost by other and other part isnt.

In the other hand, you have "zero sum game", where everything earnt by someone is lost by other.

Is there a name for a game where part of what a person or group earns is part of what other person or group loses, and other part of what this first person or group earns isnt part of what other person or group loses?

As far as I know the definition is yet to be extended beyond two person games, but you seem to be looking for some notion of antagonism.

A two player game is antagonistic if given any two outcomes A and B, if player one prefers outcome A then and only then player two prefers outcome B.

Read more here.


Does vNM rationality depend on the good chosen? The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function, such that the person will tend to maximize the expected value of u. For this reason, the hypothesis that people satisfy the von Neumann-Morgenstern rationality axioms is known as expected utility theory. Now in my question here, I asked about a confusion I had concerning the Ellsberg paradox, one of the major challenges to expected utility theory.  But as I thought more about it, it seems to me that the fundamental issue was more general than the Ellsberg paradox.

Consider some good X. Let $L_1$ be the lottery that gives you a guaranteed 2 units of X, and let $L_2$ be the lottery that gives you a 50% chance of 1 unit of X, and a 50% chance of 3 units of X.  Then my question is, is it always consistent with the von Neumann-Morgenstern axioms to prefer lottery $L_1$ to lottery $L_2$?  Or are there some goods X such that it's inconsistent with the vNM axioms to prefer $L_1$ to $L_2$?

Well, suppose that good X is dollars.  Then if u is the vNM utility function, then the expected utility of $L_1$ is equal to $u(2)$, and the expected utility of $L_2$ is equal to $.5u(1) + .5u(3)$.  And it's certainly not inconsistent with the vNM axioms for $u(2)$ to be greater than $.5u(1) + .5u(3)$; that just means the person has diminishing marginal utility/risk aversion.

But now let's choose a different good X.  Consider a raffle where four raffle tickets are placed in a hat, a single ticket is pulled out, and whoever the ticket belongs to wins a 100 dollars.  Let good X be raffle tickets in this raffle.  Then the probability of winning a 100 dollars is equal to .25 times the number of tickets you own.  So under this scenario, the expected value of $L_1$ is $.5u(100)$, and the expected value of $L_2$ is $(.5)(.25)u(100)+(.5)(.75)u(100) = .5u(100)$.  Thus the expected value of the two lotteries are equal, so it is irrational to prefer $L_1$ to $L_2$.

So what is going on here?  How is preferring 2 units of X to a 50% chance of 1 unit of X and a 50% chance of 3 units of X vNM-rational for one good X but not vNM-rational for another?  Just to add to the absurdity, what if someone were making a decision between lottery $L_1$ and $L_2$ where good X  is dollars, and then was planning to use the money he made to buy raffle tickets?  Then wouldn't the choice between $L_1$ and $L_2$ where X is dollars reduce to the choice between $L_1$ and $L_2$ where X is raffle tickets?

Any help would be greatly appreciated.

Thank You in Advance.

In the Von Neumann-Morgenstern theory, arguments of the utility function are final consumption goods. The utility function is extended over lotteries by linearity but it does not really make sense to assume that the individual "consumes" the lotteries L1 and L2 in your scenario with the raffle tickets: what he ultimately consumes is the 100 dollars monetary prize. Therefore there is no reason to expect something like diminishing marginal utility over lottery tickets - but only over final monetary prizes.

This property comes from the independence axiom: intuitively, the decision-maker views randomizations over lotteries and randomizations over final consumption goods differently. This behavioral pattern (that you find paradoxical) is usually called Reduction of Compound Lotteries. In your scenario, it says that the agent views the lottery L2 and the lottery that is computed by compounding the second-order probabilities as equivalent objects. There are some reasons to question the relevance of this axiom if you want to dig deeper (for instance, it has been found that Ellsberg-like behavior is associated with an aversion to compound lotteries).

I hope it helps.


In the UK, does the rate of annual price increases in food consistently beat inflation? How can we tell? Informally, I've often seen it claimed that the price of food always goes up. Certainly, I do notice when the price of my £5 food bag goes up 50p or when my £1 milk goes up 20p. Yet, whenever I've asked those with an interest in economics why they aren't investing in stockpiles of food, they laugh and tell me that doing so would be to bet against human prosperity and that over time, the price of food goes down. Clearly, both side cannot be correct. I've tried to look in to this on my own, for example I've tried to use the data available at https://tradingeconomics.com/united-kingdom/food-inflation however, I've noticed that the common measures of inflation are often based on food prices, and I suspect that the measures of "food inflation" will be somehow influenced by some other measure of inflation, so I've reached the point where I believe that I will need the help of the more skilled folks here. Is there an easy answer to this question?

The short answer is: No, the changes of food prices in the UK sometimes beat inflation, but not always.

To answer the question, you can simply look at the long term development of food prices in real terms. Note that "real" in the economic context generally refers to something being adjusted for inflation.

The graphic below, shows this development. It was taken from the Department
for Environment Food & Rural Affairs. You can access the underlying data here:

Now, why is it so often informally and apparently wrongly claimed that the price of food always goes up? I cannot provide you with a definitive answer, but I would assume that it is connected to the negativiety bias and the fact that most people generally tend to forget about inflation. Why do they forget? Well, maybe the italian economic-historian Carlo Cipolla was actually right.

Lastly: Does the fact that food prices have indeed risen in real terms in the UK, during certain periods, mean that human progress has indeed been going backwards, for a while?
No, not necessarily. We need to be aware that not only the price of the food we consume changes, but also its quality. For example: Regulations on food retailers, that grow evermore tightly, could lead to a continous increase in food prices but also reduce the number of foodborne illnesses. Human prosperity could therefore be growing, even while food prices increase.
This also means, that in some cases, it might indeed be rational to bet on an increase of food prices in real terms. Just dont stockpile food, the warehouse costs will almost certainly outweigh the gains and most food doesnt tend to get better as it ages.


Numbers of right and left gloves Question? I assumed that numbers of right gloves at the horizontal axis and numbers of left gloves at the vertical axis. Therefore, two goods are essential and indifference curves are L-shaped. However, I want to ask that if my left hand is broken and I cannot wear the left glove for 12 months, does the indifference curve look like https://ibb.co/BfmF53H  Also, what can I say about its utility function? Can I say that its utility function looks like $U(x,y) = x^\alpha$

I don't think it is appropriate to apply the such static visualization to dynamic problem. Let us for a second forget about the graph - the graph is just a visualization of the indifference curve.
If two things are perfect complements which are consumed in 1:1 ratio their utility is given as:
$$u(x, y) = \min \{x, y\}$$
In this case (before you break the arm) the indifference curve will indeed look like L. If you break your arm the utility function would have to change but if we assume that the second good $y$ does not give you any utility it will just default to some utility of one variable $u(x)$.
However, for the $u(x)$ we cannot meaningfully plot an indifference curve and neither we can do it for $U(x,y) = x^{\alpha}$. Why? Because indifference curve is by definition a curve along which utility of consuming some combination of $x,y$ is constant. If $y$ does not gives us any utility then the person will always just consume maximum $x$ possible. Why should the person even care about $y$ at all? In such case the concept of indifference curve becomes meaningless as there is nothing to be indifferent about. You always just consume as much $x$ as possible.


Why Certainity Eqivalence in PIH only holds for quadratic utilities In my current macro economics course, it has been stated that there is certainty equivalence in the random walk permanent income hypothesis ("which implies individuals act as if future consumption was at its conditional mean value and ignore its variation") only holds if the utility is assumed to be on form $$ u(c) = c - ac^2/2 $$
I have consulted the coursebook but could not find any rigorous proof or intuition of this. Could anybody help please?

Certainty equivalence in the context of the Permanent Income Hypothesis implies that $u'(E_t[c_{t+1}]) = E_t[u'(c_{t+1})]$, which only holds if marginal utility $u'(\cdot)$ is linear (by linearity of expectations) and thus only if actual utility $u(\cdot)$ is quadratic.

To see where this comes from, consider the utility maximization problem of a representative household over an infinite horizon where consumption stream $\{c_t\}$ and asset holdings stream $\{a_{t+1}\}$ are chosen, taken as given the real interest rate, fixed at $r$, initial wealth $a_0$ and a stream of income $\{y_t\}$. Lastly, take utility to be quadratic over consumption: $u(c_t) = \alpha c_t - \frac{1}{2}c^2_t$ with sufficiently large $\alpha$.

So the household's maximization problem is

\begin{equation*}
\begin{aligned}
& \underset{\{c_t, a_{t+1}\}}{\text{max}}
& & E_0\sum_{t=0}^{\infty} \beta^{t}u(c_t), \text{ where } \beta = \frac{1}{1 + \rho} \text{ , } \rho > 0 \\
& \text{s.t.}
& & c_t + a_{t+1} = (1+r)a_t + y_t & \forall t.\\
\end{aligned}
\end{equation*}

$$
$$
Therefore, the Lagrangian for this maximization problem is

\begin{equation*}
\mathcal{L} = \sum_{t=0}^{\infty} \beta^{t} \{E_t[u(c_t) + \lambda_t((1+r)a_t+y_t-c_t-a_{t+1})]\}.
\end{equation*}
$$
$$

The first-order conditions of the Lagrangian are
\begin{align}
\frac{\partial \mathcal{L}}{\partial c_t} &= \beta^{t} u'(c_t) - \beta^t\lambda_t = 0 &&(1)\\
\frac{\partial \mathcal{L}}{\partial a_{t+1}} &= -\beta^{t}\lambda_t + \beta^{t+1} (1+r)E_t[\lambda_{t+1}] = 0 &&(2).
\end{align}
$$
$$

Solving for $\lambda_t$ using (1) and substituting into (2) gives
\begin{align*}
u'(c_t) = \beta (1+r)E_t[u'(c_{t+1})].
\end{align*}
$$
$$

Take $\rho = r$ in this economy for simplicity. Thus $\beta(1+r) = 1$:
\begin{align*}
u'(c_t) = E_t[u'(c_{t+1})].
\end{align*}
$$
$$

Since utility is quadratic, marginal utility is linear which implies that the expectation of marginal utility is the marginal utility of the expectation:
\begin{align*}
u'(c_t) = u'(E_t[c_{t+1}])
\end{align*}
which implies that
\begin{align*}
c_t = E_t[c_{t+1}]
\end{align*}
since $u'(\cdot)$ is injective. Thus we have certainty equivalence.


Understanding Tertiarization of the Economy Trying to understand some of the core mechanics of tertiarization in developed economies.

According to the WorldBank,

  "As incomes continue to rise, people’s needs become less “material”
  and they begin to demand more services—in health, education,
  entertainment, and many other areas.

  Meanwhile, labor productivity in services does not grow as fast as it
  does in agriculture and industry because most service jobs cannot be
  filled by machines. This makes services more expensive relative to
  agricultural and industrial goods, further increasing the share of
  services in GDP."

Trying to understand in a bit more detail some of these claims though, such as:

Why does higher income imply less "material" demands, i.e. products specifically formatted as services rather than goods (couldn't rich people in theory just crave more expensive pharmaceutical drugs, textbooks, and gaming consoles, rather than associated healthcare, education, and entertainment services)?
Why can't most service jobs be filled by machines?  Does this just mean as technology stands today (vs. roombas, retail kiosks, self-driving cars, etc.)?  What if any inherent characteristics of services make them more difficult to automate?
Why does inefficient production make services more expensive, and this make them a higher percentage of GDP?  (Here I'm just trying to understand the economic principles involved)

Thanks!
Benji

I' m not sure its a law, its what has happened because manufacturing productivity has moved faster. Indeed, the robot economy might well get rid of most service jobs and we'll all be making or programming service robots for each other.

It's related to this paper Buera-Kaboski, Rise of the Service Economy
But here are some potential explanations:

Maybe after you eat and get dressed you want to be entertained. Entertainment needs novelty, creativity, showmanship, etc. These will always be services because they are a constantly changing stream that needs to be adapted. Imagine a machine that produces new TV shows for you. You would still buy a stream of new ideas for the machine to produce TV shows with contemporary content.
Maybe its best understood as a relative statement. Richer people/countries can have a consumption level that demands more tailoring and specialization that existing manufactured goods provide: Gap produces all kids of clothing, but you want something just a little more specific for you, a tailored suit that's better than the off the shelf one. Naturally, tailored, consumer specific consumption is more a service than a good, because in its nature it is not mass-produced.
In general, goods are produced for the masses, (Bill Gates cannot buy a better iphone than you can), so as a country gets rich, it moves towards services....

  Why does inefficient production make services more expensive, and this make them a higher percentage of GDP? (Here just trying to understand the economic principles involved)

This seems counterintuitive right?: Why would they become a larger part of the economy if they are inefficient? Clearly, this depends on the exact substitutability of products and the rate of satiation.

However, in principle, its not difficult to imagine how this happens. Suppose we can only eat about 2000 kilo-calories a day. Back when we were eating 1000 kc/d, increasing farm productivity increased out consumption of food, and potentially the size of our income we devoted to food until we hit the 2000 kc/d. But as farm productivity increases more, we eat the same, but it costs less and less to produce it, so we devote less and less of or budget to it. Which means we devote more and more to services...


Is it possible to eliminate the U.S. national debt? A political science teacher of mine has said that the U.S. national debt has grown way beyond reach and is now just a political talking point with no real value.  He says that there is no point in trying to pay it back and that it should be left alone since all the money is fiat, thus "imaginary".  What's your take on this?  Is it still possible to pay off the debt in 'x' amount of years without experiencing hyperinflation?

Yes, I imagine there's reason to contest that claim. Consider the GDP to debt ratio. While it has risen over time and with the recent recession, it was not too far away from Germany which is considered, I think, the absolute picture of fiscal health.

Consider also the critical point that the US government does not have a chance of death like a normal citizen. For example, if you take 30 year loan from JP Morgan, they consider the possibility that you might die. It is critical that they acquire this money before that happens- or they will lose their investment! The government does not have such concerns, and as a result face supernaturally low interest rates. Furthermore, they can pay back debt at a leisurely pace, extend their debt frequently, and if the interest rate is below the rate of inflation (Which it has been!), then they actually earn money by waiting to pay it back.

One of the main reasons for the increase in the debt-to-GDP ratio has been not an increase in spending, but a noticeable decline in government income.  The US tax rates are at historic lows. Even worse the US GDP has been smashed by the recession. The debt could be paid back eventually if it were politically feasible to raise taxes while keeping expenditures constant. The banks of the world have bet billions, trillions if you count derivative and second-stage investments, on this feasibility.

Finally, despite the fact that it is fiat money, it would be very unwise to act as if the debt didn't exist.  Note the panic over congress's threat to default. The consequences of even contemplating a default included: higher future interest rates, lower GDP, and  typically, a devalued currency. Conversely, if money is printed to cover the debt, the consequence is hyperinflation, leading to widespread drops in the standard of living. In my estimation,  if the United States did go into a spontaneous and total default, or hyperinflated to pay the debt- this would likely be the greatest economic disaster of all time, given the size of the US GDP currently. This is not hyperbole- I do not think there is a serious macroeconomist who would disagree.


How to find the points on a budget line? Hulk goes to the gym 20 times a month. His income is 1,000 per
  month and his visits to the gym cost $4 per visit.

  Draw Hulk's budget line for visits to the gym and all other goods,
  show the consumption bundle that maximizes his satisfaction, and
  draw the indifference curve through that point.

How do I find the quantity and price for "all other goods"?

You generally set the price of "all other goods" to \$1, as "all other goods" is usually measured as "dollars worth of all other goods." Then the maximum quantity of all other goods is just the available income. Then to find the quantity of other goods Hulk buys, just find out how much money is available after he vists the gym 20 times.


Method of Lagrange multipliers with random variables I'll illustrate the issue I'm having with a simple problem.

Let $c_1, c_2 \in \mathbb{R}$, and $Z$ a real-valued random variable. Let $u:\mathbb{R} \rightarrow \mathbb{R} $ be a differentiable function, and $f(c_1,Z)$ be a real-valued function that is differentiable with respect to $c_1$.

The problem is:
Maximise: $u(c_1) + \mathbb{E}[u(c_2)]$
such that $c_2=f(c_1, Z)$

This problem is easily solved by direct substitution, and the answer is

$u'(c_1) + \mathbb{E}\left[u'(f(c_1,Z)) \frac{\partial f(c_1,Z)}{\partial c_1}\right] = 0 \label{answer}$

The issue is how to write down a Lagrangian whose extrema correspond to the solution of this problem in the normal way.

My first instinct was to write
$\mathcal{L} = u(c_1) + \mathbb{E}[u(c_2)] + \lambda(c_2 - f(c_1,Z))$.

However, this doesn't seem to make sense.
If you treat $c_2$ as if it is a random variable, then the derivative of  $\mathbb{E}[u(c_2)]$ with respect to $c_2$ gives zero, and this can't possibly give the right answer.
On the other hand, it doesn't make sense to treat it as non-stochastic either, since it is 'forced' to be stochastic by the constraint.

Question: How do I write a Lagrangian whose extrema correpond to the solution of the above optimisation problem?

If you treat $c_2$ as if it is a random variable, then the derivative of
  $E[u(c_2)]$ with respect to $c_2$ gives zero.

Why? Such an assertion doesn't follow from anywhere. The subtleties lie elsewhere. The problem with the Lagrangian considered by the OP

$$\mathcal{L} = u(c_1) + \mathbb{E}[u(c_2)] + \lambda(c_2 - f(c_1,Z))$$

is that it also is a random variable since now $Z$ appears outside the expected value (The direct substitution approach followed by maximization with respect to $c_1$ only, does not create any such issues).

Now, do we /  can we maximize a random variable? Well, no, because the essential characteristic of a random variable is that it is a function whose value cannot be set by command and control.

But one could say "ok, let's pretend that this Lagrangian is not a random variable, and just write down the conditions for maximization, even though we know that we can't force the solution".

But this won't work: if one attempts to do it one will eventually obtain

$$u'(c_1) + \mathbb{E}\left[u'(f(c_1,Z))\right] \cdot  \frac{\partial f(c_1,Z)}{\partial c_1} = 0 $$

which is not the same as the condition obtained through direct substitution, because here the partial derivative is outside the expected value.

(for those who may think "hey, then how do we apply maximization procedures in the maximum likelihood approach" the answer is that there, nothing is random anymore when we get to apply the maximization steps).


Does real GDP control for changing preferences? This claims that real gdp does not account for changing preferences.
However, if preferences were to change for sneakers and subsequently pushes the price up, won't this be reflected in the changed price of a basket of goods?

I think the confusion here may be about the phrases "control for" and "account for".
Real GDP "controls for" prices, meaning that if prices change (say every price doubles), then real GDP shouldn't change either.
In contrast, real GDP does not "control for" preferences, because if preferences change, then real GDP will also change.

The phrase "account for" is ambiguous and could mean either "control for" (as described above) or "is affected by" (pretty much the exact opposite meaning).


Is weak global economy always a "headwind"? In the most recent (Mar. 20, 2019) FOMC Press conference, Powell said this:

  So, global economy was a tailwind for the United States
  in 2017.  That was the year of synchronized global growth, and we
  began 2018 expecting and hoping for  more of the same. What happened
  instead is that the global economy started to gradually slow,  and now
  we see a situation where the European economy has slowed substantially
  and so has the  Chinese economy, although the European economy more.
  And just as strong global growth was a  tailwind, weaker global growth
  can be a headwind to our economy.

Question

His logic makes sense, and yes this is a world of interconnected financial markets, but I still wonder is Powell's assertion axiomatic here with the larger community of economists?

Just merely playing devil's advocate, I would suspect that because of the Eurozone troubles in recent years, this helped the dollar stay stronger than it would have otherwise, citaris paribus. Not to say that currency valuation is everything, but is there really no counter argument for Powell's stance?

Randomly, I came across a compelling counter-argument just today which I will share below. I'm not sure I buy into this theory whole-heartedly, but there are some valid points and it's worth reading through, even just for the sake of generating more discussion:

  America benefits when everybody is worried about problems abroad, and
  as a result of that they buy dollars. What does that do for America?
  Well, a stronger dollar keeps a lid on consumer prices for Americans
  and it keeps a lid on interest rates for Americans. Also if people are
  buying into dollars and dollar denominated assets, it helps sustain
  asset prices. That's a double win; the worse things get abroad the
  better things get in the United States. But it works the same way in
  reverse. When people have a more optimistic outlook on global growth,
  then they don't need the dollar as a safe haven. And now the dollar
  starts to fall. That means we now have upward pressure on consumer
  prices. That puts upward pressure on US interest rates. And that puts
  downward pressure on US assets, because there is no longer demand for
  US treasury bonds, for US stocks, for US real estate, because now
  people want to invest internationally. That's where the money will go
  because that's where investors will find growth, and that will in turn
  hurt the US economy. -- Peter Schiff


Obj function yielding independent goods demand functions I know that if the objective function (aka utility) is homothetic, demand functions will be linear in income. So for an homothetic demand function to give goods independent of prices other than their own, one has to have a Cobb-Douglas function as it also has to be homogeneous of degree zero.
My question: can someone supply an example of a class of preferences yielding price independent demand functions $x_i = g(\frac{y}{p_i})$? (no prices nor income in preferences, just quantities)

[Challenge to think, not to give long proofs please. Just sketch proofs with the important steps if feel it's important]

So if we take a simple example with 2 goods and consider the consumer's problem:

$L=u(x,y)+\lambda(I-p_xx-p_yy)$

This yields the ratio of FOC:
$u_1/u_2=p_x/p_y$

Now plugging these guys into the budget:

$I=p_xu_1^{-1}(u_2p_x/p_y)+p_yy$

A sufficient condition is $u_1^{-1}$ be hod -1 to make $p_x$ drop out. But I don't think it's necessary.

Now I'm not exactly sure what that means (the inverse of the marginal utility of a good is homogeneous of degree -1), but a great thing to think about.


China: sectoral data I'm looking for economic data on China's main sectors (output, factor prices etc). I haven't really seen anything with a long sample -- with the possible exception of Cheremukhin/Golosov/Guriev/Tsyvinski (2015). The Economy of
People’s Republic of China from 1953.

Does anyone know if there are any good sources available? thanks.

Good data sources from China are hard to come by. For official data, you can find nearly all available data series through the company called CEIC, although this is somewhat expensive. In general, the history of many of these series doesn't go very far back either, since it is only in the last decade or two that China has really become serious about collecting economic data. If you want something that goes back to before 1990 or so, there are perhaps academic sources that do this (I don't know them), though this data will probably be based on very rough estimates in that case.


These two estimators are equal? I have a question so basically.
I have two model $$y= X_1b_1+X_2b_2+u$$
And $$X_2=y\beta_1+X_2\beta_2+v$$
I want to show $b_1=\beta_1$
Are these estimators are equivalent?
$$b_1= (X_1’M_1X_1)^{-1} X_1’M_2y$$
And
$$\beta_1= (X_1’M_2y)^{-1} (X_1’M_1X_1)$$

They are both OLS estimators but generally $\beta_1 \neq b_1$.
In statistics broadly speaking estimator is just some rule, method, or criterion for arriving at an estimate of the value of a parameter. According to Stachurski: A Primer in Econometric Theory, pp 217:

An estimator is a statistic used to infer some feature $\gamma(P)$ of an unknown distribution $P$. Thus a statistic becomes an estimator when paired with and compared to feature of the distribution. Nothe that there is nothing in the definition of an estimator that implies it will be a sensible estimator of the target feature, let alone a good one.

Consequently, by definition if you use the following formulas:
$$b_1= (X_1’M_1X_1)^{-1} X_1’M_2y$$
$$\beta_1= (X_1’M_2y)^{-1} (X_1’M_1X_1)$$
for an inference they become estimators. Moreover, both of these look like OLS estimator. So in that sense they are the same type of estimator.
However, running the same estimator will not give you the same result when you change position of dependent and independent variable (in fact OLS estimator will be biased if there is reverse causality so it does not make any sense to do it in the first place). Consequently generally speaking $\beta_1 \neq b_2$.
In fact in your specific case:
$$y= X_1b_1+X_2b_2 + u \implies X_1=y\frac{1}{b_1}-X_2\frac{b_2}{b_1}-\frac{u}{b_1}$$
Consequently, we have:
$$\beta_1 = \frac{1}{b_1}; \beta_2 = -\frac{b_2}{b_1}; v = -\frac{u}{b_1}$$
Trivially since $\beta_1 = \frac{1}{b_1}$,   $\beta_1 \neq b_1$, save for some special cases such as when $b_1=1$ for example.


Why consumption is defined as $ C_t:= \left(\int^1_0C_t(i)^{\frac{\epsilon-1}{\epsilon}}di\right)^{\frac{\epsilon}{\epsilon-1}} $ I am reading Monetary policy, inflation, and the business cycle: an introduction to the new Keynesian framework and its applications by Gali.

In section 3.1 he presents/defines the consumption as
$$
C_t:= \left(\int^1_0C_t(i)^{\frac{\epsilon-1}{\epsilon}}di\right)^{\frac{\epsilon}{\epsilon-1}}
$$

$\epsilon$ is the elasticity of substitution and $i$ indexes the goods available for consumption. It is related to the New Keynesian Model.

Can someone give me verbal explanation of why it make sense to define the consumption this way?

$C_t(i):$ How should interpret the $i$-line?

For some reason Ubiquitous edited this information into the question, rather posting it as an answer:

  $i$ indexes the goods available for consumption

Integrals are just sums with a lot of components (technically infinite). Here the space of goods is assumed to have large dimension, rather than just consisting of two or three types of goods.


Why is the Dollar Index strong after the Fed dropped the Fed Fund Rate? I have a query about the current forex market. In 16 March 2020, the US Federal Reserve Bank announces to cut the interest rate to 0%. This move supposedly weaken the Dollar Index, but why for a sudden movement it becomes stronger?

It is always very hard to precisely identify the causes of a particular index variation. Here, note that the U.S. Dollar Index (DXY) is a measure of the value of the US dollar relative to a basket of foreign currencies. So, the DXY Index goes up when the U.S. dollar gains value when compared to other currencies. Given that the economic slowdown is global, the US dollar could strengthen relative to other currencies


Other factors that affect the supply of money I've read that it is not a hard-and-fast rule that the overall money stock growth rate speeds up in response to an accelerated expansion of the monetary base and a growing money multiplier. If this is the case, what factors unrelated to central bank policy and the lending propensity of commercial banks would cause this theoretical deceleration of money stock growth?

I assume that this question is related to this question on money growth - link to question

The monetary base and velocity completely pin down the wider monetary aggregate. The behaviour of acceleration is slightly trickier, but I will attack it here.

I will firstly use continuous time for simplicity. I will also use my own notation, which is explained.

Let $M$ be whatever wide monetary aggregate you want to study, and $B$ be the monetary base. Velocity $V$ is defined:
$$
V = \frac{M}{B}.
$$
Importantly, this is a definition, and always holds. There is no reason to ascribe changes in velocity to any particular factor, such as preferences of banks.

Then, the rate of change of the money stock is:
$$
\frac{dM}{dt} = \frac{d(BV)}{dt} = B\frac{dV}{dt} + V\frac{dB}{dt}.
$$
Since we are interested in the percentage rates of change, we define growth rates as the time derivative of the variable divided by the variable. That is,
$$
G_M(t) = \frac{\frac{dM}{dt}}{M},
$$
$$
G_B(t) = \frac{\frac{dB}{dt}}{B},
$$
$$
G_V(t) = \frac{\frac{dV}{dt}}{V}.
$$

Then, we see that:
$$ G_m(t) = \frac{B}{M}\frac{dV}{dt} + \frac{V}{M}\frac{dB}{dt}.
$$
Since $\frac{B}{M} = \frac{1}{V}$ and $\frac{V}{M} = \frac{1}{B}$,
$$
G_m(t) = \frac{\frac{dV}{dt}}{V} + \frac{\frac{dM}{dt}}{M} = G_V(t) + G_B(t).
$$
Since you are interested in acceleration, that would be $\frac{dG_M}{dt}$, which is given by:
$$
\frac{dG_M}{dt} = \frac{dG_V}{dt} + \frac{dG_M}{dt}.
$$

In other words, to characterise the acceleration of the money supply, you need to look at the acceleration of the monetary base and the acceleration of the velocity. If we refer back to the question on the money supply in the 1990s, you would have had to calculate the annual percentage change of velocity, and not look at the level of velocity (which is what was displayed).

If we return to discrete time (and observed data are discrete time), the relationships above become approximations. You would have to take the first differences, to get the rate of change, and the difference of the rate of change to get acceleration. For annual data, that means we end up comparing data two years apart, which may break the continuous time approximation.

Since this question asked about other factors influencing the relationship between the base and wider money: there are none. The above equations hold by definition. The question why velocity would change is a more difficult question.


How to calculate average buy price when you buy, sell and rebuy I wanted to get my avaerage buy price for some stocks I bought and see if I made money.

So far for just buying and then later selling I have been calculating the avaege buy price using this formula

((stockamount * price) + (stockamount * price)) / (stockamount + stockamount)

so If I buy 10 shares at 2.00 and 5 shares at 3 I would get average buy price of

((10 * 2.00) + (5 * 3.00)) / (10 + 5) = 2.33

This is how I have calculated the average sell price as well.

Recently I have bought some shares, sold them at a higher cost, and then re bought some when they slightly went under what I sold them at.

I have no idea how to figure out my average buy price in this situation because I re bought some.
here is sample data
bought 10 @ 2.00
sold 7 @ 3.00
bought 2 @ 2.50
I thought maybe doing something like this

((10 * 2.00) - (7 * 3.00) + (2 * 2.50)) / (10 - 7 + 2) = 0.8

It does not make any sense that my average buy was 0.8

I have searched but cant find the answer to a buy, sell and rebuy. if someone knows what the correct formula is to calculate the average buy price when you buy, sell and rebuy please let me know.

Thanks!

I am a Canadian, and under Canadian tax laws, I think there are at least two ways of determining your cost basis for shares. I am not going to get into the details of tax accounting; please see a qualified tax professional for advice.

However, if you just want to track your profit and loss for analysis purposes, the standard way of determining the book value of your positions is to track the average cost. You track the number of shares you own, and their total cost.

When you buy more shares,

the total cost goes up by the total you paid in the transaction (=(# shares in the transaction) * (transaction price)),
the number of shares increases by the amount in the transaction

You get the average cost by dividing the total cost by the number of shares.

When you sell, the price you sell at does not matter for the determination of your average cost. You reduce the number of shares by the number of shares in the transaction, and you reduce the total cost by the (average price)*(number of shares in the transaction). This means that selling does not change the average price, just the number of shares.

Your profit on selling is based on comparing the selling price to the average cost. This would be the “cost of goods sold” in inventory accounting. (If you want more details on this subject, you could look for primers on inventory accounting on the internet.)

What you appear to want to do is to roll the profits or losses from a sale into the total cost. That is, if you made a profit, use that to lower the “total cost” of the shares so that you can compare that average of that “total cost” to the market price, and quickly tell if you are profitable.

Although that might be convenient, it probably would not be acceptable under most accounting conventions (so no textbook will tell you to do it that way). It also would give some strange-looking results. If you made \$1 million profit on some shares, and then sold all but one of those shares, you would have a “cost” of about -\$1 million for that one share. Most people would look at you funny if you showed them that number on a spreadsheet.


State variable or jump variable In my OLG model, I have two law of motions for capital and pollution
\begin{align*}
&K_{t+1} = s_t\\
&P_{t+1} = (1-\delta)P_t+\rho K_t
\end{align*}
where $K$ is capital, $s$ is the saving from the last generation and $\rho, \delta$ are exogenous parameters. Pollution in my model is just a by-product of the use of capital. Firms and households do not take it into account when making decisions in each period. I know that $K$ is a predetermined (state) variable, but I am not sure whether pollution ($P$) is a state variable. In my numerical simulation, one of the absolute value of the eigenvalues is greater than one and the other one is smaller than one in my two-dimensional system.
Originally I think both $K,P$ are state variables. Any comments to my misunderstanding will be appreciated.

I'm assuming pollution is a bad in consumer utility (as is typically seen) or otherwise relevant to some agent's payoffs -- if it's not, then $P_t$ is irrelevant and you might as well ignore it.
$P_t$ is a state variable: it's something which describes the history of the system, and is necessary to compute utility. See page 117, Definition 3.1 in these notes for a more detailed definition of state variables ("utility function" = "contribution function"), the section has some more interesting discussion as well.
If pollution appeared in utility and you were solving a planner's problem, I think there would be no confusion since you would need $P_t$ to calculate the decision rule. Where your problem gets a bit different is that the agents don't use it to compute their decision rules. Mechanically, that makes your calculations a bit simpler: optimize agents' objectives over potential values of $K_t$ only, since the decision rule is going to be "flat" over $P_t$.
That an eigenvalue is bigger than one suggests that pollution or capital in this economy will "explode". But that doesn't bear on whether $P_t$ is a state variable or not.


Reductionism, value and market economics If I'm not mistaken, the economic value provided by a business entity to the community is just one kind of value. We tend to put numbers to things such as stock price, revenue, profits and so on. However, there is an aspect of value that cannot necessarily be measured, such as benefits to a local community.

Is there any great loss when we don't take into account the non-economic factors? Has there been any good discussion in the literature on this?

You are mistaken. Economics doesn't actually concern itself with measurable quantities, but rather with the behavioral functions that give rise to measurable quantities (such as price, investment, etc). The most obvious example of this is the utility function, as they are unique up to scale – meaning that there are several (actually infinitely many) which nonetheless do the same thing.

Consider the prisoner's dilemma, for instance: we might introduce for each player a scale factor which multiplies his whole payoff matrix. But no matter how we change those payoffs, so long as the structure of those matrices is preserved so will be the behavior of the prisoners. So nothing really changes. But that is fine, because what we're not interested in modelling is the value of the choices to each player, but how the players choose.

So it isn't necessary to introduce any concept of the measurable economic value of anything so long as we might say that it is preferable to something else. Which is to say that we might model the behavior of any agent without introducing a cardinal measure: we can do fine if his choices are merely ordered (this is the idea behind Revealed Preference, which was initially formulated by Paul Samuelson as an alternative to utility functions, but which was later on found to be equivalent to them).

But to answer what's bugging your mind: there isn't practically anything even mildly relevant to human life which economists won't deal with. Because in so far as people's choices are observable, they can be treated by an economic model. For instance, there's a chapter in the Handbook on the Economics of Leisure which is called The Economics of Sleep and Boredom. I've also seen a paper once on the economics of suicide (there's actually a small literature on this). Another example – though less odd and more important – is Becker's theory of crime, which takes crime out of the domain of other social sciences (which might explain it in terms of marginalization, poor education, etc) and into the domain of expected utility and choice theory (i.e. what are the odds the guy think he has of getting away given the circumstances).

Contrary to popular opinion, dealing with money and crunching numbers is often the least important and most boring part of an economist's job. Most often economists are concerned with figuring out why people would do what they do.


Seminal papers that later were proven to contain errors I was reading on institutions, and I came across Acemoglu, Johnson and Robinson (AJR) paper on The Colonial Origins of comparative development: An Empirical Investigation, and this paper seemed so 'perfect' that spawned a lot of other papers based on the data of ancient settler mortality rate and how it was used by AJR as an IV for the current quality of Institutions in former colonies.

However, as I began searching more on this paper, I found out that the paper is in fact ridden with errors, specially on data treatment. (Albouy's 2012 comment on the same paper, published by The American Economic Review)

I would like to know, if, besides this paper on development economics, are there any other seminal papers, in any area of economics, that later on were proven to have crucial mistakes/errors that invalidated the paper conclusions?

My favorite example is the initial formulation of Arrow's impossibility theorem in the first edition of Arrows' "Social Choice and Individual Values" (1951). In the first edition, Arrow claimed that, together with 4 other conditions, the following domain condition

  ``The domain $\mathcal{D}$ is sufficiently extensive so that there exists at least one free triple of
  alternatives. (A triple is called free if all conceivable
  combinations of individual orderings of this triple actually occur in
  $\mathcal{D}$" (rewording from Blau(1957))

implied that there exists no social welfare function $S : \mathcal{D} \rightarrow \mathcal{R}$, where $\mathcal{R}$ is the set of all possible orderings (i.e. complete and transitive binary relations) over the set of alternatives $A$.

This was later showed to be false by Blau (1957) The Existence of Social Welfare Functions" Econometrica Vol. 25, No. 2 (Apr., 1957), pp. 302-313 who provided a counter-example.

Blau also showed (among other things) that the theorem could be corrected by replacing the above domain condition by the following condition

  Universal domain : the domain $\mathcal{D}$ of the social welfare function contains every possible profile of preferences over the set
  of alternatives $A$ (with $|A| \geq 3$).

Arrow later corrected this mistake in the second edition of Social Choice and Individual Values (1963), and the formulation of Arrow's theorem using the Universal domain condition has now become standard.

This being said, the initial error in the first edition of Arrow's book was rather minor, and the solution proposed by Blau does not reduce in any strong sense the importance of Arrow's result and approach. Intuitively, the conclusion remains that on a vast domain of relevant economic problems, no social welfare function satisfies a set of rather basic and reasonable conditions.

So this might not be exactly the kind of errors you were looking for (definitely a seminal paper though!), but I like the example so much I could not resist posting it . If such brilliant people like Arrow make these kind of mistakes, I guess it takes a little bit of the pressure off for everyone else?


Is measurement error in self-reported health a problem in this scenario...? I am running regressions to estimate the impact of health conditions on life satisfaction.

I have read a paper that showed that there is likely to be measurement error in the self-reported health variables in that those who do not work are more likely to report health problems to justify not working.

My question is, is this a problem for my estimates? I include various dummy controls to capture employment status so do I simply control for this potentially problematic bias due to measurement error?

Or, is the bias still there in which case I guess it would be a downward bias? Does my use of panel data and fixed effects make any difference?

Check the correlation between health status variables and employment status. Start with simple pairwise correlations and then perform auxiliary regressions where you regress a health indicator on the employment status variables.

If there is visible explanatory power in employment status for health indicators, you may want to treat health indicators as endogenous variables and employment status as instruments. Depending on the number of variables, this may be the Two-stage Least Squares estimator.


Do any social welfare functionals, other than maximin, meet all of Arrow's conditions plus invariance regarding ordinal level comparability? In the literature on social welfare functionals, the only example I've seen of a functional which meets all of Arrow's conditions–––or at least utility analogues of Arrow's conditions–––plus invariance regarding ordinal level comparability is Rawls' maximin. E.g. Sen in On Weights and Measures (1977, p. 1544) cites maximin as his case of a functional meeting all of these conditions. Maximin orders the alternatives by the welfare of individual who is worst off. I assume that the inverse of maximin–––i.e.  the alternatives are ordered by the welfare of individual who is best off–––would also meet these conditions.

Is there any work on other social welfare functionals which meet all these conditions? (I'm aware that if we tweak these conditions slightly we can derive other functionals, but I'm interested in the case in which we keep them unaltered.)

If not, is this evidence that maximin, and its inverse, are the only normatively sensible social welfare functionals that meets all these conditions? Or is it just evidence that people aren't so interested in this set of conditions? (If there is a clear reason why this set of conditions is uninteresting, I'd love to hear it).

Thanks for any help!

Utility analogues of Arrow’s conditions:

Utility analogues of Arrow’s conditions are Arrow’s conditions redefined for Sen’s welfare functional framework.  Instead of taking a profile of orderings as input, Sen's functional takes a profile of utility functions as input: $U \ = \ <u_{i_1}(X), \ u_{i_2}(X), \ \dots \ , \ u_{i_n}(X)>$. $U$ is defined on $X \times N$; each individual, $i \in N $, is paired with each alternative, $x \in X$, and the result of each pairing is the utility derived by $i$ from $x$. $\mathcal{U} \ = \ \{U^1, \ U^2, \ \dots \ , \ U^n \}$ is the set of all possible utility profiles. $\mathcal{U^*}$ is the set of all utility profiles which meet a particular domain restriction. $\mathcal{R}$ is the set of all possible orderings of $X$. A social welfare functional can then be defined as: $f: \ \mathcal{U^*} \longrightarrow \mathcal{R}$. The final ordering given by profile $U^1$, $f(U^1)$, is denoted: $R_{U^1}$. We can then define utility analogues of Arrow's conditions:

Unrestricted Domain$’$: The domain of $f$ is the set of all possible utility profiles: $\mathcal{U}^* \ = \ \mathcal{U}$.

Weak Pareto$’$: $\forall x, y \in X$, $\forall i \in N$: $( \ u_i(x) \ > \ u_i(y) \ ) \ \Longrightarrow \ (xPy)$.

Non-Dictatorship$’$: $f$ does not single out one individual $i \in N$ such that, $\forall U \in \mathcal{U^*}, \ \forall x, y \in X$: $( \ u_i(x) \ > \ u_i(y) \ ) \ \Longrightarrow \ (xPy)$.

Independence of Irrelevant Utilities: $\forall U^1$ and $U^2$ $\in \mathcal{U^*}, \ \forall x, y \in X$: $(\forall i \in N \ (( \ u^1_i(x) = u^2_i(x) \ ) \land ( \ u^1_i(y) = u^2_i(y) \ )) \ \Longrightarrow \ (( \ x R_{U^1} y \ ) \ \Longleftrightarrow \ ( \ x R_{U^2} y \ ))$.

There are at least two other examples of SWFs that satisfy these conditions.

The first is a positional dictatorship.  Let N be the number of individuals (assume it is fixed).  For any k between 1 and N, the kth positional dictatorship SWF orders social alternatives in terms of the preferences of the "kth best off" agent.  Formally, given any social alternative x, let v(x), be the vector of utilities of all individuals for x, but ordered from lowest to highest.  The  kth positional dictatorship SWF is then defined by the kth component of the function v.  If k=1, we get the maximin.  If k=N, then we get the "maximax" ---what you call the "inverse" of the maximin.  If k=[N/2], we get effectively "dictatorship of the median individual".   The point is not that these rules are normatively attractive (they aren't) ---but they satisfy your axioms.

Another possibility is the so-called leximin or lexicographical maximin rule.  This is the lexicographical extension of the maximin, obtained by ranking social alternatives according to the vector-valued function v from the previous paragraph, but with coordinates treated lexicographically.  Thus, alternative x is better than alternative y if it has a higher minimum utility value. If x and y yield the same minimum utility, then we compare them by looking at the utilities of the second-worst off individual in x and y.  If these individuals also have the same utility, then we look at the third-worst off individuals, and so on.

This SWF is very similar to maximin, but it satisfies a stronger version of the Pareto axiom.

For more information, I suggest you look at the 2002 article by Claude d'Aspremont and Louis Gevers entitled "Social welfare functionals and interpersonal comparability", which is Chapter 10 of the Handbook of Social Choice and Welfare volume I (Arrow, Sen and Suzumura, eds.).  You could also look at Chapter 2 of the book Axioms of Cooperative Decision-Making, by Hervé Moulin (1988).  In particular, Theorem 2.4 on page 40 of Moulin's book might be useful to you:  it says (roughly) that the positional dictatorships and their extensions (such as leximin) are the only SWFs satisfying ordinal level comparability and a few other mild conditions.


Consumer demand: a function of present endowment? I don't know about you, but each time I go shopping for groceries, my purchasing decision takes into account what I already have at home. I don't make only one demand decision for my entire life the day I become a consumer, and afterward never buy anything ever again. Rather, each and every day, my daily demand for goods is a different function than it was yesterday. Similar to the concept of marginal utility, my daily demand for goods depends in part on what goods I have already have acquired yesterday (and all the days before that in which I have been a consumer).

Let's take a concrete example. Whether I want to buy a soda today depends partly on whether or not I already have one in my possession at home that I could drink. Namely, if I purchased a soda yesterday and it's still in my fridge, I don't want to buy one today; on the other hand if I don't have a soda in my fridge, I do want to buy a soda today. My particular demand function for soda, as I just described it, depends on my present endowment of soda.

However, in the way demand is traditionally modeled, the amount of a good $x$ you wish to buy, $x(p,w)$, is a function only of prices $p$ and wealth $w$. The amount of each good you already have in your possession does not enter as a parameter in the demand function.

(Admittedly, your wealth, which enters in your demand function as a single parameter $w$, CAN be calculated from your present endowment of goods, as a linear combination of their respective market prices. But it's not the actual quantities of those endowments that enter into the demand function -- only the total money-value of all your endowments, in units of the numeraire good. That is, only the amount of the numeraire good you possess actually enters as a parameter into the demand functions for non-numeraire goods.)

I am sure that classical demand theory is not flawed. At the same time, there is a disconnect in my mind between how I think about demand (which makes sense to me only in the context of one's present endowments), versus how demand is traditionally modeled. Can someone help me bridge this gap?

Although it's often left unstated, demand for a good is measured as quantity per unit of time.  Broadly, the longer the time period over which demand is measured, the smaller the (proportional) effect on demand of the initial endowment.  Whether you have a soda in your fridge one morning may make the difference between your demand for soda that day being $0$ or $1$. But over the next year, if you often consume sodas, it may make the difference between your demand being $n-1$ or $n$, only a very small proportional difference if $n$ is large.  For this reason, even at the individual level it can often be appropriate to ignore endowments as a determinant of demand for frequently consumed goods.

At market level, a further consideration is that the effect of endowments may average out over many individuals. At a certain time, for example, A has a recently purchased washing machine, B's washing machine is in mid-life, and C's is old and needs replacing soon.  In the absence of changes in income or major improvements in washing machines, it may be that in any year approximately the same proportion of people have a demand for a new washing machine, so that both the aggregate endowment of washing machines and the market demand for new washing machines are approximately stable.  Again, therefore, it could be appropriate to ignore endowments.

But there are also many situations where neither of the above apply and it is important to consider endowments as a factor affecting demand.  These include: in consumer markets, take-up of goods embodying new technologies; in housing markets, the size and condition of the existing housing stock; and in commodity markets, stocks of for example wheat or copper held by commodity traders.


Why is Mises "permitted" to define "Economics is an a priori science", if a priori is not trustworthy? Why is Mises "permitted" to define "Economics is an a priori science", if a priori is not trustworthy?

In philosophy of science and natural sciences a priori as a method of knowing has long been identified to be sufficient only in special cases and more broadly mainly just among the formal sciences (mathematics, ...). By sufficiency I mean that it's sufficient for obtaining enough information in order to make empirically accurate predictions.

Since economics is about empirical things (people, resources etc.), then defining economics as an a priori science just seems very naive, if not even dangerous, because when combined with politics, such economics could propose anything and then claim validity to it, because "well it's an a priori science". What if one claimed that "Islam is an a priori science"?

Although I disagree with von Mises, he was reacting to what he saw as a very real problem, which was the use of relatively primitive statistical methods to describe behavior.  In fact, Leonard Jimmie Savage's work on probability and statistics should have been sufficient to meet his objections, although the computational speed would not have yet existed for that to have been worthwhile.

The challenge the Austrians have is that they are really arguing that no regularities exist in human behavior.  They do not see it that way, but probability and statistics are about the discovery of regularities.  Their position is that humans are too unique to be subject to statistical measurement.  All of economics could be solved axiomatically, in his understanding.

I would agree with him, as long as you got every axiom correct and the set was complete and properly partitioned for all possible cases.  Of course, the only way you could know that would be empirically and that would defeat his argument.

Although other branches of economics use axiomatic assertions, they then check to see if the predicted behavior really happens that way.  If so the axioms are at least not disconfirmed.  Most assumptions are also things nobody would disagree with.

For example, there is a proposition that humans prefer some things to other things.  If you also assume that for any pairing of goods, we will call them x and y, then either y is not dispreferred to x or x is not dispreferred to y, or neither or dispreferred to each other. If you add transitivity where for all triples x,y,z then if x is not dispreferred to y and y is not dispreferred to z then z is not dispreferred to x.

If those conditions hold, then it can be shown by theorem that it must be true that a utility function exists such that if the utility of x is not less than the utility of y then y is not dispreferred to x.

If those assumptions do not hold, then something else is true, but if they do hold then the entire mathematical theory of functions opens up to economics.  With the addition of some other mild assumptions, then calculus becomes available.

These do not need empirical checking because it is the only possible outcome, by force of math.  To go much past this point, however, becomes tenuous.  For example, must some of these functions be concave or are there circumstances where they could be convex.  If they can be convex, do real-world examples of this convexity exist?  Do real-world examples of the concave case exist?  Are there forced implications from either case or the existence of both cases?

These questions can only be approached empirically.


Effects of increased income over short and long run in AD-AS equilibrium model I've read in a few places that increased income/wages shifts SRAS to the left, which makes sense because firms' costs are increasing to pay for them. My textbook says that there's no effect on aggregate demand, but this doesn't make sense to me because if people have more income to spend then at each given price level of goods in the economy the amount consumers are are willing to buy will increase, shifting aggregate demand to the right (at least in the long run).

Side note: I'm asking because I'm curious about what this means for the monetarist/neoclassical view of macroeconomic equilibrium; specifically, why aggregate demand does not change between long and short run and why aggregate supply moves to the intersection of LRAS and AD.

Because higher wages do not necessarily mean that national income increased. From macroeconomic perspective national income is output. Higher wages in these simple models do not necessarily translate into higher output.

For example if these higher wages come from company’s profit then on one hand one (worker) household income increases but another (entrepreneur) household income decreases. Assuming all households have the same marginal propensity to consume this would not affect aggregate demand or national income. This is not necessarily realistic assumptions and there are more complex models that relax it, in that case higher wages could boost aggregate demand.

Also the side note is the same question you already asked here.


Universal carbon price To pre-face this, I am not an economist by education. Recently I have read a significant number of policy papers concerning climate change that make the claim, a priori, that a universal carbon price is the most efficient method for decarbonising the economy.

I am looking for a justification of this claim?

The justification goes back to the work of Pigou in the early 20th century. The essence is this: the burning of fossil fuels creates a negative externality: a cost that is incurred, but not by that consumer, but by the general population, and for a century or so.

This in essence creates a kind of "social subsidy": the price does not fully reflect the costs. This means that fossil fuels are over-consumed, relative to the economically efficient quantity.

As I wrote on that other answer: the "Economics Help" site explains the issue

The deadweight loss from fossil fuel consumption is the red striped triangle: this comes about because fossil fuel producers do not have to pay for their pollution, leading to a competitive advantage, and an artificially high quantity sold Q1 at price P1.

This inefficiency can be corrected (in long-run equilibrium) if the externality is priced back in - which is what the carbon price is intended to do.

Given the presence of fossil-fuel incumbents, their lobbying power, and their decades of direct and indirect subsidies, it is highly likely that a carbon price set at the marginal social cost of carbon would be an insufficient signal. A very helpful one, but insufficient on its own.