In auction theory, why is my own valuation a random variable? Auction theory typically (always?) begins by assuming that each bidder's valuation is a random variable. Now, it might seem reasonable (at least from a Bayesian perspective) for you to treat other people's valuations as random variables. After all, you don't know their valuations! However, what justification can there be for treating your own valuation as a random variable when deciding on how to bid? And are there any approaches which do not begin with this assumption?

Edit: Here's another way of posing the question. In the context of auction theory, people normally seem to define a strategy as a function mapping from my (random) valuation to my bid. But assuming that I know my valuation, why not simply define my strategy as my bid?

In most of the literature I have read on private value auctions you do actually know your own valuation in the auction, it is your private information. It has a distribution from the point of view of others, who can only guess at your valuation.

Another interpretation would be that your valuation is actually random before getting detailed information on the object you are bidding on. How much would you pay for this bottle of wine that I have here on my shelf? Oh, it depends on the wine? Then without knowing the exact type of wine and assuming it has some random distribution your valuation is also a random variable. Once you learn the exact type of the wine you learn your own 'type', which is modeled as getting a private signal about your valuation.

In case of noisy observation your valuation can actually be random. E.g. I tell you the type of wine but you have never had it before. Or in case of gas companies, they have an inexact estimate about the yield of a gas field. Their 'real' valuation depends on the 'real' yield, without knowing that they can only bid based on some expected values.

You seem to not understand the concept of "random variable". The term "random variable" does not refer to a variable that is unknown, it refers to a variable that has a nondeterministic relationship with other variables. For instance, when you draw cards in poker, the result is a random variable. Just because you end up knowing that you ended up getting particular cards doesn't make them not random variables. You can still ask what the probability of getting those cards is. And since your opponents' actions will be based on that probability, you'd better be able to figure out what that probability is. If you're thinking "Well, I know that I have a pair of kings, so clearly the probability of having a pair of kings is 100%", you're probably not going to do well. To do Bayesian reasoning, you need to know what your prior probability of getting a pair of kings is.

For a more complicated example, suppose you have a population with mean $\mu$ and standard deviation $\sigma$. You then take a sample and calculate the sample mean. You then want to calculate the 95% confidence interval. This is an interval such that there is a 95% chance that your sampling procedure will result in a sample mean within the interval. This is often presented as "I have this sample mean, and there's a 95% chance that the true mean is within this measurement error". But this is suggesting that the true mean is some random variable with some probability distribution. But it's not a random variable, it's a fixed parameter. It's the sample mean that is the random variable, and it's the sample mean that has a probability distribution. Just because you've already taken a sample, and know what its sample mean is, does not mean it's not a random variable. There is a nondeterministic process that turns a population mean and std into a sample mean. The sample mean depends on the population mean, but does so nondeterministically, and so is a random variable. Similarly, you valuation is being modeled as coming from particular parameters, but doing so nondeterministically.

Presumably, your bid will be based on how much value you think the good will generate for you. This will in turn be based on what information you have received about the good. And what information you receive can be modeled as a random process. Basically, you have a good space G. You have some data space D. You have some valuation function V. Given a particular g in G, there is some distribution of D: p(D=d|G=g). Given a particular d, there is some valuation v: v = V(d). You want a strategy, given v, of choosing a bid. v is a function of d, which is a nondeterminstic function of g, thus v is a random variable depending on g. Given a particular v and a prior on the distribution of G, and the conditional distributions of d on g, you can use Bayesian reasoning to find the distribution of g. You can then find the bid that maximizes expected value (i.e. the value for each g, weighted by their conditional probabilities).

As for why the bid shouldn't just be your valuation: there's no reason to think that your valuation will be an unbiased estimator of the good's true value. Furthermore, the expected value of a bid has a complicated relationship between the bid and the good's true value. If you win the auction, then the value of your bid is the difference between the value and the bid, but the probability of winning the auction depends on your bid and the other participants'. Thus, even if you did have an unbiased estimator of the true value, you shouldn't use it as your bid; you need to take other participants' bids into account.


What are examples for the phenomenon that more (or better) information makes everybody worse off? More information is usually considered "better". Let's say a rational agent chooses optimally given his information on the circumstances of a particular decision problem. Then providing him with more or better information makes him (weakly) better off.

Other agents might be made worse off in the process, and total welfare might even decrease. Danove et al. (2003) e.g. argue that the introduction of mandatory "report cards" in New York and Pennsylvania in the 1990ies to evaluate bypass surgeries reduced welfare because it incentivized doctors to avoid treating very old or sick patients. In this example all patients got more information, and some of them, but not all, ended up worse off.

But there are also circumstances where providing agents with more information makes everybody worse off. When visitors are about to leave a crowded theater, truthfully informing them that a fire just broke out behind the curtain might have disastrous consequences for all of them. Informing the public that a particular bank is in trouble could trigger a bank run that leaves everybody worse off.

What are other such phenomena? I am looking for examples (in theoretical models or in the real world) of the latter kind, where exogenously providing a group of agents with more or better information leads to a new equilibrium which is Pareto inferior compared to the old one.

Traffic reports are another type of information that potentially makes everyone worse off.

A recent working paper (Wiseman and Wiseman 2019, https://drive.google.com/open?id=10B6VudYJOQB5w2UVBrYEjYc5wwzGZc8Z) shows this in a simple model of traffic.

I quote from the paper, "...public information about road conditions tends to increase average travel time when...3) the scale of the traffic network is large." This corresponds to their Theorem 3, where "...in a scaled-up version of any environment with excess capacity, traffic reports increase expected travel time."

Yet another broad way of thinking about your question is in terms of monitoring structures of repeated games. A recent paper (Sugaya and Wolitzky 2018 JPE, http://economics.mit.edu/files/11455) look at imperfect monitoring in cartels and show that less transparency can facilitate collusion, making all participants better off.

Cortisol

Cortisol is a hormone similar to adrenaline that is used in emergencies. One of its effects is to shut down the immune system for a short period (while that emergency lasts) to save energy (there's no need for that when the lion chases you).

(Mis)using this effect, long-term stress can cause your immune system to be reduced, and make you sick. Panicking about a situation over which you have no control but plenty of information (e.g. the Covid-19 pandemic where the only defence is your immune system and reducing the risk of getting it) could cause more harm than less information.

Sleeping more helps the immune system, but stress could disrupt that as well.


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.

https://www.imf.org/external/np/seminars/eng/2008/fincycl/pdf/adsh.pdf

I think maybe this can help you


Homogeneous of Degree Two Utility Functions and Homothetic Preferences. The understanding that I am not clear is in when do homothetic preferences represent a utility function and vice-versa. My solution to the problem is posted below the problem:
A consumer’s preferences are described by a utility function that is homogeneous
of degree two: For all $\alpha > 0$ and $x \in R^{L}_{+} $ ,
$u(\alpha x) = \alpha^2 u(x)$
The problem that I am not getting clear is:
Q) "Are this consumer’s preferences homothetic? Show that they are or give a counterexample."
My solution:
According to Mas Colell et al. "Microeconomic Theory" (chapter 3, page 50)

Therefore, this given consumer's preferences are not homothetic as it doesn't generate a utility function that is homogeneous of degree 1 (HOD(1)). A counter example would be a utility function that is HOD(1) like the Cobb Douglas Utility Function
$ U(x_1, x_2) = x_{1}^{\alpha} x_{2}^{1-\alpha} $
To conclude, this consumer's preferences are not homothetic as it represents a utility function of HOD(2). While , according to Mas Colell et al. preference $\pmb{\succsim}$  is homothetic $\textbf{if and only if}$ it admits a utility function that is HOD(1).
Could you please help me in understanding where I am going wrong with what Mas-Colell mentioned above "necessary and sufficient condition" and how a utility function that is HOD(2) implies that $\pmb{\succsim}$ is homothetic.
Thanks.

First of all, in order to provide a counterexample, you need to construct a utility function that is homogeneous of degree two, but is not homothetic. Therefore, the counterexample you gave in your solution doesn't work.

To prove the statement directly, let $u(x)$ be a utility representation that is homogeneous of degree two. That is, $u(\alpha x)=\alpha^2 u(x)$. Therefore, if $x\sim y$, which means $u(x)=u(y)$, we have
$$u(\alpha x)= \alpha^2 u(x)=\alpha^2 u(y)=u(\alpha y).$$
This means $\alpha x\sim \alpha y$, and hence the preferences are homothetic.

We can also use the proposition in MWG: A continuous $\succeq$ is homothetic if and only if it admits a utility function $u(x)$ that is homogeneous of degree one. One caveat is that the utility representation is unique up to monotone transformations, so even if one representation $u(x)$ is not homogeneous of degree one, the preferences could still be homothetic if a monotone transformation of the representation, $\phi(u(x))$, is.

In this question, if we consider a monotone transformation $\hat{u} (x)=(u(x))^\frac{1}{2}$, this $\hat{u}(x)$ still represents the preferences $\succeq$. Notice that
$$\hat{u} (\alpha x)=(u(\alpha x))^\frac{1}{2}=(\alpha^2 u(x))^\frac{1}{2}=\alpha (u(x))^\frac{1}{2}=\alpha\hat{u} (x),$$
meaning that this new representation is homogeneous of degree one. Therefore, by the proposition above, the preferences are homothetic.

actually if a utility function is HOD(2) then it is not HOD(1), therefore, you can conclude (as Mas Colell states), that it does not represent an homotetic preference relation.

As a supportive example, consider an economy with just 1 good and a consumer whose preferences are HOD(2) and can be represented by the utiliy function $u(x)=x^2$.

It is easy to see that $u(\cdot)$ is homogeneous of degree 2 (for $\alpha>0$):
$$u(\alpha x)=(\alpha x)^2=\alpha^2x^2=\alpha^2 u(x)$$
however you also know that $\forall \alpha\neq1$ you have $\alpha^2u(x)\neq \alpha u(x)$ therefore you conclude that $u(\cdot)$ is not HOD(1). At this point you can use Mas Colell's proposition and conclude that this kind of preferences is not necessarily homotetic.

What Mas Colell means with "necessary and sufficient" is that as long as $\succeq$ is continuous, homotetic and rational you can always rationalize it as with a HOD(1) utility function; furthermore, as long as the utility representation of a preference relation is HOD(1), you can always prove that $U(a)>U(b)\Rightarrow a\succeq b$ where $\succeq$ is rational, continuous and homotetic (cfr. Mas Colell pag.96, excercise 3.C.5).


How does "buy low, sell high" relate to supply and demand? I'm taking introductory microeconomics, and I'm trying to consolidate my understanding by looking at some real world examples.
In a perfectly competitive market, there are many consumers and suppliers who are price takers. They are constrained to buy or sell at the accepted equilibrium price due to many competitors.
Therefore, we should expect $P^* = P_D = P_S$ for a certain good or service in a perfectly competitive market. However, having been to a foreign currency exchange at an airport, this does not seem to be the case! They are willing to buy an item (eg: USD) at a lower rate, but they sell it at a higher rate. So it seems that $P_D < P_S$ for the traders (looks similar to a tax wedge), assuming they are both buyers and sellers of the US dollar in the same market.
This example confuses me, as there seems to be two prices instead of one. In the textbook, if I were to buy $Q^*$ items at $P^*$, I should be able to also sell $Q^* $ items at $P^*$, not $Q^*$ items at $P < P^*$. Other examples of this can be seen whenever sellers and buyers are allowed to post their own listings; there always appears to be a price gap.
How do I explain these real world examples using the concept of supply and demand in a perfectly competitive market (and on the graph)?

In the comments @henry already provided you with the correct conceptual answer, I will try to offer some extra intuition and way how this could be modeled. Currency exchange is a combination of a retail market with service market so here if you would want to visualize it with supply and demand you would have to use two diagrams for both parts of the market.
If that still sounds too exotic just imagine classical retail. A supermarkets will first purchase its produce (let us say carrots) from carrot farmers. This will be separate market where supermarkets are the buyers and where they jointly together form demand and where farmers are suppliers. On this 'market for carrots from farms' there will be supply and demand and price given by the equilibrium.
However, once supermarkets acquire carrots then they will sell them on second retail market to regular consumers. On this second market, let us call it 'market for retail carrots' supermarkets are the suppliers and regular consumers are part of the demand. This market will have its separate price that might be different from the 'market for carrots from farms'. This however does not mean that market is not competitive because supermarket has additional marginal costs for warehousing those carrots, if they sell them just for price that covers these additional cost the market would be perfect (of course, in real life the market might not be perfect, but the point is  you can't just say it from the fact that there is a price differential).
In the same way the exchange window at an airport can be thought of operating at two distinct markets. At a market where it buys currency from individuals where the exchange windows are the customers and part of demand and people are the suppliers, and then second market where the exchange window operates as a retail and act as a supplier and people who buy currency are the buyers.
Again this is all consistent with perfect competition. Consider the following simple model:
Exchange window sells USD at price $P_H$, but buys currency at $P_L$ and exchange window additionally has to pay the person sitting at the window wage $w$ for facilitating intermediation (let us assume that wage is paid per unit of currency exchanged to simplify calculation).  Let the quantity here be the number of USD exchanged ($Q_{USD}$). Now this can be fully consistent with perfect competition. Let us suppose market is perfectly competitive so $P_H$ is treated by firms as being exogenously set (e.g. see any introductory economics text such as Mankiw Principles of Economics). This means that the profit function of this exchange window will be given by:
$$\Pi = P_H Q_{USD} - P_L Q_{USD} - w Q_{USD}$$
Now take the FOCs and we get:
$$ P_H - P_L - w =  0 \implies \underbrace{P_H}_{\text{price}} = \underbrace{P_L + w}_{\text{Marginal Cost}} $$
Hence, here we have literally a textbook example of  perfectly competitive market, where $P_H>P_L$ (e.g. a situation where firm buys low sells high). Yet there is no additional markup as price that the firm provides is exactly equal to marginal cost so the markup $\mu=1$ and we have perfectly competitive outcome.
The intuition here is that for the exchange window buying currency from people is part of their cost, but then they have other costs (e.g. wage in example above and in real life also capital costs etc) since the exchange window is in business of providing intermediation service. In perfectly competitive market price at which firms supplies product will be equal to marginal cost, but here the marginal cost equal not just the cost of accruing the currency from people in the first place but also marginal cost of intermediation.
Lastly note, that this is of course not enough to prove that exchanges are competitive, rather this is proving the opposite. Namely, a difference between price at which firm buys product and price at which it sells product in itself does not tell you anything about whether market is competitive or not. $P_H>P_L$ on both competitive and non-competitive markets. Here you would have to add more reasoning to argue it is competitive, like in a question you mention that when it comes to exchanges there are usually many firms offering the same service and so on. Or you could actually try to empirically estimate marginal costs of the firm and see if indeed firm just sells its product at marginal costs or if the prices are higher indicating both presence of markup and market power.

Are Price-Cost Markups Rising in the United States? A Discussion of the Evidence
According to this source market power is the ability of a firm or dealer to markup prices of output goods over the marginal cost of input factors.
https://www.bc.edu/content/dam/bc1/schools/mcas/economics/pdf/jep.33.3.3.pdf

The  markup  of  price  over  marginal  cost  is  a  basic  measure  of  market  power.  With perfect competition in the goods market, a profit-maximizing firm will set price equal to marginal cost, and the markup will be equal to one. With imperfect competition, the firm produces at the quantity where marginal revenue equals marginal cost, and price will exceed marginal cost. In seeking to measure markups, an immediate hurdle is how to measure marginal cost—a variable that must be estimated or inferred rather than being directly observed in a market transaction like prices or revenues. Economists specializing in industrial organization have developed ways of estimating markups for particular firms and industries.

Teaching The Bid-Ask Spread And Triangular Arbitrage For The Foreign Exchange Market
https://files.eric.ed.gov/fulltext/EJ1193295.pdf
According to this source currency dealers buy currency at the bid and sell at the ask with the difference described as the bid-ask spread.

International banks serve as dealers who make a market by standing ready to buy or sell foreign currencies for their own accounts.  The bid price represents the price a bank dealer is willing to buy for a currency and the ask price is the price a bank dealer is willing to sell for a currency.  Therefore, bank clients buy at the ask price from the dealer and sell at the bid price to the dealer.  The bid-ask spread, the difference between the ask price and the bid price, is the compensation (transaction  cost) to the dealer (bank  clients).   The bid-ask spread and bid-ask relationship are basic parts of the FX market microstructure.  Students who are familiar with these topics are able to better comprehend the theory and practice of the FX market.

Networks, Crowds, and Markets: Reasoning About a Highly Connected World
https://www.cs.cornell.edu/home/kleinber/networks-book/
https://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch11.pdf

A trader’s payoff is the profit he makes from all his transactions: it is the sum of the ask prices of his accepted offers to buyers, minus the sum of the bid prices of his accepted offers to sellers.

In the next section, we’ll work out the set of possible equilibria for the trading network in Figures 11.3–11.5, by first dissecting the network into simpler “building blocks.”  In particular, these building blocks will correspond to two of the basic structures contained within the network in Figures 11.3–11.5: buyers and sellers who are monopolized by having only a single trader they can deal with, and buyers and sellers who benefit from perfect competition between multiple traders. In the process, we’ll see that network structure and access to alternatives can significantly affect the power of participants in the market.


Is inequality a micro or macro economics issue? In a clear and comprehensive blog post, Tejvan Pettinger describes economics problems. He starts by making brief considerations on scarcity, enumerates the fundamental economic problems (what/how much produce, how to produce, whom to produce to) and then goes to specifics, commenting about micro and macro economic problems.
For me, it seems fair to conceptualize "microeconomics" as a bottom up approach for economy, in which the focus is the study of the behaviors and interactions of the economic agents (producers and consumers) facing scarcity, and "macroeconomics" as a top down approach whose goal is the study of the great economic aggregates like unemployment and inflation, for example. As such, it surprised me that Pettinger sees inequality as a microeconomic issue instead of a macroeconomic one: aren't macroeconomic tools intended to stimulate growth or redistribute income by means of monetary/exchange/fiscal policies? Isn't the goal of macroeconomics policies to grant country-wide sustained economic growth to benefit the society as a whole? In a way, isn't microeconomics the "Invisible Hand Science", according to which everyone including you and I seek our own benefit and helping the society by accident in this process?
Hope you guys can shed a light on that doubt of mine.

Inequality and public policy has actually its own field (Public Economics) so it does not narrowly fit in either of those categories, but given that most research and work on inequality is of microeconomic character (see Stiglitz Economics of the Public Sector 3rd ed) I think it is fair to put inequality under microeconomics if you have to make such binary choice as it fits there better.
First let us get the definitions of micro and macroeconomics straight. Following Mankiw Principles of Economics pp 27:

Microeconomics is the study of how households and firms make decisions
and how they interact in specific markets.
Macroeconomics is the study of economy-wide phenomena.

Neither of them is top-down or bottom-up, in fact most macroeconomics models are build upon micro-foundations (in fact even you do research in pure macro you need to learn a lot of microeconomics), so by your descriptions in your question they would both be 'bottom-up' - although I do not think it is sensible to talk about these fields as top-down or bottom-up. The distinction is based rather on the scale at which you are looking.
When it comes to inequality, often the appropriate level of analysis is microeconomic analysis. For example, do you worry about income inequality? Well income inequality arises from the fact that people are heterogeneous in their ability. Hence you need to study how this affects rewards they get for their labor supply on a labor market. Such analysis does not require tracking of inflation and other macro factors that would likely just 'muddy the waters'. To study that you want some micro models not macro models where everyone is aggregated to an 'representative agent' (some sort of average human). Similar arguments would apply to most topics to be considered in the realm of income inequality.
Macroeconomics, also touches bit on inequality as there can be interplays between inequality and economic growth (and growth is definitely macro topic). Or unemployment benefits or redistribution from people who have high marginal propensity to save (usually rich people) to ones with low propensity to save (usually poor) can be considered macroeconomic stabilizers. But macroeconomics does not really concern itself with inequality per se. If it would empirically turn out that poor people have higher propensity to save than rich people from pure macro perspective there should be redistribution from poor to the rich.
This is not to say that there is absolutely no research into inequality where inequality would be in the main focus and the research is just using macro models/tools. But this strand of literature is miniscule compared to microeconomic literature devoted to this topic.
For example, consider this. In Romer Macroeconomics, which is the standard widely used graduate macro textbook the word income tax is printed only 8 times. In the Varian Microeconomic Analysis you have separate sub chapter on optimal taxation, separate chapter for welfare analysis, separate chapter for public goods etc.
This is not because macroeconomists would want to ignore inequality but it is simply not considered to be part of the subject matter. This primarily comes to the fact that macroeconomists often have to aggregate when they try to describe whole economy. In order to aggregate you need to introduce average households, average individuals, average firms etc. Once you aggregate whole population to set of average individuals then income/wealth inequality amongst those averages is zero.
There are macro models that also look heterogeneous agents but even there you will usually have just some small limited number of options. For example, having two households that are different and each is supposed to be an avatar of their own category. It is possible to still introduce more heterogeneity into macro models but the more heterogeneity you include the complexity of the model raises disproportionately. This is less problematic in microeconomic models and thus they are preferred.
Lastly, it is possible that in the future this will change and people studying inequality and policy economics in general will start focusing more on macro models and treating inequality as a macro phenomenon. From my own experience work on inequality from macro side is nowadays more common then when I was undergraduate. Nonetheless, as of now I don't think anyone could reasonably disagree with statement that most inequality work focuses solely on micro  (for example, almost whole literature on optimal income taxes and transfers is microeconomics) or uses micro models. Hence, if you have only two options I think it makes more sense to put it under microeconomics and I think this was why the author did that.

From the cited blog article:

[A]n underlying feature of economics is concerned with dealing how to allocate resources in society to make the most efficient and fair use of resources. The main issues are:

What to produce? How to produce? For use (in consumption) by whom?

Then the article describes economic problems under the classification of microeconomics or macroeconomics. However the problems of economics listed in the article arise in the context of psychology, justice, law, and politics. The general idea that economics is an independent discipline with two domains called microeconomics and macroeconomics is a convenient and somewhat useful fiction. This truth is reflected in the idea of "fair use" of resources.
All political-economic systems must solve coordination problems which seem to be inherent in the efforts to decide what goods to produce, how to produce those goods, and how to distribute the goods. These are also political justice systems because the efforts and outcomes are judged to be fair or unfair in the perception of human observers.
A microeconomic model for an ideal free market abstracts away from the problems of justice, fairness, and failed coordination by assuming that all social transactions are voluntary consent agreements (contracts). In this model if everyone performs their contracts according to the agreed terms, and no one breaches their duties, and all benefits and harms are internal to the parties to the deal, then coordination is maximized. All the problems in economic thought occur exactly because the contract system is not perfect due to the nature of human social relations. These coordination failures have features that could be recognized as micro or macro in character, however, the root cause is that coordination failure seems to be a feature of social psychology.


Lotteries and expected utility Suppose we have the following four lotteries:

$L_{1}=[(1,\$1)]$

$L_{2}=[(0.01,\$0),(0.89,\$1),(0.1,\$5)]$

$L_{3}=[(0.9,\$0),(0.1,\$5)]$

$L_{4}=[(0.89,\$0),(0.11,\$1)]$

If our agent says that he prefers $L_{1}$ to $L_{2}$ and prefers $L_{3}$ to $L_{4}$, then he is not following the expected utility assumption of independence (also known as substitutability).

Anyone know how to explain this?

Your example is the classic Allais paradox.

I think the best way to see how the preference pattern $L_1\succ L_2$ and $L_3\succ L_4$ violates independence is to visualize it geometrically. Consider the following figure:

Observe that
\begin{align}
L_2&=L_1+(0.01,-0.11,0.1)\\
L_3&=L_4+(0.01,-0.11,0.1).
\end{align}
Therefore, the indifference curves passing through $L_1$ and $L_4$ should be parallel. Since $L_1\succ L_2$, the latter lottery should lie below the IC through $L_1$. By implication of the parallelism of the ICs, $L_3$ should also lie below the IC through $L_4$. But we're given that $L_3\succ L_4$. This means that $L_4$ lies below the IC through $L_3$ (the blue dashed line). Since parallelism of ICs is a necessary condition of independence, the agent's preference is inconsistent with independence, because it can only be justified by a set of non-parallel ICs.

Alternatively, you can think of the inconsistency between the agent's preference and expected utility theory in the following way.
Suppose expected utility theory holds. Then $L_1\succ L_2$ is equivalent to the inequality
\begin{equation}
u(\$1)>0.01u(\$0)+0.89u(\$1)+0.1u(\$5).
\end{equation}
Adding $0.89u(\$0)-0.89u(\$1)$ on both sides, we get
\begin{equation}
0.89u(\$0)+0.11u(\$1)>0.9u(\$0)+0.1u(\$5).
\end{equation}
But this second inequality is simply saying $L_4\succ L_3$, which is contradictory to the agent's preference.

The expected utility of $L_1$ and $L_2$ are:

$E(L_1)=\sum_{i=1}^{n=1}{p_iu_i}=1*1= 1$ $

$E(L_2)=\sum_{i=1}^{n=3}p_iu_i=0.01*0+0.89*1+0.1*5= 1.39$  $

Therefore if the agent says that he prefers $L_1$ to $L_2$ then he is not following the expected utility assumption of independence as $E(L_2) > E(L_1)$.

Similarly with $L_3$ and $L_4$

$E(L_3)=\sum_{i=1}^{n=2}p_iu_i=0.05$ $

$E(L_4)=\sum_{i=1}^{n=2}p_iu_i= 0.11$ $

Because $E(L_4)>E(L_3)$, if the agent says he prefers $L_3$ to $L_4$ then he is also not following the expected utility assumption on independence.

Hope this is helpful!


Can't we measure the growth in the income levels of poor? Inflation has been a challenging aspect
of policymaking. In such situations growth in
the income levels of the population living below
the poverty level can never be measured
accurately (due to higher infation poverty section will
show higher income) . My question is: Due to higher inflation why cannot we measure growth in the income levels of the population living below poverty line accurately?

That's not specific to poor, any income increases with inflation.

The real problem is that the poor receive goods for free (charity, squatting, rent nonpayment) so their real income can never be measured.


What institutions are examples of "shadow banking"? I often hear the term shadow banking tossed around when discussing the United States and Chinese economies. What exactly is shadow banking and could you give examples of some specific companies that act as "shadow banks"? I have been told that in China, shadow banking refers to informal loans that are not written up in any documentation. Is this correct?

While whomever told you about "shadow banking" in China is correct that in an international context, the term can often refer to informal banking arrangements (the earliest use of the term); however, these days, it is usually used in the sense first coined by Paul McCulley in a speech he delivered ("Teton Reflections") at the 2007 Jackson Hole conference. He described them as:

[T]he whole alphabet soup of levered up non-bank investment conduits, vehicles, and structures...
Unlike regulated real banks, who fund themselves with insured deposits, backstopped by access to the Fed’s discount window, unregulated shadow banks fund themselves with un-insured commercial paper, which may or may not be backstopped by liquidity lines from real banks.

Structured investment vehicles, as noted by Kitsune, are certainly one type of shadow bank, but nonbank broker-dealers, certain real estate investment trusts, and particular hedge funds can be viewed as types of shadow bank. The question to ask in determining whether an entity is a "shadow bank" is twofold— do they:

perform credit, liquidity, or maturity transformation; and
fund themselves through uninsured wholesale deposits (without recourse to liquidity facilities)?

As a direct answer to your question, Pozsar, Adrian, Ashcraft, and Boesky (2010) say:

Examples of shadow banks include finance companies, asset-backed commercial paper (ABCP) conduits, structured investment
vehicles (SIVs), credit hedge funds, money market mutual funds, securities lenders, limited-purpose finance companies (LPFCs), and the government-sponsored enterprises (GSEs).

I strongly recommend clicking on that link and taking your time to browse the map on page 2.
It's worth noting both that many of these entities have existed for long periods of time without incident, and that due to choices in how banking is regulated, shadow banks are often the result of a desire to both limit the scope of regulation and to limit the risk of failure within the scope of regulation— which has the effect of pushing intermediation activities outside the regulated sphere.

Shadow banks are banks that authorities do not like, so they give them an ominous name. They are institutions that do not adhere to the rules and regulations the Federal Reserve and other governments have set up to keep track of their citizens. Here is an example:

http://www.chinalawblog.com/2012/10/getting-money-out-of-china-thats-illegal.html

  Ms. Chu ran an underground bank, according to defense evidence cited by the Hong Kong judges, an operation that they said would match people who wanted to bring money into China illegally with those who wanted to get it out illegally. These strangers would deposit money in each other’s accounts — one inside China, the other in Hong Kong. Money doesn’t actually cross the border, making it difficult for regulators to track.

  In one of Ms. Yan’s transactions, Ms. Chu directed her to deposit 3 million yuan (roughly $480,000) into a mainland bank account in the name of a stranger, also a client of Ms. Chu’s, the court said.

  The same day, another stranger deposited checks worth the same amount that Ms. Yan had deposited on the mainland, converted into Hong Kong dollars, into an account Ms. Yan owned at an HSBC branch in Hong Kong. HSBC, which hasn’t been accused of wrongdoing, declined to comment.

  Funds don’t actually cross the border, but the clients essentially moved money from one jurisdiction to the other, evading the $50,000 limit.


Ben Bernanke Portfolio Balance Effect I have a question based on reading some speeches and research papers, mainly by Ben Bernanke, on the portfolio balance effect. Here is Bernanke in a recent paper he authored where he describes the portfolio-balance effect as one of the two principal channels of large-scale asset purchases:

  "The portfolio balance channel depends on the premise that securities are  imperfect substitutes in investors’ portfolios, reflecting differences in liquidity, transactions costs, information, regulatory restrictions, and the like. Imperfect substitutability implies that changes in the net supply of a security affect asset prices and yields, as investors must be induced to rebalance their portfolios (Bonis et al., 2017). In principle, the two channels of QE can be distinguished by the fact that the signaling channel operates by affecting expectations of future policy rates while the portfolio balance channel works by changing term and risk premiums."- Bernanke (2017), in a paper that can be located here: https://www.brookings.edu/wp-content/uploads/2017/10/bernanke_rethinking_macro_final.pdf

I'm having some trouble here understanding the finance of this. In particular, how does this channel necessitate imperfect substitutability? I understand that the argument hinges on 'habitat preferences' -- certain investors prefer, say, a specific type of security -- but I haven't been able to put the pieces together.

As a potential example: let's say that we have an investor who will only deal with 5-year Treasury bonds due to either preference, risk appetitive, liquidity requirements, and so forth. The Federal Reserve then purchases 5-year Treasury bonds. Bernanke seems to suggest that the reason that reductions in the supply of these securities will increase their prices and reduce their yields is that investors don't view other securities as perfect substitutes. Is the argument perhaps that, if our investor considered 7-year bonds a perfect substitute, the increase in the price of the 5-year bond would cause him to sell off his supply of 5-years for a significant capital gain and purchase some other security? Or, for that matter, his portfolio would consist of such a wide array of different maturities that buying 5-year bonds wouldn't impact his behavior at all, as he would just replace it with any other bond.

I know this has something to do with elasticity of demand, but I just haven't been able to piece together the logistics of imperfect substitutability, hopefully, leading to a rebalancing of investor portfolios and a decline in interest rates across asset classes in a broad-based way.

I'd appreciate any insights people might have on this.

My argument is that he is just looking to find a justification for a policy choice he made, and so there is no reason to believe that his arguments are completely coherent.

We need to understand why he is making such arguments in the first place. If interest rates are purely the result of expectations (term premium equal to zero), the purchases themselves have no direct effect on yields, only as the result of signalling what the Fed will do (the first channel). However, the Fed could achieve the exact same effect by just saying that the economy stinks, and they will not raise rates for a really long time.

In order to find a justification for the decision to purchase bonds (instead of just talking), he needs to argue that the change in supply affects bond yields. The problem with that argument is that the front end of the yield curve does a pretty good job of tracking expectations, regardless of the state of supply and demand in the bond market. (One can look at how market participants use front end pricing as an estimate of what the central bank will do in the next few rate setting meetings across all the major markets as an empirical validation of that assertion.)

Therefore, we need some reason to believe that the short maturity bonds are somehow different from long maturity bonds, i.e., there is some form of segmentation. This way, one can hope that supply and demand affects long-term bond risk premia more than short-term premia (which would sound plausible to most bond market analysts). What matters is that the term structure of the term premia is changing due to the supply effect. One can come up with different verbal explanations for why term premia move, they will end up being indistinguishable in practice. That said, we need to ignore the possibility that other factor affect term premia, such as returns volatility (which would be suggested by portfolio theory).

The obvious issue with this argument is that Fed purchases are not the only factor affecting supply and demand in the bond market. Why are those other factors being ignored?


Why do people buy negative interest rate bonds? I get that people buy long term government bonds, because of how safe it is, and if there would be a recession the government would just print more money and could pay it back.

But why would anyone buy a bond, that yields a negative return? If i would just keep my money in fiat, it would just depreciate in the 10 years, but after the 10 years it would still be more than investing it in a safe negative rate.

Some pictures and text are from Schroders, Marketwatch and other websites, but I don't remember all them.
Of note, Germany first sold negative-yielding bonds in Aug 2019, €2bn worth of 30-year bonds that offer no interest payments at all.
1. Better than holding cash
Cash is obviously most liquid, but some central banks like Japan impose negative interest rates on cash deposits, which trickles to the rate banks charge institutional investors.
Then highly liquid but only slightly negative yielding government bond looks better! Because the UK government unlikely will default, bond buyers are just paying a small sum to the government to guard your money, like in a vault!
2. Wagering that there are other “bagholders.”
Investors who buy negative-yielding bonds are betting on the value of the securities to keep rising. Although investors buying bonds with subzero interest rates are paying for the privilege to hold a bond, they can profit way above their cost if the security’s price rises.
For example, if you expect a central bank to buy more assets,  bond buyers can rely on the central bank to hoover up their negative-yielding securities.
In July 2020, an auction for €4 billion euros of 10-year German government bonds TMUBMUSD10Y, 0.644% sold at $-0.26%$, but at a premium price of 102.6 cents to the euro. The benchmark bund is now trading at a price of a 106.9 cents to the euro,. So  investors who bought this at auction would've gained around 4% from the price increase alone.
3. Bonds as deflation hedge
When prices fall, most asset classes don't perform well in deflation. An exception are fixed interest government bonds! Because they fixed  their coupon and principal, they retain their value and will positive real (inflation-adjusted) return, if inflation $<$ their yield. In other words, a negative yielding bond can  positive real return if there is deflation. So you can hedge against deflation with negative-yielding bonds.
4. Currency hedging can transform negative yields into positive yields.
Negative yields don’t mean negative income for some bond buyers. Unlike European and Japanese investors, US investors are often paid to hedge against fluctuations of foreign currencies because U.S. interest rates are much higher than in other developed markets like Europe and Japan.  Currency hedging can annualized return 3% for U.S. investors, like  American fund managers, buying negative-yielding  euro-denominated debt like European government bonds, according to Jens Vanbrabant, senior portfolio manager at Wells Fargo Asset Management.
In Sep 2009, the 10-year German Bund yield at -0.6% looked unattractive to US investors.But currency hedging is priced at the difference between US and German short term interest rates, which can be positive even if a central bank cuts interest rates. Since US short term interest rates are much higher than Germany's, US investors are paid money to hedge euro exposure! With currency hedging, US investors can earn 2.2% when investing in German 10 year bonds (see Figure 2 by Schroders), higher than the 1.6% available on US 10 year Treasuries.

5. Diversification benefit
What other bolt holes can weather volatile global equity markets, Brexit, US-China trade war?
Traders like volatility to a degree, but they try to diversify the risk so their portfolios aren’t fully exposed to the market's unpredictability. So buying notoriously safe bonds is a risk-averse strategy. You'll lose some money for that safety, but that loss can constitute ‘over-performance’ if other asset classes tumble. When risky assets sell off, negative yields on government bonds may be overshadowed by their proven ability to rally during recessions. Even at negative yields, bonds still are important. Figure 3 by Schroders  proves the 3-year rolling correlation between German Bunds and the German DAX stock market index. The two strong negative correlated, if you overlook the period between 2014 and 2017 when the European Central Bank’s (ECB) quantitative easing raised higher bond prices (lower bond yields) and higher stock prices.

Bonds  perform well when equities don't, vice-versa. In times of distress, you must reduce risk like this! If you are running for safety,  capital leave stocks to government bonds. Even if negative-yielding bonds lower your return compared to normal conditions, they can still reduce portfolio risk.
6. Roll down the yield curve later.
You're assuming the bondholder is holding it long term, but many don't.
In periods of uncertainty, demand for bonds increases, which makes their price increase. So you can profit from buying and selling government debt. If you think this  volatility will last, buy bonds now in the hopes that more investors flock to them later. You don't even need fellow investors to buy them! The central banks may be the ones to buy bonds to try to stimulate the economy.
Bond buyers can take advantage of the yield curve’s slope, which still can be steep even for negative-yielding bond markets in Germany and Japan. For example, a trader can buy a negative-yielding 3-year bond and sell it after a year. Since debt prices inversely correlate with yields, all else being equal, the value of the 3-year bond should be higher than, for example, a 2-year bond.
So long as shorter-term bonds' interest rates are more negative than their longer-dated counterparts,  the long-term bond's price should rise closer to maturity. But they can profit from this “rolling down the yield curve” as a short-term strategy, and must sell the bond well before maturity, because the bond will trade only at par when it expires.
For example, the Swiss 10-year bond was yielding -0.1% in Jan 2009. But at 22 August 2009, it had returned 5.6%! Negative yields can still positive return! Of course, this works both ways. Any rise in yields can make you lose money.
7. Some institutions are legally required to buy bonds! Liability matching with negative yields
The other reasons are about speculation or managing risk. But institutions can be legally mandated to buy bonds with negative yields.
Certain institutions must follow rules dictated by the banks, pensions funds or insurance companies who provide the bulk of the capital. Those rules mandate the managers to invest just in certain things like investment-grade bonds. Regulators force some clients to buy certain assets, like banks can only buy liquid assets.
Liability-relative investors, such as insurance companies and pension funds, don't care the absolute return or yields from bonds. They often buy bonds to “match”  their liabilities. The present value of these liabilities is calculated in many ways, but factors in government bond yields. For example, in Sep 2009 in the euro area, insurance industry used negative rates up to the 11 year maturity point (Source: EOPIA. See data from 31 July 2019). These liability-driven market participants can buy negative-yielding German Bunds to match a future liability . Their values will move in tandem with each other.  If they don't buy negative matching assets, they'll be exposed to significant risks if interest rates fell further.

The reason nobody else has cited: repo collateral.

https://alhambrapartners.com/2020/03/18/theyre-here-negative-ust-yields-finish-off-the-collateral-case/

"Collateral calls mean in some cases using gold as a last resort (which gets dumped immediately) and in others the buying of pristine collateral at any price. Gold is slammed while T-bill prices skyrocket, their yields plummet. For those unlucky enough to have neither option in front of them, fire sales of assets including stocks and other risk credits...

... Given these market fire sale conditions, obvious signs of gross systemic illiquidity, the Fed’s auctions should be bid full up to the limit each and every one. The demand for liquidity, any spare liquidity, is through the roof curiously everywhere except here.

The answer can only be collateral. In order to bid for the Fed’s bank reserves in any of these FRBNY operations, you have to post some of eligible MBS, agency debt, or UST’s. And when you do, whatever collateral you put up becomes encumbered (which means no repledging)."

A debt instrument, even if negative yielding, can still provide fuel for "rehypothecation", esp. in the off-book, unmeasured by monetary aggregates, shadow banking / eurodollar system.

If you look for "answers" to the repo rate spike in fall 2019

https://www.google.com/search?q=repo+rate+spike

... what you'll almost never hear is the idea that quantitative tightening, or the easing of quantitative easing - which tightened supply in the bond market - might have contributed to overnight repo rates touching 10%. Note that this also impacted the actual IOER, threatening to "uncork" the real overnight interbank rate. This would mean total loss of control by the Fed.

Overnight components overview:
https://www.newyorkfed.org/aboutthefed/fedpoint/fed15.html

Typical msm article about the repo blowup:
https://www.bloomberg.com/news/articles/2019-09-16/repo-market-chaos-drives-overnight-rate-up-by-most-in-months

Keep in mind, price is inverse to yield. More supply -> lower price -> higher yield. If you look at the yield of the benchmark US 10 year over the last few years, you'll see it climb into autumn '18, which was the first "blip" in the repo market. It made a double top around 3% with its 2014 high, and has been tanking ever since.


Will an increase in interest rate cause short run aggregate supply to shift? Most business borrow for financing their purchases of raw material and capital etc. Shouldn't a interest rate rise cause cost of production to increase, therefore shifting SRAS to left? Thanks in advance.

Yes, however a supply shift as a result of interest rates can be (sticky).this is why after a stock drop, a recession can take 1 year- 18 months to occur. So when we look at economic indicators over the past year, the 10-year approaching 3% has not led to a reduction in aggregate supply. It may not be until FY 18 Q4 that we see a drop a significant drop in in supply. Supply and interest rates do not have a “flexible” relationship, but instead a “sticky” one in which supply may not drop immediately, but over time your answer is correct.


Are there historical cases of country A printing the currency of country B for the main purpose of economic warfare? I recently read in a news article that a large amount of Libyan banknotes printed in Russia were seized in Malta following an order coming from the USA. Both Russia and the USA have geostrategic interests in this part of the world so I assume this action is probably linked to an economic warfare operation. Banknotes normally include a large amount of security features that prevent people to easily counterfeit them but I assume that for large countries like China, Russia or the USA it is not a big deal to print banknotes of a foreign country. In time of war it can be quite interesting for a large country to print a lot of banknotes and spread them in the economy of an adversary country to destabilize its economy. But putting apart the above mentioned news article I wasn't able to find evidences of such a scenario so my question is :
Are there historical cases of country A printing the currency of country B for the main purpose of economic warfare ?

Very obscure historical example:
From 1287 to 1295, the Danish nobleman Stig Andersen Hvide was leading a band of outlaws from the island of Hjelm supported by the king of Norway against the king of Denmark. Stig managed to kidnap expert coin makers and bring them to Hjelm, where they produced counterfeit Danish coins.
This allowed Stig and his supporters to buy up all the supplies they wanted in Danish merchant cities. The heavy inflation and the problems it caused for the Danish economy made it difficult for the Danish king to afford assembling an army against Stig.

Slightly different but perhaps relevant. A friend of mine spent some time during the late 1960s transporting counterfeit American Express Travelers Checks into Laos, that the CIA was using to fund its operations. He traveled on US military transport aircraft from Saigon to the capital of Laos (whose name I forget). The amount was significant, suitcases full. Apparently this was done with the tacit acceptance of American Express. He never told me who he passed them to in Laos but I presume some warlord paid for them with discounted cash, and I suppose that they stayed in Laos being used as a medium of exchange, and were rarely if ever presented to AmEx for redemption.


What will happen to the reserves at the Fed? Banks currently have 2.7 trillion Federal Reserves that they hold at their Federal Reserve account. It's part of the monetary base and these reserves were created when the Fed purchased bonds in their QE program.

What will happen to these reserves? How will they get back to the Fed? How will they be retired and won't they have to be used to pay off the treasury bonds the Fed is holding?

http://research.stlouisfed.org/fred2/series/NONBORRES

That's a link to it.

Reserves are drained (destroyed) when the Fed sells the debt or allows it to be paid off.


Estimating price elasticity of demand I have 25 quarterly observations and I want to estimate price elasticity of demand. I intented to use GMM-IV estimator. However, I read that it is not good for small samples. What can you suggest me? Please keep in mind that I am not econometrician by profession.

Unfortunately for your case all GMM estimators suffer from finite sample bias. In the presence of an endogenous explanatory variable the GMM estimator is only consistent.

There's not much you can do to remedy this issue, except collect more data. Check for consistency of sign and magnitude of estimates between OLS and GMM, as well as sensitivity to instrument choice (if your model is over-identified).

Price elasticity of demand is computed as follows:

Percent Change in Quantity Demanded (Qd) / Percent Change in Price (P)

Say you have price and demand quantity data from two years (t=1,2).  To calculate change in Q demanded you would do the following:

[(Qd in t=2)-(Qd in t=1)] / (Qd in t=1)

The process is the same for price (substitute P for Qd above).

Elasticity may be calculated for other variables as well; not just price and demand.  For example, if you wanted to see how a 1% change in IQ affects the relative change in a student's GRE score you could.  This is done by messing with logs and regression functions.

Hopefully this helps you out a bit.


Why must the rate of GDP growth be positive? There are always expectations that GDP should be growing at a certain rate. This is what I see in the newspapers. I am not an economics major and this is a very basic student question. After adjusting for level of prices, meaning that forget about inflation and price related issues, it is expected to grow at say $2\%$. Why is this a case and what should it be driven by? Assume there is an economy that only produces apples, for simplicity. So, it is expected to make $2\%$ more apples every year? So the growth would be driven by the larger amount of goods produced? Why is this economy expected to make more apples every year?

You would expect the rate of growth to be generally positive because inventing things or inventing more efficient ways of doing things, is generally a one way process - things don't get un-invented. So we would expect things that are made by machines to be made ever more quickly as the machines evolve and improve. Periods of negative growth are likely to correspond to some financial cock-up (e.g. asset bubbles) or increasing scarcity of some natural resources for which a replacement can not be found.

The expectation that an economy's GDP should grow every year is largely an extension of humans' general desire to consume more goods and services. When individuals become more productive (get a raise, grow a family business, etc.), quite frequently they choose to consume more goods and services or invest more rather than cutting back their personal production and enjoying more leisure time. This is not universally true. In fact working hours have generally decreased. But on aggregate, decreases in working hours have not kept paced with productivity gains.

There are also demographic factors.

Any factor that increase population such as immigration or children creates more desire for consumption. With more people desiring to produce, the expectation that GDP should grow is clear--though this does not directly affect GDP per capita.
If you think about a typical person in a western country, productivity tends to increase over time. However, after retirement the desire for leisure time is deemed more valuable. Production decreases (or ceases). The consumption of goods and services often goes down too.

But it is entirely possible that this preference will (in the aggregate) change at some point. Some advocate for such change using the terms minimalism or simple living; there is much variety in how the idea is promoted. If a large number of people prefer to consume less, or simply consume the same while their productivity increases, then we might not expect growth in GDP (per capita).

Similarly, if the population ceases to grow, we may expect to see lower GDP, though perhaps not lower GDP per capita.


Does a negative interest decrease the money supply? If there is less money, its value increases.
There is less liquidity when there is less money.
Does a negative interest decrease the money supply?

Especially when people don't need money: they saved it up but nobody needs it -- nobody needs to borrow it from them so they saved up for their pensions and now they want to buy a pension but nobody really needs their money. So a negative interest rate is established to entice them to spend it: a little late because they are buying pensions but OK. They are too old to spend it well. They think the washer will outlive them. So they leave the money in the incinerator of negative interest bank accounts. Then there is less and less money. Now somebody wants to sell something (liquidate it) but there isn't that much money there at the moment. It was burnt. The money becomes a kind of commodity that people are willing to pay more assets for. The asset price in currency is lower. People think, hey cool: Let as much people as possible have their money burnt so that my cash becomes more valuable. Run on the bank. But then it turns out that the CB really can print money...

Here's a story. I guess it can be what happened in the repo market recently.

Definition of Money Supply:
The money supply is the entire stock of currency and other liquid instruments circulating in a country's economy as of a particular time. Because of it's definition, the money supply can only be affected if a central bank prints or burns currency. Thus, technically, rates don't affect it per-se.

Velocity of money and money in circulation:
What you may be thinking of is related more with how much money is in circulation and how fast it changes hands.

Effect of negative rates:
In theory, when rates go up, money flows into bonds and "leaves" circulation. By the same logic when rates go down, money flows out of bonds and "enters" circulation.


Computational economics What exactly is computational economics? For example, does certain software for calculating/predicting/visualizing cost of manufacture falls under computational economics?

Taken right from the society for computational economics:

  Computational economics explores the intersection of economics and
  computation. These areas include agent-based computational modeling,
  computational econometrics and statistics, computational finance,
  computational modeling of dynamic macroeconomic systems, computational
  tools for the design of automated Internet markets, programming tools
  specifically designed for computational economics, and pedagogical
  tools for the teaching of computational economics. Some of these areas
  are unique to computational economics, while others extend traditional
  areas of economics to new areas through computational techniques.

I would say that calculating cost of manufacture is too trivial to fall under this category - unless it's a monopolist who has to take into account equilibrium responses of his suppliers and demanders to his choices.

The algebraic formulas in microeconomics can be tabulated for a large number of conditions and then the results averaged or otherwise adjusted before being presented graphically. This is one kind of computational economics. So the answer to your question is affirmative.

But by far the most interesting form of computational economics is in macroeconomics, when the situation of a country is simulated as time passes. Unfortunately, due to the failures to properly express the configured situation in what I regard as logical terms, these forecasts are made to be inaccurate and wrong. (In many cases this is deliberate, because there are strong political reasons for making the associated assumptions.) I am not talking about the effects of sudden changes, simply the ability for a situation to tend to a greater amount of equilibrium (self-stabilize).

The model that I use goes back to the situation before John Bates Clerk combined the factors of land and capital (offensively from A. Smith's explanation of the factors and returns on production). Were this situation to be correctly and better expressed, then we would have a greater degree of accuracy in simulating the changes. My method for response to the effect of the external changes is original and will also greatly help this process, for which my soon to be released book "Consequential Macroeconomics" should provide the answer.


Should we get rid of the Penny? Jeff Gore has suggested scrapping the 1 cent coins a few years ago. Why doesn't the US cancel the pennies? Is it that terrible to the economics to keep the copper coin?
As mentioned in the comments, Greg Mankiw has also discussed it here:

Per year, the average citizen wastes 12 minutes paying with pennies.
That’s like half of an episode of The Office. Twelve minutes is also
the length of the first human spacewalk by Soviet cosmonaut Alexey
Arkhipovich in 1965.
Mankiw also estimated this 12 minutes of wasted time costs the U.S.
economy approximately $1 billion every year.

Should we get rid of the Penny?

No. That would be as foolish as suppressing a symptom instead of addressing the illness.

The reason why "a penny does not buy a penny" --or being more accurate, why it no longer buys a penny-- is that currency depreciation has been policymakers' answer for too long and for too many issues.

The permanent, excessive printing of money inevitably weakens the purchase power of the USD. Metal prices, like everything else, go up where economic problems are "addressed" by issuing more bonds, giving more subsidies, ignoring the rapidly changing demographics, and pretending that welfare state still is sustainable.

The weakening of a currency by inflationary measures is not limited to rendering coin metals out of reach. At some point, even the cost of paper on which money is printed can also exceed the purchase power of the denominations printed on that paper. History has many examples of this.


GNI versus GNP for Measuring Development In the calculation of the Human Development Index, Gross National Income (GNI) is used rather than GNP.

I've searched around on the internet, but I haven't found a clear explanation of what the precise difference between GNI and GNP is. Wikipedia defines GNI as "total domestic and foreign output claimed by residents of a country" and the GNP as "market value of all the products and services produced in one year by labour and property supplied by the citizens of a country." Just like the income and expenditure approaches to calculating GDP yielding the same result, it seems to me that GNI and GNP should be at least theoretically equal.

What is the difference between GNP and GNI, and why use one over the other for measuring development?

GNP measures production, so is a better measure of how the country is doing in the long term at accumulating fixed capital and developing. Fixed capital has a much higher return than the financial capital that GNI is typically derived from. However, both measures are usually very similar, except for some tax havens such as Ireland that have significantly more GNI than GNP.

Suppose a country consisted of one individual making trillions of dollars on the stock market and boosting GNI without any national product. If they don't own any fixed capital, this would be a very bizarre economy and not really "developed".

On the other hand if a country has lots of production but has a negative GNI because, say, a domestic company issued a massive dividend to overseas investors that year, then the country could still be called "developed" because it has real people and factories and so forth.

Neither of these cases have anything to do with reality of course, they're just examples.


Is the BEA double counting benefits in Personal Income? The BEA (US Bureau of Economic Analysis) that produces the GDP and GDI also prepares a summary of Personal Income for the nation.

In that it includes employer contributions for both private pensions and insurance as well as the employer contributions for government social insurance such as social security and medicare.

Later on "transfer payments" from both private and government programs are also added.

Finally, personal payments for social security etc are deducted.

To me it seems that including employer contributions that are not available as income and are counted later in transfers seems like double counting and also doesn't agree with elementary macro economic texts that define national personal income as not including such contributions. In fact these contributions are carried into "Disposable Personal Income" which seems clearly wrong. Am I missing something?

6/15

After reading the comments, part of the issue may simply be that I'm not good at accounting, but I understand part of this better. I agree there is no double counting. But, in the image below (just looking at social security)

I'm OK with gross "personal income" at the aggregate level including line 8 and the net of lines 18 and 25. But if one thinks of Social Security as a big savings account, then line 8 belongs in personal savings and not disposable personal income. No?

Statistical Agencies do not necessarily obey the habits of Economic Theory. There is no "mistake" here (certainly, there is no double-counting), but a different approach to what each concept means or "should mean" (which sometimes is also a consequence of historical precedence).

For the fun of it I post below how the same data could be arranged to conform with standard theoretical economics, where we make a point of distinguish between income earned, taxes in the broad sense, transfers, consumption, saving.

ALTERED/RE-ARRANGED BEA TABLE 2.1. "Personal Income and Its Distribution"

Thats why transfer payments are not supposed to be counted in GDP, only private and government wages and salaries. But there is no way to tell what the BEA actually does, and this would be the least of their inconsistencies anyway.


Difference between Maximum Output and Potential Output In macroeconomics, what is the difference between potential output and maximum output? Or they are simply equivalent concepts? If they are different, how can we graph it in comparison to LRAS on AD-AS model?

Potential output and maximum output are often interchangeable and be used in place with each other. Another term is Maximum Potential Output, but the most commonly used is Potential Output. This google search shows that all the results on the first page use the term Potential Output instead of Maximum Output.


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

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

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

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

Go beyond the numbers

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

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

Simple, you have a perpetuity, thus will need to discount all future cash flows to find Net Present Value, which essentially is the net worth of your company:

100 * 200$ * 12 months * 50% = 120,000$

You will then divide that by your interest rate, perhaps your average weighted cost of capital, WACC. Let’s say it is 5%.

120,000 / 0.05 = 2,400,000$

Which would be the Net Present Value of all your future cashflows; given the information you provided.

This is true because you specified a specific cashflow without growth for all eternity, hence the value of your cash flow in year 50 is going to be worth very little in today’s money.

EDIT: Forgot to take into account that there are 12 months in a year; answer has been updated.


Reference request on "post-scarcity" economics? Some friends and I have been discussing, speculatively, what might happen in the future after technology/increased automation greatly reduces the need for human labor.

The Marxists / leftists among us think that there will be a coming class conflict as more and more of the productivity gains from automation are captured by an elite, and that there will be a widespread political push from the left for something approaching a basic income.

Other, less left-leaning folks among us worry that there will be a collapse in aggregate demand as the purchasing power of a sizable, jobless part of the labor market essentially exits the economy. How government might respond to that is unclear.

I have the equivalent of an undergrad degree in economics and figured that there had to be some good discussion out there.

Can anybody point me to any papers or extended discussions of this topic?

A related question is in asking when (if ever) will we be post scarcity. The paper Are We Approaching an Economic Singularity? Information Technology and the Future of Economic Growth by William D. Nordhaus should be of use.

Abstract:

  What are the prospects for long-run economic growth?, the present
  study looks at a more recently launched hypothesis, which I label
  Singularity. The idea here is that rapid growth in computation and
  artificial intelligence will cross some boundary or Singularity after
  which economic growth will accelerate sharply as an ever-accelerating
  pace of improvements cascade through the economy. The paper develops a
  growth model that features Singularity and presents several tests of
  whether we are rapidly approaching Singularity. The key question for
  Singularity is the substitutability between information and
  conventional inputs. The tests suggest that the Singularity is not
  near.

(emphasis mine)

Another possibility is to consider those sectors, like digital media, where we are already post-scarcity, in that marginal costs are zero or very near to it. I recommend Carl Shapiro and Hal Varian's Information Rules for an accessible and interesting discussion of the economic issues that arise in this setting.

As colossus pointed out, technology advance is not associated with Unemployment. Malthus argued upon scarcity, but he has been proved wrong. As you hold an undergraduate economics degree, you might already know that economics "best friend" is history.

There's no reason to talk about a future technology boom, as we have already experienced it. There's not any similar technology boom in history from that of 20th-21th century. Not even close. Also, Marx has been proved wrong on this subject. Austrians have worked extensively against Marxist Theory (most notably F.A. Hayek and L. von Mises).

About the political tendencies and the left. After WW2, Greece and Korea suffered a civil war between communists and non-communists. Koreas' split is well known, but people do not know much about Greece. In Greece the communists lost, but the implications were tremendous. Left parties (socialists) abused communist ideals and they deindustrialised the economy. Also, they created class conflicts and massive statism was in favor. They created an economy full of rigidities and inefficiency. They gave tremendous power to unions and they abolished any concept entrepreneurship. Some Greek quick facts:

Greece extracts top quality olive oil, better than Italy (except Sicily) & Spain but it cannot export since there is no factory to put it in bottles.
The only industry that operates properly is commercial shipping (1st in the world), because it has nothing to do with Greece as the most shipping companies are off-shore.
1/10 of population (NOT labor force) works in the state
Specialized young people work as delivery boys etc because there are no industries to give them work.
Unions have the right to blockade or use violence anytime they want
Greece's GDP before crisis was that high due to consumption (i.e. AE) and there was not any Investment.

Conclusion

Are the left parties the right way to go in first place? Democracy by its nature gives more power to lower classes than upper ones. What will happen if there is a party that is willing to redistribute blindly just to keep happy only the lower classes? We all know that upper classes have more political influence than lowers, but if a party achieves to keep happy the lower classes then they will vote them again and again. Therefore, here's a spiral where the government manipulates the masses to vote them, the investors will leave as they will not afford to lose money, and competitiveness will fall.

Edit:

F.A. Hayek, Road to Serfom: Hayek's Nobel awarded extensive
work against interventionism and socialism.
Mises, Ludwig Von. Economic Policy, Thoughts for Today and Tomorrow.
South Bend, IN: Regnery/Gateway, 1979 (Socialism Chapter)
Representation of Malthusian fallacy