Selecting the best utility function for households I have little to no background in micro, but I'm learning about utility functions.

It seems that there are many forms of utility functions for households. In general terms, how does one go on to select a given functional form. Are there a class of utility functions for households that are better than others? How does one even judge better, in this context? Does the selection of a utility function depend on the context and analysis at hand?

According to Wikipedia and this notes from HKU, the indirect utility function is part of consumer theory, and is defined as the maximum utility that can be attained given a consumers' money income, and goods prices.  It reflects both the consumer's preferences and market conditions.  It is a model which helps to understand how consumers optimize their expenditure considering the price of products.

The model considers a consumer who faces a world with only two products with fixed prices and one limited budget, and is represented by a perpendicular axis graph, with each axis representing the quantities of each good, and both axis converging on quantity 0.  A descending diagonal line is then drawn to represent all the possible quantities of good A and good B the consumer could buy by spending his entire budget.   This line is called the goods bundle line, the price of both goods is reflected in the steepness of this line.

Another descending line is then drawn called the marginal utility function, this line tends to be concave and not straight, due to the theorem of diminishing marginal benefits.  The line represents all the combinations of quantity of good A and good B that give the consumer the same level of benefit.  In fact you could draw a whole map of concave lines, all parallel to each other, and each would represent the total quantity of good A and B needed to achieve a certain fixed level of "satisfaction" by the consumer.  This map of lines would represent the consumers' absolute "tastes and needs" sort of speak.

The consumer, in consumer theory, will try to select a bundle which combines just the right amount of both products, and will spend the whole entire budget on doing so, in order to obtain the greatest possible benefit in his consumption process.   The decision of how much to spend on each product is represented in the graph by the intersection of the goods bundle line and the one marginal utility function it intersects tangentially with.  Any other products bundle in the goods bundle line will not be as beneficial to the consumer as the one where the goods bundle line tangentially intersects one of the utility functions.

This is how you can finally build the indirect utility function, by fixing the price for both goods and making the budget a variable.  Now for each level of budget you´d get one single point in the goods bundle line where the benefit is maximized for the consumer, and if you put together all the dots, one representing the optimal goods bundle for each level of budget, you'd construct the indirect utility function.  It is called "indirect" because of its' indirect correlation with the price of goods.  Budget level thus now becomes irrelevant, and what molds the consumers decision making are prices of goods in the market and the consumers' preferences.

So my answer to your first question, "In general terms, how does one go on to select a given functional form.?", would be that I don´t think the techniques for figuring out a particular utility function, for one or a group of specific individuals, belongs to the economics realm.  Because it would involve practical modeling and not just the economic theories any more. I'd say that question could find a better answer in the finance realm.

My answer to your second question, "Are there a class of utility functions for
 households that are better than others?", is yes.  Consumer theory describes one utility function for any given person and price level of goods A and B.  But if the price of any of the products in the consumer's bundle changes, the utility function reshapes given the consumers preferences.  Also if the consumers' preferences or needs towards any of this products change, that would result in the reshaping of the utility function.

My answer to your third question, "How does one even judge better, in this context?", is you can't judge better in reality.  Perception of the benefit for consuming is subjective, and this subjectivity is embedded in a consumers' map of marginal benefit functions, and through it in the resulting utility function. This makes it impossible to quantify and thus to measure.  Making it only possible to estimate.  So people use this theory to understand the phenomena in a general level, like predicting the behavior of entire economies, or a whole segment within them.

And for your last question, "Does the selection of a utility function depend on the context and analysis at hand?", my answer is yes; and I quote from this book:  -What exactly is a “good”? The answer lies in the eye of the modeler. Depending on the problem to be analyzed, goods might be very specific, like tickets to different world series games, or very aggregated like food and shelter, or consumption and leisure. -

In any case I strongly suggest you specify if your question is theoretical or practical, in order to get a more accurate answer.


Perpetual Youth Model I am reading the famous paper of Blanchard,1985. There are some fundamental stuff that I did not really get.

1) Why they call it "perpetual youth"?
2) On page 225, he mentions the cohort size. So, for example does it mean that there are "x" numbers of individual of age 20. But this number x declines when the time goes to infinity? Does it mean that at a given date $t$, there are people with age between $0$ and $\infty$ ?

I haven't read the paper in full detail (I should, it's interesting) but let me give you my interpretation of the paper's title.

Blanchard uses a constant probability of instanteneous death for each agent. As mentioned in footnote one of the paper this is most realistic as assumption for people between 20 and 40. Agents in the model therefore are like young people for their entire life, hence the title.

As for your question 2, the way I read the paper yes there are many people alive of all ages. After all at each instant in time a new cohort of size p is born (and starts dieing off immediately at rate 1/p). So eventually at time is infinity that cohort will have completely passed away.


Interchangeability between knowing an event obtains with probability 1 and knowing an event obtains with absolute certainty? In the literature of interactive epistemology, for a player, knowing an event obtains with probability one and knowing an event obtains with absolute certainty are different. Is there a nontrivial (say, it could be the case, an event is a proper subset of the event that player $i$ knows this event obtains with probability one, but never the case for knowledge operator with absolute certainty) proposition that could serve as an example to show they're not interchangeable in the language which consists of two corresponding knowledge operators, a set of states of world, set relations, set operations, and all logical connectives.

If you take the standard Aumann model, but allow for states occuring with probability zero, you can taje some nonempty event $N$ such that for the agents prior $p$, one has $p(N)=0$. Let $K\cap N=\emptyset$ and $p(K)>0$. If the agent knows $K\cup N$ but not $K$, then she assigns probability $1$ to $K$, even though she does not know $K$.


Problem with defining liquidity I have heard multiple times that a consistent definition of liquidity does not exist. The two wikipedia articles describing liquidity (Market liquidity and accounting liquidity) lack a discussion of this apparent problem within economics. Could someone perhaps provide a reference to a discussion of the problem of defining liquidity and maybe provide a brief summary of the issue?

Etymology and Introduction

As a concept to measure the interchangeability of assets and money, liquidity is a new word. It first appears in 1923 in a use by Hawtrey (The Oxford English Dictionary (1989)). The underlying idea however is much older. Menger (1892) calls a good more or less saleable according to the facility to which it can be disposed of at current purchasing prices with less or more diminution. He is talking about the origin of money, and not the disposition of financial assets, but this concept of saleability is very much like the modern concept of liquidity. This sense of saleability goes back at least as far as Jehan Palsgrave's usage in 1530 (The Oxford English Dictionary (1989)). Although the absence of liquidity is now commonly referred to as "illiquidity", Marschak (1938) offers "frozen" as an alternative that did not catch on.

Hicks (1962) says that the use of the word liquidity in a financial sense was popularized by Keynes and the Macmillan Report in the 1930's (Macmillan Committee of HMSO (1931)). In The General Theory, Keynes says that liquidity justifies money trading at a premium over bills or bonds and causes the existence of an interest rate. Hicks teases from Keynes' Treaty on Money (Keynes (1930)) that one calls an asset more liquid than another if it is "more certainly realizable at short notice without loss."

This quote is more ambiguous than it may seem at first glance. Hicks offers several interpretations. The first, which he flatly rejects, define liquidity as the difference between the price the owner carries on his books for an asset and the price they could sell it for on the market. The second, is an interpretation of marketability. Hicks defines a security as marketable if it is sold just as well after negotiation, search and advertising as it is without it. That is, we can compare the liquidity of two assets by the relative sacrifice one makes from a rapid sale. He claims this interpretation is "more appealing" but still not what Keynes meant. He understands Keynes's definition of liquidity to require perfect marketability, but even perfectly marketable assets can be more or less liquid. The difference here is in the moments of the asset's price. Among marketable financial assets, we can regard them as more or less liquid by using a utility function to manage the trade-offs between maximizing the desirable odd moments (e.g., positive mean and skew) and minimizing undesirable even moments (e.g., variance and leptokurtosis) of asset returns.

Definitions of Liquidity

A treatment of market liquidity is critical if we are to realistically model the behavior of markets of financial assets that are traded with transaction costs. The liquidity literature primarily follows three meanings of liquidity. The first and oldest class of measures of liquidity relate the size of loss to the amount of notice. That is, what is the fraction of the best possible price that a seller can net as a function of time allotted to conduct a loss minimizing sale? Keynes's definition is a specific example where he is interested only in short notice. For example, compare trying to sell a round lot (100 shares) of IBM stock today with doing the same with a home. The IBM shares will sell without diminution. The home will sell at an enormous discount because of product heterogeneity, heterogeneous buyers, and the skipping of time consuming risk avoidance techniques (e.g., title search and property inspection). A classic statement of this sense of liquidity comes from Hirshleifer (1968). He calls liquidity "as asset's capability over time of being realized in the form of funds available for immediate consumption or reinvestment -- proximately in the form of money." Admati and Pfleiderer (1988) also care about liquidity in this first sense. They see exogenous liquidity events (say a change in margin requirements) causing a "demand for immediacy" (a term also found in Grossman and Miller (1988)), that is, the willingness to sell rather than wait when doing so costs the seller. According to Greenbaum (1971), who called this the L1 definition of liquidity, the earliest work on this sense of liquidity was in Tobin's unpublished manuscript. Pierce (1966) elaborates this notion and explores this measure in the context of commercial bank portfolio management.

The second meaning understands liquidity as the expected time to sale without diminution. Returning again to the example of selling the lot of IBM stock and a home, the expected time to getting the best price on your shares of IBM is almost zero (at least during business hours and with access to a computer or phone) whereas, on average, the home would take a few months to sell optimally. Lippman and McCall (1986) explore this sense of liquidity. They take an agent as choosing a stopping rule $\tau^* \in T$ of all possible stopping rules to maximize expected net receipts (under that stopping rule) of $E [R(\tau^*)]$. They define liquidity as $E [\tau^*]$, the expected time to sale under the optimal stopping rule. Krainer and LeRoy (2002) also suggest this expected time to sale under an optimal selling rule a measure of liquidity.

The third definition of liquidity involves the uncertainty of an asset's value. As discussed above, Hicks (1962) sees this as the critical attribute of liquid assets. Proponents of this definition argue that it is of little importance if you can sell an asset on short notice and with small loss if the asset itself is worth little when you need it. That is reasonable as long as investors are risk averse. Tobin (1958) introduces this sense of liquidity in a framework of risk averse investors and uncertainty of future interest rates. Tobin's paper resolved the paradox (to economists) that consoles (perpetual bonds) have higher expected rates of return than cash investments. Lagos (2008) is able to explain much of the risk-free-rate and equity-premium puzzles in an economy with riskless, liquid assets and risky, illiquid ones when agents hold assets for the liquidity services.

Deaton (1991) equates a model's liquidity constraints with limitations on borrowing future income. In that sense, liquid assets are more effective in moving income though time. Holmstrom and Tirole (1998) also explore this meaning of liquidity as a way of storing wealth between periods in search of recommendations for efficient market making of financial assets and optimal provision of liquidity services by the government. Hovakimian, Opler, and Titman (2001) continue to explore this inter-temporal liquidity concept in economies with human capital that creditors cannot seize or make claims upon. He experiments with two an extra features, either no short selling of physical capital or limited borrowing by agents.

The concept of liquidity is a mixture of the attributes of liquidity discussed above. Households without liquid assets want to borrow with their illiquid assets as collateral. They cannot do so. Creditors are unwilling to lend because in the event of default, lenders will have to sell collateral with serious discount from the true value, with long waiting times for finding a good selling price, or with unfavorable co-movement (e.g., covariance or other forms of joint distribution) with other asset holdings. This idea of liquidity as having wealth when you need it is similar to the CAPM insight of weighting future returns by the marginal utility. Krainer and LeRoy (2002) argue that the CAPM holds for illiquid assets as well as liquid ones, but that observing the relevant shadow prices is difficult. However, the ambiguity of asset values in the presence of illiquidity (explored later) ensures that these shadow prices will not be unique. The general idea is that illiquidity can drive a a wedge between the discounted expected risk adjusted returns and the price for which you can sell an asset. As such, the traditional CAPM model is not entirely appropriate. An area for future investigation is expanding the CAPM to make this distinction. Holmstrom and Tirole (2001) was one attempt to so, but focused on firm decisions and not investor valuations.

Can the Alternative Definitions of Liquidity be Reconciled?

Here is an example of the wedge between expected returns and price that also highlights that an asset can be liquid in one sense and yet is illiquid in another. Imagine an investor with a US Treasury bond with a 14% coupon in a market where newly issued bonds have a coupon of 7%. Selling these highly appreciated bonds (which traded far above par) would require paying significant capital gains taxes, while holding them involves minimal credit risk and the interest would be state and local tax exempt.  Therefore, to sell would be expensive for the owner and therefore illiquid in sense 1. Nevertheless, these securities could surely be sold rapidly though the secondary US Treasury Bond market and there would be little benefit to waiting and therefore highly liquid in sense 2. It is certainly the case that assets that are liquid in one sense are often liquid in the others too. But as this example shows, that need not be so.

Therefore we cannot collapse these three definitions into a single numerical measure of liquidity capturing all the desired attributes. Even if we could, Hicks (1962) and Admati and Pfleiderer (1988) have concluded that liquidity is an ordinal property. Marschak (1938) suggests measuring the distinct properties of liquidity separately. Pierce (1966) disagrees that such an ordering is possible, at least with respect to sense 1 of liquidity. He says that "apart from those assets that are perfectly liquid and those for which sale prior to maturity is impossible, assets cannot be uniquely ranked by degrees of liquidity." His example is an asset A that is easy to  sell well with short searches (but no better after long ones) and an asset B that sells more poorly than A for short searches and better than A for long ones. Pierce also notes (in describing the weakness of his notion of liquidity) that "the price per unit often depends on the number of units sold." This allows for another example of the crossing behavior, where one asset may be more liquid at small quantities but less liquid for large ones.

Admati and Pfleiderer (1988) argue that liquidity of the third type actually encourages liquidity of the first type. They argue that commodities with successful futures markets have demand for immediacy because price volatility and risks of delaying sales are large (illiquid in sense 3). Such markets also help spread the fixed costs of market making (waiting around for buyers and sellers to want to trade, as well as infrastructure) across a large number of market participants.  In contrast, home sellers are less concerned
with short-term price volatility and instead prefer an extended search for potential buyers.

Alternative Definitions

Krainer and LeRoy (2002) argue that liquidity is a feature of markets and not of assets. They offer as a first example that a Ford automotive factory is illiquid but Ford stock is liquid. A second example is a pool of mortgages which is more illiquid than than the underlying mortgages. However, perhaps it suffices to refer to an asset's liquidity as its liquidity in the most liquid market an agent can trade it in. Tobin calls reversibility "the value of the asset to its holder expressed as a percentage of is contemporaneous cost to the buyer" (Tobin and Golub (1998)). Hahn (1990) sees asset liquidity as being closely related "to the cost reversing a decision taken earlier." His example is that for economic agents, the cost of selling an asset in period 2 will factor into the decision to invest in it in period 1. This meaning of reversibility is a mixture of sense 1 and sense 2 of liquidity. If waiting for suitable trading opportunities is the expensive part of reversing a trade then reversibility is primarily the second sense of liquidity. However, if transaction costs are the expensive part of reversal then the first sense of liquidity will be the relevant one. Marschak (1938) develops a concept of plasticity that is essentially this concept of reversibility. He considers plasticity as a
more general concept than saleability that includes flexibility. Greenbaum (1971) is an early reference that notes the interrelatedness of reversibility and liquidity.

Jones and Ostroy (1984) see an essential attribute of liquidity in the related measure of flexibility. Financial investments that leave agents with a larger set of intermediate and final choices are more flexible. Lippman and McCall (1986) are similarly interested in liquidity as flexibility. They show in a simple search model that if the investor opportunity set changes over time, even risk neutral investors will demand a more
liquid asset because it improves the expected returns of their portfolio. Hahn (1990) also sees liquidity as tied to the "speed of response to new information," but it is hard to see if this is a cause of liquidity or caused by it. Intuition suggests the former. Few market participants, high transaction costs and other direct causes of illiquid markets all make it more difficult to trade on new information. Further, the trees model
of Lucas (1978) shows that prices can move even in the absence of trade. Frequent trade is not synonymous with liquidity.

The frequency of order arrival is a determining factor of liquidity in markets with market makers. This implies that markets need not be liquid to have fast adjusting prices. Flexibility can be about more than investment opportunities. If agents are borrowing constrained and goods can be purchased only with liquid assets, then agents must hold some liquid assets to purchase goods for immediate consumption, even though doing so does not maximize their portfolio return. If consumption opportunities vary over time then agents will hold relatively more ready assets to take advantage of fleeting consumption opportunities. If agents were not so constrained, then they could simply borrow against their illiquid assets (repaying debts as the returns arrived or when prudent sale was possible) to consume as they like. This is also true for investment flexibility. If investors could borrow against their illiquid assets then they would not need liquid holdings to take advantage of future investment opportunities. The necessity of holding liquid assets for consumption purposes is one motivation for the money-in-the-
utility function (MIU) literature. The MIU framework puts money, an asset without consumption value nor any investment return, into the utility function as a reduced form representation of all the ways that money (as the most liquid asset) makes consumption easier and more efficient.


Effects of ACA individual mandate vs AHCA surcharge The US Congress is currently considering a new healthcare bill, the AHCA, which would replace the existing healthcare bill, the ACA.

One of the major changes is the way each bill encourages people to maintain health insurance coverage:

ACA existing law: (in general) if you do not have health insurance for part of the year, you pay an additional tax based on how long you were not covered.
AHCA proposed law: (in general) if you have a lapse in coverage for more than 63 days, insurance companies are allowed to charge you up to 30% more for 12 months.

I am not an economist, but IMHO, the goal of these provisions should be to both encourage people to obtain coverage if they don't have it, and also discourage people from ending coverage if they do. It seems to me that the current ACA meets both of those goals, however, the proposed AHCA does not encourage people to obtain coverage once they have lapsed for 63 days. In fact, the AHCA appears to discourage people from obtaining coverage once they have lapsed for over 63 days. Of those in the group that have lapsed, those that need the coverage the most (regardless of price) are still going to purchase insurance, so this would increase the density of high cost people in the overall pool, leading to increased premiums for everyone.

Is the above analysis correct, and if so, why would this change be proposed? (I find it hard to believe that the economists involved in writing the bill would have simply overlooked this.)

Working off of Josh's answer let's do a case study based on a real world example. On Friday, before leaving for a 7 day cruise through the eastern Caribbean, I went to the Dr and got a prescription for Tramadol, a pain reliever to treat an injury. I went to all of the usual suspects, Walgreens, CVS, etc, and found that with my insurance, the cost for 15 50mg pills was 60 dollars. Using the app GoodRX, I was able to reduce this cost to 44 dollars. I decided to pass. Fast forward two days to find me sunning in the Dominican Republic but unable to enjoy myself because of the injury so I found the nearest pharmacy and was able to purchase a blister-pack of 20 50mg pills for 13 US  dollars without a prescription (Tramadol is not regulated like a narcotic as it is in America). These were not knock-offs but the actual meds. How could this be, I wondered. So I asked the pharmacist. He told me that drug manufacturers make all of their profits in America, marking up the same drugs that sell in other countries for reasonable prices to exorbitant prices and then offer modest discounts to insurers, not to mention the profits of the pharmacy. Why can one script be 90 bucks at Walgreens and only 4 bucks at Walmart?  The simple answer is greed and slothfulness. Drug companies and pharmacies rely upon the laziness of Americans and our willingness to get screwed and our eagerness to bitch about problems without the slightest intent on fixing them.

The moral of this story is that when it comes to managing health care costs, one of the major issues is the regulation of pricing. While I am an ardent believer in capitalism, we must limit the margins charged by drug manufacturers and suppliers alike. The government must modify Medicare Part D to include price controls and introduce these same controls into the ACA or we are doomed to ruination.


Cournot game with 2 firms I have given

2 firms in a market with constant marginal costs and no fixed costs
market demand has $D(p)$
The ﬁrms play a Cournot game

I'm supposed to Calculate the equilibrium quantity for each ﬁrm and the market equilibrium quantity and price. Also I have to find the implied proﬁt for each ﬁrm.

My approach:

Isolate the profit functions as $\pi_i = F(q_A, q_B)$ for $i \in \{A, B\}$
Then I compute marginal costs using that MC = the derivative of total costs w.r.t. Q
Then use that MR = MC for each firm, and solve for $q_A, q_B$
Then using this I was able to find the equilibrium quantity for each firm by substituting one into the other
Finally I subbed these quantities into $D(p)$ to get the equilibrium price

Among my results, I get that $q_A = q_B$. I'm not sure if I've solved this correctly but it seems to make sense to me that the firms have the same equilibrium quantities due to it being a Cournot game.

Was the approach correct?

The approach is correct, but it is not true that firms have the same equilibrium production quantities because we are dealing with Cournot competition - it is because the firms have the same profit functions. You can see for yourself with an example that if the two firms had different cost functions, they would not necessarily produce the same outputs as each other.

The step of "substituting one into the other" implicitly uses the concept of Nash equilibrium, i.e. each firm's production quantity is a best response to the other's. Given that $A$ produces some amount $q_A$ and $B$ knows it, $B$ would make the amount $q_B^*$ is profit-maximizing for $B$. Then we fix $q_B^*$ and find what $A$ would make as a profit-maximizing response - call it $q_A^*$. If I then fix $q_A^*$ and find $B$'s profit-maximizing response is the same $q_B^*$, $(q_A^*,q_B^*)$ is a Nash equilibrium: each firm's action is optimal, given the other's. This line of reasoning can be implemented by a solving a system of two equations, given by the profit-maximizing condition $MR=MC$ for each firm that you mentioned.


if all income is spent on consumption how will it change or affect the economy Imagine all incomes being spent on consumption would such a system be in a position of no change.

No, at least not if you mean "final consumption", that is spent on goods and services solely for our own enjoyment.

We produce goods and services with capital and labour (and natural resources and technology and human capital, but for simplicity let's put those under capital as well). The thing is that capital detoriates over time. My computer at my work place will have to be replaced at some point. The plough of the farmer will break down eventually. The natural gas that I use to heat my house will run out eventually, although potentially not during my life time.

To make up for these losses we need to invest some money in replacing the lost capital and finding replacements for non-natural resources. That is we need to invest money. If we'd only spend all our money on final consumption goods eventually we'd run out of capital and wouldn't be able to produce all those goods.


Why does competition work for capitalism? As far as I know, capitalism is based on competition:
If two(or more) companies produce similar products that compete against other, these companies are in a competition.
Because the objective of a company is to earn as much money as possible, the company will try to maximise the selling of their product. However, because normally there are more than a single company, every company has to sell their best possible product for the lowest price without making enough profit. That leads to a situation where the consumer gets a very good product for a very fair-realistic price.

My problem here is, that this only works if every company only can make the decision about what price they make for what quality once. Like in the prisoner's dilemma.
The prisoner (the company) will (usually; if he is sane) make the decision to betray his member (->Game Theory).
The point is the ideal strategy changes if this 'game' will be repeated forever (is identical to a situation where nobody knows, when the game ends). The strategy any sane prisoner would take is to not betray his gang-member, however, if his member betrays him he will betray him, too, until his member does not betray him anymore.
Because this is a simplified version of a real competition, real companies should act like the prisoners: make a high price until the competitor make a low price. However, no company would make a low price because although they would make better profit in short term, the company would make better in longterm if they made the unspoken deal with the other companies.

So why is it not like this in real world, or is it like this and I haven't noticed that yet?

When two companies produce commodities and/or services that are substitutes then they are simply producing for a market that allows the presence of two or more substitutes.

  "...If two (or more) companies produce similar products that compete against other, these companies are in a competition"

Two firms do not necessarily compete with each other when they are supplying substitutes in the market.

What needs to be clear is that qualifying a market as competitive amounts to making a series of statements about the way the participants in the market behave, their numbers, how potential new participants can interact with the market, the relevant time scale etc.

Narrowing the focus on two members of a market and claiming that they are in competition is not warranted by the assumptions. Nothing has been said about the structure of the market they are embedded in. They could eg be simply trying to flood the market with alternatives to a third commodity so as to narrow the market share of a third producer; the possibilities are really unbounded.

  "...Because the objective of a company is to earn as much money as possible, the company will try to maximise the selling of their product."

The objectives of firms are really as diverse as is the number of industries and producers immense. "Making money" is not always a single operative constraint. Firms have a plurality of goals and obtaining liquidity is one of them. How binding that goal is depends on a host of issues like the market they are embedded in, the firm's size and relative position in the market, probably its access on financing etc.

Profit maximization is an assumption about the behavior of firms which is historically relevant and analytically useful but it is not always the case that firms are maximizing profits. They may be going for market share, or they may be simply optimizing some other metric. And, of course it could very well be the case that they are just winging it!

  "...However, because normally there are more than a single company, every company has to sell their best possible product for the lowest price without making enough profit..."

Again, this claim is not universally true. The number of firms in the market is not always a guarantee of 'quality' and 'affordability'. What matters is the cost structure of the industry, the technology and the assumptions about the market structure. Also, profits that vanish to zero is, again, a feature of the competitive model; not what 'really' obtains.

Now, as far as the 'Prisoner's dilemma' is concerned: In an one-shot game the best thing to do is to 'defect'. In a repetitive setting, that is also open-ended (no predetermined end date) I think that anything goes. You would have to make more assumptions about the number of players and their strategies over time (and in response to others') in order to arrive at definitive conclusions.

The short and non-definitive answer to the question of why don't firms collude when involved into price-competition with each other would be that there are laws that prevent them from that ie the fundamental cost structure of the game is different than what the 'dilemma' posits.


With interest rates and inflation in the U.S. low and growth moderate, where is the money going? Question is basically in the title. With interest rates so low for such a long period of time, I wonder where are that injected cash has gone?

I realize that the economy has definetly grown quite consistently for years now, but the middling growth and simulatenous near-zero interest rates would seem to indicate that the economic climate is so bad in the country that we basically have to ignite a nuclear bomb to boil a pot of water.

Is that the case? It doesn't seem so, and it seems worrying that maybe this cash from monetary policy is somehow disappearing into thin air as we create it or disappearing somewhere problematic

The money is not going anywhere. In fact, it never even "left the building". The banks simply increased their reserve balances with the Federal Reserve, mainly because the Fed began paying interest on reserves in October 2008.


How to set a minimum wage How does a country set an optimum minimum wage, i have went through loads of website but none of them give me a satisfied answer. For example, median of a country's income, percentage of GDP and such seem too shallow and unfair as a medium of calculation.

What criteria define an optimum minimum wage? Is there even such a thing?

The reason why you haven't found a satisfactory answer is that there isn't one. There are several and depending on who you ask you will get a different answer.

Some people will say that the optimum minimum wage is 0 and that the state should note interfere in the matter. Laissez-faire.

Some people wants the minimum wage to cover basic living expenses. What that entails varies widely but is usually connected to the general economic level of the country. In some countries it covers only the cost of basic food for 1-2 people. In others it covers rent, utilities, food, a tv, a mobile phone.

Some people want the minimum wage to be as high as possible. Some unions.


Is the economy a zero-sum game? Theoretically speaking, if all the Earth's inhabitants were to save money and invest, is it possible for everybody to get, let's say, a 4% yearly return for everyone?

Is the economy a zero sum game (where if someone gains, others lose) or not?

Certainly the economy is not a "zero sum game" (whatever that means). There has historically been a positive aggregate net return on capital investment - there doesn't have to be a loser for every winner.

That said, economists generally believe that as the stock of aggregate savings increases, the return will go down; this is a consequence of diminishing returns to capital. Hence it's not possible for everyone to save an unlimited amount at 4%.

To be a little more concrete, economists often use a constant-returns-to-scale production function $F(K,L)$, taking capital $K$ and labor $L$ as inputs, as a first-pass way of thinking about the world. In this simple model, net aggregate savings equal capital $K$. Holding $L$ constant, the extent to which more $K$ will push down the net return to capital $r=F_K-\delta$ (where $F_K$ is the marginal product of capital and $\delta$ is the depreciation rate) depends on the elasticity of substitution of the function $F$.

With a high elasticity of substitution, $K$ can increase substantially without $r$ falling very much, as the economy continues to find productive applications for capital despite its relative abundance; with a low elasticity of substitution, a rise in $K$ can result in a large drop in $r$.

Example. A common form for $F$ is Cobb-Douglas, which corresponds to a constant elasticity of substitution of 1. If the gross capital share of production is $0.35$, then we write $F(K,L) = K^{0.35} L^{0.65}$. The marginal product of capital here is $F_K(K,L) = 0.35 \cdot (K/L)^{-0.65}$, implying that the elasticity of $F_K$ with respect to $K$ is -0.65.

Now, if we suppose that initially $r=0.04$ and $\delta=0.06$, then the elasticity of $r=F_K-\delta$ with respect to $K$ is $-0.65\cdot (0.1/0.04)=-1.625$. This means that if we increase capital $K$ by 10%, the net return $r$ will decrease by approximately 16.25%, or $4\times .1625 = .65$ percentage points, from 4% to 3.35%. This is a pretty substantial decrease!

Indeed, since $1.625 > 1$, in this case net capital income $rK$ to capital decreases as $K$ goes up; remarkably enough, if savers accumulate more, they earn less, as the decline in the net return per unit of capital overwhelms the increase in capital.


Visualization tools for game theory: Game trees There are many ways to draw a sequential game 'by hand'. By drawing the game I mean this:

Displaying players' decision points, available actions and payoffs.

Is there any way I can do this in R or a similar high level programming language? To be precise: I do not want to plot geometric equations, I want to define a structure (players, points, connections, payoffs) and have the program plot it.

I am currently browsing the 'igraph' package but I am having some difficulty labeling so I am wondering if there is a better way.

LaTeX with forest

The forest package of LaTeX allows you to draw game trees with pretty simple syntax. After copying a pre-set template into the LaTeX preamble, one can build up the game tree using a nested [] syntax, then the program takes care of node placement/spacing/etc.

pros: customizability (you can annotate the game tree in any way you want) and font/style consistency
cons: inputting the game tree elements (player/action names, payoffs, info sets) is still somewhat manual, especially if the tree is large; and a somewhat steep learning curve if you're not already familiar with the TikZ package

Here's an example from the forest manual ("Decision tree" in Section 5.1):

\begin{forest}
decision tree
[N,plain content
  [I;{p_1=0.5},plain content,elo={yshift=4pt}
    [{5,1};a]
    [II;b,plain content
      [{1,2};m]
      [{2,3};n]
    ]
  ]
  [II;{p_2=0.5},plain content,elo={yshift=4pt}
    [;c
      [{1,0};z]
      [{2,2};t]
    ]
    [;d
      [{3,1};z]
      [{0,0};t]
    ]
  ]{\draw[dashed](!1.anchor)--(!2.anchor) node[pos=0.5,above]{I};}
]
\end{forest}

Game Theory Explorer

The game theory explorer is developed by a few people at LSE. It allows users to input matrix-form games or build extensive form games through a GUI. It also seems capable of converting between normal and extensive form games. Additionally, the software comes with a solver that looks for Nash equilibria of the inputted game.

pros: GUI; solver; no need for local installation; (limited) customizability
cons: no support for annotation; font/style inconsistency with rest of document

Screenshots:


IS-LM - Effect of interest rate on price level I'm starting to study the Keynesian theory, and I have just read that the increase of interest rate ($r$) will lower the price level ($P$). I tried to understand this using the IS-LM model (I mean, visually through the curves or through the equations), but I am stuck at this reasoning.

If I consider the LM curve and its idea, we will eventually see the following curve:

This represents the interest rate in the y-axis and real money in the x-axis. Now, if I want to know the effect of an increase in $r$ (from $r_1$ to $r_2$), I can say that the real money will be lower, and considering $M$ constant, this implies that $P$ increases. I am aware that this result is obviously not correct, how could I understand this change in $r$ in terms of the IS-LM curves correctly?

There are two different way to present the IS-LM model, one with a vertical money supply line, and one with a horizontal interest rate line. Consider the second one, as it represents better what central banks actually do nowadays.

If the r goes up, this means the central bank has increased its benchmark interest rate (it can mean a host of other things, but I am assuming your IS-LM model does not include risk premia and the like). The horizontal r line shifts upward. The point where this line intersects the money demand line implies that the real money supply is lower. This does not tell us much: it just tells us that the central bank, in order to achieve the higher interest rate it wants, has decreased the nominal money supply M, so that, given the money demand, the interest rate goes up. One could represent this equally well with a vertical line, as I mentioned, but that representation makes it seem as if the central bank targets a given level of money supply. It does not: it targets the interest rate.

Anyway, Patricio is right in saying that, to really track what happens to P, you need the AS-AD model. However, the basic mechanics can be understood intuitively in the IS-LM. The shift in money supply shifts the LM curve leftward, so Y decreases. We move upwards left along the IS curve, as the increased interest rate (endogenously) decreases I (the opportunity cost of investing is larger, so less people invest). The resulting decrease in demand lowers the price level (this is just basic S-D logic, no AS-AD needed). If the central bank wants to keep to its target interest rate, it further increases the M in response to the decrease in P, so as to keep M/P at the level conforming to its target interest rate.

There are some more dynamics in the AS-AD curves after this that have to do with wage rigidity and inflation expectations, but I will leave it at that, as I don't know if you've seen this already.


Best resources to self-educate myself in economics I want to learn Economics by myself and I'm looking to build a path with people who're in this field to how and in what order should I learn Economics, I did some research and I've found many resources to learn from and I'm sure all of the information could be helpful to me in the future but I'm quite sure that not all of the material is practical. I'm ready to invest as many hours and buy all of the books required in-order to learn the material but there's just one thing to keep in mind in this path that I'm asking you to help me build which is: Practicality of the material and how fast I could start to use this knowledge to do trial and error to maximize my learning with the available resources of money I currently have.

If I'm to give a single reference on learning six years of economics by yourself, it would be

MIT Economics Course

http://ocw.mit.edu/courses/economics/

The MIT has the best graduate economic program, and its undergrad program is definitely in the top 3. The faculty is technical-oriented, which means a lot of math, so you'll be well prepared.

The list of requirements included in a syllabus of each course says what other courses you must complete before approaching this one. So, you'll know your learning path in advance.

Each course includes lecture notes and recommended literature.

I'd also keep in mind that while you save money learning this way, the process is quite difficult (especially due to solving math problems alone) and puts you out of sync with institutional aspects of formal education. Like, it's harder to enroll in a grad program or get an advantage in employment.


Why is there a deadweight loss in this lemons market? Is there a deadweight loss in this used car market and why?

On the plums side we can make a pareto improvement by exchanging information and matching 200 buyers and sellers who will gain from trade.

On the lemons side, we can't say for certain that it is inefficient. Lemons are being exchanged at the expected value of a car (50% of cars are plums and 50% are lemons) which is 12k. This becomes the maximum WTP of an ignorant buyer, so the exchange is not inefficient, there are equity issues but not efficiency issues. A Pareto improvement is not possible because any gain that buyers make when given information (they will keep their money in their pockets) is a loss to sellers. (Is this correct? the sale of 600 lemons is Pareto efficient but why can you not return to this point once you're off equilibrium without making sellers worse off?)

So is the deadweight loss the 400k on each side, or just the 400k in the plums market, or is it something else - 2 million on the right hand side for example because the true WTP is 16k? What do you think?

You can calculate the total social surplus (= CS + PS) in this equilibrium and compare it to the social surplus in the efficient allocation of cars.

Equilibrium allocation

The equilibrium (under asymmetric information) has price equal to $12000$. Thus, in the lemon's market,
\begin{align}
CS_L&=(8000-12000)\times1000=-4000000\\
PS_L&=\frac12\times(12000-2000)\times1000=5000000.
\end{align}
Total social surplus in the lemon's market is
\begin{equation}
TS_L=CS_L+PS_L=1000000.
\end{equation}
In the plum's market,
\begin{align}
CS_P&=(16000-12000)\times400=1600000\\
PS_P&=\frac12\times(12000-4000)\times400=1600000.
\end{align}
Total social surplus in the lemon's market is
\begin{equation}
TS_P=CS_P+PS_P=3200000.
\end{equation}
Joint surplus from the two markets:
\begin{equation}
TS=TS_L+TS_P=4200000.
\end{equation}

Efficient allocation

Efficiency occurs when lemons are priced at $8000$ and plums at $16000$. Note that in both markets, since demand is perfectly elastic, consumer surplus is zero at the efficient allocation. So total surplus is the same as producer surplus.
\begin{align}
TS_L^*&=\frac12\times(8000-2000)\times600=1800000\\
TS_P^*&=\frac12\times(16000-4000)\times600=3600000\\
TS^*&=TS_L^*+TS_P^*=5400000.
\end{align}

The gap between $TS^*$ and $TS$ is the DWL. The inefficiency arises from the fact that, in equilibrium (with asymm info), some cars are in the wrong hands: the last 400 lemons sold and the potential 200 plums that were unsold.


Can a continuous preference be represented by a discountinuous function? I can think of some examples, but what can be an outline of the proof?

Indeed you are correct that a continuous utility function can be represented by a discontinuous function. However, I am not sure what you mean by proof beyond an example; an example is a proof of this fact.

For completeness, here is an example we can take $\succeq\,\subset \mathbb R \times \mathbb R$ to reflect the usual ordering (i.e., $x \succeq y$ iff $x \geq y$). Clearly this is a continuous ordering as its contour sets are intervals. The utility function
$$ U(x) = \begin{cases}
x &\text{ if } x < 4 \\
x + 1 &\text{ if } x \geq 4
\end{cases}
$$
is discontinuous, but represents $\succeq$.

Any such function is necessarily have a continuous representation as well.


Characteristics of market liquidity The characteristics of market liquidity, accoridng to Kyle, are tightness of the market, depth of the marekt and resiliency of prices. By referring to tightness, it descriebes the cost of turning around a position over a short period of time. Does this mean the cost to change your position in a risky security from short to long in the short term? The depth reflect the size of an order flow inovvation required to change prices a given amount, and this means the order flow necessary to induce prices to rise or fall by $1\$$. But what is the intuition behind resilienc of the market? It confuses me a little in the way Kyle sets this.

Each of the aspects mentioned by Kyle points to a useful definition of "liquidity."
Tightness of the market refers to the bid-ask spread, the price difference between the highest bid price across all venues and the lowest offer price across all venues. Theory by Black (1971) suggests that the size at the inside bid and offer will, however, be small. So this measure of liquidity is useful for a small order or a a baseline for larger orders.
Depth of the market refers to the rate at which size cumulates if you add orders sizes moving away from the bid-ask spread. We often model this by thinking first about the slope of those cumulated sizes. If a market has a lot of depth, we can trade large orders and will not need to pay much beyond the bid-ask spread.
Resiliency of prices refers to the rate at which the order book refills. If you were to exhaust the inside bid or ask (or even a few price levels beyond that), resilience measures how quickly those levels will refill with new orders.
For more on these ideas, I would suggest reading up on market microstructure. Hasbrouck's Empirical Market Microstructure is very good as is Foucault, Pagano, and Röell's Market Liquidity: Theory, Evidence, and Policy.


utility function always negative In a problem set, I found a strange utility function: $U(c)=-1/2(c^* - c)^2$, where $c^* =$ positive constant level of consumption. Does this function have economic sense?

Remember that utility function only matters ordinally... that is, you only care if $u(A) > u(B)$, and $u(A) = 100$ with $u(B) = 10$ is the same thing as $u(A) = -1000$ and $u(B) = -1000.0001$ (both have $u(A) > u(B)$.)


The impact of news in the stock market? I am currently working on a large sample of textual data from news articles. I was just wondering whether there exists any studies which tries to explain the market anomaly known as "The-Day-Of-The-Week effect" or the "Weekend Effect" with news articles or news in general?

What kind of news can impact the stock market in such a way?

I don't know about the "Weekend Effect" but a paper by Scott R. Baker, Nick Bloom, and Steven J. Davis try to answer to the question What triggers stock market jumps?. They show that some news can indeed impact the stock market.

Drawing on next-‐day newspaper accounts, they develop new evidence about the forces that trigger large daily jumps in national stock and bond markets. They read and code next-‐day interpretations of 200 or more daily jumps per country in recent decades, yielding five main results.

The Global Financial Crisis (GFC) of 2008-‐09 exhibits very high counts of daily equity market jumps around the world. Looking back to 1885 for the U.S., the Great Depression is the only period with equal or greater jump frequency.
U.S. developments trigger equity market jumps across the globe, especially during the GFC. Jumps sourced to the U.S. are hugely more important than jumps sourced to Europe except for European countries, where the counts are similar.
Policy news triggers about 20-‐25% of equity market jumps in most advanced economies and a larger share in other countries (e.g., China=33%, and India=46%).
News about the macroeconomic performance and outlook accounts for 23-‐38% of equity market jumps in advanced economies, and less in other countries.
For U.S. government bond yields, news about the macroeconomy triggers 65% of the jumps; adding news about monetary policy as well accounts for 93% of the jumps.

See also Nick Bloom's CEPR Vox column.


Can government and people spend money foolishly be a main cause of inflation? Can government and people spend money foolishly be a main cause of inflation?

For example if the the arm race happen in two country unwisely, two country will be focus on a military product instead of civilian use product, then some resources will not be use effectively based on the production possibility curve

I am wondering if inflation will happen if people don't know how to balance out which combinations of product is best for them

No, it cannot cause inflation. Inflation is a general rise in the price level, a decrease in the purchasing power of money. While military spending, for example, could cause inflation if paid for through seigniorage (essentially, devaluing a currency by printing more of it), there's neither any reason in theory nor any empirical evidence to support the idea that inflation would result from military spending per se.

Intuitively, if spending were shifted toward military expenditures and away from consumer expenditures, the price of consumer goods would likely fall, not rise. Similarly, the effect on producer prices would be ambiguous, as the price of consumer goods would likely fall, while the price of military goods would likely rise. If prices aren't rising, you don't have inflation.


Why would a politician sollicit foreign investors to come and buy real estate? In the Netherlands we have a shortage of affordable housing. Especially in urban areas, especially housing in the price ranges affordable for young people and middle and low incomes.
This is pretty much a constant, of course now that the economy is doing well and the house prices are rising again, after the 2008 crises, it is even more true.
A couple of years ago - at a period in time when affordable housing was a scarce but real estate prices were not going through the roof - our then Minister for Housing was on television in Singapore asking investors to come buy ('invest in') Dutch real estate.

Here is a clip in Dutch, shown in a late-night show: "Starters op de woningmarkt - Zondag met Lubach (S09)"

Why?
Could there ever be any benefit for citizens when investors buy existing real estate? They are not building new houses.
Could there ever be any benefit in a situation where affordable housing is already scarce?

The owners of existing housing certainly benefit from increased demand and higher prices for their assets. The total benefit to society may be positive or negative, depending on whether current owners win more than current non-owners lose (from higher prices if they want to buy and become owners).

Higher price of housing makes new buildings more profitable, benefiting the construction industry.

The politician may favour certain groups over others, for example the construction industry is usually a large donor in election campaigns. So the politician may want real estate prices to rise even if it is on average bad for the country.

`Invest in' need not mean buying existing housing, but it could mean building new buildings and selling the apartments in them. This could increase availability and decrease the price of housing.


What do we know about the causes of global income inequality? According to the IMF, the GDP per capita in the USA is about \$57,000 per year. In many central African countries the figure is more like \$500 or less. These examples are indicative of the incredibly broad spectrum of levels of development observed globally.

What is the state of the art as far as economists are concerned in explaining where these income disparities have come from? Why have countries like the US grown so much quicker that those of central Africa?
What do we know about the prospects for closing this gap in the future? What are the main prerequisites for very poor countries to begin to grow quickly?
Is there a sense in which developed countries could be said to be perpetuating global inequality (for example, via unfavorable trade policies), or is the state of the developing world largely independent of "the West"?

Three questions, but I think they are fairly closely related (in the sense that the answer to 1. might well also answer 2. and 3.) so I am asking them all together here.

I have to say I do not believe in simple all encompassing answers. The reasons behind the differences are probably complex and multitude, varying from country to country. Below are some answers that one runs into and I think these probably account for a share of the inequality.

The book Why Nations Fail deals with the first question extensively. It is a highly acclaimed work (though personally I was not always convinced by their reasoning) by renowned economists Daron Acemoglu and James Robinson. Their basic argument is that inclusive democratic institutions lead to greater growth because it safeguards business and economic interests of the people.
Hence they see the biggest obstacle in undemocratic cultural traditions and lack of institutions.
An argument I read somewhere (perhaps it was the Dictator's Handbook) is that developed countries prefer dictators in power to fledgling democracies in other countries. The reason is that fledgling democracies are not very stable, and that is bad for investment. Also dictators may be bribed more cheaply to disregard their people's best interest. (For example they may not implement environmental regulation for a price. The same may be said for democracies, but the price is usually higher.) In this way business interests in developed countries may directly contribute to dictatorships, which according Acemoglu and Robinson is what hinders economic growth.


Fed, Asset prices, and the Economy Often you hear people speak about how the Fed has created a fake economy, or one that is propped up with their support, and that they have artificially raised asset prices. What does this exactly mean? How as QE created a fake economy?

As a comment noted, without a reference, it is difficult to give a definitive answer. However, I have often run into similar phrasing in financial market commentary, so I will offer an initial guess as to what you read. This answer is just giving an initial idea as to what topics you could search for to get more information.

This phrasing is often used by members of the Austrian school of thought in economics. (The name "Austrian" refers to the fact that many of the founding members of the school of thought came from Austria.)

The Austrian school is very free markets oriented, and highly critical of government interference in the economy. The Austrian Business Cycle Theory - which I am not an expert on - argues that interest rates are important for planning in the private sector. If the central bank sets the interest rate away from the "correct" level (I am unsure how they phrase this technically), this leads to distortions in private sector activity (away from where the private sector would have naturally been). This leads to imbalances and eventually a crisis/recession. Since the economic activity is not "natural", it is often referred to as "fake." (Since interest rates are determined by the price of bonds, this is the link to asset prices and QE.)

The Mises Institute link to website would be probably the best site to learn about Austrian economics.

However, the Austrian school is not well-represented in academia at present. Most other economic schools of thought currently do not take the Austrian criticisms very seriously. Austrian thinking has not changed much over the past decades, and most non-Austrians view them as having been debunked a long time ago. As a result, it would be difficult to find recent authoritative criticisms of Austrian business cycle theory. In other words, it would be probably be hard to find criticisms of the idea that QE has led to a "fake economy." For example, from the post-Keynesian perspective, it is unclear how we can even define "fake" in this context.

I believe that if you wanted to pursue this, you would need to look further into Austrian theory, and ask a narrow question about a particular topic.


Understanding GDP vs Real GDP I am totally new to Economics. I have issues understanding GDP and real GDP. I have listed 3 statements below, can someone tell me if those makes sense ?

GDP Gross Domestic Product is used to get an idea of the nations economic development.
GDP excludes production that does NOT go through markets hence, GDP is not considered as a good measurement to measure the economic development.
Real GDP on the other hand is inflation-adjusted unlike GDP alone. and can be the best choice to use to measure a countries Economic development.

Yes but note economic development is more broad than just GDP. GDP measures economic output of a country and higher GDP correlates with higher development and it can be also used as a measure of economic development but more narrowly GDP is just a measure of output.
This is correct, GDP can’t measure things like home production. It’s a disadvantage of GDP but I would not necessarily say it implies it’s not a good measure. Sometimes alternative measures can be even less appropriate but if you care mainly not just about output but development there are certainly measures that might be more appropriate. For example, often development economics uses the number of people in absolute poverty as development indicator, or access to education or other factors. There is also Human Development Index (HDI) that includes GDP but tries to also combine more indicators in it such as environmental quality and again education. But for some research purposes GDP might still be the best development indicator - it’s highly case specific. For example, GDP is quite objective and data on it are easily available, even if you would consider HDI superior measure, GDP might still win thanks to data availability as having large number of observations is often important.
Yes real GDP is inflation adjusted. This is important because value of money changes across time dollar today is not same dollar as dollar year ago. This situation is like if in physics length of a meter would change every year. Real GDP corrects for this. However, this only adjusts for changes in value of dollar across time. If you are doing some cross-country comparison you should also think about adjusting for purchasing power parity (the fact a dollar can have different buying power across countries).


What would be the economic effect of widespread instances of individuals paying off consumer debt? In light of the economic impact of the recent shutdowns in response to COVID-19, the Australian Government is considering bringing forward planned tax cuts, that were do to be implemented gradually over the next five years. The tax cuts themselves aren't too large compared to other economic stimuli currently in action, but I read the following statement on a Guardian article:

The Australia Institute paper, by senior economist Matt Grudnoff, concluded that bringing forward the income tax cuts was an “ineffective stimulus”.
He cited the “simple fact of economics that high income earners are more likely to save or pay down debt with the tax cuts, rather than spend the extra funds to help stimulate the domestic economy”.
“A more effective way to stimulate the economy would be to invest heavily in direct employment programs or focus on supporting those who are doing it tough by maintaining or increasing the current rate of the jobseeker supplement.”

This left me wondering what happens to the wider economy when people decide en masse rather than spending their disposable income on consumer goods/services, to instead  pay down their debt and save/invest?

This left me wondering what happens to the wider economy when people decide en masse rather than spending their disposable income on consumer goods/services, to instead pay down their debt and save/invest?

tl;dr: Answer depends on the situation/time horizon you are talking about. In long run increasing saving and investment will have no negative impact on economic activity. In fact it can even lead to higher long-run economic growth.  However, in short-run and in recession (especially one where economy is in a liquidity trap) it would lower everyone real incomes and depress economic activity.
Full Answer:
To see what mechanisms are in play here we can use little bit of math. This can be done with the standard goods market equilibrium model (see Blanchard et all Macroeconomics: a European Perspective)  Let us start with output/GDP definition for closed economy:
$$Y =C+I+G \tag{1}$$
where $Y$ is the economic output (which in economics must also be equal to people's incomes so I will be using output/income interchangeably). $C$ is consumption, $I$ is investment and $G$ is government spending. In order to get some meaningful answer from the above identity we have to specify what the consumption is. In order to make everything simple lets assume linear consumption function:
$$C= c_0 + c_1 (Y-T) \tag{2}$$
Where $c_0$ represents your autonomous consumption -  consumption you will consume regardless of your income, $c_1$ is your marginal propensity to consume, if $c_1=0.75$ that means you will consume $3/4$ of your disposable income and save the rest and finally $Y-T$ is income minus taxes which is the disposable income.
If we substitute $C$ back to the GDP definition and solve for $Y$, we get the goods market equilibrium:
$$Y = \frac{1}{1-c_1}\left( c_0+I+G-c_1T\right) \tag{3} $$
This shows that the level of economic output $Y$ will actually depend both on consumption and investment (and investment in turn depends on private savings as it is the sum of private and public saving). However, it also shows that if people's marginal propensity to consume increases (that is when $c_1$ becomes higher) the whole output multiplier $ \frac{1}{1-c_1}$ becomes higher and hence for any level of autonomous spending, investment or government spending the output will be higher.
Nonetheless the above is all just a short-run partial equilibrium analysis. Such analysis is appropriate when we are in recession and where investment is unresponsive because for example an economy is in a liquidity trap (a situation where increase in savings wont necessary fuel more investment). However, in long-run we have to acknowledge that investment is not just independent as the formula (3) suggests but also depends on income and interest rates as investment as mentioned above arises from private and public savings.
If we make just one very simple change to the model above and assume that investment is given as $I= I_0 + d_1 Y -d_2 i$ , where $I_0$ is autonomous investment, $d_1$ is the fraction of income that is invested, $d_2$ is parameter which determines how investment respond to interest rates and $i$ is an interest rate, then the goods market equilibrium will be given by:
$$  Y = \frac{1}{1-c_1-d_1}[c_0 + I_0 + G − c_1T] - \frac{d_2}{1-c_1-d_1}i \tag{4}$$
In this case you can see that the multiplier is given as $\frac{1}{1-c_1-d_1}$ so multiplier is given by spending not just on goods and services but also by investment spending - if people lower their marginal propensity to consume but increase marginal propensity to invest to offset that nothing will change. Furthermore, ceteris paribus increasing the amount of savings lowers the interest rate (which is the price for savings that can be used as investment).  So once we let investment to vary depending on interest rates and income we see that what matters is the amount of all spending no matter whether it is spending on goods and services or investing.
In addition the above is still missing explicit model for money-market and behavior of firms if I would add that in a result would show that in the long run all savings are transformed into investment either directly (which is modeled here) or indirectly through their effect on overall price level but an exposition of full model would be too complex so if you are interested you have a look at some undergraduate textbook (all models presented here are taken from the above mentioned Blanchard et all Macroeconomics but they will also appear in any standard macro book with perhaps different notation).
Furthermore, the discussion above does not factor in economic growth and saving and investment is crucial for economic growth. The main growth model used in modern economic literature are the Solow growth model in which increase in saving rate can result in short to medium term higher economic growth, but not really in  a long run per capita growth which will in the model be determined by the rate at which technology progresses. However,  for that to happen the economy still requires some level of saving - the model just shows that trying to increase the level of saving in the long run steady state wont make difference (See Romer Advanced Macroeconomics).
However, recently in literature endogenous growth models are becoming more popular (Romer even got his Nobel Prize in economics in  2018 for his work on them) and in such models savings rate actually can increase even long run economic growth (again see Romer Advanced Macroeconomics).

PS: This is little bit of an tangent and hence I included it as a post scriptum but actually this:

He cited the “simple fact of economics that high income earners are more likely to save or pay down debt with the tax cuts, rather than spend the extra funds to help stimulate the domestic economy”.

this is actually not entirely accurate - or at least taken out of context (probably journalist misunderstood statement about particular tax cut as a general one). You can always design a tax cut that specifically targets poor. For example suppose we have flat tax rate of $40\%$ we can always decide to cut tax rate to let's say $10\%$ only for people below some income threshold. Rather the issue is that taxes generally have lower multiplier attached to them and hence they affect output differently. From equation (3) you can see that if government spending $G$ increases by 1 the output will increase by $\frac{1}{1-c_1}$ but if the government decreases taxes output increases only by $\frac{c_1}{1-c_1}$ and on interval $0<c_1<1$ the former will be always larger as on that interval $\frac{1}{1-c_1}>\frac{c_1}{1-c_1}$. This also holds just in short-run though.


Does quantitative easing favour banks? The reserve bank recently announced it would print $100B over 6 months, and spend this buying back gov bonds.

Will this policy advantage the financial sector over other parts of the economy?
Why doesn't the reserve bank give this \$100B to treasury directly, so that fewer bonds need be issued to support gov spending?
Alternatively, why doesn't the reserve bank distribute this \$100B directly to ordinary households (e.g. \$4k per resident)?

Will this policy advantage the financial sector over other parts of the economy?

I do not see how this would a priori advantage the financial sector over other parts of the economy. This policy is done to stimulate economic activity by putting pressure on lowering the long-term interest rates and to push pressure on inflation and lower exchange rate. Such expansionary monetary policy is conventionally considered to stimulate real economic activity in the short-run (see any undergraduate macro textbook for example Blanchard et al. Macroeconomics: a European Perspective). There is no reason to a priori think this specially advantages banks over other sectors, as this is macroeconomic policy with aim to stimulate the whole economy, although banks will likely benefit as well.

Why doesn't the reserve bank give this $100B to treasury directly, so that fewer bonds need be issued to support gov spending?

This is for several reasons. First, giving money directly to government would mean that money supply is permanently being increased by that new money (technically that money could be still destroyed in some ways but not unliterary just by central bank). When central bank buys government bonds the money supply is expanded only as long as the government bonds are not repaid. Central banks still have option of scrapping the bonds and hence making the money supply expansion permanent, but they also have other options. Central banks will usually want to expand money supply in recession but in expansions they might want to contract it. They could contract it also with other ways (like increasing reserve rations), but open market operations are usually one of the preferred tools of central banks.
However, this does not affect government budget negatively. Any interest that government pays to central bank is then returned to the government. So from the perspective of government this debt has no cost. In fact such extra demand on government bonds will likely make it cheaper for government to issue bonds on primary market so if anything it might indirectly help it.
Also, the reason why it is done on secondary market rather than primary market, is that central bank is supposed to be independent from government. Hence they try to always keep arms length relationship with it.

Alternatively, why doesn't the reserve bank distribute this $100B directly to ordinary households (e.g. \$4k per resident)?

This is what is called 'helicopter money'. Some economists are in favor of such policy, however arguments are being made that it threatens central bank independence. Helicopter money is very close to fiscal policy and if people learn they could get 'free money' from central bank they might put political pressures on central banks being involved in such transfers beyond what is warranted by monetary policy. It is argued that any fiscal policy should be done by elected representatives and not by unelected technocrats, and helicopter money is very fiscal-esque.   See more on this in Reichlin; Turner; Woodford (23 September 2019). Central bank independence is in economic profession revered in similar way as in law profession independent judiciary or in journalism independent press so anything that threatens central bank independence is hard sell. Of course, this raises additional question of why the central bank independence is so important - exploring that is beyond the scope of this answer but you can read more about it in this ECB explainer.    In addition in most countries this would not even be legal although laws can be changed.

Edit:
Theory above aside, even when we look empirically at aggregate measures of bank profitability we can see that in the post 2007 they are low, as you can see from the figure below which plots price-to-book ratio for banks, which is a measure of profitability and expected profitability that stock prices capture (see Carletti, Claessens, Fatás, Vives 18 June 2020, and sources cited therein).

QE was not common before 2007 and became quite commonplace after, due to the Great Recession. Hence, there is not much evidence to suspect that banks are somehow 'getting rich' out of QE. Furthermore, of course the above is just raw data so it has to be interpreted with caution. One could argue that maybe there are some other factors that depress  bank profitability inspite of all the QE.
However, when we look at some serious research it actually confirms that QE together with negative interest rates and other recent bank regulation erode bank profitability (e.g. see Florian 2018).  Hence, if anything there is research and evidence supporting the idea that QE, combined with other policies central banks nowadays commonly pursue, makes banks less profitable not more.


How to find the elasticity of substitution for the general CES-function? I have to find the EOS for the general CES-function defined as

$$
y = (a_1x_1^p+a_2x_2^p)^{1/p}
$$

I first find $MP_1$ and $MP_2$ to find $MRTS$. We have that

$MP_1 = \frac{\partial y} {\partial x_1} = \frac{1}{p} (a_1x_1^p+a_2x_2^p)^{1/p} \cdot pa_1x_1^{p-1}$

$MP_2 = \frac{\partial y} {\partial x_2} = \frac{1}{p} (a_1x_1^p+a_2x_2^p)^{1/p} \cdot pa_2x_2^{p-1}$

and thus

$MTRS = - \frac{MP_1}{MP_2} = - \frac{a_1x_1^{p-1}}{a_2x_2^{p-1}}$

By definition EOS is given by

$$
\sigma = \frac{d(x_2/x_1)}{dMTRS} \frac{MTRS}{(x_2/x_1)}
$$
so to find $x_2/x_1$ I have done the following. Let $\theta = - \frac{a_1x_1^{p-1}}{a_2x_2^{p-1}}$ then we have
$$
\frac{1}{\theta} = - \frac{a_2x_2^{p-1}}{a_1x_1^{p-1}} \Rightarrow \frac{x_2^{p-1}}{x_1^{p-1}} = - \frac{1}{\theta} \frac{a_1}{a_2} \Rightarrow \frac{x_2}{x_1} = (- \frac{1}{\theta} \frac{a_1}{a_2})^{\frac{1}{p-1}}
$$
Thus
$$
\sigma = \frac{d(- \frac{1}{\theta} \frac{a_1}{a_2})^{\frac{1}{p-1}}}{d \theta} \cdot \frac{\theta}{(- \frac{1}{\theta} \frac{a_1}{a_2})^{\frac{1}{p-1}}} = -\frac{1}{p-1}
$$
which does not give the desired result that $\sigma = \frac{1}{p+1}$. Where am I doing wrong?

four things :

The desired result is actually
 which is the answer you are getting if you multiply the negative into the denominator( you can cross-check on https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution)
. However, you have made the following mistakes.
NON CONSEQUENTIAL ERROR: Your first error is when you differentiate to get MP1 and MP2. In both these cases, the long term should have power : (1/p - 1 ). This term gets canceled hence doesn't affect the solution.

Further MRTS(marginal rate of technical sub) = MP1/MP2 and not - MP1/MP2. This is because MRTS is the absolute number of factor x2 that has to be given up to employ one more unit of factor x1 while keeping the production constant( moving along the same isoquant curve). MRTS is always taken as positive. This is because the negative sign of the slope simply implies the "giving up" which is implicit in the definition of opportunity cost.
However, in both of your mistakes, your error got canceled due to the symmetry of the numerator and denominator. Hence you are actually getting the right answer.  Your method is a little long. I am posting here the way I do it :


Identifying assumption meaning I am hoping to get a good explanation regarding what is meant by an identifying assumption.
In many articles, under empirical strategy, authors state that:

we exploit firm level variation to identify the effect
we exploit industry level variation to identify the effect

Examples:

The paper examines the effect of bank runs on lending. We exploit variation in the structure of banks' liabilities to identify banks that were more vulnerable to the run.

We exploit the variation across geographically distinct commercial real estate markets to establish conclusively that loan supply shocks emanating from Japan had real effects on economic activity in the United States.

"Identification" is the most loaded term in econometrics. There are multiple cheap talk equilibria with regard to its meaning. It is used with different intended (but related and overlapping) meanings, in different contexts, by people with different orientations, with different levels of precision.
Therefore you will get a range of correct answers.
Here is an attempt covering a few of the variations, going from the theoretical end of the spectrum to the empirical.
Statistics
A statistical model is a one-to-one mapping $\theta \mapsto P_{\theta}$ from a given parameter space to a family of probability measures.
It is the one-to-one property of the mapping that makes the model "identified".
No two different elements in the parameter space can give rise to observationally equivalent data generating processes.
In statistics, a model is therefore, by definition/assumption, always identified.
(This can be seen in the assumptions for all the foundational results, e.g. Neyman-Pearson.) Statisticians never speak about identification, because they don't have to.
For example, for
$$
y = \beta x + \epsilon \quad (*)
$$
where $(x,\epsilon)$ is bivariate normal, to specify a model for population $(x,y)$ parametrized by $\beta$, one must assume that $Cov(x, \epsilon) = 0$. Without imposing this assumption, different $\beta$'s could give rise to the same distribution for $(x,y)$. In econometrics, which is much more explicit about the identification issue, the condition $Cov(x, \epsilon) = 0$ will sometimes be called an identification assumption.
Structural Models
If one tries to construct a statistical model by adding unobserved disturbances to an economic model, identification needs to be addressed.
In order to make the resulting structural econometric model identified, usually one needs to make certain assumptions, either of economic or technical nature. These are called identification assumptions.
For example, suppose there are $n$ firms in Cournot competition with private constant marginal costs $(c_1, \cdots, c_n)$ drawn from joint density $f(x_1, \cdots, x_n)$.
The econometrician observes firms' output $(q_1, \cdots, q_n)$ and market price $P$ and would like to identify $f$. One possible identification assumption is that the Jacobian of the FOC system
$$
\frac{d P(Q)}{dQ} q_i + P(Q) - c_i = 0, \, i = 1, \cdots, n,\, \mbox{ where } Q=\sum_1^n q_i
$$
is non-vanishing. Then, by the Implicit Function Theorem, $(q_1, \cdots, q_n)$ maps one-to-one locally to $(c_1, \cdots, c_n)$. This implies the model, parametrized by the observed quantity $(q_1, \cdots, q_n)$, is identified, at least locally.
The empirical interpretation is that sufficient variation in the trade-offs faced by the firms
allows you to identify $f$.
There are more interesting examples where the identification assumption
puts restriction on economic agent behavior, etc.
Empirical Usage-Consistent Estimation
So far, identification is purely a property of the mapping from parameter to data generating processes. Identification is a prerequisite for estimation but by itself it makes no mention of the sample.
There are also contexts where an econometrician speaks about a specific estimator that's designed to estimate a specific parameter in a specific model.
An assumption under which the estimator consistently estimates the parameter is called an identification assumption.
For example, given time-series data $(x_t, y_t)$ generated by
$$
y_t = \beta x_t + \epsilon_t, \; t = 1, 2, \cdots, \quad (**)
$$
the parameter $\beta$ "can be identified by OLS $\hat{\beta}$" under the assumption that $Cov(x, \epsilon) = 0$.
In $(*)$ and $(**)$, the condition $Cov(x, \epsilon) = 0$ and the terminology are the same, but "identification assumption" have different (but clearly related) meanings.
Empirical Usage-Causal Inference
When one is interested in establishing causal effect, a condition imposed on the model that allows for causal interpretation of the estimate is called an identification assumption. Yes---$Cov(x, \epsilon) = 0$ for the linear model would fall under this category also. Often it is strengthened to  $E[\epsilon|x] = 0$, which is more interpretable for causal inference.
Similarly, when $Z$ is an instrument, the exogeneity condition $Cov(Z, \epsilon) = 0$ is an identification assumption.
For diff-in-diff, the parallel-trends condition is an identification assumption.
For regression discontinuity design, the identification assumptions are that, first, there are no other discontinuities except the forcing variable, and second, agents cannot manipulate the forcing variable.
The corresponding empirical design (e.g. IV/DID/RDD/etc) is sometimes called the identification strategy.
In this context, "identification" is not a binary condition. One could have weak identification, e.g. a weak instrument.
Used in this sense, an identification assumption clearly needs to be justified when it's claimed to hold empirically. In other words, one needs to justify that the corresponding  variation is exogenous---e.g. the variation of the instrument is exogenous, etc.
In your quoted example,

The paper examines the effect of bank runs on lending. We exploit
variation in the structure of banks' liabilities to identify banks
that were more vulnerable to the run...

vulnerability to a run is clearly a endogenous variable in relation to lending. The claim is then the empirical design in question uses exogenous variation in the structure of banks' liabilities---as an instrument/forcing variable/whatever---to circumvent endogeneity and achieve identification.


How would banking in EU change if taxpayers withdrew their support for Deposit Guarantee Scheme? Disclaimer

The question pertains mostly to EU but I believe counterparts to Deposits Guarantee Scheme exist world-wide.

Assumption

Let’s suppose that support for liberal ideas and free market rises in European nations what results in taxpayers withdrawing their support for majority of state’s interventions in the free market, including Deposit Guarantee Schemes. Taxpayers would also demand that the minimum capital to open one’s own bank would be dropped from 5mln Euro to 100k Euro, so that the competition in the banking sector is at a much higher level that it is nowadays which is an interesting topic in itself but let’s just focus on DGS exclusively.
I am far from judging who would benefit on that or whether such a situation is even likely - it’s simply an axiom for this question.

Question

Now, given that Fractional Reserve Banking model makes it impossible for banks to guarantee even a small fraction of deposits in their own capital as clearly banks juggle money supplies rows of magnitude higher than they own, what can we reasonable expect to happen if taxpayers turn their back on banks and demand banks to provide their own guarantees?

I presume that once the taxpayers’ guarantees are gone, for banks to be perceived as a safe place, they would have to own capital that at least equals the deposits to be handed over to them?

Otherwise, I cannot see what would people base their trust to banks on?

References

Directive 94/19/EC on DGS

DGS FAQ

Based on the discussion in comments, the core of your question appears to be "What would happen if European governments stopped providing deposit insurance?"

The question and answer about the US deposit insurance program here provides useful background, but the short answer would be that we would expect bank runs to be more likely, though how much more likely would be a function of the institutional relationships between banks, banks' access to liquidity backstops, the extent of bank regulation, and economic fundamentals. This is because (as discussed in the linked answer) private deposit insurance doesn't entirely relieve depositors of monitoring burdens, and private deposit insurers lack the ability to discipline the banks they insure without potentially creating bank runs.

Theory aside, it's not difficult to find examples (particularly historical examples) where deposit insurance has not existed, and while bank runs were generally more likely in those cases, they were not always common, as emphasized by Calomiris and Gorton (1991). Institutional arrangements such as credit mutuals, where shares in the depository institution are allocated based on deposits, can mitigate run risk, for example. A decent review of banking from an industrial organization view can be found in Neuberger (1998).


Why do firms bother to produce at equilibrium quantities if at equilibrium quantity, MR < MC? For almost all demand curves, the resulting marginal revenue curve is often to the left of and steeper than the demand curve. The marginal cost curve has its distinctive U-shape, and a particular portion of the marginal cost curve is the supply curve. So the result can be shown below:

The figure above indicates that in almost any case, because MR is to the left of D, if a firm produces the quantity at market equilibrium, MR < MC, which means that the firm would be actively losing profits.  So, why do firms even bother going to market equilibrium - from a theoretical standpoint?

The MC curve can only be seen as a supply schedule for the individual firm if it is a price taker. In the case you depicted, however, we have imperfect competition. A profit-maximizing firm will thus produce where MR=MC, and charge a price that will induce consumers to purchase this quantity (which can be read off the demand schedule). In this sense, there is no "disequilibrium": the firm is doing the best it can (so it has no reason to change), and total quantity demanded is equal to total quantity supplied (i.e. there is market equilibrium).


Value added by sector of economic activity I am trying to make a pie chart of value added by economic activity (as a % of gdp). I am trying to use data from world bank for each of the four sectors: manufacturing, agriculture, industry, services http://data.worldbank.org/indicator/NV.IND.TOTL.ZS?display=default , but surprisingly the percentage share for each of those sectors, for one country do not add up to 100 but to 120. Why is that?

The first line of your World Bank link gives you the explanation:

  Industry corresponds to ISIC divisions 10-45 and includes
  manufacturing (ISIC divisions 15-37)

Hence, if you add up industry and manufacturing you count some activities twice, the divisions 15-37 that is.

But even if you take this into account you should not find 100% if you are adding up the value added of all the activities. Gross domestic product (GDP) is not the sum of the gross value added (GVA) of all the activities but:

  GDP = GVA + Taxes on products - Subsidies on products

According to Statistics Explained

  Gross value added of the total economy usually accounts for more than
  90 % of GDP

So, the message is to check carefully the definitions and concepts used by the World Bank.


Why is Money Necessary? I've heard a lot of different economists bullet point a few main ideas as to why money is necessary. However, I'd like to get an ultimate rundown list. What are the major reasons why money is necessary for a culture to thrive?

There are issues with this question as currently written.

I will attempt to offer a partial answer by responding with a different question. If money did not exist, how would governments in modern developed countries impose taxes?

Historically, rulers would impose taxes in kind: forcing peasants to serve in the army, or taking a portion of the harvest. This is not particularly easy to see how a modern government could achieve this in a politically acceptable fashion.

So if you can find a way to allow taxation without money, you have found a way for money to not be necessary in a modern developed country.


What's the advantage of repurchase agreements over collateral backed loans? Is there any material difference between a repo and a collateral backed loan?
The one I can think of is that the collateral is owned by the lending party during the loan. So if the Fed uses this with treasuries they get to collect interest on it.
Why did the Fed adopt this as a tool over simple buying and selling? It seems to provide the same effect to the money supply and they don't need the interest from the treasury collateral given they return most of their money to the Treasury every year.

Repo and Securities Lending
https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr529.pdf
Nominal page 2:

A repurchase agreement is the sale of securities coupled with an agreement to repurchase the securities, at a specified price, at a later date (see Duffie (1996) and Garbade (2006)). Securities lending agreements are economically similar to repo agreements.4 Both agreements resemble a collateralized loan, but their treatment under the U.S. bankruptcy law is more beneficial to cash lenders:    In the event of bankruptcy, cash lenders can typically sell their collateral, rather than be subject to an automatic stay as would be the case for a collateralized loan.

Two advantages are

Repo are short term self-liquidating positions which automatically run off the balance sheet under the terms of the deal; and

Collateral under Repo deals is available for sale by the lender if the counterparty goes bankrupt.


How to find the maximum profit in a graph? We know the maximum profit will occur at the quantity where the gap of total revenue over total cost is largest. But how can we find such gap?

Short answer:
Shift the profit line parallel downward until it only touches the loss function in only one point. That's the point where the maximum gap occurs.
Reason:
The maximum occurs where Marginal Cost=Marginal Revenue.
You can see this from basic profit maximization:
$\max Profit = \max (Revenue - Cost) $
We solve by taking first derivatives, call them $D$, and setting to zero.
Hence $D Revenue - D Cost =0$. Note that what we mean by Marginal Revenue and Marginal Costs are just first derivatives of Revenue and Cost, respectively.
So clearly Marginal Cost = Marginal Revenue.
Graphically this means the slope of the cost function equals the slope of the revenue function at the maximum profit point. This is because the first derivative gives the slope of a function.
So shift the revenue function parallel downward toward costs until it only touches on one point. They have the same slopes at that point. This is because a) revenues here are linear (a straight line) and have the same slope everywhere and b) a straight line that touches a function in one point only (called a tangent) has the same slope as the function at that point.
So that tangent point is your profit maximization point.
Similarly, if you shift revenue upward to the other tangent point with costs, you will find the maximum loss point.


Did the financial crisis affect the retirement patterns of Baby boomers? Baby boomers are retiring and have been for a few years already. The financial crisis potentially made a large fraction f them change their retirement plans. Is there some measure / study of this effect? Are there any references to look at?

I don't know if you'd find these specific references helpful to look at, but I hope it's a good start. Quandl has a database called Social Security Administration and if you search "retirement" within the database, you will see datasets on number of retired recipients of social security, along with their spouses and dependents, and the average monthly amount they receive. Data goes back to the 1960s. Another database, Federal Reserve Economic Data, also shows retirement data such as federal employee retirement plans and funds. Data goes to back to the 1940s. You'd have to search for "retirement" within the database. Both these databases are free to access. Hope this helps. [Disclosure: I work for Quandl]


Quoting convention for Gold in the early 1900s I was looking at some historical references on gold prices over the past century and I noticed that London gold prices are written as "$x$ s. $y$ d" (e.g., '$121 \text{s}. 1.75 \text{d}$'). I'm wondering how I'd go about converting this into pounds. Thanks!

Have you considered googling the subject?
By doing so I have found:
https://en.wikipedia.org/wiki/%C2%A3sd

  £sd (occasionally written Lsd) is the popular name for the pre-decimal currencies once common throughout Europe, especially in the British Isles and hence in several countries of the British Empire and subsequently the Commonwealth. [...] In the classical Roman Empire, standard coinage was established to facilitate business transactions. 12 denarii were rated equal to 1 gold solidus – a 4th-century Roman coin that was rare but which still circulated; and, since 240 denarii were cut from one Roman libra of silver 240 denarii, therefore, equalled one pound (livre in France, peso in Spain, etc.). [...] Different monetary systems based on units in ratio 20:1 & 12:1 (L:S & S:D) were widely used in Europe in medieval times. The English name pound is a Germanic adaptation of the Latin phrase libra pondo 'a pound weight'. [...] In writing, there were several conventions for representing amounts of money in pounds, shillings and pence: £2.3s.6d. (two pounds, three shillings and sixpence)


Fixed Effects Interpetation I have some issues understanding the intuition in Fixed Effects models,
and the sources of variation they imply. For a concrete example, consider
the following regression specification:

$$r_{ist}=\gamma_{i}+\delta_{st}+\epsilon_{ist}$$

The LHS in the above equation is to be interpreted as the rating
that a worker $i$ receives at time period $t$ in sector $s.$ The
RHS is composed of three terms. The first term represents a worker
fixed effect- think of this as a dummy variable that takes a value
of 1 for worker $i$ and 0 for all $j\neq i$. In this sense, the
design matrix would consist of dummy variables for all workers (no
constant term), and the variable for worker $i$ would take on the
value $1$ when considered in this matrix. The second term represents
$\delta_{st}$, or a sector-year fixed effect. This is basically a
coefficient on a dummy variable for a particular sector-year cell. How is one to interpret this?
There are a total of $st$ of such dummy variables. The third is an
error term. My first question is, how does on interpret the value
of a particular $\hat{\gamma}_{i}?$ Also, how does this relate to removing
the variation at the worker level and the sector year level. What
variation are we removing? What does it intuitively mean to remove
variation? Finally, think of adding a set of covariates as:
$$
r_{ist}=x_{ist}'\beta+\gamma_{i}+\delta_{st}+\epsilon_{ist}
$$
 Now, how is $\beta$ being identified? If we take into account individual
and sector fixed effects, how is $x$ varying? Would one not interpret
that $\beta$ is identified by holding constant $i$ and holding constant
$st$ , we vary $x_{ist}$. But if we are holding both $i$ and $st$
constant, there is no variation in $x.$

I apologize for the multiple questions asked here, but I think the questions are quite inter-related.

Interpretation of FE: $\delta_{st}$  is the mean rating in each sector in each time period.

Contrived Example:  Over time, public opinion of workers in the library sector improved and their rating r improved. On the other hand, those in the used-car sector became seen as less reliable and their rating r declined.  We capture this with $\delta_{st}$ .

Identification of B (intuition):

x must vary within individuals i of the same sector s every time period. Otherwise $\delta_{st}$ will be co-linear.
x must vary within individuals i along time periods t. Otherwise $\gamma_i$ will be co-linear.

Basically, $\gamma_i$ can be identified separately from $\beta$ because individuals change over time.  And $\delta_{st}$ can be identified separately from $\beta$ because they individuals are heterogeneous within each time period and sector.