Why is market absorption of issued US Treasury Bonds (with the Fed purchase plan) a problem?

Why can't the Treasury and the Federal Reserve agree upon a controlled issuance and instant procurement of UST bonds "straight from the printing press"?

Treasury bonds are not “printed” at a “printing press,” the only “printing press” is run by the U.S. Mint, where they print Federal Reserve Notes (e.g., dollar bills). Treasury Bonds/Notes/Bills are sold at auction.
Not sure of the exact statute that forces this, but the Federal Reserve does not bid at auction, they buy in the secondary market. This answers your question.
Update: a FAQ on the Fed website: link.

Why subject the market to the ambiguity ...

Because there is no legal alternative, other than changing Fed operating procedures to having them cap bond yields. (One can search for discussions of “yield curve control” for more details.)
As for financial market commentary, it is not always reliable, so statements made there need to be taken with a large grain of salt.


Intuitive explanation of $S(p,w)\cdot p=0$

This is a general mathematical property of the second derivative/Hessian matrix of multivariate functions that are homogeneous of degree one.

The Expenditure function $E$ is homogeneous of degree one in prices. Why?
If all prices change in the same proportion (which is how we check for the mathematical property of homogeneity), relative prices do not change. If relative prices do not change, the quantitative composition of the minimum-cost compensated consumption bundle in order to achieve a given utility does not change at all. Then, since all prices have increased by the same proportion, budget shares remain the same, and the Expenditure needed to achieve the same utility, rises in that same proportion: homogeneity of degree one.

By duality, the Hicksian demand vector is the gradient of the Expenditure function, $H = \nabla_p E$.

The Hicksian demand vector, gives us minimum-cost quantities demanded. Due to the homogeneity of degree one of the Expenditure function, the inner product of the Hicksian demand vector times the price vector equals the Expenditure function. This also should be intuitive: we just multiply each quantity demanded by the unit price that must be paid for it, and by summing these products we obtain the total Expenditure we must incur in order to acquire the minimum-cost bundle for given utility.

So we have  (simplifying differentiation notation) $ E = H\cdot p$ while also $\frac {\partial}{\partial p}E = H$. Therefore also

$$\frac {\partial}{\partial p}(H\cdot p) = H \implies H + \frac {\partial H}{\partial p}\cdot p = H$$

and it must be the case that

$$\frac {\partial H}{\partial p}\cdot p = 0$$

So the Hicksian demand vector is homogeneous of degree zero in prices (mathematically, this is a consequence of Euler's theorem for homogeneous functions, i.e. that if a function is homogeneous with degree of homogeneity $k$, its gradient has degree of homogeneity $k-1$).

But the 1st derivative (Jacobian) of Hicksian demand (which is the Hessian-matrix of second derivatives of the Expenditure function) is the Slutsky matrix, $\frac {\partial^2 E}{\partial p^2}=\frac {\partial H}{\partial p} = S(p,w)$. So $S(w,p) \cdot p = 0$.

So the result stems from the homogeneity of degree one of the Expenditure function. Is there an intuitive explanation, analogously with the intuition behind the homogeneity of degree one of the Expenditure function? Well, the former comes directly from the latter, so it is difficult to come up with a "separate" intuitive argument. One could informally say that compensated quantities demanded are "independent" of (not affected by) price variation when relative prices remain the same. Then in geometric terms, this means that the vectors of rates of change of compensated quantities demanded (which is what each row of the Slutsky matrix contains), are orthogonal to the price vector.


So your EOQ expression is suggesting that the optimal order size is for about $438$ items each time.

You can check the result if you wish.  Suppose you order in batches of $Q$:

The average annual number of batches ordered is $\dfrac{3600}{Q}$ so the average annual cost of ordering is $£\dfrac{72000}{Q}$
The average number of items held in inventory is $\dfrac Q2$ worth $£\dfrac{3Q}{2}$ at a holding cost of $£\dfrac{3Q}{8}$
So the combined ordering and holding cost is  $£\dfrac{72000}{Q}+£\dfrac{3Q}{8}$
For $Q=437$ this gives about $£328.6347$; for $Q=438$ this gives about $£328.6336$; for $Q=439$ this gives about $£328.6341$. This suggests that $438$ may indeed be the best order size
You can check the calculus: the derivative of $\dfrac{72000}{Q}+\dfrac{3Q}{8}$ is $\dfrac{3}{8} - \dfrac{72000}{Q^2}$ which is a increasing function of $Q$ and is zero when $Q^2=192000$ i.e. $Q \approx 438.178$, and this would minimise the combined cost


The MRS is a function of $x$ and $y$. The fact that $y$ doesn't appear in the formula simply means that this function is constant in $y$.

The linearity does not imply indifference. It means that an additional value of $y$ is valued equally by the agent irrespective of his baseline consumption. In your example, this contrasts with the marginal utility of consuming $x$ which is decreasing with the baseline consumption since the function $u$ is concave in $x$.


If there are 4 years to maturity now, it will only be 3 years to maturity next year.
E.g., initial year is 2000, bond matures in 2004. In 2001, it’s 3 years to 2004.


Could indexation of wages help Argentina?

It seems that you answered your own question?

If the government's estimation of inflation rates are not credible, how can the government effectively index to inflation?

In any case, the first best solution to inflation in the long run is almost entirely an independent, competent central bank that has the capacity to raise interest rates, limit the money supply, and bring inflation under control. (And have a government that doesn't interfere with the central bank.)


When to invest into additional products?

Other than the generic calculation of "Present Value", there's no rule of thumb as such. Your decision should largely depend on your knowledge of the market, your capital and other production inputs, whether the licenses are substitutes, the marginal profit each one would bring, and so forth.

If a license has an expiration date, you might want to postpone the purchase till peek season is approaching. That way, you are not cash-strapping yourself unnecessarily. Also, there is always a possibility that some substitute and more affordable software might be released (or be noticed by you) sometime soon. For instance, would you buy a license if you find an open-source equivalent elsewhere?

On the other hand, the deployment of a specialized software might take time to stabilize, whence you would need to assess whether that would disrupt business operations.

Another aspect to consider is that by spending more of your remaining --and arguably vital-- resources, you are placing "more eggs in the same basket". That type of management is discouraged unless you have the certainty that your business will be profitable.

Knowingly or not, during your decision-making you'll inherently be applying many principles of economics and finance. There is just no tool or test that gives the precise type of guidance you are seeking.


Sequential vs. trembling hand perfect equilibrium

Yes. In a normal form game, every Nash equilibrium is also a sequential equilibrium. But not every Nash equilibrium is trembling hand perfect. Consider the game in which each of two players has two strategies, A and B. Both players get payoff 0 except in one case: they achieve positive payoffs if they both choose A. Then (A,A) and (B,B) are two Nash equilibria of this game. Both are therefore also sequential equilibria. However, (B,B) is not trembling hand perfect. If there is even the smallest tremble in player 2's choice, player 1 has a strict preference for A. Only (A,A) is trembling hand perfect. The generalization of this is that Nash equilibria in which some players play weakly dominated strategies are not trembling hand perfect.


What was the "invariable measure of value" problem and how did Sraffa solve it?

The working paper by  Kurose & Yoshihara (2014) addresses both of your questions.
What was the "invariable measure of value" problem:
According to the Kurose & Yoshihara:

An invariable measure of value can be defined as a measure that is invariable
with respect to changes in both income distribution and technique (Ricardo, 1951A,
chap. 1). The advantage of the invariable measure of value, if it exists, is that we can
distinguish between the variations which belong to the commodity itself and those
which are occasioned by a variation in the medium by which values or prices are
expressed, when relative prices change (Ricardo, 1951A, p. 48).

The invariable measure of value problem is the problem of finding such measure. Ricardo considered gold/silver money as good although flawed approximation. The authors provide more detailed overview of the idea at the start of chapter 2.
How did Sraffa 'solve it':
I put the '' around solve it as whether he indeed solved the issue is somewhat up to the debate (see the paper sec. 2.3), but the Sraffa's solution was as as follows (Kurose & Yoshihara, 2014):

... Sraffa (1960) revived the concern about the invariable measure of value, which had fallen into oblivion since the so-called Marginal Revolution.
Unlike Ricardo, he divided the problem of identifying an invariable measure of value
into two parts: the first is to search for a measure of value that is invariable with
respect to changes in technique, left aside the change in income distribution, and
the other is to search for a measure of value that is invariable with respect to the
change in income distribution, left aside the change in technique. Sraffa concentrated
on the latter by constructing a special, composite commodity termed the standard
commodity. He also demonstrated an interesting relationship with respect to income distribution if the standard commodity is adopted as the numéraire: the linear
relationship of income distribution.

Again you will find more detailed overview of Sraffa's solution in the paper as well as generalization of said solution by the authors.


How does price-elasticity of supply affect the incidence of tax on consumer and producer

You are right: both the price-elasticity of demand and the price-elasticity of supply affect the respective proportions for producers and consumers of the burden of a per unit tax imposed on sales by producers.

The proportions depend on the relative slopes, which reflect price-elasticities, of the demand and supply curves. Considering the elastic supply case in your diagram, the slope of the demand curve between points AE is much steeper than that of the supply curve between CE.  Hence E is much closer, in the vertical (price) dimension, to C than to A. Thus the post-tax price to consumers (p2 corresponding to A) is much further from the pre-tax price (p1 corresponding to E) than is the post-tax price to producers (p3 corresponding to C),and so most of the burden falls on consumers.  For the inelastic supply case the position is reversed.  A detailed explanation may be found in this NTRC paper (see section III).


If a company buys a robot, it's part of investment. If a person buys a car, it's part of consumption. Why?

Because there is a definition of what is production and what is consumption, and households are generally outside the production boundary. From the 2008 System of National Accounts (at 6.24):

  Economic production may be defined as an activity carried
  out under the control and responsibility of an institutional
  unit that uses inputs of labour, capital, and goods and
  services to produce outputs of goods or services. There
  must be an institutional unit that assumes responsibility for
  the process of production and owns any resulting goods or
  knowledge-capturing products or is entitled to be paid, or
  otherwise compensated, for the change-effecting or margin
  services provided.

The distinction therefore has nothing to do with cars versus robots, and everything to do with who purchases the car or robot. A car purchased by a consumer is considered consumption, but a car purchased by a firm is considered investment. This is intuitively reasonable; the stream of transport services that a household receives from owning an automobile is generally consumption, and likewise for a business it is generally an input into production. While it's true that a car owned by an individual may be used both for production and consumption, the point raised by denesp is precisely why no distinction is made: we simply do not know how people are using their personal cars at any moment in time, and it's probably not worthwhile to spend the resources to know, so we use the ownership of the automobile as a proxy for how it is used.

However, one might reasonably argue that even though the purchases are made by consumers, one should count the stream of transport services received by the household as consumption, and capitalize the purchase of the automobile. This is how we treat housing, as described in part in the answer here. Indeed, this point has been raised even by researchers at the US Bureau of Economic Analysis:

  The treatment of consumer durable goods other than owner-occupied housing as
  final consumption expenditure rather than as fixed capital formation is also a long-standing
  criticism made by many users of the national accounts. Consumer durables are similar in
  many ways to owner-occupied dwellings, but the treatment in the accounts is quite
  different. The owner of a dwelling is treated as an owner of an unincorporated enterprise
  that produces housing services, but consumer durables are not assumed to provide services
  within the SNA production boundary (SNA 6.89, 9.40). Many durables, such as cars, trucks,
  and furniture, can be used either by consumers or by business enterprises—the SNA
  definitions count their purchase by households immediately as final consumption
  expenditure whereas they are to be capitalized by enterprises. “Extended” national
  accounts developed by researchers such as Eisner, Jorgenson and associates, Kendrick, and
  Ruggles and Ruggles include the services of consumer durables (for a review, see Eisner
  1988). Fraumeni and Okubo (2001) illustrate the possible options of capitalizing motor
  vehicles or all consumer durables.

Why this is not done is a fair question, but I would speculate that (in the US at least) the answer is probably simply that given the limited resources available to the BEA, this potential improvement to the national accounts simply isn't as high a priority as other projects.


Why do firms bother to produce at equilibrium quantities if at equilibrium quantity, MR < MC?

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


Where can I find information on relationships between different commodities?

Quick answer, as I'm on my phone, but product by product input output tables can be obtained from Eurostat for EU countries, and are probably your best bet.  Individual countries may have more detail from their own National Statistical Institutes' websites.

The production functions in these are derived under some fairly strong assumptions, though, and you're certainly not going to get 30000 products worth of detail!

OECD also have some as well, and there are a number of multi-country input output tables available. I hear SE Asia do this well, but I don't know what data are publicly available. Countries which use hybrid transformations to produce IO tables may be able to provide you with their technology assumptions matrix, which might help you distinguish joint production from by-production.

This is all quantitative data, though, and you need to be careful about imports. If you can get an imports matrix as well, that would help, although if you're only looking for qualitative info, if you stick to tables for larger economies the problems should be mitigated.

You might be able to find more detail on a qualitative basis elsewhere, but I'm afraid I don't know from where.

Editing to add links and further detail:

Eurostat collect datasets from EU members and make them available here.

Note that some of the tables will be industry-by-industry (IxI) rather than product-by-product (PxP).  The former will do in a pinch, but it's not strictly what you're after.

OECD provide data for a wider range of countries as part of their STAN database but again these are IxI.

The UK do produce PxP tables under a hybrid technology assumption, available here but I would add the caveat that the UK have not carried out a full purchases inquiry since before a change in classification from SIC 2003/NACE Rev. 1 to SIC 2007/NACE Rev. 2, so you could see the odd spurious cell as a result of the correlation matrix method used for their conversion.

Your best bet (at least as far as IO tables go) is probably the tables produced by the US BEA.

Their Total Requirements: Commodity by Commodity table (also known as the Type I Leontief inverse) has a 389 commodity breakdown.  This isn't a PxP table as such; each cell shows (in monetary terms) how much of each input (labelled on the row) is needed to make one unit of output of the product labelled on the column in the whole domestic supply chain.

It sounds like you want something more like a direct requirements matrix, which gives only the things directly used to make that product, not including the things used to make the things used to make the product, and the things used to make those etc. etc.  For this you want the direct requirements matrix, which is unfortunately only provided on an IxI basis.  You might want to go ahead and use this, or you could try to back out the direct requirements matrix (also known as the A-matrix) mathematically.

Ordinarily I'd say just invert your total requirements matrix and subtract EDIT(it from) the identity matrix, but looking at the spreadsheet I'm seeing some negatives, which shouldn't happen with a Type I Leontief inverse by construction so I'm not sure what's going on there; I'm guessing some of final demand has been endogenised.  It may be worth digging into their methodology or getting in touch with BEA to discuss this.  They may even be able to directly provide you with something suitable.

You'll likely find that there are a lot of cells with (relatively) very small values in either approach; for a qualitative analysis I'd suggest setting a threshold value and setting anything below it to 0 and above to 1, or just picking the largest n cells in each column to look at.

One final caveat: Product-by-Product tables are basically never compiled from directly collected data, and are in a sense an inherently synthetic beast.  Instead they are constructed from Supply and Use tables, which are much closer to directly collected data.  These both have product-by-industry dimension, with the supply table showing what each industry produces, and the use table showing what each industry consumes.  If you can make use of those instead, then that's preferable to using IxI or PxP tables.

If you want to learn more about input-output, I can recommend some books.

The first is "Input-Output Analysis: Foundations and Extensions" by Miller and Blair, which seems to be the bible among academics on the subject (I would add a warning that I find their presentation of the Type II Leontief model suboptimal for applied work, but this shouldn't be an issue here).

Thijs ten Raa has a book, "The Economics of Input-Output Analysis" which is a bit more high level (not to mention shorter!).

If you don't want to fork out the cash, the Eurostat manual on Supply, Use and Input-Output Tables is available online but is heavily geared towards construction of the tables themselves.  If you're looking for detail on how Supply and Use tables are converted to Input-Output tables, my favourite mathematical presentation online is actually that from the 1968(!) version of the UN System of National Accounts which you can get from the UN here.

There's also a UN Handbook on Supply, Use and Input-Output Tables due to be published sometime this year, which I'd recommend looking at when it's finally published.


Question about the relationship between Weak Axiom and Slutsky Matrix

It is almost true.

There are examples of demand that have a negative definite Slutsky matrix but fails the Weak Axiom.

However, if we ask that
$$v \cdot S(p,w) v <0 $$
whenever $v \not = \alpha p$ for any scalar $\alpha$ (i.e. $S$ is negative definite for all vectors except those proportional to price), then the Weak Axiom holds.


How to interprete independence between treatment indicator and outcomes?

Note that this section in the book starts with the counterfactual that each agent has an outcome $y_0$ without treatment and an outcome $y_1$ with treatment. You observe only the $y_0$ of the untreated agents and only the $y_1$ of the treated agents, but both exist for each agent. If treatment is randomized across agents then $w$ is indeed independent of $(y_0,y_1)$, but of course not independent of the $y_i$ you actually observe.


Could a bank simply eliminate a loan from its books?

If Mr. X hasn't used the money, so it's all still in a deposit account at the same bank, then the bank may be able to cancel the loan. Whether they can or not, will depend on the exact contract attached to the loan.

If Mr. X has withdrawn the money as cash, then that transaction represented a drop in the bank's liability to Mr. X of 100, and a drop in the bank's assets of cash-at-hand of 100.

If Mr. X has used the money in a digital transaction, then they can no longer cancel both at the same time, as the asset of the loan is with Mr. X, but its matching liability will be with another party.

In either of the last two cases, the bank can cancel the loan, reducing its assets by 100. The balancing transaction will be a reduction in the bank's equity of 100 - i.e. the bank records a net loss on the loan of 100, and the shareholders make a loss of 100 on the transaction as a result.

(because assets = liabilities + equity)


Bayesian Mechanism vs Prior-free Mechanism

You may need to provide more information for a clear answer. How does the mechanism look like in detail? What is the goal you want to achieve?

Regarding your first question, it is not "necessary" to show that a mechanism is prior-free but it is a nice-to-have feature. Whether it is of first-order importance, as always, depends on the circumstances.

For example, Myerson's optimal (revenue-maximizing) auction requires that the seller allocates her object to the buyer with the highest "virtual valuation", $v_i - \frac{1-F_i(v_i)}{f_i(v_i)}$. This construction depends on $F_i$ (the cdf of $i$'s value distribution) and its derivative. That is, in order to design the optimal auction, the seller needs a prior about $i$'s value - and if this belief is way off, the designed auction can be far from optimal.

As another example, consider a bidder in a first-price auction. How should this bidder figure out an optimal bid if they have no clue about how the other bidders' valuations are distributed? Do they even know the mean or even the support of this distribution?

If a seller simply wants to allocate her good efficiently, i.e., to the buyer with the highest value, she can set a second-price auction without a reserve price. It is a (weakly) dominant strategy for each bidder to bid the true value and no knowledge about priors is required (for the bidders or the designer).

A participant in your double auction may know the support $[0,1]$, but what is the optimal price to be submitted if they don't know the value distributions? So what goal do you want to achieve with this double auction?

Mechanism designers refer to research weakening assumptions on common priors as following the "Wilson doctrine" (yeah...) because of this quote:

  Game  theory  has  a  great  advantage  in  explicitly  analyzing  the
  consequences  of  trading rules that presumably are really common
  knowledge; it is deficient to the extent it assumes other features to
  be common knowledge, such as one player’s probability assessment about
  another’s preferences or information.

  I foresee the progress of game
  theory as depending on successive reductions in the base of common
  knowledge required to conduct useful analyses of practical problems.
  Only by repeated weakening of common knowledge assumptions will the
  theory approximate reality. Wilson (1987)

Bergemann and Morris have done some nice research on this issue. Maybe you want to read this essay or get a copy of their book.


There are many online. I don't recommend any of them, unless you're looking for a structure to guide you through. Business plans must suit the idea, and not otherwise.

You can find generic templates out there, but I believe they should work as a guidelines - i.e., things you should include. But the point of a business plan is to explain everything about an idea/project and explore the outcomes from there. If you are able to explain every single detail of your idea, you'll find some weaknesses - which you must include, of course - and your exercise is now to think about how can you over come those weaknesses.

Some questions for you to consider:

Who are you? Why are you proceeding with this idea?
What is the idea? What is the product? Why is it so different?
Where are you/your firm located? Why? Any particular reason? Where should it be located if you could?
What is your market? Age, type, profession, gender, etc etc
How do you expect to reach out to those people about the idea? After that, how do you want them to buy your product/service?
(At this point, you can perform the so-well-known SWOT analysis and other similar matrices (BCG matrix, for instance).
How are you going to finance yourself? Why? Why or why not loans, business angels, credit, etc etc ? What is your financial strategy? How are you going to manage the (few) cash you will have?
Are you going to invest on marketing? If so, how, why, why not?
Okay, you go some sales. What are you going to do with the cash you just earned? Why? For how long are you keeping that strategy
How are things going to unfold once you get it running? Why? Why not in a totally different way?

There are no identical business plans. You have to adequate yours to your idea. A quick example: When there is a physical product, you must include the design, explain it, whys and why not. When there is a service, for instance, perhaps it is better to explain why is it different than other solutions (you know, reinventing the wheel, not inventing it).

I hope these will help you work something around.


Do unsold goods still make it into the GDP?

2.5 m. Because GDP calculates the final price of Factory goods produced,consumption- which the workers and suppliers spent their cash, and a few other components.


$$\require{cancel}$$

Notice that if $\dot x_t \neq 0$, then $\Delta \dot x_t \to 0 \implies \Delta \to 0$

$$ \lim_{\Delta\to 0} \frac{f(x_{t+\Delta}) - f(x_t)}{\Delta} = \cancelto{f'(x_t)}{\lim_{\Delta \dot x\to 0} \frac{f(x_t + \Delta \dot x_t) - f(x_t)}{\Delta \dot x_t} \dot x_t}= f'(x_t)\dot x_t$$

If $\dot x_t = 0$, then $f(x_t)$ is a constant function.


If a best-response dynamic converges, does it converge to a Nash equilibrium?

Given that the system does converge, i.e. $a_i^t=a_i^{t+1}=a_i^*$ for all $i$ after some $T<\infty$, and that $a_i^{t+1}\in BR_i(a_{-i}^{t})$, it follows that $a_i^*\in BR_i(a_{-i}^*)$ for all $i$. Hence $a^*$ is a Nash equilibrium of the underlying game.


Maybe not what you are looking for, but a related concept is regret. Orphanides and Zervos (1995) is a classic paper on rational regret in a health economics concept http://www.jstor.org/discover/10.2307/2138580?uid=3739840&uid=2&uid=4&uid=3739256&sid=21106216442271

There's also plenty of irrational regret papers, mostly just boiling down to hyperbolic discounting models.


The third line of p.45 denotes:

$MC_{t+k|t}=\psi_{t+k|t}/P_{t+k}$

but this is probably not the answer you are looking for.

Going from eq. (9) to (10), multipliy the right-hand side by $\frac{P_{t+k}}{P_{t+k}}=1$ (you can always multiply by one), the numerator goes into $\Pi_{t-1,t+k}$ (together with $P_{t-1}$), the denominator goes into $MC_{t+k|t}=\psi_{t+k|t}/P_{t+k}$.


Is there a solution to the Joker's game in The Dark Knight?

Suppose first that the groups are not altruistic and care only about their own survival. It is not exactly a prisoner's dilemma since the outcome obtained by mutual cooperation (if both groups wait) is not Pareto-improving: everyone dies in that case. The only equilibrium is that one of the groups destroys the other boat as soon as possible; and any action played initially by the other group is possible in equilibrium, since this team is indifferent between waiting and triggering other the bomb (they will die one second later anyway).

As @Alecos_Papadopoulos wrote, the game becomes more interesting if the groups have pro-social preferences. For instance, they might be reluctant to sacrifice the other group and prefer that everyone dies (including themselves). If there is no uncertainty, the outcome is trivial: the only equilibrium is that both groups wait until the Joker triggers the bombs.

The most interesting scenario is the one in which the types of the groups are uncertain: each boat can be either selfish or altruistic. In that case, it seems reasonable (but other specifications are possible) to assume that cooperation is desirable only if the other group is also altruistic, but if the other group is selfish the individuals prefer to kill them first and survive. The equilibrium strategies are the following:

If the group is selfish, it triggers the bomb of the other group as soon as possible (it is a dominant strategy).
If the group is altruistic, its initial action depends on its beliefs about the other boat. If it is sufficiently optimistic (i.e it believes that its opponent is altruistic with a sufficiently high prior), the group waits. If it has not exploded one second later, the group understands that it faces an altruistic opponent and therefore waits until the Joker kills everyone. Notice that the explosions happen either at $t=0$ (as soon as the game starts) or at midnight (when the game ends) but never in between.


Proof of Expected utility theorem with three outcomes

In order to do that, you need to define $u(·)$ as a utility function on "sure things" rather than on lotteries. In your example, you need to think in terms of the set of possible prizes to the lotteries. Say the set of possible prizes is given by $R$ and asume that is finite. For any $r\in R$, define $w_r$ as a lottery that pays $r$ in every state of nature. Then, it should be clear that

$$x \sim \sum_i p_i w_i,$$

(and similarly for $y$ and $z$) where $p_i$ denotes the probability of state $i.$ Given that, as you mention, it must be the case that two equally desirable lotteries receive the same expected utility, the utility assigned to $x$ needs to be

$$H(x)=H\left(\sum_i p_i w_i\right).$$

The first chapter of Huang, C. and Litzenberger, R.H. Foundations for Financial Economics, North Holland, 1988 explains in detail why the function representing the preferences $(H(·))$ has to be linear, and, with linearity stablished, you get the expected utility representation because

$$H\left(\sum_i p_i w_i\right)=\sum_i p_i H(w_i).$$

The only thing left is to define $u(r) \equiv H(w_r),$ i.e, $u(r)$ is defined on outcomes, while $H(w_r)$ is defined on lotteries. This is why we say that $u(r)$ is a utility function on sure things, because $r$ receives the same utility level that a lottery paying precisely $r$ in every state of nature.

Of course, expected utility is most useful in settings with large outcomes spaces and/or large lotteries spaces. In a restricted setting such as yours, you're probably best served by assigning values ("utilities") to lotteries themselves (as you did in your question). Again, a more rigorous proof can be found in Huang and Litzenberger, op.cit.


implied volatility, how to get parameters?

The implied volatility is defined as the volatility parameter that gives you the option price currently trading on the market. That is, you will observe market quotes for option prices or implied volatilities and you use the Black-Scholes formula to convert from one to the other. The implied volatility is not therefore something you computed based on stock price data, it's really a price determined by the market.

There are as many implied volatilities as there are options traded. In fact, options are frequently quoted in implied vols. You have one implied volatility for every strike price and for every maturity. This defines the "Volatility surface". Instead of the strike price you frequently see on one of the axes the "moneyness", that is the ratio of current price to the strike price.

Take a look at this graph.
https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/23316/versions/2/screenshot.jpg

That means, for example, that the 3-month 1-moneyness implied vol is the volatility parameter that you need to input in the BS formula to obtain the observed market price of the 3-month 1-moneyness call option.


What are the alternatives to currency devaluation?

The only alternative is what is often called "internal devaluation". This basically means reducing the actual (domestic) prices of goods in a country.

This is what is often called as increased "competitiveness". It is most often achieved through cutting wages or slowing down wage growth. This is because wages are most often a huge cost factor and the price of capital (which is often bought internationally) is harder to reduce just like that. However there is also the phenomenon known as "downward nominal rigidity", which means people don't accept lower nominal wages, so it's very difficult to lower wages. Much harder than increasing them. In fact, in practice, it's easier to increase inflation to reduce real wages than actually reducing the number printed on your check at the end of the month. However in this case, we want deflation (reduction in prices) to boost exports, so the whole matter gets more complicated.

Technically a devaluation only makes all your domestic goods cheaper abroad. This can also be achieved by just reducing your prices of course. However, as we saw, this is difficult. Also there is a coordination problem, as each industry would have to adjust (thousands of prices must adjust) for the same effect as the exchange rate adjusting (one price adjusts).

Milton Friedman used to compare this to daylight savings. We could all just agree to push all our appointments and activities by an hour for some time, which is hard (this would be internal devaluation). Or just change the time for the same effect (exchange rate devaluation).

A surge in quality is technically also an alternative, but not possible always and especially not short-term.


Asymmetric (in sign) cross-price derivatives in consumer-theory problem

MWG proposition 3.G.2 is the one you’re thinking of, but that applies to Hicksian demand’s hessian (constant utility). What you solved for is the Walrasian demand, so we want to look at the Slutsky matrix.
$$S_{lk}(p,w) = \partial x_l(p,w) / \partial p_k + \partial x_l(p,w)/ \partial w * x_k(p,w)$$
First term: uncompensated change in demand of good l due to a change in $p_k$ (when multiplied by $\partial p_k$)
Second term: effect of wealth change on demand of good l (when
multiplied by $\partial p_k$) [https://scholar.harvard.edu/files/basilico/files/mwg_flashcards.pdf]
If you check the symmetry of this matrix (in our case l and k are x and y), I believe it should work out.


Rentier capitalism vs investment capitalism?

A share is an entitlement to the ownership of a company. Such ownership brings several benefits like voting rights and dividends, and the owner is free to sell such ownership whenever s/he wants, making a capital gain (or a loss) in the process.

Why is this the case? Well, it was like that with the first publicly listed stock-owned company (the Dutch East India Company). In terms of incentives, it fosters the allocation of (financial) capital to new ventures by giving those taking the risk to benefit from it. It has proven a highly successful legal arrangement to foster businesses and investment.

Another common legal arrangement is that of non-profit corporation. These organisations are usually started by a group of people, which contribute capital to it (albeit this is not represented in the form of shares). Sometimes they transfer the ownership to a foundation. In any case, these companies cannot distribute profits to the owners.

Finally, as you say an alternative legal arrangement would be one were ownership of shares do not lead to income via dividends, but such shares still allow for capital gains. In fact, some shares pay no dividend at all (as a matter of fact, the taxonomy of shares is quite diverse). As this article explains:

  investors who buy stocks that do not pay dividends prefer to see these companies reinvest their earnings to fund expansion and other projects which they hope will yield greater returns via rising stock price.

So in principle you could set up a company that does not issue dividends in order to foster its growth. Naturally, this could be changed in the future through a motion in an annual general meeting of shareholders. There are also plenty of companies who decide not to pay dividends in order to foster expansion (e.g. Apple until a few years ago). Yet, many of these companies, and particularly in the last decades, have decided to execute share buybacks rather than foster expansion and investment. This is, the company buys their own shares with its profits, which fosters price growth and hence expands capital gains. This is part of a wider short-termist trend that some have denominated "Quarterly Capitalism".

There is very interesting new research about the consequences of this "quarterly capitalism" on investment and growth. Check here, here, and here. The latter concludes:

  We show that capital no longer flows more to the industries with the best growth opportunities because, since the middle of the 1990s, firms in high q industries increasingly repurchase shares rather than raise more funding from the capital markets.

This evidence gives a rather counterintuitive result (at least from the normative meaning of the words), which is that a rentier capitalism might be better for investment and growth than an investment captialism.


Why doesn't the ECB implement the same fiscal and monetary policy that the FED used to save the US economy?

The ECB faces a unique challenge in that the Eurozone is a monetary union without a fiscal union. Because each country has autonomy over their own fiscal policy and there is no separate Eurobond, it is unclear which countries' bonds the ECB would buy to perform Quantitative Easing. In the US this is easy because of the presence of US Treasury Bonds that  the Federal Reserve can readily purchase.

Also, since the Eurozone is composed of so many different economies, the main goal of the ECB is inflation control. It is extremely hard to set a blanket policy to cover the whole Eurozone when there are so many different economies in different states right now. Setting an interest rate very low or performing quantitative easing over the whole Eurozone, which is very hard because of the lack of fiscal union, would undoubtably be good policy for countries like Greece and Portugal, but would be the wrong policy for a country like Germany that currently has a strong economy.


In control systems engineering, there was the "Aizerman Conjecture" (the transliteration of Aizerman varies) that argued that a linear time-varying system was stable if the parameters (state matrices) at all times corresponded to stable systems. However, counter-examples were found to this conjecture.

About the only way to show that a time-varying system is stable (for example) is to find a Lyapunov function that holds at all times. This is generally going to be difficult.

Something like graphical analysis would be technically invalid, as you are violating assumptions that are in place. You are pretty much going to have to derive any results from first principles.


How can we measure the size of the new uber-driver-type economy?

Those are important and difficult questions to answer. Regarding Uber, Jonathan Hall (Uber) and Alan Krueger (Princeton) wrote a joint paper on An Analysis of the Labor Market for Uber's Driver-Partners in the United States. The paper provides the first comprehensive analysis of Uber's driver-partners, based on both survey data and anonymized, aggregated administrative data. The following figure documents the exponential growth in the number of active Uber driver-partners in the United States from mid-2012, when uberX was launched, to late 2014.

Source: Hall and Krueger (2015)

More generally, they point out that the Bureau of Labor Statistics (BLS) publishes a supplemental module to collect information on various forms of contingent and alternative work arrangements in the Current Population Survey (CPS) in 1995, 2001, and 2005 that provides the most informative data available, although it is now somewhat out of date. The BLS contingent worker supplement also measured the share of workers in alternative work arrangements, including independent contractors. Workers in the sharing economy can work part-time or full-time, or participate on a temporary or permanent basis, but they are almost universally working as independent contractors while they are participating in the sharing economy. Thus, evidence on independent contractors can provide relevant background for understanding the nature of the labor market in a sector that overlaps with the sharing economy.


What's the role for official intervention in the Balance of Payments?

The Balance of Payments is supposed to be a form of double-entry bookkeeping, in that every transaction has two opposite effects, often in different accounts.  Hence the word balance. In fact it might be considered quadruple-entry bookkeeping, as there are another two effects on the foreign side too.

For a country's Current Account to be in surplus there must be some net income, for example from the sales of exported goods and services exceeding the purchase of imported goods and services.

The surplus could be represented by a debt owed by the foreign importer to the domestic exporter. If the exporter uses this to invest in the foreign country then this counts in the Capital Account (or the Financial Account as the IMF calls it) which balances the Current Account.  But even if it simply remains as debt or as the exporter's balance in a foreign bank, this still counts as other investment and balances in the same way.  If the foreign importer pays in domestic currency then that reduces the outstanding liabilities to foreigners, again with the same net effect on the Financial Account.

If somebody actually turns a debt into money, then it amounts to an investment in the liabilities of the foreign money-issuing authority (typically its Central Bank).  Bringing the foreign money home and selling it to somebody else domestically for domestic currency makes no difference to the impact on the Current or Financial Accounts, unless you sell foreign currency to the domestic Central Bank in which case it turns into a change in the Central Bank's Reserves.


Why do we need a restriction of a game to prove the given statement?

It is because the set of strictly dominated strategies changes as we eliminate strategies.

The point of the proof is to show the result for ANY $R$ such that $R \rightarrow_{S}R'$.

Look at Example 7 in the next page of the paper.

In $S$, there is only one strictly dominated strategy, and we remove it and get $R$ (hence $S \rightarrow_S R$).
Now look at $R$. There is a strictly dominated strategy that was not one before (in $S$), removing it get $R'$ (hence $R \rightarrow_S R')$.


Corporate Finance: From External Financing Needed(EFN) to Sustainable Growth Rate

We can replace growth rate in the formulation as below
$$\frac{A_0}{S_0}gS_0-\frac{L_0}{S_0}gS_0-PM(1+g)S_0b=0$$
$$(A_0-L_0)g-PMS_0b-PMS_0bg=0$$
$$g=\frac{bPMS_0}{A_0-L_0-bPMS_0}$$

In the paper you linked the author assumed $A_0$ and $L_0$ to be total assets and total debt (pg.11); therefore $A_0-L_0=E_0$
$$g=\frac{bPMS_0}{E_0-bPMS_0}$$
$$g=\frac{b\frac{PMS_0}{E_0}}{1-b\frac{PMS_0}{E_0}}$$
$$g=\frac{b\times ROE}{1-b\times ROE}$$


Your "counterexample" also violates condition $\alpha$: $y=C(\{x,y,z\})$ but $y\ne C(\{y,z\})$. So it's not really a counterexample.


list of math intense graduate level microeconomics books?

Mas-Collel is very popular. It is very math-heavy. Every idea and concept is done pretty rigorously and it pretty well covers everything. The book is a very slow read and is sometimes uneven. Very detailed in some sections and not as good in others. That said, in my experience, it is the graduate microeconomics bible. If you have a question, your answer is somewhere in there.


Uncovered interest parity and asymmetric capital controls

In principle it shouldn't really matter that a sub-population (in this case the locals) have capital restrictions, so long as the unrestricted population is sufficiently large.  The UIP model only needs that the capital can flow - it doesn't mind who is doing it.

In this case, so long as the foreign investors have not completely left, then in aggregate the restriction shouldn't make a difference.

Furthermore, if foreign investors are able to short sell to locals (which I think they can?), then you can even create extreme capital outflows.


Actually, the expression more money supply is not clarifying at all (i) which effect is desired and (ii) what really occurs, whence your (really natural) question.

What is implicit behind this expression is that commercial banks will have an easier access to (re-)financing. If commercial banks play their role of Money multiplier -- which is not that obvious since they may prefer to clean their balance sheets --, they will basically be more prompt to grant credits. Put differently and using an abusive but pedagogical term: they will be psychologically more prompt to waste money, and thus to stimulate demands here and there.

Since growth is very often conceived as being demand led, more demands (of goods or whatever) at a constant level of supply (of those goods or whatever) in turn means inflation, until levels of supply, here and there, adjust and create jobs, generate dividends, etc...

To conclude and summarize

  Basic Reason of Why the Money Supply Needs to Increase?

Because one needs commercial banks to be more relax and play their role.

  what would be wrong with keeping it the same as the economy grows [...]

The economy cannot really grows without leverage.

  [...] or contracts

Bubbles may form and explode sooner or later in this case, which is nothing desirable.

Adjusting the money supply is a difficult balancing exercise for central banks.


Substitutability vs complementarity of efforts

In problems like this, complementarity and substitutability are often defined with respect to the cross-derivatives.

Write $v_i(\cdot)$ for the derivative of $v$ with respect to its $i$th argument. Thus, $v_i(a_1,\ldots,a_n)$ measures how much output increases if $i$ increases his effort slightly.

Now let's think about the derivative of $v_i$ with respect to $a_j$: $v_{ij}(a_1,\ldots,a_n)$. If $v_{ij}>0$ then an extra unit of effort from $i$ yields more output when $a_j$ is high (and vice-versa). We say that $i$'s and $j$'s efforts are complements because extra effort from $j$ makes $i$'s effort more effective (and vice versa).

Conversely, if $v_{ij}<0$ then extra effort from $j$ makes $i$'s effort less effective, and this is often taken as a definition of substitutability.


What Was the Accuracy of Macro Model in the Phillips' Machine (MONIAC)?

Phillips himself claims writing about Moniac like machines in 1950: "The accuracy obtained depends on the precision with which the machines are constructed, but there is no difficulty keeping it within about $\pm$ 4%" (p.284)
The article also points out that at the time of writing he was still building the MONIAC at LSE, but had already constructed one in Leeds. I suppose the LSE version turned out to be accurate upto 2%, and hence the conflicting informaton.
Economica, New Series, Vol. 17, No. 67. (Aug., 1950), pp. 283-305. Here's a link

Two unrelated fun-facts:
The MONIAC features in Terry Pratchett's Discworld novel: Making Money. As always in Pratchett's novels there are a lot of references to roundworld reality: introduction of paper money, outsourcing, inflation due to money dilution and many others
The Dutch have an expression "To have money like water" which in the Dutch context obviously means to have lots of money. The MONIAC is one of the few cases where it can be interpreted literally.


How has decreasing quality (or the need to pay more for the same quality) tracked with inflation?

I will respond to a few points.

The first thing is that although I am old enough to be able to complain about declining quality in many products, it is very unclear how widespread it is. Official methodology takes into account quality changes already. However, it appears unlikely that the change of agricultural production is captured, as that is not really observable at the supermarket.

Over a multi-decade span, things like the CPI have inherent flaws with measuring changes. This is known as “the index number problem.” I am not too familiar with this, so I will let the reader ask another question, or do a web search for more information.

At the same time, the belief is that the CPI overstates changes in the cost of living. In the US, this was the subject of the Boskin Commission.

  There is probably a well known marketing/business school of thought about this pattern of getting consumers to pay more for what they are already paying for.

If we are talking about agriculture, this is off-base. All the changes made were the result of research in agriculture. One can debate the wisdom of the philosophy (like organic farming proponents do), but changes made were considered “best practice.” (Note that even organic farmers look at agricultural research to raise crop yields.)

  How can I track cost of living with quality of living. Is there any metric that would help identify what I'm referring to "shadow inflation" that affects product quality?

If you go to the Bureau of Labor Statistics website (link), I think you will find a statement to the effect that “the CPI is not a cost of living index.” You might get an explanation about that distinction (or ask another question here about the distinction).

At present, the CPI methodology distinguishes between organic/non-organic food. So the inflation rates now are not affected. If you want to compare versus the 1950s, building a new index is going to be nearly impossible, since it seems unlikely that you could find the equivalent of organic prices in the 1970s. All you could do is try to make an adjusted cost-of-living comparison from an earlier period to the present. However, given the large changes in the consumption basket, it is unclear how meaningful that is.


Are there economic models that predict (only) a medium/long-term negative effect of protectionism?

This is not exactly what I was looking for, but seems "good enough":

I found a recent empirical paper by IMF staff (Furceri et al., 2018) applying Jorda’s local projection method to a panel of data of 151 countries over 1963-2014. They found/predict negative effects from the first year after the measures are introduced, but the effect size on output looks pretty small and given the confidence band it can well still go up for some years after the measures are introduced.

They also have bunch robustness checks (alternative models) which mostly preserve/confirm that conclusion

The "drop early years (<1980)" seems to produce a different enough result on output though (in that robustness graph), but I can't find any commentary on that particular check in the paper. I guess it's because it still falls within the 90% confidence region of the base model. The paper does point out in its introduction that older data had more protectionism:

  Our panel of annual data is long if unbalanced,
  covering 1963 through 2014; more recent data is of greater relevance, but older data
  contains more protectionism. Since little protectionism remains in rich countries, we use a
  broad span of 151 countries, including 34 advanced and 117 developing countries.

As an US addendum, regarding the Trump economy in particular, Kenny LJ answered another (much broader) question by citing/meniotining Fajgelbaum et al. (March, 2019)

  We analyze the impacts of the 2018 trade war on the U.S. economy. We estimate import demand and export supply elasticities using changes in U.S. and retaliatory tariffs over time. Imports from targeted countries declined 31.5% within products, while targeted U.S. exports fell 11.0%. We find complete pass-through of U.S. tariffs to variety-level import prices. Using a general equilibrium framework that matches these elasticities, we compute the aggregate and regional impacts. Annual consumer and producer losses from higher costs of imports were \$68.8 billion (0.37% of GDP). After accounting for higher tariff revenue and gains to domestic producers from higher prices, the aggregate welfare loss was \$7.8 billion (0.04% of GDP). U.S. tariffs favored sectors located in politically competitive counties, but retaliatory tariffs offset the benefits to these counties. We find that tradeable-sector workers in heavily Republican counties were the most negatively affected by the trade war.

So noticeable effect on trade already, but very small on GDP, percentage-wise. Given the IMF/Fuceri model, we don't really expect a large impact on GDP anyway.


They do consider it. The precise mathematical formulation is usually
$$
-\frac{p_1}{p_2} = \text{MRS}(x_1,x_2)
$$
or
$$
\frac{p_1}{p_2} = \left| \text{MRS}(x_1,x_2) \right|
$$
in the basic cases, when MRS is a negative number (the slope of the indifference curve at basket $(x_1,x_2)$).


Rationality and Common Belief in Rationality in Brandenburger & Dekel (1987)

The concept that Brandenburger and Dekel (1987) call an "a posteriori equilibrium" is roughly the same as what Dekel and Siniscalchi call an "epistemic type structure for a complete information game" in which all types are rational and there is common belief in rationality. Therefore, Brandenburger and Dekel's Proposition 2.1, together with the remark that immediately follows the proof of Propoistion 2.1, is roughly the same as Theorem 1 in Dekel and Siniscalchi.


Mythbusters - Determine optimal boarding strategy based on time and satisfaction score

I would start with your generic
$$f(t,s) = t \times s$$
and, instead of add weights or factors to this, I would add other variables related to time and satisfaction like:

boarding time as function of luggage management ($TL$) times baggage number ($B$), and time to go to seat row ($T_g$) vs time to actually sit ($T_s$) for the different seat types (Window, Mid, Aisle) per number of passengers ($N$)
satisfaction as function of easiness of boarding ($E$) (think about the WilMA and families with little kids), functionality of luggage positioning ($F_b$), amount of distraction required ($D$) (e.g. boarding while listen to loud music or boarding while talking at the phone distract from the boarding and leads to errors).

A proposal can be
$$f(TL, Tg, Ts, W, M, A, N) = (TL\times B)+(TG\times N + \frac{N}{3}W + \frac{N}{3}M + \frac{N}{3}A)$$
$$f(E, Fb, D) = E \times Fb \times \frac{1}{D}$$

$$\mbox{boarding strategy score}=f(TL, Tg, Ts, W, M, A, N) \times f(E, Fb, D)$$

and I would start assigning weights while conducting some more simulations (I understood that Mythbusters example refers to single trials only for each strategy).

In my opinion, advantages / disadvantages are not coming from equations itself but from the methodology. Without more robust experimental data, all equations above, and even more factors, are arguable and contestable.

I also would not add "money" in the model, but rather added value for the airline vs added value for the passenger, and things will easily escalate: you may find that keep people stuffed in tunnels and in line waiting to enter the aircraft, or waiting in airports for delays or flight cancellations, can increase exposition time for advertisement boards, therefore potential revenue for airport services, therefore ...utility functions of delays.


How do Trade Costs work in International Trade?

The quotation comes from James Anderson and Eric Van Wincoop "Trade Costs"  in the Journal of Economic Literature Vol. XLII (September 2004) pp. 691–75 and a preprint of the article is available

The calculation is trying to find the equivalent to an ad valorem tax by which the price of manufacture increases by the time of retail sale.  Essentially it is saying transportation multiplies price by $1.21$ (a $21\%$ increase), tariff and non-tariff border related trade barriers multiply by $1.44$ (a $44\%$ increase), and retail and wholesale distribution costs multiply by $1.55$ (a $55\%$ increase) combining to multiply by $1.21\times 1.44\times 1.55=2.7$ (a $170\%$ increase).

This figure being over $100\%$ is not an issue.  For example you could imagine a high tax on a packet of bottle of perfume costing $\$10$ before tax: if the tax rate was $170\%$ ad valorem this would add $\$17$ tax and make the after-tax price $\$27$.

There are plenty of caveats: domestic commerce also faces retail and wholesale distribution costs as well as some transport costs.  Some goods see smaller costs, such as high-value low-weight goods seeing lower transport costs, or cross-border trade involving a short distance and a free-trade area, so this is in a sense a weighted average across goods and countries.

The article goes into considerable detail on the methods used for the calculations and possible implications for trade models.


Are there papers in evolutionary game theory that are influential in economics?

Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.

Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.

I disagree with your assertion that EGT is seldom applied or that it has not been  influential.  Both of the papers referenced above appear in RePEc's list of the
top 1% of citations.

Allowing preferences to 'change' can generate just about any equilibrium you want, so the premise behind EGT is a tough sell in many economic models - not to say compelling research hasn't done so.  The bottom line is that it isn't a part of the atmosphere where mere mortals can tread.

EGT has, in fact, been applied to many problems in economics as well as those traditionally parsed by the other social sciences - particularly the evolution of social norms, political representation, voting, and distributive justice.


First of all, you need to expand the definition of a vector. It is not only quantities having maginitude and direction. While I agree that is the representation in $\mathbb R^2$, it is not always the case. Think of a vector as a representation of any ordered group of numbers $(x_1,x_2,...,x_n)$ and forget completely that you ever thought these implied magnitud and direction.

We think of commodity bundles as vectors and not as quantities by themselves because we want to be able to explain consumption choices as bundles. Let me give you an example with a bundle of 2 goods, $(x_1, x_2)$. Think that $x_1$ is the amount of coffees that you can buy whereas $x_2$ is the amount of packets of sugar that you can buy. We want to be able to compare, say, $(2,1)$ with $(1,2)$. I agree, we could analyze both the choice of both goods separately, but ultimately we want to know what is the optimal consumption bundle and not the optimal amount of sugar and coffee separated. Now, did I say something that entails magnitude? Or direction? No.

Bottomline, yes, we are thinking about quantities of goods, but when we say vectors, it means bundles of quantities of goods. That is ultimately what happens in the real world.


Was the aid in the Marshall Plan a loan?

The plan did involve loans but was mostly in the form of grants (gifts). As the Wikipedia entry states:

  The Marshall Plan [...] consisted of aid both in the form of grants and in the form of loans. Out of the total, 1.2 billion USD were loan-aid.

Since the total economic support the program involved was of \$13 billion in contemporaneous time (roughly \$132 billion in Sept 2017 money), only 10% approx of the aid was in form of loans.

  The UK received 385 million USD of its Marshall Plan aid in the form of loans. Unconnected to the Marshall Plan the UK also received direct loans from the US amounting to 4.6 billion USD. The proportion of Marshall Plan loans versus Marshall Plan grants was roughly 15% to 85% for both the UK and France.

The last payment of these loans by the UK government was done in 2006. Apparently, the last payment from the French occured in 1962.

  Germany, which up until the 1953 Debt agreement had to work on the assumption that all the Marshall Plan aid was to be repaid, spent its funds very carefully. Payment for Marshall Plan goods, "counterpart funds", were administered by the Reconstruction Credit Institute, which used the funds for loans inside Germany. In the 1953 Debt agreement the amount of Marshall plan aid that Germany was to repay was reduced to less than 1 billion USD. This made the proportion of loans versus grants to Germany similar to that of France and the UK. The final German loan repayment was made in 1971.


Any invention that replaces human labor puts an end to that specific task. Glass recycling eliminates (or decrease) the need for silica-gathering task. Typewriter eliminates the need for printing press typesetter. Etc.

Those people whose tasks are eliminated will get reallocated to their most productive use. This might be in the form of job change (silica miner move to coal miner), or might be in the form of task redefinition (the book Prediction Machines describe how self-driving school bus might shift the main task of a school bus driver to an adult who oversees and "teaches" the schoolchildren.)

Going back to your question, recycling also creates new jobs. They need people to sort bottles, maybe drive a recycling truck, etc. So whether an invention leads to more or less job is ambiguous.

Added: While the effect on a specific industry might be quantifiable, if you take into account job mobility, etc. then the effect on the whole labor market is ambiguous.

Regardless, an invention that increases productivity should increase the size of the pie. We can produce more from the same resources. How that bigger pie is divided, however, is another very important question altogether.


Paper where an integral in the constraint of an optimization problem is treated as infinite sum

Some papers that come to my mind are ;

-Calvo and Obstfeld (1988, Econometrica)

-Endres et al (2014, Resource and Energy Economics)

-Traeger et al. (2012, European Economic Review)

In these papers, the objective function has two integrals but as these models are treating an overlapping generations model, there is a such aggregation that one of the integrals disappears because it is not possible to have an integral on an Hamiltonian. Otherwise, it is not possible to solve it by standard methods.

I am not sure about but this so take it with precaution, this kind of problem with two integrals on the objective function could not be solved by optimal control techniques but by calculus of variation.

There is a very good section about constraints with integrals on textbooks of

-Kamien and Schwarz (Dynamic Optimization : The Calculus of Variations and Optimal Control in Economics and Management)

-A. Seierstad and  K. Sydsæter (Optimal Control Theory with Economic Applications)


Understanding Tertiarization of the Economy

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

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

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

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

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

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


TFP estimation in R by using prodest and estprod packages

You get the error because your ID is string and the prodestLP function has a problem with that here - leading to incorrectly specifying that replacement matrix in this case.
You can solve this issue with:
 DataA$ID<-as.numeric(as.factor( DataA$ID))

once you declare the ID as numeric the code works:
     mod2 = prodest::prodestLP(DataA$va,
+                            fX = DataA$l,
+                            sX = DataA$k,
+                            pX = DataA$m,
+                            idvar = DataA$ID,
+                            timevar = DataA$Year,
+                            opt='optim',
+                            exit = FALSE,
+                            tol = 1e-100)
>
>  omega = prodest::omega(mod2)

with output:
    summary(mod2)

-------------------------------------------------------------
-               Production Function Estimation              -
-------------------------------------------------------------
                   Method :    LP
-------------------------------------------------------------
                               fX1       sX1
Estimated Parameters      :   0.107     0.458
                             (0.012)   (0.052)
-------------------------------------------------------------
N                         :  4397
-------------------------------------------------------------
Bootstrap repetitions     :  20
1st Stage Parameters      :  0.107     0.249
Optimizer                 :  optim
-------------------------------------------------------------
Elapsed Time              :  0.02 mins

-------------------------------------------------------------

summary(omega)
       V1
 Min.   :-3.452
 1st Qu.: 1.428
 Median : 1.842
 Mean   : 1.778
 3rd Qu.: 2.202
 Max.   : 4.492

Update these are the packages I am running and code before the one shown above (also I am running R  version 4.0.2 (2020-06-22)):
rm(list = ls())

Data <- read.csv("~/R studio/excercises in randomness/tfp2/Gmail/LV.csv")

 View(Data)

 pckg<-c("plm","readxl","dplyr","ggplot2", "broom","prodest", "estprod")
 #install.packages(c("plm","readxl","dplyr","ggplot2", "broom","prodest", "estprod"))
 lapply(pckg, require, character.only = TRUE)

 head(Data)

 summary(Data)

 DataA <- Data %>%
         filter(NACE == 'A') %>%
         filter(VA > 0, L > 0, K > 0, M > 0) %>%
         mutate(l = log(L),
                va = log(VA),
                k = log(K),
                m = log(M))


Is the amount of tax that consumers pay the same as the amount producers pay?

Tax is payed by the party it’s levied on, but I think your question is about tax burden and loss of consumer/producer surplus.

In this case both producers and consumers loose the same amount of their surplus, as you can calculate the lost area which is for both of them 40.

However, in real life this does not have to be symmetric. It depends on the elasticity of the demand and supply. As a general rule the more elastic demand the higher share of the tax burden goes on producers and the more elastic supply the higher share of burden is shifted to consumers.


Well I havent read the paper but this is what it looks like to me:

Compute $R_t$ - the rolling average for month t.
$R_t > 0 \Rightarrow  R_{t+} = R_t \wedge R_{t-} = 0$ and$R_t < 0 \Rightarrow  R_{t-} = R_t \wedge R_{t+} = 0$


What institutions are examples of "shadow banking"?

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.


person owns object, loses it and refuses to buy it the second time. Is it really an example of sunk cost fallacy?

I see two questions here. Are all fallacies that are based on sunk cost, sunk cost fallacies? Does the example above describe likely human behavior?

The earliest mentions of the sunk cost fallacy seem to come from the following paper.

  Arkes, H. R., & Blumer, C. (1985), The psychology of sunk costs. Organizational Behavior and Human Decision Processes, 35, 124-140.

The definition given is as follows:

  The sunk cost effect is a maladaptive economic behavior that is manifested in a greater tendency to continue an endeavor once an investment in money, effort, or time has been made.

The loss of an object A is a sunk cost as whether or not you owned A in the past is not relevant to whether you should own it in the future. To be less likely (or more likely) to purchase the object A in the future is irrational behavior (a fallacy) related to sunk cost. However, it isn't clear whether it is a sunk cost fallacy based on the definition above. You could argue that you put effort into not owning the object (by losing it). And thus by continuing to put effort into not owning the object (by not purchasing it again) despite that not being the optimal decision, you are committing the sunk cost fallacy.

A clearer argument is that you put effort into owning the object (by purchasing it once), and thus you are more likely to continue to put effort into owning the object (by repurchasing it) based on the sunk cost fallacy. And this latter argument sounds more likely to me, but I have no evidence to back this up.


Capital Recovery Factor for Hyperbolic Discounting

I'll just expand upon what I've said in the comments as an answer. The sum $$\sum_{t=0}^n \frac{1}{1+rt}$$ will not have a nice closed form. However what wikipedia has done is approximate this sum as an integral. The integral will just be $$\int_{t=0}^n \frac{dt}{1+rt}=\frac1r\ln(1+rt)|_0^n=\frac1r \ln(1+nr)$$ Which is basically what you've got without multiplying by the principle value, and relabelling some variables. Now something to watch out for is that this will be off by a small constant. If you look at the diagram below, there is some error area that the integral fails to pick up, so it will actually be slightly smaller.

In this case however you know the error area is below 1 (because if you imagine sliding each error area into the first square (purely horizontally it will not fill it all up)

 and above one half, (draw a line between the corners of each error area to make a triangle and each triangle is half the area of the corresponding rectangle, so the sum of all the triangles is half the area of the unit square)

So since the error is between 1 and a half, for large n it should be pretty insignificant, and this is a pretty good approximation.


What are some theoretical explanations for deviations from the efficient market hypothesis?

I think this piece by John Cochrane represents a typical defense of the efficient market hypothesis from this kind of critique. Here's another. The basic summary is that market efficiency does not imply that expected returns cannot vary or that bubbles will not happen. Bubbles should be unpredictable, and variation in expected returns should be driven by risk or discount factors. Whether that's the case for the financial crisis is definitely a matter of debate.

Do people believe in efficient markets? I think that varies a lot from field to field. It might be more useful to say that efficient markets are usually the null or prior that academics in finance and economics work with when they try to understand something. That is to say if you want to use some data to try to convince them that financial markets aren't efficient, you face an uphill battle, but the struggle isn't impossible.


which type of goods maximum utility function represent?

$u = \max(x, y)$ represents the preferences over two substitute goods that cannot be consumed together. For example - tea and coffee. In the event that the consumer gets x quantity of tea and y quantity of coffee, consumer choose to consume only one of the them depending on the quantity. He always choose the one that is offered in larger quantity and throws the one that is offered in smaller quantity.


Why doesn't stock market help to boost the economic growth directly?

First there are some inaccuracies in your question.

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

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

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

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


Economics' position in the hierarchy of sciences (hard vs soft)

There is actually no clear cut consensus on where Economics belongs (although it is fair to say most would likely put it into category of social science). Some authors consider it to be science, some social science, some even moral science, and some even argue it should have its own category.  A good paper that tries to answer this question for economics is  Hudson (2017).
According to the author:

Is economics a science or a social science? Arguments have been made for both orientations, i.e. that economics is a social science (Frey 1999), a science (Frey 1999) and even a moral science (Schabas 2009). In terms of sciences it has been linked with physics, with many physicists doubling as, or transforming into, economists and a subpart of physics, econophysics, specifically evolving which deals with economics (Stanley et al. 1999). There are also links with biology (Marshall 1920; Daly 1968). Frey (1999) argues economics is a social science as it is part of those sciences which deal with actual problems of society, i.e. it is the subject matter which makes it a social science. However, he also points out that in practice economists tend to fill the journals with axioms, lemmas and proofs, i.e. they adopt what they perceive as a scientific, and particularly a mathematical, methodology. Mayer (1980) argues that economists act as though economics is a hard science and this is reflected by their sophisticated use of mathematics. However, he then goes on to argue that econometrics is not sufficiently advanced to enable us to test theories as a hard scientist would.

The literature review above is good place to find out the different views on what economics is. In addition the paper itself is not just a literature review but also itself tries to answer the question by examining how similar economics is to other fields. Hudson (2017) further concludes:

With respect to the question posed in the title of this paper, our view, in part informed by these results, is that the subject matter of economics places it clearly as a social science, but many in the discipline act as if it were a science. Economics has gradually developed into an interdisciplinary subject that uses scientific methods, for example setting out and formally testing hypotheses, and particularly a mathematical approach, to solve social science problems. This dual aspect may explain why it fails to fit neatly with either as in fact it combines elements of both. It is a social science pursued with more quantitative rigour than much of the rest of the social sciences. This emphasis on technique then pushes economics and economists away from the other social sciences and in some sub-disciplines towards maths. Placing economics as a science, emphasises technique above subject matter. But there is then a danger that technique becomes an end in its own right, rather than a means to an end, i.e. a vehicle which allows a more refined analysis of economic issues which have wider relevance. Often, for example when developing a new econometric technique which subsequently becomes widely used, this is justified. But sometimes this is not the case, which helps explain the relative isolation of the discipline as noted earlier. This does not mean that economists should abandon their quantitative focus, but that they should always strive to ensure that their work contributes, directly or indirectly, to an understanding of a real world issue. This is consistent with Frey’s (1999) observation that economics is part of those sciences which deal with actual problems of society, but that most economists attempt to imitate the sciences and that economics can be regarded as a branch of applied mathematics. It is also consistent with the view that that economics, particularly neoclassical economics, is the most mathematical of the social sciences (Porter 1996).

However, I would not take the above conclusion immediately at face value (author also cautions against that) since the cluster analysis done there could not take into account everything what you would ideally want to and it focused only on research in one country (UK). As you can see since this is still being debated and articles about this published in 2017 this is still not completely settled question (although to be fair most would likely classify it as a social science). Also, as noted in the excerpts above the issue is that economics is quite close to the border between social and hard sciences (some authors say it is social science that acts like hard science or draw parallels with biology) making it difficult to classify.

PS: Actually the Comte's 19th century idea of 'hierarchy of the sciences' is problematic in itself.  The problem is that a field on its own cannot be neatly put into such hierarchy because it consists of many sub-fields that are heterogenous. For example, when it comes to fields like game theory economics can run lab experiments while in astrophysics researchers have to rely almost solely on observational data.
Consequently, once you break fields into sub-fields you will find that subfields from various fields can be on top of the hierarchy while other subfields from the same fields can end up at the bottom.


Bananas and oranges in communist countries

there actually were some bananas in communist countries. There was just shortage of bananas and other products as well such as toilet paper etc.

As this article from Financial Times shows, there actually were some bananas in East Germany.

  Near the queue, locals were doling out used toys and bananas (the West Germans believed the East Germans didn’t know what bananas were). “But we had bananas from Cuba,” Meinfelder says in exasperation.

So there were bananas in communist countries but there was a shortage of them, and as with other products their availability for you dependent on your contacts and what (political) class you were member of (shopkeepers would often set aside high in demand products for friends). Prominent members of party had access to things ordinary people not in special shops reserved for them and so on.

Why there was a shortage of bananas?

Because, centrally planned economies are very inefficient when it comes to aggregating the information about what consumers want compared to market economies which aggregate the information using price system. Moreover, price system provides not just information to market participants but also gives them incentives to behave in a way to avoid surpluses and shortages on the market, whereas in the centrally planed economies there are no efficient mechanisms to achieve that.

For example, central planners might decide that the quantity of bananas they want to import should be some $x$ based on their calculation of how much bananas an average person could eat in a year. Afterwards, the central planners decide on price not in a way which they think the supply equates the demand (and in fact central planners are even not able to get such information since market mechanism is absent - so they cant do that even if they would wanted), but in a way they believe it is appropriate by making guesses or following some political/ideological/moral criteria.

For example, if a demand for bananas is given by $D_{b} = 100- p $, where $p$ is the price,  and supply of bananas is given by $ S_b= -10 + p$ (lets say this is the supply at which Cubans are wiling to send bananas to East Germany) then at a market price $p=45$ there will not be any shortage of bananas. At price $\$55$ people will demand exactly $45= D_b$ bananas and supply of bananas will also be exactly $45 = S_b$.

But if someone just arbitrarily decides to set price to $\$20$ - maybe the political leadership wants to make bananas affordable to everyone, the demand for bananas at $\$20$ will be $80 = D_b(\$20)$ while the Cubans will only be willing to supply $10$ bananas $S_b(\$10) = 10$. Hence people will want to buy 80 bananas but stores will only have 10 and there will be shortage. During shortages goods are often being allocated through personal favors, or first come first served system, or goods might be reserved for members of 'upper class' (i.e. politburo) and so on. This is why many communist countries experienced long ques shortages and economic malaise in general.


Why would the economy return to equilibrium at full employment after a supply side shock?

I guess it depends on the model you are considering, but in the basic AS-AD model it should happen via adjustment in the labour market: if $Y_t > \bar{Y}$, then there will be upward pressure on the nominal wages (employment is higher than equilibrium employment, therefore workers ask for higher wages), to which firms respond by increasing prices, inducing an increase in inflation. As inflation expectations adjust, the SRAS shifts leftward. The adjustment stops when workers' real wage demands are met by firms (which is, when inflation expectations are realised) and output is back at $\bar{Y}$.


Competition between utilities like ports

In America, on the West coast, unions negotiate a common contract:

  Ironically, the International Longshore and Warehouse Union is a
  beneficiary of the same forces that are killing unions everywhere
  else: Its workers are the folks who unload the stuff that comes in
  from abroad. Those workers are sitting right at the bottleneck through
  which all that foreign competition flows to the U.S., and due to some
  smart planning by the union in earlier decades -- such as insisting
  that the West Coast ports would bargain as a bloc so that they can't
  play different locals against each other -- they can cork that
  bottle anytime they want. That gives them the ability to extract a
  little tariff on all that trade. Their rake-off is a tiny fraction of
  the overall flows, but that still translates into substantial sums for
  the few thousand workers who are holding onto that cork. The more
  trade, the better the concessions the ILWU is able to extract -- and
  the worse workers in other unions do.

Where Have All Our Wages Gone? by Megan Mcardle

There used to be a pre-anti-trust era railroad cartel in the USA:

  The [Joint Executive Committee (JEC)] was a cartel formed by the
  railroads which controlled eastbound freight shipments from Chicago to
  the Atlantic seaboard in the  I  88os. The agreement was publicly
  acknowledged, as it preceded the passage of the Sherman Act (1890)
  and the formation of the Interstate Commerce Commission (1887). ...
  The JEC cartel agreement took the form of market share allotments
  rather than absolute amounts of quantity shipped. Firms set their
  rates individually, and the JEC office took weekly accounts so that
  each railroad could see the total amount transported. Total demand was
  quite variable, and the actual market share of any particular firm
  depended on both the prices charged by all the firms and unpredictable
  stochastic forces.

On the Incidence and Duration of Price Wars (Porter (1985))


When the Fed increases the money supply, does any of the additional supply go directly to the government?

The answer to this question is maybe (but most likely not).

The most common method central banks use to increase money supply (assuming they control their own monetary policy) is through open market operations. Open market operations is when the central bank purchases or sells treasuries in the secondary market (typically). The answer to your question depends on where the central bank buys the treasuries.

If the central bank uses an open market purchase of treasuries in the secondary market, then the money goes to the entities which sold them the treasuries, so none of the money would go directly to the government. However, hypothetically in some countries where corruption is prominent, there may be a situation where the government forces the central bank to purchase treasuries in the primary market (directly from the government). In this situation, all of the money that is being pumped into the economy would go directly to the government.


Nominal GDP is often more quoted in media and in politics than the GDP in PPP, but that doesn't make it be less important. In fact, as stated by 1muflon1 on the comments, economists typically like to measure differences between comparable things, so when comparing GDPs there are usual corrections done on purchasing power parity, as well as inflation.

The PPP indicator has been present in literature for a long time, mentioned in the early 1500's, and translated to modern terms since 1918. It's regularly calculated by international bodies (such as the UN under it's International Comparison Programme).

The GDP PPP is also regularly used in real life by institutions such as the OECD, IMF and World Bank to make recommendations on economic policy, and by traders to better assess when stocks and currencies might be under- or over-valued. This article on investopedia provides a concise overview.


This is extremely common in institutional markets, and is called a "repo" transaction - short for Repurchase agreement

In a repo transaction, you "sell" the bond to the bank and agree to buy it back again at a fixed price in the future (regardless what the actual market price may be).  This is the same business model as pawnbroking.  If you fail to buy the bond back, the bank gets to keep the bond.  The reason it is done as this sale-and-repurchase, rather than collateral (which is economically identical) is that it makes handling a default much simpler.  If you default on a collateralised loan, the lender still has to apply to take full ownership of the collateral, which can delay matters (such as under chapter 11 protection).  In a repo transaction, the bank already legally owns the bond and has it in custody, so it is much simpler.  It is worth noting, that although they have bought the bond from you the repo agreement (GMRA - "General Master Repo Agreement") specifies that the original owner retails "full economic interest" in the bond - that is they get any interest payments from the original bond.

That said, this is most commonly done for Treasury bonds in highly rated countries (US, UK, Germany etc.).  Since the bond is collateral for the loan banks are less keen to lend you for bonds that are risky, as should the collateral become worthless, then the loan becomes unsecured.  For this reason repo transactions in EM bonds or Corporate Bonds tend to have a significant "haircut".  The haircut is the difference between the value of the bond and the amount borrowed.  So in your example, a repo transaction of a poor country bond the bank may take a 20% haircut, so to buy \$10m of the bond, you would borrow \$8m and pay for \$2m yourself.  The logic here is the same as when you mortgage your house, the bank won't usually lend you the full value of the house.

As you might have guessed from my example using millions, repo transactions are done between banks and institutional investors, not the man-on-the-street.

For extensive details see: ICMA Guide to Best Practice in Repo


Devising a model for inflation for a closed points system

If your points are exchangable for rewards, the fundamental value of the points is entirely driven by the exchange rate between points and the rewards. (People may value the points more or less than the fundamental value for any number of reasons.)

This means that the inflation rate is entirely driven by the administered exchange rate - up until the point the program runs out of rewards. If you want to prevent the possibility of running out of rewards, the total supply of points must be held less than the redemption value.

This is similar to the operation of a gold standard. In the classical gold standard, a country’s currency (in principle) is exchangeable at a fixed rate against gold. (In practice, the implementation of gold standards changed over time.) You should be able to find a lot of resources on gold standard systems.

If you have a fixed supply of rewards, and you want to keep the exchange rate stable, you would need to find a way to drain points from the system - a tax.

In terms of motivating people, the major question is the value of the rewards. If people don’t want your rewards, your points will have little value.


There is a potential conflict of interest (not only for a chairman but also for any director or employee who owns shares in the company) arising from the possibility of insider trading.  Suppose the chairman of a quoted company has a large shareholding and, through their position, becomes aware of information, not yet disclosed to the market, that means the company's prospects are not as good as previously believed.  They might then want to sell shares immediately, rather than waiting until the information has been disclosed and as a result the share price has fallen.

Since directors including chairmen are supposed to act in the interests of the company and its body of shareholders, there are two possible conflicts here.  Firstly, by focussing on whether to sell their own shares and arrangements for doing so, a chairman might neglect their duties to the company at a critical time for it.  Secondly, the selling of a large block of shares would tend to depress the share price to the detriment of other shareholders.

This is not to say that a chairman should not hold shares. A relatively small shareholding would be unlikely to give rise to a serious conflict of interest. In many countries (see here) the issue has to some extent been addressed by making insider trading illegal (although the detailed rules differ between countries).


Can the Machina Paradox be solved by expanding the choice set?

No, I would not say that this resolves the Machina paradox, because it is exactly the same as the Machina paradox: the paradox does indeed require from you to look at the three possible outcomes. The M-C/W/G book discuss only the $B$ and $C$ outcomes because it is there where the paradox focuses on whether a violation of the axiom of independence may happen.

But most importantly, Machina did not argue that all people will have preference ordering $A>C>B$. He argued that it is reasonable, for evident psychological reasons, to expect that some people may... So some others will have the ordering $A>B>C$, which does conform to expected utility framework.

The first will say "I cannot watch a movie about Paris after losing the trip - I will smash the TV!" The second will say "Well, tough luck. At least I will see it on screen and keep dreaming about it". Both seem like behaviors that could be anticipated by "usual" human beings.

The point of the paradox is not to show that Expected Utility (EU) is invalid for all people -only that it may be violated in reasonable situations, i.e. situations that may characterize a lot of people and may happen often.

What paradoxes like this examine and contemplate, is the degree to which EU represents adequately the "majority" of people in some sense, and so whether it is valid/useful/not-misleading as a core theoretical assumption in economic models, or not.
And this is a matter of degree, a quantitative matter. This is true for almost all assumptions in theoretical models in social sciences.