Why does the aggregate consumer spending decrease due to to lower expected future disposable income instead of MPC? This illustration is from Krugman's macroeconomics textbook, it's supposed to illustrate following situation (assuming that it happened for many people):

  Conversely, suppose you have a good job but learn that the company is planning to downsize your division, raising the possibility that you may lose your job and have to take a lower-paying one somewhere else. Even though your disposable income hasn’t gone down yet, you might well cut back on spending even while still employed, to save for a rainy day.

In other words, the shift allegedly happened due to bad news about expected future disposable income.

By the way, here is the aggregate consumption function on which the plot above is based ("A" stands for the aggregate autonomous spendings by consumers, "YD" stands for aggregate disposable income of households):

But I don't believe that the plot will shift like this in response to such bad news, it seems to contradict what I learned about microeconomic autonomous spending (I believe that the same must be true for aggregate autonomous spending). It's spending that you just WON'T reduce, they are too critical. You will tap into your savings, you will borrow or ask for charity, you will break the law, - but you absolutely WON'T reduce your autonomous spendings. You don't save money by decreasing your autonomous spending when you hear bad news, you just won't, it's your bare minimum that MUST be spent.

What I imagine will happen instead is that the marginal propensity to consume will decrease, increasing savings of people before the storm arrives, consequently changing the slope of the (aggregate) consumption function.

I understand that it's a textbook, so my reasoning must be wrong and the textbook must be right, but I fail to see mistakes in my reasoning.

But I don't believe that the plot will shift like this in response to such bad news, it seems to contradict what I learned about microeconomic autonomous spending (I believe that the same must be true for aggregate autonomous spending). It's spending that you just WON'T reduce, they are too critical. You will tap into your savings, you will borrow or ask for charity, you will break the law, - but you absolutely WON'T reduce your autonomous spendings.

This is sort of correct, but not completely. In a narrow sense autonomous spending is a persons spending when her or his income is 0. As you mentioned consequently many textbooks use examples like people always must eat even if they dont earn any money. However, that suggest that autonomous spending is set at a bare subsistence level and that is not true.

It was already recognized by Adam Smith in his magnus opum the Wealth of Nations that what is and what isnt necessity, and thus something that would determine autonomous spending, is context dependent. As Adam Smith writes:

  linen shirt … is, strictly speaking, not a necessary of life. Greeks and Romans lived, I suppose, very comfortably though they had no linen. But in the present times, through the greater part of Europe, a creditable day-labourer would be ashamed to appear in public without a linen shirt, the want of which would be supposed to denote that disgraceful degree of poverty which, it is presumed, nobody can well fall into without extreme bad conduct.

Hence, autonomous spending can change and it is dependent on the 'opulence' of society in general as well as of the individual. For example, if you would be a relatively rich commodity trader and you would be fired from your job (hence reducing your income to 0) you would not dis-save just to consume on subsistence level, but dis-save enough to maintain the minimum you would consider necessary for yourself. If you expect that long term you wont be part of the upper status class but will have to become middle class person you can move your autonomous spending to the level consistent with whats necessary for such person to live. Hence changes in expected income can move the whole consumption function up and down.

The slope of the consumption function (or the marginal propensity to consume) changes when person decides to consume smaller or larger fraction of their total income not just when consumption falls. For example, if your income is 1000 and your MPC is 0.6 you consume 600 and save 400. If your income is 500 you would consume 300 and save 200. In such example income changed but MPC remained the same.

MPC can change with income but empirically the poorer people have higher MPC than richer People. I dont have the Krugman's book but many textbooks include examples where the MPC is hold constant by assumption as a thought exercise and only changes to income are considered in similar fashion.

However, I also agree that the Krugman's wording is confusing as he talks about "saving for a rainy day", which can to many readers suggest MPC should decrease.


Accounting profit in macroeconomics as compared to microeconomics In Macroeconomics (2019) on p.103, it is argued that the reason there exists profit in an economy is that most firms own rather than rent capital. Thus:

But, Microeconomics assumes a different definition of economic profit. It is the surplus after deducing opportunity cost and implicit costs.
Why is there a difference in the definition of accounting profit between the fields of Macroeconomics and Microeconomics?

There is no difference in definitions. In macroeconomics the economic profit is also surplus after accounting opportunity cost and all  other implicit and explicit cost.
What the equation above says is just that the accounting profit also contains return to capital. That also hold in microeconomics for any firm that owns and uses capital in its production function.
For example, typical microeconomic profit equation will be given as:
$$\Pi = PF(K, L) − wL − rK$$
where $P$ is price, $F(\cdot)$ output, $w$ wage, $r$ return, $L$ labor and $K$ capital. In the equation above the firm rents capital from some other firm. However, if If firm owns its capital rather than rent it the $rK$ will belong to the firm owner and be part of their profit (you can think of it as firm 'renting' capital from itself).
The equation above simply states that the accounting profit will be sum of economic profit (i.e. surplus after all costs are accounted for) plus any return on the capital they provide.
In fact in both microeconomics and macroeconomics this extends even further. If firm owner provides also labor/entrepreneurial labor, then the accounting profit will be actually given by $\text{accounting profit}  = \text{Economic Profit} + wL + rK$.
Again this is not something that would be different in economics. To see this just rearrange the expression for economic profit.
$ \text{Economic Profit}  = \text{accounting profit} - wL - rK$
The above literary tells you that economic profit is surplus after accounting the explicit and implicit costs of labor and capital. The wage and rent should already reflect the opportunity costs of using that labor and wage elsewhere.


Black-Litterman---in what way are expected returns hard to estimate? In the Wikipedia article about the Black-Litterman model, it states that the motivation
behind model is that "it is difficult to come up with reasonable estimates of expected returns." Why is it that expected returns are difficult to estimate, whereas the covariances are not?

Your question relates more broadly to modern portfolio theory, and can be illustrated via mean-variance analysis of a univariate time-series. The extension to the multi variate (normal) setting, is trivial. Below I use the term accuracy, in a non-formal way, relating to the variance of an estimator. In particular, when the variance of an estimator can be reduced, take this to mean the estimator can be made more accurate.

Short story: The variance of the estimator for the variance of returns can be reduced by taking more observations (finer observations - up to a limit), whereas this is not true for the variance of the estimator of the expected returns. In this sense, it is more difficult to accurately estimate expected (mean) returns compared to variance of returns.

To see why, consider a time-series of returns, and assume the mean (per unit time), $\mu$, and variance (per unit time), $\sigma^{2}$, are constant over non-overlapping time intervals of frequency $h$. Here, $h$ represents daily, or monthly, or quarterly periods, etc. Further assume that our time-series data are observations over time intervals of length $\Delta$, where $\Delta<<h$. Then, define $n=h/\Delta$, as the number of observations of returns during a time interval of $h$.

For the $k^{\text{th}}$ observation interval (of length $\Delta$) during a period of length $h$, without loss of generality, we can assume that the price process for an asset is given by $$S_{k+\Delta}=S_{k}\exp{(\mu\Delta+\sigma \sqrt{\Delta} \epsilon_{k})},$$ where $\epsilon_{k}$ are iid normal. The logarithmic return (over period $\Delta$) can be written, as
$$X_{k}=\mu\Delta+\sigma \sqrt{\Delta} \epsilon_{k}.$$ For mean-variance portfolio theory, we require estimates of the true values of $\mu$ and $\sigma$, since they are of course, unknown. Call these estimators $\hat{\mu}$ and $\hat{\sigma}$. To answer your question, we only need consider the properties of these estimators.

First
$$\hat{\mu}=\sum_{k=1}^{n}X_{k}/h, \quad \mathbb{E}(\hat{\mu})=\mu, \quad \text{Var}(\hat{\mu})=\sigma^{2}/h.$$

Importantly, the variance of $\hat{\mu}$ depends upon the total length of the observation period and not on the number of observations.

Now consider, the (biased) estimator for $\sigma$:
$$\hat{\sigma}=\sum_{k=1}^{n}X_{k}^{2}/h, \quad \mathbb{E}(\hat{\sigma})=\sigma^{2}+\mu^{2}h/n, \quad \text{Var}(\hat{\sigma})=2\sigma^{4}/n+4\mu^{2}h/n^{2}.$$

The bias can be neglected (see reference for details).

Importantly, the accuracy (variance) of the estimator for $\sigma$, $\text{Var}(\hat{\sigma})$, does depend upon the number of observations, $n$ - for fixed $h$.

The consequence of this is, for fixed $h$, by taking finer (smaller) observations intervals, $\Delta$, the accuracy of the variance estimator can be improved ($\text{Var}(\hat{\sigma})$ can be reduced). This is not true of the variance of the estimator of the expected (mean) return, $\text{Var}(\hat{\mu})$, whose accuracy can be improved only by increasing the observation period, $h$.

The reference for this is

Merton, R. C. On estimating the expected return on the market. J. financ. econ. 8, 323–361 (1980).


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

Necessary Caveats When Discussing Slavery:
First before tackling this question it is important to note that this issue is broad and complex. This is because there is no single 'slavery'. For example, slavery under the Roman Empire was not the same as slavery practiced in US south (see Tamin; 2017). Furthermore, even within a given society there might be different parallel forms of slavery. This is especially true if you count as slavery all 'unfree labor' such as indentured servitude or serfdom which were similar to slavery (Russian serfs could even be bought and sold see Kolchin 1990).  Hence it is extremely difficult to generalize about an institution that has been practiced differently all across world and time until very recently, and making exhaustive review of all forms of slavery and unfree labor is beyond scope of stack exchange. As a consequence I will mainly focus in my answer on the sort of slavery that existed in the US although I will try to keep thigs as general as possible.
Second, when we discuss whether slavery made an economic sense we have to distinguish between economic sense from point of view of society and point of view of few private individuals. For example, mercantilism is demonstrably not economically beneficial to society and generally tends to make economies poorer than they could be without it, which you can learn from any international economics textbook (see Krugman et al (2018) for example). Yet despite of that you could historically find many merchants who became fabulously rich thanks to mercantilist doctrines. North Korean or Venezuelan institutions also make local elites extremely rich but are arguably disastrous to the general level of economic welfare in their societies. If government would give a company monopoly on apple production it would greatly benefit the owners of said apple company but  hurt consumers much more so on net basis it would be not economically desirable to have it.
Slavery from Private Perspective:
From narrow private perspective slavery was profitable. For example, according estimates provided by Conrad & Meyer (1958) the slave owners in antebellum US could expect to see return in excess of $10\%$ during certain time periods. According to Fogel & Engerman (1974) returns of plantation owners using slave labor were comparable to those in manufacturing.
Generally speaking if slavery was not privately profitable for people engaged in the slave business they would not continue to do it on any large scale. Yes even if it would not be profitable some individuals could have kept slaves as a some sort of Veblen good to signal their high status, and I am sure historically some wealthy individuals kept slaves for only this purpose, but on any economy-wide scale slavery would not persist if it would not bring benefits to the slaveholders themselves.
Slavery from Societal Perspective
From a societal point of view the economic literature suggest slavery had more costs than benefits. For example, Anderson & Gallman (1977) argue that slave ownership is detriment to specialization. The reason for this is that if you own slaves you own them whether demand for your goods is high and low. Slaves are essentially a fixed cost for a business because you need to shelter them and feed them even if you dont have any work for them whereas free laborer can be just fired and hired at will. As a response slave owners were often not engaged in just one single line of business (like just picking cotton) but had to also diversify and use their slaves for various tasks.
However, such diversification is detrimental to economic welfare and even economic growth as specialization leads to both higher efficiency and hence allows economies to produce more, but what even more specialization can also have dynamic effects that allow economies to grow more faster (inventions & discoveries are usually made by specialist not by 'jacks of all trades'). Consequently, Anderson & Gallman argue that slavery in long run stifled the economic growth in south and hence been detrimental to southern economies even if for the slave owning elite benefited from such system. Other authors such as Genovese (1976) went even so far as to claiming that slave ownership was detrimental to the development of 'capitalism' as it discouraged  development of towns and commercial centers.
Furthermore, generally from a development perspective we recognize two types of institutions (see Acemoglu and Robinson Why Nations Fail);

Inclusive Institutions - “inclusive economic institutions… are those that allow and encourage participation by the great mass of people in economic activities that make the best use of their talents and skills”

Extractive Institutions - are defined as the opposite of the above inclusive institutions (and authors even mention slavery as prime example of extractive institution).

And developmental research shows (again see Acemoglu and Robinson) that extractive institutions are detrimental to economic development. In fact the authors argue that most of the differences between 'rich' and 'poor' countries today can be explained by the fact that  countries that are high income today tended to adopt inclusive institutions while the low income countries mostly relied on extractive institutions. Now slavery is only one of myriad of institutions so it is possible that a country would manage to develop even despite of it. Also the contrary holds a country where most institutions are highly extractive but does not have slavery will still not be able to develop itself. Nonetheless, their research suggests that slavery would be detrimental to economic development.
An concrete example of study that looks at unfree labor would be study of Dell (2010) that using regression discontinuity (in order to ensure exogeneity) examines the long‐run impacts of the mita, an extensive forced mining labor system (which is very close to slavery) in effect in Peru and Bolivia between 1573 and 1812. Results show that this system had persistent effect on lowering household consumption by around 25% and increases the prevalence of stunted growth in children by around 6 percentage points in subjected districts today (long after the system was abolished). Furthermore, the study shows this system had also persistent negative effects on other developmental measures such as integration of road networks and that also the regions that used to had mita are less industrialized and focus more on subsistence farming even today.
There are also some studies that highlight that slavery also had some positive economic impacts. For example, Williams (1944) argues that even though slavery was overall detrimental to economies of Americas it helped to develop international financial networks and in turn international banking has first order effect on economic development. Nonetheless, international financial systems would most likely develop thanks to the international trade eventually anyway so the benefits of slave trade were likely just indirect.
Furthermore, all of the above does not even take into account the welfare cost associated with the loss of utility experienced with by the slaves themselves. This utility loss was undoubtedly tremendous and any economic analysis from societal point of view has to take it into consideration.
Lastly, as pointed out by Giskard in his +1 comment, slavery was not abolished just due to economic reasons (and the same can be said about serfdom or myriad of other extractive institutions). Moral and socio-political factors play role as well. For example, top US public economists are generally in favor of well regulated market for kidneys as this poll shows, yet US does not have such market and this is most likely because most voters would consider such market immoral regardless of any general welfare benefits. Consequently, one should not assume that some economic policy exists or ceases to exist solely because it is or ceases to be economically efficient. You should also note that slavery was most prevalent in the  past when democracy was not ubiquitous as today, and even countries that had democracy extended franchise only to the land holding elites (which were also most likely the ones to own slaves) and was further restricted based on other ethic or gender characteristics. Thus extension of franchise probably played big role in abolition of slavery and other forms of unfree labor but these are questions for political scientists, historians, sociologist and anthropologists to answer.


Is it possible to have transferable utility in non-cooperative games? Transferable utility is a concept that seems to be associated with cooperative game theory and coalitions. I would like to know if there are any examples of transferable utility in non-cooperative game theory.

Well, in a lot of mechanism design uses money and assumes agents' valuations are quasilinear. So monetary payments are essentially "transferable utility".


Terminology for "part" of extensive form game How should I call a "part" of an extensive form game which is neither (i) a subgame, nor (ii) a stage in a repeated game?

For instance, consider the class of games constructed by "stacking" 2 Stackelberg games, but where the identity of the player who choses first in the second part may depend on the actions in the first part.

I believe these kinds of games are not strictly speaking repeated games (right?).
If that's correct, I cannot really speak of the first "part" of the game as the first "stage" (or can I?).

Do you know of any standard terminology to talk about such "parts" of games which are not strictly speaking stages of repeated games?

Edit: if you can substantiate your answer with examples of papers where the terminology you propose is used, that would be even better.

A "part" of an extensive form game that is not a proper subgame because it does not start at a single node but an entire information set would be called "continuation game". This terminology is fairly standard (Perfect Bayesian Equilibrium).

However, I think what you are after is a stochastic game which consists of several states. Each state corresponds to a different game. In your example there would be two states: One state for each player $i\in\{1,2\}$ being the Stackelberg leader. Then you also need a transition process that maps the period-1 state and the period-1 action profile into a probability distribution over period-2 states. You then find equilibria for all state games in period 2 and proceed to solve for equilibria in period 1 with the corresponding (probability-weighted sum of) continuation payoffs.


Pooling equilibrium in akerlof's lemon market with certification cost Consider a market for 300 used cars where 1/3 of all cars are good quality cars and the rest are bad quality cars. All these cars are owned by (potential) sellers to begin with and each seller owns only one car. Suppose the value of a bad car is 20 to the buyers and 10 to the seller The valuation of a good car, however, is 100  for a buyer and 50 for a seller. Assume the number of buyers on the market exceeds the number of sellers and as a result seller and the bargaining power(the price of any car in the market will be its value to the buyer)
Question: Suppose there exists a certification test costing C that can identify good cars with certainty. However, bad cars can also pass the test with probability 1/4 (and fail with, remaining probability). Consider the possibility of a pooling equilibrium, in which both sellers of good cars and bad cars choose to undertake the test. Find out the range of certification test cost C for which such a pooling equilibrium exists.
My attempt: without certification buyers are willing to pay the average price i.e. is $$140/3=46.67$$The price of a good certified car in the pooling equilibrium will be $$200/3=66.67$$ assuming that buyers know that test can certified lemon as a good car with probability 0.25
and that of lemon is 20.
Therefore, $$0< C <16.67$$
i.e C can be anything between what buyers are willing to pay less valuation of good cars to seller $$(66.67-50)$$
I am having doubts in my attempt. I am not sure if it is correct or not.
It would be of great help if someone helps me with this.
Thank you.
Edit: After certification, lemon will be sold for an average price of 40.
Rationale of my attempt: Suppose C=17, then the net benefit to a seller after certification is 23>20(=value of a bad car to seller) for lemon and 49.67<50(=value of good car to the seller) for a good car. Therefore, the seller of good car will opt out of certification.

We are looking for a pooling equilibrium where both types choose to certify their cars.
The certification has two outcomes $\{success,\;failure\}$.
The buyer faces three possible types of histories: (1) (type $h_1$) a successful certification, (2) (type $h_2$) an unsuccessful certification, (3) (type $h_3$) no certification. (each of these histories are followed by a standard lemons market probem with a price offer from the seller and a buy/not buy decision from the buyer).  Then, by Bayes rule (wherever possible), the interim beliefs following history $h$ are:

$Pr(good|successful\; test) = \frac{2}{3}$
$Pr(good|unsuccessful\; test) = 0$
Off path Belief: $Pr(good|no\; test) = 0$.

Game following history $h_1$:
Buyer's maximum willingness to pay is $\frac{2}{3}100+\frac{1}{3}20 = \frac{220}{3}>50$. Hence the equilibrium price in this game $p(h_1)=\frac{220}{3}$ and both types sell their cars.
Gross Payoff for either type: $\frac{220}{3}-C$

Game following history $h_2$:
Buyer's maximum willingness to pay = 20 <50. In this case, the equilibrium price is $p(h_2)=20$ and hence only the lemons sell.
Gross payoff to lemons: 20-C
Gross payoff to good cars: 50 - C

Thus the expected payoff to Lemons if they choose to certify: $\frac{1}{4}\frac{220}{3}+\frac{3}{4}20 -C = \frac{400}{12}-C$.
The expected payoff to Good cars following certification: $\frac{220}{3}-C$.

Off-path choices (history $h_3$):
To sustain this equilibrium, neither type should deviate to no testing. Given off path beliefs, the buyer's maximum willingness to pay is 20<50. Hence only lemons are sold in this scenario, yielding payoffs 20 and 50 for lemons and good cars respectively.

Pooling can be sustained when:

$\frac{220}{3}-C>50 \implies C<\frac{70}{3}$, and
$\frac{400}{12} - C > 20 \implies C<\frac{160}{12}$

Hence pooling is an equilibrium as long as $C<\frac{40}{3}$


Why is the Free Rider Problem a problem? Why is it bad that someone can use something like a park or an emergency room without paying?

According to the standard criterion used to evaluate welfare (Pareto efficiency), the problem with 'free riding' is that goods are not produced even though they cost less to produce than they are worth to consumers. That means that we are forfeiting an opportunity to help people without harming anyone else.

To illustrate using a standard example, suppose that 10 people live on a street, and that each would value an additional street light at £100 (i.e. each would pay up to £100 to bring a new street light into existence). The street light would cost £101 to produce, but if produced can be used by all for free: this is known as 'non-excludability'. Will it be produced? If people are self-interested, then the answer is no. Although any resident would benefit from the street light, building it would cost them £101, which exceeds the benefit (£100). That's a problem since the total benefit (10 x £100 = £1000) greatly exceeds the cost of the light. If the inhabitants could be compelled to pay for the street light, sharing the cost equally, then they would all be better off.

I should stress that, from the perspective of Pareto efficiency, the problem with 'free riding' has nothing to do with 'equity'. To use your example of parks, the problem is not that people get to use the park without paying. Rather, the problem is that, since people are expected to free ride, the park won't be created in the first place.


Computing the core in a transferrable utility game An allocation $x^{*}$ is said to have the core property in a game of $N$ players if there is no coalition $S \subseteq N$ that can improve upon $x^{*}$. The core of a game is the set of allocations with the core property.

Now, a coalition $S$ will block an allocation $x$ if there exists a feasible $\widetilde{x}$ such that $\widetilde{x} \succ_{s} x$ for all $s \in S$.

As a practical matter, to determine the core of a cooperative game we usually must compute the allocations that any coalition $S$ will not block (i.e. the allocations that cannot be improved upon). If we denote this allocation as $A_{S}$ then we can write the core allocation $\mathcal{C}$ as $$\mathcal{C} = \bigcap_{S \in 2^{N}} A_{S}  $$

Now in any game with more than two players it can be tedious to compute the core.

I am wondering, if I knew the game was a transferable utility game, is there any way to compute the core more efficiently?

This is mostly a question about the consequences of a game being a transferable utility game, and whether this provides any information that is useful to computing the core. Although I am familiar with the definition of transferrable utility, I was never really comfortable with what it's practical implications were for the game.

It depends on the set of feasible allocations for the coalitions $S$. Suppose for all $S$ a best allocation exists (the sum of the individual utilities of the members of $S$ is maximal). Then as in usual cooperative games each coalition can be assigned this best utility sum as its value $v(S)$. Let us denote the utility vector each player gets from an allocation by $x$, and the sum of utilites players get from this by $x(S)$. An allocation is in the core iff
$$
\forall S\subseteq N: x(S) \geq v(S).
$$
This is a slight simplification of what you wrote, because instead of comparing all allocations to $x$ we first find the 'best' allocations for each coalition and only compare these to $x$.

If you make further assumptions about the coalition values $v$, e.g. if you assume the game is convex (this is true for exchange economies) then the calculation may be simplified a bit, as the core of a convex game is the Weber set.


Does elasticity vary along the Demand/Supply curve or is it a summary statistic of a curve? I know that the Demand curve has elastic and inelastic regions but when we say horizontal demand/supply curves are elastic or vertical curves are inelastic, in that case, does the elasticity still vary along the curve?

More specifically, one of my lectures gives Elasticities of various items such as 0.09 for Gasoline and 0.8 for soda drinks. Are these values just taken on a specific point? If yes, how can they be used to describe the complete curve of a specific item.

Yes, elasticity varies along a curve. No, elasticity is not a summary statistic of a curve.

Definition. The elasticity of demand, $Q_D$, with respect to price, $P$, (or price elasticity of demand) is defined as this number: $$\frac{\partial Q_D}{\partial P} \div \frac{Q_D}{P}.$$

Example. Suppose $Q_D = 100 - P$. Then the price elasticity of demand (PED) is $$\frac{\partial Q_D}{\partial P} \div \frac{Q_D}{P}=-1\div\frac{Q_D}{P}=-\frac{P}{Q_D}=-\frac{P}{100-P}.$$

  More specifically, one of my lectures gives Elasticities of various items such as 0.09 for Gasoline and 0.8 for soda drinks. Are these values just taken on a specific point?

Yes. Elasticity estimates are usually point estimates.

Note though that sometimes they're some sort of a mean or average estimate. (In such cases anyone reporting such estimates should be very careful about how exactly these estimates were defined.)

  If yes, how can they be used to describe the complete curve of a specific item.

You're right. They don't describe the "complete curve".

Note. With soda, prices probably don't fluctuate too much. So elasticity estimates are probably reliable.

In contrast, with gasoline (or more generally energy), we have to be more careful. Indeed, there's an extensive literature on this topic with estimates all over the place.

Here for example is a table from a recent meta-analysis (Labandeira, Labeaga, and López-Otero, 2017) where ranges of elasticities from various studies are reported:


Question about Changes in Surplus Will Both Consumer and Producer Surplus decrease as a result of a decrease in demand? Or is this not possible?

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

Thank you!

Simply shifting the demand curve down will typically reduce the combined surplus, especially the producer surplus.  But you could devise two non-parallel demand curves, one below the other, where consumer surplus rose, for example like this:

If the demand curve fell from the higher to the lower red curve, than the combined surplus would fall by the orange and brown amount while the producer surplus would fall by the green and brown amount.  But the consumer surplus could rise, providing that the green amount is larger than the orange amount.  You could achieve this without such kinky curves, but it might not be so obvious.

If consumers' tastes (or utilities) change then with a constant budget constraint, demand could increase for other products, raising the combined  surplus for those.


Factor-augmenting technologies (Acemoglu and Restrepo 2018c) In that paper, they consider the following production function:

$Y = F(A_KK,A_LL)$.

Where:

  K denotes capital, L is labor, and $A_K$ and $A_L$ denote capital-augmenting
  and labor-augmenting technology, respectively. We assume throughout
  that F is continuously differentiable, concave, and exhibits constant
  returns to scale. Let $F_K$ and $F_L$ denote the derivatives of F with
  respect to capital and labor. We focus on competitive labor markets,
  which implies that the equilibrium wages is equal to the marginal
  product of labor:

$W = A_L F_L(A_KK,A_LL)$.

Why? Shouldn't simply be:

$W = F_L(A_KK,A_LL)$.

Without the $A_L$ multiplying the derivative?

Chain rule! To make it simple call $\tilde{L} = A_L L$ and $\tilde{K} = A_K K$, so that

$$
Y = F(\tilde{K}, \tilde{L})
$$

so that

$$
\frac{\partial Y}{\partial L} = \frac{\partial \tilde{L}}{\partial L}\frac{\partial F}{\partial \tilde{L}} = A_L F_L(A_K K, A_L L)
$$

the trick here is that you should read $F_L$ as the derivative of $F$ with respect to its second argument.


Why is the labour supply independent of the wage in this case? Consider the model $\max U = \ln c + \ln l$ subject to $c=Lw$ and $1=l+L$, where $c$ denotes consumption, $l$ leisure, $L$ the labour and $w$ the wage rate.

The optimal choices of $L$ and $l$ can be easily computed to be 1/2. I don't understand the intuition why the labour supply decision is independent of the wage rate in this case.
Is it possible to argue in terms of substitution effect and income effect of a wage rate change?

For some intuition, rewrite the problem as the consumption problem $\max_{(c, l)\in\mathbb{R}_{+}^{2}} (cl)^{0.5}$ subject to the constraint $c/w + l \leq 1$.
The optimal level of $l$ is then given by $l = 1/2$ as per the usual solution for Cobb-Douglas preferences.
The intuition for why $l$ does not depend on $w$ in this example is the same intuition for Cobb-Douglas consumers, who spend a fixed fraction of their income on each good.


Literature Request: how does the house quality distribution change endogenously over time? Is there existing literature on how the distribution of housing quality changes with time? For example, literature saying "using 2000 as a baseline distribution $X$, the housing quality distribution is $1.2X$ in years when GDP is rising and $0.8X$ in years when GDP is decreasing." This is of course very naive, but hopefully it gets my point across. Perhaps housing price distribution could be used as a proxy for house quality, as there may not be data on the latter.

A paper of interest but it is mostly about trend changes in quality and not business cycle fluctuations:

  This paper employs a new national data set to estimate constant
  quality dwelling prices for four regions of the country. The data set,
  collected by the National Association of Realtors, provides sale
  prices, locations, and characteristics of 5581 dwellings sold during
  the years 1986–1992 inclusive. The paper provides the first national
  hedonic analysis based upon transaction prices of sample dwellings.
  The estimated equation implies that more than half of dwelling price
  increases during the period resulted from quality improvements in
  dwellings.

New Hedonic Estimates of Regional Constant Quality House Prices (Millsa and Simenauerb (1996))

Because housing is a long lived asset and it is somewhat unusual to significantly change the size of a house after it is built we could explore your question with the quantity and quality of new housing, assuming existing housing is largely unchanged. The US Census's New Residential Construction Survey has rich information about new housing. For example, on Characteristics of New Single-Family Houses Sold one can see many attributes of new houses including size, bedrooms, bathrooms, number sold, and much more. The Median and Average Square Feet of Floor Area in New Single-Family Houses Sold by Location table goes back annually to 1978. So you could compare it with RGDP per capita to get an idea of how this varies with wages.


How should I evaluate my startup?(specific question) If I have a startup that produces a product that I estimate to sell 100/per month, with 50%profit, and $200 is the customer price of each product, How can I evaluate this business to find investors?

First of all, valuation, especially for startups, is a topic without much consensus on the single way to do it. You can take several approaches, such as DCF, multiplayer, prepetuity and EVA (or residual income).

One frequently used way to make a valuation of projects and businesses is to use the Discounted Cash-Flow model, where you estimate the profits and losses for each year, including the financing and the depreciation you would have from the initial investments. This will give you the expected net result of the project, discounted to today (the net present value).

As some startups have difficulties in projecting costs and revenues, alternatives such as the multiplier method are used by some entrepreneurs & investors. I do not consider this method very accurate, as it is easily manipulated by the choice of multiplayer.

Go beyond the numbers

If you're looking for investors to fund your large initial investment, you usually need to provide proof that you can actually sell to your customers. If you could get customers to sign already a future commitment to buy this would help investors trust you and fund you.

You can also try to resort to debt or public grants for starting a business, or try to anticipate some sales revenue to finance your startup. Get legal advice  before signing with an investor, this is critical to ensure you still get a fair share of the deal.


Can the cyclicality of the real wage be used as a measure for the degree of competiveness in the labour market? When reading the answers to this question of mine, I'm left wondering if cyclicality of real wages can be seen as an indicator for the nature and degree of competition in the labour market.

In perfect competition, we would have high procyclical wages, under monopsony acyclicality.

What would be the cyclicality, if the labour market could resemble a oligopoly(a highly unionized market could resemble an oligopoly, right?), or if the labour market worked as if in monopolistic competition?

In general, no. The procyclicality of wages can also It could also be a measure of labor market frictions instead of the level of competition.

For an example that highlights the difference, consider an economy where only union electricians can do electrical work and where the union controls the members and their hours. If the union can frequently and costlessly adjust their total labor supply, then they don't have a lot of friction in their supply but they (by construction) have limited competition through their monopoly labor supply.  On the other hand, laws mandated costly separation processes for employees such as 2 years severance or, more extremely, lifetime employment make it very difficult to adjust the quantity of labor supplied but this isn't exactly a competition issue. There could be many employees, many employers, and no licensing restrictions and yet this could still significantly dampen the cyclicality of the real wage by making employment not adjust to cyclical productivity shocks.

This might be somewhat splitting hairs because both restrict the adjustment of labor demanded but conceptually they are quite different.

Additionally, there may be reasons related to other features of the economy or the way that the data is gathered for wages to be less procyclical in one place than another. For example, measurement error attenuates statistical relationships towards zero so in two otherwise identical countries, if one has wage measured with more error then the correlation between wage and your favorite business cycle measure will be shrunk towards zero in that country relative to the truth.


Finding optimum market value of vintage car I am trying to find first and second order conditions for the following problem:
$$P(t) = V(t)e^{-rt}- \int^t_0 me^{-r\tau}d \tau $$
I managed to find the first order condition:
$$P'(t) = V'(t)e^{-rt} -  rV(t)e^{-rt} - me^{-rt} =0 \\
V'(t) = rV(t)+m $$
According to our textbook this is correct, but I have problem finding SOC.  We learned before that SOC are found by taking second order derivative and examining if it is > or < than 0.
When I try to find $P''(t)$ I get:
$$P''(t) = V''(t)e^{-rt} -  rV'(t)e^{-rt}-  rV'(t)e^{-rt} + r^2V(t)e^{-rt} + rme^{-rt}$$
But the textbook says that the second order condition should be:
$$D=V''(t) -rV'(t)$$
this looks like the derivative of $V'(t) = rV(t)+m \implies V'(t) - rV(t) - m = 0 $
but I don't understand why that is correct. Previously when deriving SOC we always just took the 2nd derivative of the function so how come that does not work here?

Note that, from your SOC:
\begin{align}
P''(t) &= V''(t)e^{-rt} -  rV'(t)e^{-rt}-  rV'(t)e^{-rt} + r^2V(t)e^{-rt} + rme^{-rt}\\
&=e^{-rt}\Bigl[\underbrace{\color{red}{V''(t)-rV'(t)}}_{=D}-r\underbrace{\bigl[V'(t)-rV(t)-m\bigr]}_{=0\text{ from FOC}}\Bigr]
\end{align}


When the base year changes, does it affect data at current prices as well? I'm trying to collect current GDP data for India from 1990-2016. But, India changed its base year in 2011. So, to get a continuous series, do I have to change the data to a common base?

Yes,

If you initially had GDP data at some base year $Year\;x$ for some $Year\;y$

$$I_{\frac{Year\;y}{Year\;x}} = \frac{GDP_{Year\;y}}{GDP_{Year\;x}} \times 100$$

If your base year has now changed to some base year $Year\;a$ for some $Year\;b$
, $a > x$, then you should convert the GDP data from year $b$ onwards to reflect the initial base year, $x$.

$$I_{\frac{Year\;b}{Year\;x}} = I_{\frac{Year\;b}{Year\;a}} \times I_{\frac{Year\;a}{Year\;x}} $$

Further proof,
$$\frac{GDP_{Year\;b}}{GDP_{Year\;x}} = \frac{GDP_{Year\;b}}{GDP_{Year\;a}} \times \frac{GDP_{Year\;a}}{GDP_{Year\;x}} $$

This way you will be able to get a continuous and consistent series based on some base year, $x$. If there were multiple base years, the data would be meaningless since it would reflect on changes with regard to different periods of time - ie, you would not be able to draw a definite conclusion.

An index compares the value of the current year against the value in the base year.
In this case, you might be looking for the current GDP value for every year from your data-set. As an example, if $$I_{\frac{2001}{2000}} = 110, \; and \; GDP_{2000} = 200, \; then \; GDP_{2001} =220.$$

When comparing data with changing base years, for eg,
$$I_{\frac{2001}{2000}} = 110, \;I_{\frac{2002}{2001}} = 105,$$
You can see that this does not mean the GDP in 2002 is $10\%+5\%$ higher than 2000. Instead, the actual GDP =

$$I_{\frac{2002}{2000}} \times GDP_{2000} = I_{\frac{2002}{2001}}\times I_{\frac{2001}{2000}} \times GDP_{2000} = 115.5 \times GDP_{2000} = 231$$
or you can break this down to
$$GDP_{2000} = 200$$ $$GDP_{2001} = GDP_{2000} \times I_{\frac{2001}{2000}} = 220$$ $$GDP_{2002} = GDP_{2001} \times I_{\frac{2002}{2001}} = 231 $$
 Thus this is why you have to change your indexes to reflect on the same base year, since your calculated values of actual prices will differ.


Adaptive expectations I know expected inflation plays a key role in both the Phillips curve equation and the Fisher equation, but does it also play a key role in Taylor's Monetary Policy Rule?

I'm asking this as I have an assignment question which requires me to derive the DAD curve, with a different expected inflation, and I am unsure if I have to change the expected inflation in the monetary policy rule as well.

Important details are missing, but just think: whose expectations about inflation are included in the monetary policy rule? Model consistency should help you answer your question.

If you provide more details on your model, I will be happy to expand.


Determine price and cost of intermediate good Consider a world where an intermediate good is produced using a linear production function in a competitive market:

$$ Y = qAL$$

where $q$ is the price of the intermediate good, $A$ is productivity. Due to perfect competition, profits are given by

$$ 0 = \pi = (qA-w)L$$

where $w$ are wages. Due to perfect competition, we have that $w = qA$.

Now consider a final production sector where some market power exists. Why is - I believe - irrelevant to the exposition here. Due to some cost of entry to the final sector, we can determine the measure of firms in the final sector, $S$. Each of these final good firms $i$ then will sell the final good at price $p_i$. That is, we have some non-degenerate price distribution in the final sector.

Now, we have a measure $S$ of final sector firms that require the intermediate good.

Assumption 1 Let's assume for simplicity, that they all will purchase the same quantity (although the quantity is irrelevant due to the linearity of the intermediate good's production function).

How would the price $q$ be determined in this setup, with and without assumption 1?

Can there be market power for the final sector, given that there is a continuum of firms in both sectors?
If so, how does the price-setting work?
In particular, if there is market power on one side, the price should be equal to marginal cost.

However, so far, I was using the FOC $w = qA$: taking the price as given and use that as the wage. Due to linearity of the production function, I feel that I cannot determine both $w$ and $q$ at the same time here. Is that correct? What's the way to go?

One way to close the model is through the labor market equilibrium. The OP clarified that the final-goods sector does not use labor.

Let $D_y = D_y(q)$ be the total demand for the intermediate good, in quantities. Since the market for the intermediate good is competitive it will clear, so we have

$$D(q) = AL \implies L^d = D(q)/A$$

Let $L^s(w)$ be labor supply coming from the utility maximization problem of the households and depending also on the wage. Assume a competitive labor market. Then the wage will adjust to clear it. Here we have

$$L^s(w) = L^d = D(q)/A$$

which gives us a second relation between $w$ and $q$, alongside $w=qA$, and it permits to determine both simultaneously.


Econometrics - marginal effect of x on y at average values I was solving a prep Econometrics exam, with STATA output provided on two different models.
They asked me to " Estimate the marginal effect of ability (x variable) on wage (y variable) for the models of output A and B for average levels of wage and ability."
Model A is a log-log model for the given x and model B is log-linear model. The answers they provided are
Model A: ∂wage/ ∂asvabc = 0.403*(wage/asvabc), at averages we get 0.153.
; Model B: ∂wage/ ∂asvabc = 0.008*wage, at average we get 0.169

Irrespective of the numbers, I don't understand how they know whether to multiply the marginal effect by x or x/y or... Can someone help me with the logic? Or if you know the rule for this?

"They knew" because they have written down the models. Ignoring other variables, the log-log specification is

$$\ln y = \beta\ln x \implies e^{\ln y} = e^{\ln x ^{\beta}}$$

$$\implies y = x^{\beta} \implies \frac {\partial y}{\partial x} = \beta \frac {x^{\beta}}{x} = \beta \frac {y}{x}$$

I guess the OP can work out the other model now.


Supplier offers "Price Protection Tariff" w/o exit fees, and more expensive Variable Price tariff. Does that mean it is betting on the price falling? My energy supplier offers two tariffs:

The first is a "Price Protection tariff". It gives you a fixed per-kWh price for 12 months, and has no exit fees (23.28 cent)

The other is a "Variable price tariff". It has a higher per-kWh price (25.31 cent).

This appears to be the only difference.

I am a little thrown regarding the economics here.

Does this mean the company is assuming the price will likely go down?
If they believed the price will likely go up, should I not have to pay a premium for the price being fixed.
Otherwise, what would be a reason for a customer to choose the variable price tariff?

It is possible that the supplier is trying to segment the market:

For those customers who do not frequently review the pricing options, it has a "standard variable tariff" which is not the lowest price on the market
For those customers of theirs or of other suppliers who do review the options, it has a lower price option which it sets competitively, though it hopes that some of these will not review at the end of the 12 month period and will then be automatically switched to the higher price "standard variable tariff"

Whether you regard this as promoting competition or as an abuse in competitive markets is a complicated political and regulatory question


How would you draw a MSB,MSC,MPB,MPC graph for this? 'farmers would get 100% subsidy for installing micro irrigation gadgets like dripper, sprinkler etc.  the farmers should make use of this opportunity to have better yield in sugarcane, coconut, oil palm, groundnut, grams, cotton etc. while saving a lot of water.'
I am very confused how the graph will look like for this situation where farers are given subsidies , which give them a better yield thus increasing supply and helping them save water.

First of, you would not be able to infer actual data on marginal measures of social benefit or social cost from this prompt alone, as they do not indicate any such information (if they are constant or variable). You'd instead have to conjecture the explicit effects of the saving of water. In doing so, we can, more safely than not, assume that conserving water is a positive externality of this subsidy, and this marginal benefit is ..clears throat.. constant.

The subsidy being imposed, we notice that Supply (MPC) curve moves to the right; that is, for every same level of price, producers now supply more to the market.
Furthermore, we notice that the Demand (MPB) curve remains constant, as no measure that takes place should change the needs of the consumers for agricultural products.
On this we will add a constant Marginal Social Benefit; that is the positive externality of rationing on water usage. Mechanisms at work, classical economic theory suggests, would imply that the consumption of these subsidized products, saves more water; so people naturally want to purchase more of them. This being the case, the Marginal Social Benefit curve is established further to the right than the Demand curve.

One final point of equilibrium is that where $Q=Q_2$, and producers receive price $P_0$ as part of their subsidy, while costumers pay an actual price of $P_2$.
The cost of this subsidy is $Q_2 * (P_0-P_2)$.


Can a subset of variables in a lower triangular Cholesky identification scheme be ordered arbitrarily if we do not care about their shocks? For example, in a three-variable SVAR model in Favero, C. A. (2001), the author uses Cholesky decomposition to identify only money shocks by ordering it last. Thus, both $p_t$ and $y_t$ affect $m_t$ contemporaneously, and this is the only identification condition in the model.

He mentions that the identification of shocks to $p_t$ and $y_t$ do not matter in the model. We can see here that $p_t$ affects $y_t$ contemporaneously but not the reverse.
In another example in the same book, $y_t$ contemporaneously affects $p_t$ which is in contrast to the example above. Again, he seeks to identify shocks only to $FF_t$, and hence does not discuss the ordering of the non-policy block of the model. I guess it is arbitrary.

I see same thing in Primiceri, G. E. (2005). Interest rates are ordered last in the VAR. The interaction between inflation and unemployment is arbitrarily modeled in a lower triangular form, with inflation first, unemployment second. So I guess unemployment could also be first.
Another example is by Drechsel, T., & Tenreyro, S. (2018). There are 4 variables in the VAR. The only identification condition is that commodity price is ordered first in the lower triangular Cholesky identification scheme. The author does not mention how the other 3 domestic variables are arranged in the model. So I guess, arbitrarily.
So my question is, in a lower triangular Cholesky identification scheme, one does not necessarily need to have an economic theory for all the orderings of the variables in the model, right? I mean, some of the orderings can be arbitrary if one do not care about the shocks associated with these aribitrarily ordered variables in the model?

You are right.
Ordering a variable first reflects the identifying assumption that this variable will not respond contemporeneously to the other shocks in the system. You could obtain the exact same shock series via an OLS regression that includes as explanatory variables only the lags of all the variables in the VAR. Since you were happy to "assume away" all endogeneity concerns, your shock is neatly identified, and you don't care about the others. (You don't even need to impose the other zeros in the impact matrix: any rotation of the bottom-right (n-1)x(n-1) submatrix will leave the first shock unaffected.)
Ordering a variable last allows this variable to contemporaneously respond to all other shocks in the system, but it imposes the assumption that none of the variables in the system can contemporaneously respond to the shock in the last equation. Again, you could obtain the same shock series via an OLS regression including all lagged and contemporaneous values of all the variables in the VAR, since, once again, you were happy to assume away all endogeneity concerns. (Also, you don't even need to impose the other zeros in the impact matrix: any rotation of the top-left (n-1)x(n-1) submatrix will leave the last shock unaffected.)
Intuitively, the OLS-counterparts show that the ordering of the other variables doesn't matter when you're interested in exclusively the first or the last shock:

either you don't includy any of the other variables contemporaneously in the OLS regression (first shock);
or you include all of them contemporaneously (last shock).

For the shocks in between, the OLS regressions that would deliver the same shock series as the shock series obtained via cholesky include the variables ordered before the shock of interest, but not the variables order after. So here the ordering of the variables in the VAR does affect what the shock series will look like, because changing the ordering for these shocks would include or exclude some of the rearranged contemporaneous variables in the OLS regression.


Will printing more money during COVID cause hyperinflation? When COVID started, many countries started printing loads of money and handing it out to their people. Here are some examples
US is printing money to help save the economy from the COVID-19 crisis
We’re Paying for Coronavirus Stimulus by Printing Money
14 countries that are paying their workers during quarantine
Coronavirus bailouts
Why Countries Are Giving People Cash Amid the Pandemic
There are definitely people that need the support but also many that won't bother finding work because the handouts are more than what they were earning before. So if there are less people working, doesn't that imply a drop in 'Goods and Services' produced by the country? And with all the money being printed and handed out, that's an increase in money being circulated.
The article The problem with printing money does a good job of explaining the effects of unrestrained money printing when the 'Goods/Services' of a country remains constant. However, I'm arguing that goods and services are decreasing but the money being circulated has increased which is even worse.
I know of hyperinflation in Germany after WWI and Zimbabwe in more recent times from all the money printing. I'm sure there are other examples in history.
So are the countries doing all this money printing on road to hyperflation? If not, why not?

Will printing more money during COVID cause hyperinflation?

Likely not for several reasons. First, the article from economicshelp.org you mention is oversimplifying the economics, which is understandable as it is article written for non-economists, but to understand this issue we need to go little bit further.
Inflation, is simply just positive change in price level and price level of an economy is determined by the equilibrium at money market. The money market equilibrium, in its simplified form (more complex models include expectations of the quantities as well but this should suffice for this answer) is given by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY.$$
Where $M$ is the money supply, $V$ velocity of money, $P$ price level and $Y$ output.
Solving for price level and log-linearizing (so % changes in right hand side variables give us the % change in P) we get:
$$\ln P=\ln M+\ln V−\ln Y.$$
Hence, it is true that inflation depends on increase in money supply but it also depend on changes in velocity of money and real output. If money supply increases by $30\%$ and real output decreases (due to pandemic) by $10\%$ and velocity drops by $40\%$ these effects cancel out and even $30\%$ increase in money supply would not lead to any inflation.
In fact one of the main reasons why we did not see much inflation recently is that velocity of money dropped significantly as you can see from Fred data. It is not clear if velocity will pick up in near future and as long as it remains low it will be offsetting considerable amount of increase in money supply despite of significant drop of real output.
Next, it is important to understand what hyperinflation is. Following Cagan The Monetary Dynamics of Hyperinflation, hyperinflation can be defined as an increase in price level that exceeds $50\%$ per month.
This means that in terms of the simple model $\Delta M + \Delta V - \Delta Y  = 50\%$ per month.  There is simply not enough money creation going on  in most countries to hit that $50\%$ per month value to classify as hyperinflation. For example, in the US the money stock as measured by $M2$ increased during last year by $\approx 19\%$ (see Fred data). While, that is without doubt large increase relative to previous years, it is far cry from increase in money supply that would lead to hyperinflation, even taking into account drop in output due to covid. Hyperinflation would not be caused by changes in velocity either because even though it is possible it would pick up later velocity usually does not increase fast month by month.
Lastly, if there would be any signs of hyperinflation independent central banks would start acting. In countries like Zimbabwe central banks are not independent and often they are forced to expand money supply rapidly by politicians. In most developed countries central banks are independent and for most part run by technocrats. Central banks have plethora of tools to sharply reduce money supply.
Even though people often just label all money creation money printing this is really just analogy as it is easier to explain money supply increases to people that way, but in reality most money are created by banking system via lending and central banks control the amount of money that can be created by changes in interest rates on its reserves (see for example McLeay, Radia, & Thomas; 2014). Next money are also created when Fed borrows money to the government via its open market operations. Only very small fraction of money are actually printed each year and similar picture holds for most developed nations.
Consequently, if Fed or any other modern independent central bank would spot signs of not just hyperinflation but even high inflation (like $10\%$ per year) they would quickly start hiking interest rates which would slow money creation and eventually even destroy part of new money, they would stop buying government bonds or even sell them again destroying part of money supply and so on. Independent central banks are quite good 'inflation fighting machines' and empirical literature, for the most part, shows that there is negative relationship between central bank independence and inflation (e.g. see Jácome & Vázquez; 2008).
Of course, it is not literally impossible that the situation will be mishandled, and heads of central banks are still typically appointed by politicians in most countries  so there is possibility of political capture of central banks, but as the things look like now I would say that hyperinflation in most developing countries is astronomically unlikely in near future.


Why is MRS equal to Price ratio? I've seen a derivation of MRS, but it's not immediately obvious to me why letting MRS equal to the price ratio of two goods will give you the solution to an optimization problem. Can anyone link me to a paper that explains this (or explain it themselves)? It would be great to get both the intuition and mathematical derivation! Thanks in advance!

The mathematical derivation is straightforward: set up a Lagrangian for the utility maximization the consumer solves subject to a monetary constraint, then divide its partial derivatives with respects to the quantities one with another, and there you have it: MRS equals the price ratio.
The intuition behind it is that, given fixed prices (that is, a price taking situation), the ratio of the marginal utilities must also remain constant: suppose by contradiction this isn't the case, and that some good provides relatively high marginal utility. Then the consumer would profit from deviating to consuming a basket in which the quantity of said good is higher, since the increase in utility would be higher than the costs incurred.


Explain some All countries excluding residents in BIS Debt Securities Data In the BIS Debt Securities statistics:

In both column "issueresidence" and column "issuenationality" there is a category called "All countries excluding residents". I do not understand what it means. What is it used for? although I have read through the report going with the data.

Many thanks for your help!

Your link is not particularly helpful - perhaps you mean something like https://stats.bis.org/?m=6%257C346%257C644#ppq=CBS_IB_INT_C_BY_SEC_TYP_IB;pv=11~10,9~0,0,0~name

"All countries excluding residents" is a phrase BIS use for international debt securities, so represents debt or similar instruments issued by somebody in one country and held by somebody else in a different country, i.e. excluding residents (human or corporate) of the same county

Note that residents of the same country may have a different nationality or be owned by non-residents.  So for example if an American-owned subsidiary incorporated in London issues a debt security to a German-owned subsidiary incorporated in London denominated in Japanese Yen, this would be excluded from these statistics since the two banks are both resident in the UK. But if the American-owned bank in London holds a debt security issued by an American bank in New York, this should not be excluded, and should count as a US liability to the UK

BIS provides a glossary, which is sometimes helpful and sometimes less so


Inflation, Monetarism and Keynesianism Is there a strict division between the Keynesianism and Monetarism on the view of inflation. In other words, does the push and pull inflation only belong within a Keynesian framework and does inflation defined in term of balance between monetary base and supply of goods and services only belong within the Monetarism.

Alot of presentations of inflation are self contradictory to me and I thought this might be why. I.e that there is indeed two definitions of inflation not having anything to do with each other originally.

In particular I find it hard to distinguish between "An increase in the money supply" and "An increase in the aggregate demand for goods and services"

On this page ; https://www.investopedia.com/articles/05/012005.asp

The demand is governed by the existing amount of money in my opinion, i.e demand pull become secondary or a consequence of increase in money supply. Hence the "definition" of inflation as "increase in prices" seams to include two things of which we cant decide what is what.

Increase in money supply $\rightarrow$ demand pull  $\rightarrow$ prices up.

Increase in money supply $\rightarrow$ prices up.

demand pull  $\rightarrow$ prices up. (without increase in money)

The last implication donst make sense.

I thick you should return to some book about history of economic theories usch as "Modern Macroeconomics: Its Origins, Development and Current State" . Center of focus in Keynesianism/Monetarism debates was about the power of monetary/fiscal policy for combating recession.

Monetarists won and showed that monetary policy is effective at least when there is no ground for liquidity trap. Monetarists also believe that "transmission mechanisms" of monetary policy are more much broader than what Keynesian interest rate-investment mechanism ascertains. thus Monetarists as well as Keynesians accept that printing money will increase aggregate demand but through much more broader channels.

I should say that distinction between demand-pull inflation and cost-push inflation is a little tricky, because in real world (rather than in our DSGE models which are designed based on equilibrium paradigm) when central bank prints money excessively,  demand increment in  different markets will take place in a gradual manner and inflation transmits from one market to other markets step by step. According to this fact, one who just observe the input price increment in some markets, may think that there should be a cost-push inflation.

Pure cost-push inflations are mainly rooted in real shocks (namely supply shocks) rather than nominal shocks (namely demand shocks). For example droughts, wars and oil price shocks  can make pure cost-push inflation.

Finally I should say that monetary policy may be able to dampen nominal (demand) shocks, but there are some economists who argue that monetary policy should not harshly respond to supply shocks . Unfortunately in real world central banks hardly can find out whether a price increment is due to supply shocks or demand shocks.

Monetary policy is much more complicated than what Taylor Rule suggests.


Can integrals be interpreted simultaneously as aggregates and averages? (Mas-Colell et al. 1995, Proposition 4.C.4) I'm currently reading chapter 4 of Mas-Colell, Whinston, and Green (1995).
I have a problem with the way integrals are treated. For instance, Proposition 4.C.4 (p.113) states that when wealth is uniformly distributed on $[0,W]$, the aggregate and the average demand function are:
$$x(p) = \int_0^W x(p,w) dw $$

Where $x(p,w)$ is an individual demand (every individual has the same preferences, their demands only differ in the amount of wealth).

However, I think the right way to write the average would be:
$$x(p) = \int_0^W \frac1W x(p,w) dw $$
because this is the definition of the expected value.

Am I wrong? When using integrals, can I just assume that averages are equal to aggregates?
This a big problem to me because in exercise 4.C.10 it is asked to prove that $$C(p,w)=\int_0^W S(p,w)dw - S(p,W)=-D_w x(p).x^T(p)+\int_0^WD_w x(p,w).x^T(p,w)dw$$ is positive definite, where $S(p,w)$ are individual Slutsky matrices, and $S(p,W)$ is the Slutsky matrix of aggregate demand.

I thought to define $w=aW$ with $a$ uniformly distributed on some interval. Therefore, I could re-define $x(p)=x(p,W)$ and differentiate $x(p)=x(p,W)$ and $x(p,w)=x(p,aW)$ with respect to $W$. However, I'm not sure how to define an interval for $a$ such that average wealth is equal to aggregate wealth using $w=aW$.

Note: Proposition 4.C.4 is based on an example given by Hildebrand (1983) ("On the Law of Demand"). I read the article and he assumes wealth is distributed on $[0,1]$. With this interval, aggregate demand is equal to average demand. Does this mean Proposition 4.C.4 is misspelled? If it is so, I still have a problem with exercise 4.C.10 because I need an interval for a such that aggregate wealth is equal to average wealth.

I talked to my teacher to try and get a handle on the question.

You are correct that usually

$$\overline {f(x)} = \frac{1}{b-a}\int^b_a f(x) dx$$

But for the demand function there are two arguments, $w$ and $p$.

$$x(p) = \int_0^\bar W \tilde x(p,w) dw$$

The left hand side is no longer a function of $w$. The integral is to simplify wealth out of the picture, but we aren't averaging over wealth.
All consumer preferences are identical. For the sake of argument, suppose there were $n$ consumers. We aren't multiplying by $n$ on the inside of the integral, so we don't need to divide out anything (like $n$) through the outside of the integral. The "aggregation" is occurring over all consumers.


Faulty reasoning in two person card game problem I was asked this question in an interview: There are two people Mike and Cheng with one blank card each. Both write either a '0' or a '1' on it without showing the other while writing. They then simultaneously show their cards to each other. If the payoffs are as follows depending on the cards shown:

1,1: Mike pays Cheng 3

0,0: Mike pays Cheng 1

1,0: Mike receives 2 from Cheng

0,1: Mike receives 2 from Cheng

Is this game fair?

Using game theory I reason: Cheng will always play 1 because his payoff from 1 is (-2 or 3) as opposed to his payoff from playing 0 which is (1 or -2). Knowing that Cheng will prefer to play 1, Mike always plays 0 to get a payoff of 2. So the game is unfair to Cheng.

But I also reason: Mike will never play 1 because he has a payoff (2 or -3) vs playing 0 which has a payoff (-1 or 2). So Mike will always prefer to play 0 (this is also inline with the above reasoning). Knowing that Mike will always prefer 0, Cheng always plays 0 so Mike gets -1 every round. So this game is unfair to Mike.

Regardless if the game is played one round or many rounds, I am unable to conclude which is correct.

Can anyone help explain why I am getting conflicting results?

PS: Later the interviewer told me that the game is unfair and Mike always wins.

PPS: I apologize in advance if I have made any mistakes in the posting - this is my first post.

Suppose Mike plays a randomised strategy of playing "0" with probability $\dfrac58$ and playing "1" with probability $\dfrac38$

Then @Herr K.'s table becomes (in expectation)
$$\begin{array}{|c|c|c|}\hline&\text{'0'}&\text{'1'}\\\hline\text{Mike's }\frac58,\frac38 \text{ combo}&\frac18,-\frac18&\frac18,-\frac18\\\hline\end{array}$$

and there is nothing Cheng can do to get a better result than an expected loss of $\frac18$.  So in that sense the game is advantageous to Mike if Mike takes this approach

Incidentally, here Cheng can restrict expected losses to this amount by playing the same mixed strategy, and both players doing so is a Nash equilibrium


"The econony needs x workers of profession y". What does it mean and how is it derived? I keep hearing that there is not enough of some specialists in economy which is followed by some number. Here's an example:

http://www.computerweekly.com/news/2240205466/Economy-needs-300000-digital-workers-by-2020-to-reach-full-potential

  Economy needs 300,000 digital workers by 2020 to reach full potential

How is this derived? Is it reasonable?

Job market is regulated by supply and demand. To follow the example of "digital worker" - I believe that many, for example, engineers could change their job profile to become "digital workers", but in that case engineers would be suddenly in higher demand as well.

We can say that janitor contributes x to GDP and database administrator contributes y and because y > x, we need more db administrators than janitors, but in reality we need exactly the current number of janitors given their market price and we need exactly the current number of database administrators given their market price.

Also I can think of a question "How many digital workers do we need to inject into economy by 2020 so that the number of digital workers on the market in 2021 will be the same as in 2020?" and the answer could be 300 000. But how to calculate it without being simplistic?

To reiterate: what does it mean that we need x new professionals and how to calculate it?

Full-factor employment GDP (referring not only to labor but also to capital and any other factor), results from existing factor stock interacting with production technology. It is a (quasi) "engineering" relationship, not an economic one.

It says "if all labor and all capital were employed, given technology, output will reach its feasible maximum". It does not say that it is an optimal level in any sense. It does not allow for labor-leisure choice or lock-out (idle capital). It does not take into account whether current markets actually clear (or not).

Still we informally accept that "more is better" so we do examine what would it take to reach this feasible maximum, or how economic interactions, incentives, institutions etc may or may not lead us to such a full-factor employment GDP.

In the case examined by the question here, it appears that an expert body has identified an "engineering" mismatch in the composition of the labor force. Namely, this body of researchers has estimated the required compostion of the labor force that can lead the economy to "feasible maximum GDP"-and then found that the actual composition does not align with the former.

As to how one can indeed estimate such "required compositions" of the labor force, well, this is too technical to go into here, but it can be done.


Do free-trade agreements typically include clauses relating to services? Do free-trade agreements typically include clauses relating to services?

For example, reciprocal recognition of professional qualifications.

The simplest answer is: some do, some don't.

Trade in goods and trade in services are dealt with quite separately, so structurally, you wouldn't find a couple of clauses on services within an FTA.  You would generally find a chapter on goods and (possibly) another on services, reflecting the division in the WTO between the GATT (goods) and the GATS (services).

Quantitatively, there is a roughly equal split between goods-only agreements and agreements that cover both (153 for goods only and 154 combined agreements have been notified to the WTO as of December 2018).

You also often find a group of countries negotiating a goods-only FTA first, then extending to cover services later on (for example by adding a protocol to an existing treaty).  This reflects the fact that an integrated services market is usually seen as a "deeper" form of integration than tariff-free trade.


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

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

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

The Utility function here is the average score that Polly gets i.e.

$U(x_2,x_3)=\frac{max\{x_2,x_3,60\}+max^2\{x_2,x_3,60\}}{2}\\$

Where: $max^2\{.\}$ stands for second highest number.
Now this utility function can be rewritten as:

$U(x_2,x_3)= \begin{cases}\frac{x_2+x_3}{2}, & \text{ if } x_2,x_3\geq 60,\\ \frac{60+x_3}{2}, & \text{ if } x_2<60, x_3>x_2,\\ \frac{60+x_2}{2}, & \text{ if } x_3<60,x_3<x_2,\\ \frac{60+k}{2}, & \text{ if } k<60,x_3=x_2=k.\\
\end{cases}$

Plotting its level curve i.e. the IC for utility level $c$ would be a horizontal line from point $(0,2c-60)$ to $(60,2c-60)$, a vertical line from point $(2c-60,0)$ to $(60,2c-60)$ and a line from $(60,2c-60)$ to $(2c-60,60)$.

So if $(x_2,x_3)=(50,70)$ option 2 satisfies the IC's description.


Log linearising EUler equation I am trying to solve a problem that asks to log linearise following Euler equation of the New Keynesian model:

$$C^{-\sigma}_t=\beta E_tC^{-\sigma}_{t+1}(1+i_t)/(1+\pi_{t+1}).$$

The solution is given as: $$\tilde{C}_t=\beta E_t\tilde{C}-\frac{1}{\sigma}(i_t-E_t\tilde{C}_{t+1}-\rho).$$

And also there are following relationships in the steady state given $1=\beta(1+r)$, $\beta=(1+\rho)^{-1}$ and $ln1=ln \beta+r$ what leads to $r=-ln\beta=\rho$.

Can anyone explain to me how the log linearization is done? I know that the first step would be to take the logarithm of everything (and subtract the logarithm of the constant steady state parameter) or to use Taylor approximation. However I have a problem with the $(1+i_t)$ and $(1+\pi_{t+1})$ terms. Furthermore why does $1=\beta(1+r)$ hold in steady state? Note that $i$ denotes nominal interest rate.

Thank you.

UPDATE: So below I will give my solution path. I am not sure though whether it is appropriate to do it like this:
$$C^{-\sigma}_t=\beta E_tC^{-\sigma}_{t+1}(1+i_t)/(1+\pi_{t+1})$$
$$lnC^{-\sigma}_t=ln\beta+lnE_t(C^{-\sigma}_{t+1})+ln(1+i_t)-ln(1+\pi_{t+1})\qquad (1)$$
Subtracting (1) with $$lnC^{-\sigma}=ln\beta+ln(C^{-\sigma})+ln(1+i)-ln(1+\pi)$$yields $$\tilde{C}_t=E_t(\tilde{C}_{t+1})-\frac{1}{\sigma}(\tilde{(1+i_t)}-\tilde{(1+\pi_{t+1})})$$ and since $\tilde{1+i_t}=ln(1+i_t)-ln(1+i)=i_t-i$ and $\tilde{1+\pi_{t+1}}=\pi_{t+1}-\pi$:
$$\tilde{C}_t=E_t(\tilde{C}_{t+1})-\frac{1}{\sigma}(i_t-i+E\pi_{t+1}-\pi)\qquad(2)$$
$i$ is the  nominal interest rate in steady state and can  be defined as $i=r+\pi$ and $r=\rho$:
$$\tilde{C}_t=E_t(\tilde{C}_{t+1})-\frac{1}{\sigma}(i_t-\rho+\pi-E\pi_{t+1}-\pi)\qquad(3)$$

Leading us to the final equation:
$$\tilde{C}_t=\beta E_t\tilde{C}-\frac{1}{\sigma}(i_t-E_t\tilde{C}_{t+1}-\rho).$$

As you say the first step is to take log of both sides after that you are just applying the rules for logarithms and rearrange.

For example:
$$\ln (XZ)=\ln X + \ln Z$$
$$\ln X/Z= \ln X - \ln Z$$
$$\ln X^a = a \ln X$$
$$\ln 1 = 0$$

Also an important approximations that hold close to zero are applied here as well these are:

$\ln(1+x) \approx x $ for $x$ close to zero (which for interest rates and inflation which are usually just couple of percents applies).

Also Taylor approximation is actually a different way how to linearize relationship so although it’s an example of linearization it’s not necessary log-linearization. In fact the result $\ln(1+x)$ is based on Taylor approximation but it’s not log linearization because just applying logs there won’t produce loglinear expression.

Using these rules you can prove all the above solutions. I will leave the first equation for you as an exercise, for the other equations you can see that:

Log linearizing  $1=\beta(1+r)$ gives: $ \ln 1= \ln (\beta(1+r))$ which after simplification gives us $0= \ln \beta + \ln (1+r)$ or $\ln \beta = -r $

From the second equation  $\beta=(1+\rho)^{-1}$ log linearizing gives us $\ln \beta =-\ln(1+\rho) \implies \ln \beta = -\rho$. Hence you get the equality that $-r=\ln \beta = -\rho$ then you can multiply all sides by -1 to move the minus in the middle of the equality.

The $1=\beta (1+r)$ comes from the fact that rational person would want the marginal utility of consumption today and in future to be equal so actually the equation properly reads:

$$u_t^{\prime} = \beta (1+r) u_{t+1}^{\prime}$$

Which can be rewritten as: $u_t^{\prime} / u_{t+1}^{\prime} = \beta (1+r) $ and if $u_{t}^{\prime}= u_{t+1}^{\prime}$ you get the result that $1=\beta (1+r)$. Again this is because in steady state you want marginal utility of consumption to be equal in each and every period.


Why the difference in productivity and wage trend in the UK economy? In reading this article from FT, we come across two graphs:

and

Shouldn't real wages have a similar trend to productivity? Why was there that discrepancy since the 2009 until 2014? Maybe some other factor that shifted the PS, or the WS curve? It's interesting to notice that in Jun 1st 2014 began the sharp fall in oil prices, which may be the cause for the increase in the real wage we've been observing until know. It seems that workers productivity has had little impact in the behaviour of real wages...

Any help would be appreciated.

Edit: I'm including a graph with CPI in GBR with data from OECD.

Blundell, et. al (2014) offer an explanation. According to them, the UK economy experienced a positive labour supply shock over that period.

First, they present the facts in a very intuitive fashion (graph taken from the working paper version):

They argue that the supply shock was due to two factors:

changes in welfare policies that made work more attractive and tightened job-search conditions attached to the receipt of unemployment insurance beneﬁts
an increase in statutory pension age for women that strengthened their labor force attachment

I don't want to infringe copyrights so I won't include more figures, but look at Figure 14 (showing an increase in employment of older workers after the Great Recession), and Figure 15 and 16 (showing an increase in employment participation of Lone Mothers). As the authors state:

  "The age limit for youngest child was set at twelve in November 2008 for all new claimants of Income Support and was lowered to ten in October 2009, seven in October 2010 and five in October 2011." (p. 392)

That is an example of a policy fostering employment participation and a positive supply shock.


What's effect of introducing infinitely high denomination bank notes during hyperinflation? Countries that suffer from hyperinflation often print banknotes with many zeroes.

Recently I had a showerthought: Let's imagine a government suffering from hyperinflation go crazy and begin begin printing money with Googolplex denomination for example.
That's a so large number that if we would turn all atoms in the universe into paper and ink it would be still too few to write it down.

Or they simply print an infinitely high denomination "omega" bill: omega is the symbol used to denote the "infinitary" in the hyperreal number plane, which is larger than any real number.

What are the consequences of such an infinite banknote entering the circulation? Would that country in question be able to buy the entire world before the market can react?

This question seems analogous to "if I think the word infinity, does my head explode?" The answer is no. Infinity is an abstraction. You do not have to accept a piece of paper promising infinity. I would even hesitate to accept an incredibly large finite bill.

On tricky countries buying the world:
You do not buy foreign things in your own currency, first you purchase foreign currency with your currency and then you buy the foreign goods with foreign currency. Printing excessive amounts of money is not only inflationary, it also deteriorates the exchange rate of your currency to other currencies. The most your currency has to offer is being able to buy everything in your country. The total value of your currency cannot exceed this. Hence others are unlikely to trade more (e.g. the world) for it.


Does anyone recognize the shape of this residuals vs. fitted plot? Hello Stack Exchange community,

I'm running a regression on a survey dataset which consists of 45,381 individuals in 36 countries using Stata.  My model is specified as:

reg income religious `controls' [pweight=Combinwt], cluster(village)

where Combinwt is the probability weight and standard errors are clustered at the village level, since the survey is performed by randomly choosing villages in a region and then randomly choosing individuals within that village.

When I ask Stata to produce a residuals vs. fitted plot, this is the result:

I have never seen an rvf plot that looks like this before.  Does anyone have any ideas for what could explain the shape of the plot?

Best regards,

If you watch closely, you will find out that the slope of the lines is -1. I.e. the values of y along every one of the lines are exactly equal. That is you get this lines only because you have great many cases for which the left hand side variable is equal. The lines are visible because relative to the number of observations there are not that many different values of y.


Why are mortgage rates in USA so high compared to Europe? What are the main reasons of high mortgage rates in USA compared to central Europe? In central Europe mortgage rates are about 75%-100% lower than in USA.

For data on mortgage rates see:
https://www.numbeo.com/cost-of-living/country_price_rankings?itemId=106

The European Central Bank has held interest rates to an extremely low level, in large part in an attempt to boost the economies of member countries in the wake of the most recent worldwide financial crisis.  The United States economy has had a stronger recovery, and so rates in the US have risen in recent years.

This article, "How Europeans' household net worth is 'now exclusively driven' by negative interest rates" provides some detail and explanation as to why rates in the EU continue to be held to such a low level.


Is Iranian rial going to get boosted? I was reading about the Iran's economy and Iranian rial. I have read the news regarding the lift of sanctions from Ira, which had allowed the purchase of Iranian rial in America.
I was having query whether the current political scenario going to help the in boosting Iranian economy?
Will the current politics will provide an economy growth to the Iran?
If any answer I would appreciate your response.

Getting rid of sanctions will boost the currency because it will allow Iran to export more oil, thus encouraging other countries to buy more rials. It also is a sign of stability, which further appreciates the currency.

However, there is no way for you as an individual investor to know when this will take effect or whether it has been already priced in. So I wouldn't buy rials.


Synthetic Control Method I need to study Synthetic Control Method for my term paper. So can anyone suggest some book/literature from where I can study Synthetic Control Method on my own?.

There are many ressources available online

Synth is a statistical software that implements synthetic control methods for causal inference in comparative case studies with aggregate data as described in Abadie and Gardeazabal (2003), Abadie, Diamond, and Hainmueller (2010), and Abadie, Diamond, and Hainmueller (2013). The Synth package for R is also described in detail in Abadie, Diamond, and Hainmueller (2011).
A lecture on Synthetic Control Methods from Yiqing Xu.
A video lecture by Alberto Abadie himself on  Synthetic Controls for Policy Evaluation!


Efficiency in Auctions Consider a finite number of bidders, each bidding for a single indivisible object, with private independent values from some probability distribution.
There are 2 intuitive notions of (ex-post) efficiency: Pareto efficiency and the notion of efficiency that the bidder with the highest value receives the object.

Are the two ever equivalent? I can see that the second notion implies Pareto efficiency, but not the converse.

If bidders have quasilinear preferences and monetary transfers are possible, then the two notions are equivalent: If $x$ is an allocation of the object and $t$ is a vector of monetary transfers with a balanced budget (so the sum of all transfers is 0), then the pair $(x,t)$ is Pareto efficient if and only if $x$ is the utilitarian allocation (object goes to the bidder with the highest valuation).

If monetary transfers are not possible, every allocation of the object to some bidder is Pareto efficient.


How to calculate Pareto Optimal outcome in a game with a Nash Equilibrium I have at hand a two period game.

In period 1, Union decides wage offer $w$.

In period 2, firm decides on L, given wage.

Union maximizes $wL$

Firm maximizes $=(L(100-L) - wL) \quad if \quad L<=50 \quad or\quad (2500 - wL) \quad if \quad L>50 $

An SPNE of this game is: w = 50, L = 25.

I need to compute a PO allocation. I know it exsits, but I'm unsure about how to derive it from the payoffs. (Example: w = 40, L = 40. Gives both firm and union strickly greater payoffs.) But, how do I compute the set of PO outcomes from the gives functions? Or even a single PO outcome, without guesswork?

For Pareto optimality, you can ignore the timing. Also, anything you know about Nash equilibria in this game is irrelevant.

Let $v_F(w, L)$ be the payoff of the firm and $v_U(w, L)$ be the payoff of the union given $(w, L)$. What you are looking for are pairs $(w, L)$ such that neither the firm nor the union can have a higher payoff without the other side having a lower payoff. Equivalently, you want to the payoff of the firm to be as large as possible under the constraint that the union cannot have a lower payoff and you want the payoff of the union to be as large as possible under the constraint that the firm cannot have a lower payoff.

This means that $(w,L)$ is Pareto optimal if and only if it solves the following two maximization problems:

$$\max_{(w',L')} v_F~\text{ s.t.}~v_U(w',L')\geq v_U(w,L).$$
$$\max_{(w',L')} v_U~\text{ s.t.}~v_F(w',L')\geq v_F(w,L).$$

Now if you just have to find one Pareto optimum and not all Pareto optima, you can just maximize $v_F+v_U$.


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

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

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

Robot taxation is a bit like corporate income taxation. Like corporations, robots don't pay taxes, people pay taxes. In the words of Herb Stein:

I remember that in addressing the issue in the 1980s, the late Herb
Stein said that it's as if people think that if the government imposed
a tax on cows, the tax would be paid by the cows.
Are Taxes on Corporations Taxes on People? by David Henderson

There really are only three entities to tax. You can tax the people who own the robots, you can tax the people who buy what the robots make, or you can tax the income of people who work with robots. If you try to tax the robots directly, you'll end up with an effective combination of these other taxes.
In general, it is thought that the providers of capital are unlikely to bear very much of the incidence of taxation. Instead, it is thought that generally expected capital returns will adjust to keep the expected returns similar before and after the tax. This happens because capital is mobile. If the US tries to tax capital heavily investors can invest elsewhere, and will do so until after tax rates of return are equated. Robots are just another sort of capital, suggesting that it will be as difficult to tax them as any other sort of capital.
Taxing the buyers of robot produced goods is also problematic. As long as consumers can purchase imports without a special robot tariff then robotic produced imports will force domestic produced goods with a robotic tax to have a lower prices to leave consumers indifferent. Or they may not produce at all. Either way, consumers likely won't bear the burden.
Which leaves labor, the relatively immobile factor of production, to bear the burden.


Why is imputed rental income for owner-occupied housing included in the measurement of household income? In the National Income Dynamics Study in South Africa, total household income is measured by totalling labour income, government income, investment income, capital income, agricultural income, remittances and imputed rental income for owner-occupied housing (see page 48 of the user manual). Why is this last variable calculated and included? The household doesn't actually earn that income, so surely it's more a measure of wealth? Please point me to literature that backs up this methodology.

The household owns an asset, the house, from which an income can be derived. The household could decide to let the house and with the income rent another house. Alternatively, the household could decide to live in the house that they own. In the latter case household income would be lower, unless imputed rental income is considered.
So calculating and including imputed rental income serves to control household income for households' decision to let and rent or live in their own house. If it wasn't included, household income would swing considerably based on how many households decide to rent or buy their home in any given period.


Why do graphic card prices rise due to bitcoin miners? I thought it would mean more sales thus more production and more profit, so why does nvidia and amd simply dont ramp up production if the trend has been now quite a long one?

And as far as I can see it's the retailers that are upping the prices, not the manufacturers so the manufacturers could easily adapt to demand within a month or two.

Am I missing something?

I thought someone would have answered this by now.

Folks will argue but bitcoin is still a relatively new currency. A couple of regulations here, some stolen money there, and a lot of people may stop using it.

NVidia and AMD's target market (gamers and graphics designers) have a fairly predictable demand. This bitcoin thing is a new category and no one knows where it will be a few years now. Chip manufacturing (unlike say software development) is a heavy investment industry. Investment in factories, people and minerals.

It takes a while to ramp up production in order to satisfy the demand of this new category of coin miners. What if, by the time, the ramp up is completed, the miners have left?

This uncertainty is probably why they are taking it slow. let the market adjusts itself while they ramp up slowly.