The grey-haired "Quantity Theory of Money" is a good initial way to gain some clear understanding for inflation. This theory is just one equation,

$$PQ = VM$$
where

$P$ is the price level, $Q$ is quantity produced, $M$ is money supply, and $V$ is "velocity of money", which represents how "fast" money circulate, given the transactional technology and other institutional aspects of an economy. For example, in an economy where bank branches are interconnected by a real-time on-line system, money circulates faster compared to an economy where bank branches are interconnected only through, say, telegraph, which in turn move money faster compared to an economy where banks are not interconnected at all, and money has to move physically from one person to another.

Assume that we produce $Q=10$ pieces each at a price of $P=15$ kudos. Do we need $10 \times 15 = 150$ kudos to complete all buy-and-sell transactions? No. If velocity of money is, say $V=3$, we only need $M=50$ kudos to facilitate all transactions, because money circulates "three times around" (before the next production cycle is completed).

Now, in standard economic theory, economies are close to "full employment level of production factors" (which may allow for friction unemployment of humans, machines etc).

Now, assume we increase the money supply to $M=100$. The right-hand-side of the equation becomes $VM = 3 \times 100 = 300$. What happens to the left-hand-side? Well, since production cannot increase (because all available production factors are already employed), it has to be the Price level that will increase to $P=30 \implies PQ = 30 \times 10 = 300$.

Intuitively, buyers with more money in their hands will increase their demand (the demand schedule will shift rightwards in a diagrammatic representation), but supply won't change, because it cannot change. Suppliers will increase their prices since there is now "competition among buyers". Hence, inflation.

This is the most simple explanation about how increasing the quantity of money in a full-employment situation, will create inflation.


How can I estimate the disconnect between book value and market capitalisation?

The context of the question is analysis of the plans of the company, the market price, and the book value.
Primary investors provide cash or other resources to the company in exchange for original debt or equity claims against the assets of the company. The company is expected to purchase assets with the cash as it executes the business plan. Secondary investors purchase the debt or equity claims from a primary investor so the company does not get any cash from these secondary transactions. The question is how to estimate the disconnect between market capitalization and book value.
Understanding Price-to-Book Ratio:
https://www.thebalance.com/fundamental-analysis-understanding-price-to-book-ratio-3140794
The calculation of book value:

(Assets - Liabilities)

Ongoing, financially-sound companies will always trade for more than their book value because investors price the stock based, in part, on their anticipation of the firm's future growth.

The Affordable Growth Rate (AGR) is a formula appearing in the book 101 Business Ratios by Sheldon Gates. According to Gates the formula was used by Hewlett Packard. This article describes AGR

https://www.inc.com/magazine/19861201/9293.html

The AGR is a growth strategy based on two assumptions. The first is that your sales can grow only as fast as your assets. If yours is like most firms, for example, you can't increase your sales by 30% unless you increase your receivables, your inventories, and your fixed assets by about 30% as well. The second assumption is that your firm has a target debt-to-equity ratio and that your lenders are willing to continue to extend credit at that ratio. This assumption implies that as your equity grows, debt can grow at the same rate, allowing you to maintain a constant debt-to-equity ratio.

The sources of cash to grow assets, and therefore sustain sales growth, is debt, equity, and retained earnings. When a firm is taking venture risk the future cash flows in the form of retained earnings are not expected to be sufficient to cover the growth of assets in support of sales growth. When a firm is throwing off cash it has high retained earnings or profit that can also be used to pay dividends. There is another book called The Cash Flow Problem Solver, by Bryan E. Milling, which describes in detail how a company can grow too fast and cause a cash flow crisis that results in bankruptcy.
There is no direct link between market capitalization and book value because market capitalization is the last sale of one or more shares of stock in a secondary market transaction based on the desire of the buyer to own shares at that price and the seller to own cash rather than shares at that price. The market capitalization contains a liquidity premium if the shares are relatively easy to buy and sell on the secondary market and a growth or discount factor, based on expected future events, so there is a disconnect between market capitalization and book value.
If the firm is expected to remain a going concern and grow assets, sales, and profits in the future, especially after reaching cash flow break-even following new injections of debt or equity, and if it can grow from internal finance of retained earnings from operations after getting past cash flow break-even, then there is a premium in the share price above book value. There is no particular formula for evaluating the plans, asset position, debt and equity claims of a company, and there is no particular formula to forecast future sales, profits, and retained earnings, and there is no particular way to put a premium or discount factor on the share position, so there is no particular way to link market capitalization to book value.


Confirmation bias is somewhat different to the behavior you are describing. This expression describes the attitude of a researcher who interprets ambiguous data as confirming his initial hypothesis. For instance, researchers who believe that death penalty has a deterrent effect on crime would interpret any additional dataset as confirming this theory, whereas researchers who believe the opposite would interpret the same evidence as indicating that the effect is null.

The behavior that you describe might be called "post hoc analysis" or "post hoc theorizing". Scientific standards in experimental economics have been  improving recently to mitigate this bias (among other mistakes/misbehavior). For instance, many researchers who do randomized controlled trials in development economics now pre-register their analysis plan (and even sometimes a theory with its predictions) before collecting the data: by doing so, they commit to a list of statistical tests that they will run, which prevents them from changing their theory/hypotheses (and even the question of interest) after looking at the data. Of course, as @denesp mentions, this cannot generally be done with observational data, except maybe in situations where the researchers need to go through an approval procedure to get access to the data, in which case a pre-registration of the analysis plan might be imposed as part of the application.


Trembling hand perfection and weakly dominated strategies

A trembling hand perfect (THP) equilibrium may not survive iterated deletion of weakly dominated strategies, as is shown by the following example. Let game $G$ be

\begin{array}{|c|c|c|c|}\hline
&A&B&C\\\hline
A&0,0&0,0&0,-2\\\hline
B&0,0&1,1&-1,-2\\\hline
C&-2,0&-2,-1&-2,-2\\\hline
\end{array}

There are two pure strategy NEs: $(A,A)$ and $(B,B)$, with the former involving iteratively weakly dominated strategies. And yet $(A,A)$ is a THP equilibrium. To see this, consider the following sequence of totally mixed strategies
\begin{equation}
\sigma_i^k=\left(1-\epsilon^{-2k}-\epsilon^{-k},\epsilon^{-2k},\epsilon^{-k}\right),\qquad i\in\{1,2\} \text{ and }\epsilon>2,
\end{equation}
which converges to $(1,0,0)=A$ as $k\to\infty$. It is easy to verify that, for any $k$, the best response of player $j\ne i$ to $\sigma_i^k$ is $A$:
\begin{align}
u_j(A,\sigma_i^k)&=0 \\
u_j(B,\sigma_i^k)&=\epsilon^{-2k}-\epsilon^{-k}<0 \\
u_j(C,\sigma_i^k)&=-2<0.
\end{align}
Therefore, $(A,A)$ is THP.

However, the game $G'$ that survives iterated deletion of weakly dominated strategies does not contain the strategy $A$ for either player. Hence, the THP equilibrium $(A,A)$ of the original game $G$ is not preserved in game $G'$.


Do policy functions exist for Finite Horizon Dynamic programming problems?

No, they cannot by definition.
To derive a time-invariant policy function, you need to have an infinite horizon problem. This is because the structure of the solution remains the same, no matter when you look at it. Intuitively, this is because any sequence of periods from any time period to infinity looks the same. The technical conditions for this can be found in a number of textbooks (Adda and Cooper, Sargent, as well as Stokey/Lucas).

In your example, the number of periods left determine the solution structure.


Are there theories that invalidate the "tragedy of the commons"?

As you implied, the tragedy of the commons was the standard theory in Economics. This is no longer the case. However--and this is an important point--rejection of this one-size-fits-all approach to public resource management did not come from the emergence of new theories; rather, it resulted from actually studying real-world outcomes. In fact, it's for her work doing exactly this that Elinor Ostrom won the Nobel Prize in Economics. As described by the Nobel committee:

  [B]ased on numerous empirical studies of natural-resource management, Elinor Ostrom has concluded that common property is often surprisingly well managed. Thus, the standard theoretical argument against common property is overly simplistic. It neglects the fact that users themselves can both create and enforce rules that mitigate overexploitation. The standard argument also neglects the practical difficulties associated with privatization and government regulation.

Since these case studies there has been theoretical work--some of it by Ostrom herself--in order to reconcile the discrepancies between the previous theory and the observed outcomes (developed using the theory of repeated games in Non-Cooperative Game Theory).

However, what's most interesting to me is that this theory was rooted in actual observations and not the other way around (i.e. first the theorized behavior followed by real-life observations).

Did this answer your question?


Correlation over time, panel data variable

The answer (if I understand your question correctly) is a dynamic panel data model. In such models, one expresses the DGP as follows: $$y_{it}=\rho y_{it-1}+x_{it}'\beta+\alpha_{i}+u_{it}$$
 This has been studied extensively for the past 20 years.
Some classic estimators are:

a) Arellano-Bond estimator
 b) Anderson-Hsiao estimator and
c) Arellano-Bover systems GMM estimator.

I would suggest that you go with the 3rd option.  I think this one is the latest+most robust estimator. You can verify the statement. Each of these methods deals with an alternative way of consistently estimating $\rho$ by using instruments (or systems of instruments).


Monopoly: Demand Curve and Marginal Revenue Curve Intercepts

Your marginal revenue is not calculated correctly. Marginal revenue $(MR)$ is the derivate of total revenue which is equal price times quantity $TR=PQ$.
In your case $TR$ should be:
$$TR=(k+aQ)Q \implies MR = \frac{dTR}{dQ} = k+2aQ$$
If the demand is given as: $P = 120−2Q$ then:
$$TR= (120-2Q)Q \implies MR = \frac{dTR}{dQ} = 120-4Q $$
Also made a graph for you by simulating the $MR$ (red) and demand (blue) in R


There is a long tradition of using flexible functional forms for cost, utility or production functions. This can be done using a (low) order series expansion. Usually, these are Taylor expansions. For example the translog is a second order polynomial in log prices.
Of course, one could also use a Fourier expansion, which would give a function in terms of cosine and sine functions.
See for example the appendix of Griffin, Montgomery, Rister,(1987) "Selecting Functional Form In Production Function Analysis," Western Journal of Agricultural Economics


Is there a definitive way to tell if an action causes a movement or shift in a supply-demand graph?

The supply and demand curves are plotted as functions of price. Hence:

Changes in price will result in movements.
Changes in anything else will result in shifts.


How was the CES production function derived?

The CES function can be derived directly from the condition of constant elasticity of substitution.  There are various ways to do this, but the simplest derivation occurs for a homothetic production function.  Suppose we start with a homothetic production function $Q = f^*(K, L)$ and we rewrite this in intensive form as:

$$\begin{matrix} q = f(k) & & q \equiv Q/L & & k \equiv K/L. \end{matrix}$$

For this case the elasticity of substitution $s$ can be shown to be:

$$s = - \frac{f'(k)(f(k) - kf'(k))}{kf(k)f''(k)}.$$

Letting $r \equiv (s-1)/s$ and re-arranging this equation gives the second-order differential equation:

$$\frac{kf(k)f''(k)}{1-r} + f'(k)(f(k) - kf'(k)) = 0.$$

This equation has general solution $q = f(k) =  c_0 (1 + c_1 k^r)^{1/r}$ where $c_0$ and $c_1$ are constants.  Parameterising with $a \equiv c_1$ and $F \equiv c_0 \cdot c_1^{1/r}$ and substituting to obtain the extensive form gives:

$$\begin{equation} \begin{aligned}
Q = Lq = Lf(K/L) &= c_0 L \left( \left( 1 + c_1 \frac{K}{L} \right)^r \right)^{1/r} \\
&= c_0 \left(c_1 K^r + L^r \right)^{1/r} \\
&= F \left(a K^r + (1-a) L^r \right)^{1/r}.
\end{aligned} \end{equation}$$

The parameter $a$ can be interpreted as the capital intensity in production and the parameter $F$ can be interpreted as the overall efficiency of production.


Why can't goverments print money to fund their economies?

The first thing to be aware of is that money is continuously being created and destroyed through the process of fractional reserve banking (which according to the Bank of England and others is incorrectly explained in most textbooks). Under this system there can be periods in which, in the absence of central bank intervention, there will be a fall in the money supply and deflation. In these periods there would be little risk of inflation if the government printed money for whatever purpose they liked. Indeed some economists have advocated direct money printing instead of QE.

With regard to the idea that creating money for productive purposes causes less inflation because more is produced - I know that this is something that Prof. Richard Werner has emphasised in the past, though I don't have a specific reference for that to hand.


What statistics and linear algebra book do i need before reading Hayashi's econometrics

The Linear algebra part should not worry you, it is just basic linear algebra plus familiarizing yourself a bit with differentiation of vectors and matrices (and for some chapters, visualizing the Kronecker product).  Hayashi goes some length into writing out explicitly large matrices, which is virtually with no-precedent (see eg. pages 267, or 288), something that eventually facilitates understanding -as long as you don't back out from a matrix half a page large, but you really look at it.

What you should really go slow over upon is Hayashi's notation, which is non-standard in many places. So don't expect to understand through familiar notation. Be prepared for that and "read" carefully every symbol and its role. Many people's discomfort with this book is due to the notation, but they don't realize it.

As for the Statistics part: In Econometrics, since we deal almost always with non-experimental, observational data, a large part of Statistics (originating usually in Biostatistics) do not really enter (our) picture. For example, apart from proving that under certain conditions the OLS estimator is best linear unbiased, you won't see much regarding the issues of minimum variance estimation or sufficient statistics. We don't even discuss the Exponential Family of distributions and the concept of Generalized Linear Models. Also, in statistical Hypothesis testing the Fisherian spirit prevails (oozing through the Neyman-Pearson apparatus), meaning, among other things, that issues like the "power of the test" are not so often considered.

Moreover "frequentist Econometrics", which is what Hayashi presents, are considerably lighter than Bayesian Econometrics in terms of the Algebra of Random Variables and probability theory.

What really matters is a good familiarity with basic Asymptotic Theory and Stochastic Processes (for the Time Series part). Although Hayashi in most cases just states results, providing references for the proofs, nevertheless it would be good to feel comfortable with asymptotic results and properties, because in most cases, it will be all your estimators will possess. For this part, I will once more advocate A. Spanos' book, Probability Theory and Statistical Inference - Econometric Modeling with Observational Data. It is a valuable book, Hayashi or not Hayashi. It is Statistics with the Econometrics graduate student in mind.

In case you want some more specific Time Series material, Hamilton's Time Series Analysis remains a standard reference.

Finally, regarding Unit-root Econometrics and Co-Integration, the subject is inherently advanced, and I think Hayashi has done a good job in collecting and presenting the very basics.


Any major theory/model that considers return due to idiosyncratic risk?

There are no major models that come to the conclusion that idiosyncratic risk can drive positive returns. The reason is that idiosyncratic risk is diversifiable. The models, however, do in fact consider idiosyncractic risk. The theories don't forget or ignore them. It just turns out that this risk doesn't matter.

In this sense, CAPM actually does consider idiosyncratic risk. In this model, if you are perfectly rational, you will diversify your portfolio to minimize risk. This leads you to hold the whole market portfolio, in which case idiosyncratic risks are diversified away in your portfolio and therefore no longer matter. In simple terms, market risk then is not diversifiable, because once you hold the market portfolio, there's no way to diversify further. What drives returns are risk, but rational investors can remove the idiosyncratic risk through diversification. Hence, what matters for returns in the CAPM therefore is just the market risk (which you refered to as systemic risk, but that term actually means something else). That's why under CAPM, the returns are driven by the asset correlation with the market.

EDIT:

The CAPM model does not put any explicit assumptions on the number of assets available, hence the model does not require an infinite number of assets. However, the derivation is based on the decision to add an asset to an already well-diversified portfolio, i.e. adding an asset to the market portfolio.

Nevertheless, if only a handful of assets exist, then it might not be possible to diversify away all idiosyncratic risk. In that case, the CAPM does not work, because it implicity assumes enough assets exist, since it assumes a well-diversified portfolio exists to which you can add an asset. In such a case idiosyncratic risk may become relevant.

Such considerations are unlikely to be relevant in practice though. It is difficult to put a number on how many assets are necessary for idiosyncratic risk to be diversified away completely. Often, a number that is mentioned is 30-40 assets. The number required in practice is usually very realistic and far below infinity. The number of assets required for idiosyncratic risk to be completely diversified away becomes larger if assets are more correlated with each other or very volatile.

Lastly, an asset with such high idiosyncratic risk that no investor would want to add it to their portfolio cannot exist in equilibrium, because supply of the asset could never equal demand.


Find utility function given indifference curve?

VCG's comment about isolating $k$ is the correct approach.

Given $U(\cdot) = k$ and
$$z = \frac{k^\frac{1}{\delta}}{x^\frac{\alpha}{\delta}y^\frac{\beta}{\delta}}$$
raise each side to the $\delta$ power:
$$z^\delta = \frac{k}{x^\alpha y^\beta}$$
and isolate $k$
$$k = x^\alpha y^\beta z^\delta$$

Since $k$ is now a function of each of the goods in your equation, it makes sense as a function form for utility.

$$U(x, y, z) = x^\alpha y^\beta z^\delta$$
So we arrive at the Cobb-Douglass utility form.


This feels like trying to read your mind, so I’m probably wrong. I will venture an answer regardless :D . I think that what is happening is that the benefit from buying the insurance is certainly the reduction in exposure: A-C. However maybe you are thinking about the remaining exposure after buying the insurance, in that case it is (A-C) + B. So I think you are thinking about the total costs after buying insurance while the question was asking about the change in costs. I prefer the term exposure, but I thought that using your terms will make the exposition  clear.

P.S. I hope it is understood that we are not literally adding costs, since they occur in different states of the world, but rather using it as a short hand notation to focus on the relevant issues.


Why are Big Macs supposed to cost the same around the world?

Because of the Law of One Price, identical products are supposed to cost the same in different places. Since McDonald's applies standards for all the individual franchisees, the product is supposed to be identical even if it isn't perfectly identical. The law assumes there are no transportation costs. If lower costs exist in one place and there are no transportation costs you would move enough product until costs equalize. When the costs equalize the product price can equalize. This is not realistic for perishable products. The problems with this "law" are described in the limitations secton of the Big Mac Index entry in wikipedia.


I strongly suspect that an emerging important area for applications of measure theory will be in approximate dynamic programming techniques. Approximate dynamic programming (aka "reinforcement learning" in the computer science literature) has been the direction of research work in the last ~10-20 years of the dynamic programming literature. Economics is only just now starting to adopt some of these advances. For example of the direction of the DP literature, see Bertsekas' most recent 4th edition expansion of his dynamic programming series, or Powell's Approximate DP: Solving the Curse of Dimensionality. Economists are just starting to pick up some of these tools, both directly and indirectly, and I suspect that they will have a growing impact on the literature over the next few years. Some of the analytical background for convergence of these methods is topology and dynamical systems.

A good example of theoretical contribution to this type of literature from economists is Pál and Stachurski (2013), Fitted Value Function Iteration With Probability One Contractions (ungated version here). Peruse that paper and you can see the importance of a good grasp of measure theory. Stachurski's book Economic Dynamics is actually a very nice exposition of dynamic programming from this perspective, building at a pace which works for multiple levels of graduate student/professional (measure theory comes in formally at the end I believe -- I'm still working towards those insights).

Hopefully this answers your question to some degree. I'm afraid that the phrase "post-1960s mathematics" is somewhat ambiguous to me (due to my own lack of knowledge of history of maths literature), so if I've completely missed the mark, my apologies!


The argument is correct

Social Mobility and Income Inequality are simply two distinct phenomenons. Mobility is arguably the more complex one, and there are many different ways to define it. As an example, absolute mobility refers to someone earning more income in absolute terms (\$ per year), while relative mobility refers to someone earning more in relative terms (going from the 60th to the 70th percentile of the income distribution). Note that the latter could occur for constant personal income, if income of all others decline. Another major distinction is made between inter- and intra- generational mobility. I would attribute part of the reason mobility is not featured often in political discource to the ambigiuous meaning of the concept. Related to this, there is no generally accepted single indicator (like the Gini coefficient for income inequality) by which mobility could be measured.

The second reason is that measuring mobility requires repeated observations of income distributions for the same individuals, ideally over a long period of time. These kind of data are still rather rare and not available for all countries in the required quality.

The scenario you have in mind ("the guy is not poor because he is likely going to earn a lot") is essentially a prospective task where one would estimate future earnings paths. While this can be done in principle, the precision of such studies are far below e.g. a detailed analysis on poverty ratios for various demographic groups.

Summing up, measuring income inequality ignores the movement of individuals between two points in time, which should be kept in mind when talking about income inequality. Povery is much more a problem if it's not a transitory, but a permanent phenomenon from an individual perspective.


Effect of today's decision in the US to no longer mandate contraception coverage

There are different arguments here, depending on the points of view of the government and the insurance providers. I'm trying to answer to the general question on the title.

Insurance providers aim at minimizing their costs with healthcare and the probability of health issues. Free birth control not only prevents unwanted pregnancy, but might also have other health benefits. This prevention would save insurance providers from the costs of unwanted pregnancy, which are not only the birth but also psychological costs. I am not aware of any studies that would compare both situations. Insurance providers could benefit from this measure if they know that women will buy the birth control anyways, so the insurer free rides on the benefits of the pill.

The government should try to maximize the "society's profit" or well being, coming from healthcare, but also from other aspects like the fulfillment of values. The logic is to balance the "harm" inflicted by this policy to some groups (say, some religious citizens could say they feel bad for living with these policies) and the losses in profit inflicted to insurance providers or employers, with the potential benefits to society. The book Freakonomics makes an interesting correlation with approving abortion and reducing crime in New York, which could be an argument to give it for free (social benefit of less crime). Note that the argument was later refuted in The Economist, but might still be used by some people who only read the book.

Who could benefit from this change in policy, besides what is mentioned above (my own opinion, discussable)

Pharma industry, with people choosing more expensive pills when they are not covered by the insurer
Religious groups and anyone who disagrees with the concept of free birth control
President Trump, by gaining more approval from these groups
(Far fetched) Hospitals and doctors who could increase their services


What's the significance of the triangular region for calculating the deadweight loss?

I suspect your chart could look more like this:

Initially with the price and quantity at E, the combined surplus is the triangle to the left (between the orange line and the lower green line to the left of E, i.e. the pink and grey areas).

But with for example a tax, the new equilibrium has consumers paying the price at C, so the new combined surplus is still between the orange line and the lower green line, but only to the left of C (i.e. the pink area).

So the deadweight loss is the triangle CEF (i.e. the grey area) which is the loss in surplus associated with the reduced quantity.  If all three lines are straight, and the green lines are parallel then this is the same area as the triangle CDE, but not necessarily otherwise.


How do I calculate the cost per usage of a machine?

Correct approach: there is reliable information (from the vendor and/or from past experience), that the machine can perform $T$ number of tests in total before being scrapped or taken out of service. Then the cost of the machine per se allocated to the execution of one test is $10.000 / T$.

In the OP's case, a straight-line depreciation method is applied, writing-off $2.000$ per year. The problem here in the calculation $2.000/T_i$ for year $i$, is that next year, if the number of tests is more/less, one will get a different cost allocation of the value of the machine on a single test -and it will be misleading. So for economic-costing purposes this is not advised. But for purposes of reconciliation with accounting practice year-by-year, then one could accept the artificial variation, if one cannot apply the correct approach.

A mitigating approach, if historical data exist, is to take "average yearly tests performed", and divide $2.000$ with this average.


How does migration facilitate specialisation?

Workers may have different skills. If immigrant workers are good at farming then domestic workers can shift into non-farming activities.
Workers increase the total population and larger populations can sustain greater specialization. For example, with enough people we can have an artisanal pencil sharpener and professional crossword puzzle maker but a smaller population couldn't sustain that as a career.
Migrants tastes may differ from domestics and domestics may develop businesses to address these tastes. For example, bidets are not common in the United States but Kohler, an American toilet manufacturer, is happy to have its workers make them for immigrants that enjoy them.


Transitional Dynamics of consumption per capita in solow model

You're right, since in basic Solow model (with population growth and no technological progress) macroeconomic closure condition (in aggregate terms) is:
$$Y(t) = C(t) + I(t)$$
where $$I(t) = sY(t)$$
Now replacing the second in the first equation:
$$Y(t) = C(t) + sY(t)$$
Factorizing we arrive at the equation you stated:
$$C(t) = (1-s)Y(t)$$
Taking the first equation in per worker terms (multiplying both sides by $1/L_t$) and differencing with respect to $t$:
$$\dot c = (1-s)\dot y$$
Using the identity $c(t) =(1-s)y(t)$, dividing the previous expression (as you did) we get:
$$\frac{\dot c}{c} = \frac{\dot y}{y}$$
I hope this is what you are looking for.


Who is Butler in Marx' footnote in Das Kapital?

I googled "The value of a thing is just as much as it will bring." in quotes, and got several hits that show Marx referred to Samuel Butler, the author of Hudibras.

Here is one.

Here is a another, see Inscription.


Why are Canadian provinces' debt-to-GDP so much higher than the US?

The Canadian provinces implement most of the welfare state programmes. The role of the Canadian Federal Government is to set out guidelines, and undertake fiscal transfers to allow provinces to stay near national standards. Since they have much larger budgets, they necessarily end up absorbing more of the economic cycle as being an automatic stabliser (i.e. they issue more debt).

There are no balanced budget laws for Canadian Provinces. American states generally have balanced budget rules, so debt levels are necessarily low. The states that do not have balanced budget laws are pretty much forced to follow the borrowing norms set by states with balanced budget rules.

Finally, the funding mechanism is different. Canadian city governments do not issue much debt, and there is very little project-based bond issuance. In other words, debt that shows up at the Provincial level ends up being financed otherwise in the United States (and does not show up in State level debt).


It seems to me based on the 2019 JEL review of the same authors that they had published more-or-less what you ask about in a 2015 paper about monopolies and price discrimination (as an application of their BCE theory); see section 5 (and 5.1 in particular) in the 2019 paper. Here the relevant information is the monopolist's knowledge of the consumers valuation. Here are some snippets:

  The set of
  BCE is precisely the set of outcomes that can
  arise with additional information for a given
  basic game and prior information structure. If there are properties that hold for all
  BCE, we have identified predictions that are
  robust to the exact information structure.
  Identifying the best or worst outcome that
  can arise under some information structure
  according to some objective function as criterion is the same as solving an information
  design problem where the designer is maximizing or minimizing that criterion. In this
  section, we will review two such economic
  applications of information design. We will
  highlight the implications of this approach in
  the context of third-degree price discrimination.
  (Bergemann, Brooks, and Morris 2015) [...]

  A classic issue in the economic analysis
  of monopoly is the impact of discriminatory
  pricing on consumer and producer surplus.
  A monopolist engages in third-degree price
  discrimination if he uses additional information about consumer characteristics to offer
  different prices to different segments of the
  aggregate market. Bergemann, Brooks, and
  Morris (2015) characterize what could happen to consumer and producer surplus for all
  possible segmentations of the market.

  One can provide some elementary bounds
  on consumer and producer surplus in any
  market segmentation. First, consumer surplus must be nonnegative as a consequence
  of the participation constraint: a consumer
  will not buy the good at a price above his valuation. Second, the producer must get at least
  the surplus that he could get if there was no
  segmentation and he had no additional information beyond the prior distribution. In this case, an optimal policy is always to offer the
  product with probability one at a given price
  to all buyers. We therefore refer to it as uniform monopoly price, and correspondingly,
  uniform monopoly profit. Third, the sum
  of consumer and producer surplus cannot
  exceed the total social value that is generated by the good, which is willingness-to-pay
  minus unit cost of production. The shaded
  right-angled triangle in figure 5 illustrates
  these three bounds.

  The main result in Bergemann, Brooks,
  and Morris (2015) is that every welfare outcome satisfying these constraints is attainable by some market segmentation. This is
  the entire shaded triangle in figure 5. If the
  monopolist has no information beyond the
  prior distribution of valuations, there will
  be no segmentation. The producer charges
  the optimal monopoly price and gets the
  associated monopoly profit, and consumers
  receive a positive surplus; this is marked by
  point A in figure 5. If the monopolist has
  complete information, then he can charge
  each buyer his true valuation, i.e., engage in
  perfect or first-degree price discrimination;
  this is marked by point B. The point marked
  C is where consumer surplus is maximized;
  the outcome is efficient and the consumer
  gets all the surplus gains over the uniform
  monopoly profit. At the point marked D,
  social surplus is minimized by holding producer surplus down to uniform monopoly
  profits and holding consumer surplus down
  to zero.
  The main result states that we can make
  only very weak predictions about producer
  and consumer surplus. It can be understood
  as the outcome of a set of metaphorical
  information design problems. If an information designer wanted to maximize consumer surplus, she would choose point C.
  If she wanted minimize consumer surplus,
  or producer surplus, or any weighted combination of the two, she could choose point
  D. Any other point on the boundary of the
  triangle is the solution to some maximization
  problem of the information designer defined
  by some preferences over producer and consumer surplus.

  The information design problem has a
  very clear literal interpretation in the case
  where the monopolist knows the consumer’s
  valuation. She can then achieve perfect price
  discrimination at point B. However, giving a
  literal information design interpretation of
  point C is more subtle. We would need to
  identify an information designer who knew
  consumers’ valuations and committed to
  give partial information to the monopolist
  in order to maximize the sum of consumers’ welfare. Importantly, even though the
  disclosure rule is optimal for consumers as
  a group, individual consumers would not
  have an incentive to truthfully report their
  valuations to the information designer, given
  the designer’s disclosure rule, since they
  would want to report themselves to have low
  values.

  [...] One can show
  that any point where the monopolist is
  held down to his uniform monopoly profits with no information beyond the prior
  distribution—including outcomes A, C,
  and D in figure 5—can be achieved with
  the same segmentation. In this segmentation, consumer surplus varies because the
  monopolist is indifferent between charging
  different prices. [They then give a numerical example, which I omit here.]

  [...] Roesler and Szentes (2017) consider a
  related information design problem in which
  a single buyer can design her own information about her value before she is facing a
  monopolist seller. While the analysis of the
  third-degree price discrimination proceeds
  as a one-player application, the arguments
  extend to many-player settings. Bergemann,
  Brooks, and Morris (2017a) pursue the question of how private information may impact
  the pricing behavior in a many-buyer environment. There, we derive results about
  equilibrium behavior in the first-price auction that hold across all common-prior information structures. The results that we obtain
  can be used for a variety of applications, e.g.,
  to partially identify the value distribution in
  settings where the information structure is
  unknown and to make informationally robust
  comparisons of mechanisms.


The underlying force for creating specialized areas in the cities of developing economies

This is an interesting observation that has produced a lot of theoretical and empirical research in industrial organization. In fact this phenomenon also occurs in developed economies, for example with gas stations. It is also not limited to location, the broader questions being why competitors in many markets tend to produce very similar products when they could also choose to differentiate themselves more strongly. A special case of the question is also often applied to politics, where the question is why different parties tend to be very similar to each other (most of the time).

Most simple explanations are based on an old and simple game theoretic model by Harold Hotelling called the Hotelling model or linear city model. Applied to politics, this model is behind the predictions of the median voter theorem.

You can find a very good explanation of the reasoning behind the model in the links below:

http://mindyourdecisions.com/blog/2008/03/25/game-theory-tuesdays-hotelling%E2%80%99s-game-or-why-gas-stations-have-competitors-nearby/
https://en.wikipedia.org/wiki/Location_model#Hotelling.27s_Location_Model
https://en.wikipedia.org/wiki/Hotelling's_law


In the model with technological progress the capital per effective worker remains constant, implies that capital per worker grows at the rate of exogenous rate of technological progress. See Barro and Martin book, Chapter 1.


Does the case of strategic complements always result in a situation where the Stackelberg leader is worse off?

It depends on what you assume the firms know about each other.  Under full information / rationality assumptions, with identical firms, second-mover advantage disappears because the first-mover will recognize the credible threat of undercutting, and set P = MC and that will be that.

If the firms are not identical (e.g., different marginal costs) then turn order is irrelevant, because only one firm has the ability to make a credible threat of undercutting.  That firm will capture the market, whether it moves first or second.

Only if you drop the assumption of full information / rationality is it feasible that turn order would matter for Bertrand competition, because then the assessment of credible threat becomes a probabilistic one.


Why not create money to assist the post-COVID-19 economy?

First, the two examples you list here are not equivalent. In the first example some portion of money circulating in economy is destroyed by the computer virus so reverting it would just keep amount of money in economy constant whereas in the second case you actually expand money supply because people 'loosing money' due to paying rent etc does not mean money in economy is being destroyed. For example, if an economy would have $\$100$ and the computer virus would eliminate $50\%$ leaving the economy with $\$50$, printing additional  $\$50$ would just bring the money supply in economy back to $\$100$. However, when people 'loose' money because they are paying rent, buying food and so on money is not being destroyed but just transferred from person A to person B. If I have $\$100$ and pay $\$50$ rent money supply is still $\$100$,  printing additional $\$50$ would increase it further to $\$150$.

The above being said it actually makes sense to expand money supply during recessions but it is not consequence free. Money in itself is not source of wealth - production of goods and services is where wealth comes from and money is just a measuring stick for its value. If you expand the amount of money in economy and the expansion is believed to be permanent then it will eventually lead higher prices since more money will be chasing the same amount of goods and services leading to inflation. Society cannot make itself richer just by printing money.

However, inflation is actually what you want during recession because there are many market rigidities such as sticky wages which can make recession worse than they are. In recession you want wages to fall to prevent unnecessary high unemployment, but people often have long term contracts with stipulated nominal wages that would take time to renegotiate. Inflation helps to 'grease the wheels of economy' because by reducing the value of money it reduces the value of peoples' wages in real terms.

Furthermore, in recession many business might face a liquidity problems - they might be overall healthy and profitable but might have hard time to have enough cash at hand. In that kind of situation you would again want to expand money supply in order to make more cash avaiable for them so they do not need to fail unnecessarily.

For these and other reasons central banks around the world are actually expanding money supply now, although they dont do it in a direct way as you described, but rather indirectly through slashing interest rates and buying bonds (see for example how Fed responds to covid19 here). The reason why they do it in this indirect way is that many experts think that if central banks would be just sending money directly to people it would politicize them, but central banks work best when they are independent technocratic institutions. Moreover, some central banks around the world are not even allowed to just do that due to the rules under which they are set up. However, central banks still can do that indirectly by buying government bonds and letting politicians decide on how to organize transfers.

The above being said while monetary expansion during recession helps the economy, the monetary expansion itself does not make economy any richer. This is especially so in situation where the problem is that economy is actually not allowed to produce goods and services in many sectors due to lockdown. Monetary expansion does not solve that underlying problem in any way. If government would just continue sending cash transfers to households payed by expansion of money supply eventually you would just get an inflation and prices would just rise higher and higher. This would have several downsides of eroding peoples savings, at higher levels inflation could also increase uncertainty, it would create menu costs as business would be forced to change their prices too often,  shoe leather costs as people would hold less then optimal cash balances, it would create fiscal drag by pushing people into higher tax brackets, it would redistribute income from lenders to borrowers and so on. So it cannot be done just without any cost.


How to determine a corner solution? Growth Model

What the authors seem to be doing in the footnote is imposing a condition stating that if intergenerational transfers tend to infinity (say for the case of children of billionaires) there will be no growth in wealth from human capital investment.
This condition is here to just communicate that the parent views allocation between human capital of the child and physical capital as substitutes.
This is communacated by the fact that we have $w_{t+1}h_{t+1}+r_{t+1}s_{t+1}$ being concidered in the same logarithm together.
Hope this helps


Ordinal utility and monotonic transformations

You need to be clear about the definitions. Lets take:

(1) $u: X \to \mathbb{R}$ represents $\succsim$ if $u(x) \geq u(y) \iff x \succsim y$.

(2) A function $h: \mathbb{R} \to \mathbb{R}$ is monotone if $z \geq w \implies h(z) \geq h(w)$. $h$ is strictly monotone if $z > w \implies h(z) > h(w)$.

First, note that every strictly monotone function is monotone. Why? Well let $z \geq w$, and there are two cases to check: (i) $z > w$: apply the definition; (ii) $z = w$: then $h(z) = h(w)$ by the definition of equality (this is because $\mathbb{R}$ is a totally ordered set).

So immediately, we see that your condition (b) implies your condition (a). However, (b) is false (I do not understand Kanak's line of reasoning, but it is certainly wrong, although perhaps can be rationalized by non-standard definitions). To show that it is wrong, we need a counter example. Lets let $X = \{x,y\}$ and let $x \succ y$. Then $u(x) = 1$ and $u(y) = 0$ represents $\succsim$. Moreover, $h: z \mapsto 0$ is a monotone transformation. But, $h(u(x)) = h(u(y)) = 0$ does not.

Indeed, this example shows that it is weakly monotone transformations that destroy information (they need not be invertible), which in terms of the representation, indicates that strict preference gets collapsed into weak inequality.

Showing that (a) holds is a straightforward application of the definitions. (Hint: show that strict monotonicity can be defined via a bi-conditional statement).


Is it enough to prove that $x \not \succsim^* y$?

Yes, it is. Step by step:
$\lnot \exists B \in A (x,y \in A \land x \in C(B))$ is equivalent to
$\forall B \in A \lnot(x,y \in B \land x \in C(B))$ is equivalent to
$\forall B \in A (x,y \notin B \vee x \notin C(B))$ is equivalent to
$\forall B \in A (x,y \in B \implies x \notin C(B))$.
Reference: How to prove it, by Velleman


How is freelancing viewed under Marxism?

Marx addresses this about two-thirds of the way through Section 1 of the Manifesto. In the standard English edition of 1888, it reads:

  The lower strata of the middle class - the small tradespeople,
  shopkeepers, and retired tradesmen generally, the handicraftsmen and
  peasants - all these sink gradually into the proletariat, partly
  because their diminutive capital does not suffice for the scale on
  which Modern Industry is carried on, and is swamped in the competition
  with the large capitalists, partly because their specialized skill is
  rendered worthless by new methods of production. Thus the proletariat
  is recruited from all classes of the population.

So his basic argument is that, sure there might be small business owners (freelancers in this example), but that because of 1) inability to compete against large firms ostensibly taking advantage of economies of scale and 2) rapid development of technology, they become obsolete and are driven to the proletariat.


If a call may expire OTM, why won't a \$1 increase in the underlying's price necessarily increase the call's price by \$1?

The reason that a call option price does not increase one-to-one with spot price of the underlying stock is simple: A 1 dollar increase in stock price only increases the likelihood that the option will be ITM. It is not a guarantee of 1 dollar increase in payoff at maturity. Naturally the price of call does not increase by 1 dollar.

More precisely, the price of the call should increase by the probability that the option will be ITM, which is less than 1. This fact is model-independent. (Try buying calls at one dollar plus current price whenever the underlying increases by one dollar, and see what happens.)

Accordingly, any model of option prices will have this property. Consider, for example, two basic models---the binomial tree and the Black-Scholes model.

Binomial tree

Suppose the stock price today is $S$. Tomorrow the stock price can be $S+\Delta S$ with probability $q$ and $S-\Delta S$ with probability $1-q$.

The price $C$ of a European call option with strike $K > S - \Delta S$ is therefore equal to the expected payoff $(S + \Delta S - K)q$.

(To be correct, assuming risk-free rate $r$, $q$ should be the risk-neutral probability given by
$$
q e^{-r} (S + \Delta S) + (1- q) e^{-r} (S - \Delta S) = S.
$$
But this is not central to the discussion.
)

If $S$ increases to $S + 1$, the price of the call becomes
$C = (S + 1 + \Delta S - K)q$.
The increase in the price of the call is exactly the probability $q$ of the call being ITM.

Black-Scholes

In the context of the Black-Scholes,
the sensitivity of option price with respect to the underlying is called the delta of the option. It is a standard quantity that arises in delta hedging.

Let $C(S_0, K)$ denote the Black-Scholes formula for price of European call with strike $K$ maturing at time $T$.
The delta of the call is the partial derivative $\frac{\partial C}{\partial S_0}$. The delta is the increase in $C(S_0, K)$ when $S_0$ increases by 1 dollar.

As you would expect, it's immediate from the Black-Scholes formula that the delta $\frac{\partial C}{\partial S_0}$ is equal to the (risk-neutral) probability that the option will be ITM at maturity.

(In Black-Scholes, under risk-neutral dynamics, the price of the stock $S_T$ at maturity $T$ is given by
$$
S_0 e^{( r + \frac12 \sigma^2 )T + \sigma \sqrt{T} N}
$$
where $N$ is a standard normal random variable.
So $\frac{\partial C}{\partial S_0}$ is equal to
$$
P( S_0 e^{( r + \frac12 \sigma^2 )T + \sigma \sqrt{T} N} > K)
$$
where $N$ is a standard normal random variable.
)


This is often called “home production.” By default, the answer is no, but different countries have different methodologies.
This US Bureau of Economic Analysis page has some information: BEA webpage.
They produce a “satellite account” that includes this information. (Not officially part of GDP, but official supplemental information.)


What effect does a wage ratio cap have on the efficency of allocation of labour?

The effects can be quite different from a price (wage) ceiling. The baseline case where you have homogeneous, inelastically supplied labor that's free to move across different "types" of work produces no supply response in reaction to a wage ceiling, but leads to complete specialization in one type of labor or another in the case of enforced bounds on relative wages which rule out the competitive market allocation.

For companies, enforcing internal wage ceilings may be a way of trying to address problems of corporate governance - the shareholders may be trying to address a principal-agent problem by getting such a policy instituted within the company. In that case, it may well improve efficiency, but it's hard to say if there would be a significant impact on the supply of executives available for corporate management.


Confused about what is meant by adjusting for inflation

Things change in price over time. For example, a movie ticket in 1955 might cost \$.50, and a movie ticket today costs about \$10, 2000% as expensive in 2019 as in 1955. (source)

These are nominal prices. That is, what is the number of dollars I need to pay for a movie ticket?

However, these nominal prices might go up for two reasons. It could be that the item is getting more valuable. Or it could be that the dollar is getting less valuable. In other words:

(1) One is that the relative price of movie tickets might be going up. That is, movie tickets are getting more expensive relative to other goods. For example, imagine a loaf of bread also cost \$.50 in 1955, but cost \$5 today (I'm making these numbers up). In 1955, you'd have to give up one loaf of bread to have enough money to buy a movie ticket. But today, you'd have to give up two loaves of bread to buy a movie ticket. So movie tickets have gotten more expensive relative to bread.

(2) Another reason that movie tickets might get more expensive is because everything gets more expensive together. In other words, the value of the dollar drops. In 1955, you could trade a single dollar for two movie tickets, or for two loaves of bread. Today, you can't trade a single dollar for even one of either. In other words, a dollar today is less valuable than a dollar in 1955.

This second reason, where the value of the dollar drops, is called inflation.

Adjusting for inflation is a process of getting rid of any price changes that happen for reason (2). This is done by calculating (usually using something called the Consumer Price Index) what the prices of things would be if the dollar still had the same value that it did in a different year - if inflation had not occurred (we've adjusted for inflation).

According to the US Inflation Calculator, a single dollar in 1955 is 855.8% as valuable as a single dollar in 2019.

So that 2000% comparison of movie ticket prices we had before? That actually represents that movie tickets are 2000/855.8 = 2.34 (234%) as expensive in 2019 as in 1955 - a 134% increase in relative price. The rest of the nominal price increase is because the dollar itself got weaker.


LM curve: How interest rate is changing without OMOs by the central bank?

Hence interest rate is directly dependent on the OMOs.

While open market operations have a large influence on interest rates, there are other ways in which central banks influence interest rates. For example, they may increase or decrease the interest on excess reserves. Moreover, the IS-LM model does not necessarily assume the existence of a central bank. Interest rates have been set by the market far before central banks existed to influence them.

So how do interest rates rise with a fixed real money supply? Increased transactions demand leads to a increase in demand for money. If real money supply stays constant, then interest rates should rise. The following is an example.

Imagine an economy with only one good, tomatoes, and two people, Buyer and Producer. Producer produces all tomatoes. Buyer owns all 10 credits and is disposed to consume everything possible. Imagine the Producer has produced 10 tomatoes, and is willing to sell at 1 credit per tomato. Thus real GDP is 10 credits. If the Buyer purchases all 10 tomatoes from Producer, Buyer will own 10 tomatoes and Producer will own 10 credits.

The next year Buyer has magically regained all 10 credits. Maybe Buyer stole them from Producer; it doesn't matter. Producer produces 20 tomatoes. Hence, real GDP is now 20 credits. Intuitively tomato prices should go down as there is more supply and a fixed demand (from Buyer) but that would imply that real money supply has gone down. So to better illustrate the LM curve, let us assume that Producer keeps prices at 1 credit per tomato. Buyer now purchases 10 tomatoes, and has no credits left. But Buyer is determined to consume everything possible, so Buyer strikes a deal with Producer to borrow the 10 credits that now Producer owns at 10% interest. Buyer then purchases 10 more tomatoes.

In short, real GDP doubled, real money supply stayed the same, and interest rates went up from 0% (no one borrowing) to 10%.

  Also, why would someone will buy the bond from central bank when the bond prices are going down?

Central banks will sometimes sell bonds that they have purchased previously to decrease the money supply. The announcement that a central bank will attempt to do so may attract front-running speculators. In other words, basic market dynamics will apply: if no one wants to purchase bonds, then prices will decline until someone believes prices have declined enough that they will eventually start rising again even under pressure from the central bank.


What happens on a banks balance sheet when the borrower submits loan payments?

If you make a payment of \$X, then:

loan balance (bank asset) goes down by \$X, and
deposit balance (bank liability) goes down by \$X.

I.e., the bank balance sheet shrinks (as do money aggregates that  include bank deposits).

The bank may have held a loan loss provision against the loan, and so the loan may have been carried on the balance sheet at less than \$X. For example, a bank might think there is an expected loss rate on this loan of 2%, so the bank would have a provision of .02*\$X. The loan would be carried on the balance sheet at a value of .98X, not X. The creation of this provision generates a loss, causing a corresponding reduction of equity. (Note: how this is accounted for probably depends on the jurisdiction.) Note that there are no transactions associated with this loss, so it is a non-cash loss.

Since you paid off the loan in full, the provisioned loss did not materialise, and so it would be reversed. The value of the loan would be written up to \$X before cancellation. This would generate a non-cash profit, as equity would rise by the amount of the reversal of the loss provision.

In the comments, it was asked how banks make money on loans. They make money off the interest payments, which are supposed to be higher than the interest costs of the bank.


REE with asymmetric information and Bayesian Nash equilibrium?

The idea of a rational expectations equilibrium is more general than BNE. It simply means that the belief system of agents is consistent with the model and incorporates all available information. This abstract idea can be applied for games, markets or other types of interactions. BNE is a solution concept for non-cooperative games. The expectations being rational also poses no restriction on how agents in a model update their beliefs, while BNE assumes beliefs are updated according to Bayes rule.

Let me be more concrete. If you are modeling a competitive market, the REE is not a Nash equilibrium. Players are simply maximizing giving prices and information (instead of given the strategies of other players). In contrast, if you are modeling a market where the buyers or sellers are strategic (for example a Cournot model with incomplete information), the typical solution concept is BNE and it will also be an REE.

To sum up, any BNE is an REE, but the converse is not true.


What are some helpful online tools (databases, etc..) for economic analysts?

St. Louis Fed:
https://fred.stlouisfed.org/

Has very good US data.

I am not aware of a database that systematically aggregates city-level data. I recommend state government sites and, for larger cities, city government sites.


How do I determine PED from price consumption curve with slope of zero?

Since you have discrete datapoints and want to calculate PED, you will have to make assumptions, like "the data represents the general behavior of the consumption function". (You can also get more data or throw your hands up in despair.)
If you know that price has no effect on the quantity demanded, you can apply the PED formula, and get a very specific number for PED.


Supporting Hyperplane Theorem and quasiconcave utility function

This problem is quite specific to economics. The correct statement is:

Proposition
If $u(\cdot)$ is quasiconcave, strictly increasing, and continuous, then $\forall x$, there exists $p \gg 0$ and $w \geq 0$ such that $x \in x^*(p, w)$, where $x^*(p, w)$ is the Marshallian demand correspondence.

Proof

Quasiconcavity of $u$ means the upper-contour set $\succeq\!\!(x) = \{x': u(x')\geq u(x)\}$ of bundles weakly preferred over $x$ is convex.

By continuity of $u$, $\succeq\!\!(x)$ is closed.

By strict monotonicity of $u$, $x$ lies on the boundary of $\succeq\!\!(x)$.
Consider the supporting hyperplane $p\cdot (x' - x) = 0$ of the closed convex set $\succeq\!\!(x)$ at boundary point $x$ with normal vector $p$.
Since $u$ is increasing, then we can take $p \gg 0$.

Since $\succ\!\!(x) \subset \{ p\cdot (x' - x) > 0 \}$ (general relationship between the interior of a convex set and a half space given by a supporting hyperplane),
$x \in x^*(p, \,p\cdot x)$. $\Box$

Differentiability is not needed. If $u$ is strictly quasiconcave, the Marshallian demand correspondence is a function, and $x = x^*(p, w)$.
The argument above also tells us that $x \in x^*( p, \, e(p, u(x)) )$, where $e(p, u)$ is the minimum expenditure required to achieve utility level $u$ given price $p$.

Questions

Q "...$x$ lies on the boundary of $\succeq\!\!(x)$..."

A
By definition, $x$ lies on the boundary of $\succeq\!\!(x)$ if every open neighborhood of $x$ contains some $x' \in \succeq\!\!(x)$ and some
$x'' \in \prec\!\!(x)$. If $u$ is strictly increasing, this is clear. Every open neighborhood of $x$ contains some $x' \gg x$ and some $x'' \ll x$.

Q "Since $u$ is increasing, then we can take $p \gg 0$."

A
Suppose $p \geq 0$ but has a zero entry, say the first one. Let $e_1$ be the standard basis vector with 1 in the first entry and zero elsewhere. Then $x + \alpha e_1$ lies in $\succeq\!\!(x)$ for any $\alpha \geq 0$, since $u$ is increasing. Strict quasiconcavity of $u$ then implies that $x + \alpha' e_1 \succ\!\!(x) $ for some $\alpha' > 0$ (take a convex combination on this half line). This means the plane with normal vector $p$ cannot be tangent to $\succeq\!\!(x)$---this plane intersects the interior $\succ\!\!(x)$.


American economic theorist Henry George wrote about precisely this issue in his famous work Progress and Poverty published in the late 1800s, and based on his observations on the economic development of San Francisco during the gold rush.  His argument was that increasing economic development primarily benefitted landowners, at the expense of both capital and labor.  (However, since landowners were often also holders of large amounts of capital, it was primarily labor that ended up losing out.)  In a nutshell, the leverage that landowners held over the workers allowed them to push wages ever lower, creating poverty as a result of economic progress.  He theorized that taxing economic rent (at/near 100%) would eliminate speculation and thus stop the boom/bust cycle endemic to market economies, as well as providing ample revenue to the government to fund social welfare programs and to develop infrastructure.


If the Engel Curve of a Cobb-Douglas utility function is positive and linear, than does that mean it is neither a necessity nor a luxury good?

Recall the following equivalent definitions for luxury goods and necessities:

A good $x$ is considered a necessity if $e_{(x,I)}<1$.

A good $x$ is considered a luxury good if $e_{(x,I)}>1$.
As you can see, these definition do not encompass all possible scenarios, so any specific good does not have to be either a luxury or a necessity.

In the case of a Cobb-Douglas utility function $U(x,y)=x^\alpha \cdot y^\beta$ we get $x^* = \frac {\alpha I}{P_x}$. One can easily verify that $e_{(x,I)}=1$. In other words, the demand does for $x$ does not change with $I$. This means that in this case, $x$ is neither a luxury good nor a necessity.


Definition of "simple situation" is ambiguous

Consider the typical prisoner’s dilemma,

$$
\begin{array}{|c|c|c|}\hline
&{\rm confess}& {\rm lie} \\ \hline
{\rm confess} & \color{red}{-8},\color{blue}{-8} & \color{red}{0},\color{blue}{-10} \\ \hline
{\rm lie} & \color{red}{-10},\color{blue}{0} & \color{red}{-1},\color{blue}{-1} \\ \hline
\end{array}
$$

In this case it is easy to predict that each player should play confess, regardless of the the selection made by the other player. Or in the words of the problem:

  The best strategy (the one that outperforms other strategies) is to confess regardless of the strategy adopted by other players


Interestingly I could not locate quantitative data on Firing Costs (aka Separation Costs aka Severance Pay) for the US Economy. Perhaps because, as US Dpt of Labor says

  There is no requirement in the Fair Labor Standards Act (FLSA) for
  severance pay. Severance pay is a matter of agreement between an employer and an employee (or the employee's representative).

A  world map  and another one for separation costs measured in weeks of wages -but none of the two include data on US Economy.

ILO's new data base does not seem to have quantitative data on Firing Costs.

Kugler, A. D., & Saint Paul, G. (2000). Hiring and firing costs, adverse selection and long-term unemployment. deal with  some US data but qualitatively and indirectly.

Abowd, J. M., & Kramarz, F. (2003). The costs of hiring and separations. Labour Economics, 10(5), 499-530. Data from the economy of France, related to year 1992. Extensive treatment of various costs associated with labor, including costs of separation treated distinctly. Note: monetary values are in French Francs. Conversion Rate: 1 FFr = 0.152449 EUR.


Does open source software contribute to GDP?

Open source software does influence GDP in a number of ways, both positively and negatively.  The net effect of greater open source usage will depend on the economy, I think particularly on whether the economy produces or imports most of the closed-source software that is being displaced by greater open-source usage.

Here are some of the mechanisms by which open source software influences GDP:

People still pay for some open source software through donations, a mechanism very similar to the purchase price of closed source software.  E.g. the Mozilla Foundation received $4.5 million in contributions in 2015 (see p4).
Companies provide a wide range of services that rely on open source software.  In some cases this is closer to closed source development (e.g. Red Hat), where companies pay to use software systems -- even though the underlying software is open source, they pay for an "enterprise solution".  Maybe 90% of web servers are open source, but companies are still paid to provide those servers, same with companies providing virtual machines.
The use of open-source software by companies or workers that could not afford closed-source equivalents improves productivity and probably therefore GDP.
Most obviously, the use of open source software replaces some closed-source software reducing the purchase and production of closed-source software.  More closed-source development is paid, so this would reduce GDP in the country where the closed-source software is made.

As I mentioned, whether an increase in open-source usage is likely to increase GDP probably depends primarily on whether most closed-source software is domestically produced or imported.  If closed-source software is domestically produced, and this production is partly replaced, GDP could go down, unless this if offset by open-source-related services.  However, if closed-source software is mostly imported (the case in the vast majority of countries worldwide), only the value addition in wholesale and retail shows up in GDP.  Using open source instead will free up foreign exchange that can be used elsewhere.  If a chunk of this buys capital goods instead, that should boost GDP in the medium term.


To what extent can cryptocurrencies be influenced by monetary policy?

Well first if actually the cryptocurrency we are talking about would be created by central bank, then the rules that were used to create it would be by definition monetary policy even if supply of money would be fixed, since monetary policy is central bank’s control of money supply either directly or via interest rate (see Yeyati, Sturzenegger (2010), or Friedman 2001). Keeping supply of currency completely fixed at all times is a valid (although arguably very disastrous) monetary policy. Hence, to an extent that some monetary authority consciously sets up rules for cryptocurrency, that set of rules will, by definition, be monetary policy.
If we are talking about some independent cryptocurrency then the cryptocurrency is equivalent to being a foreign currency from a perspective of central bank. In such case we can’t talk about central bank directly conducting monetary policy for cryptocurrency as by the definition of monetary policy monetary authority has to be able to change supply of money, but despite of that monetary policy set for its own currency can still affect the exchange rate between domestic and cryptocurrency and thus it can affect the value of cryptocurrency.
A loose monetary policy ceteris paribus, would depreciate USD/Bitcoin exchange rate making bitcoins more expensive (for more detailed overview of how monetary policy affects exchange rate markets see  Exchange Rates and International Finance).
Central bank could decide to do what you suggested buying/selling that cryptocurrency - which is equivalent to an foreign exchange intervention. This too is technically monetary policy since this is done through control of the money supply of central banks’s currency (e.g. central bank has to create more of its currency in order to get more of the foreign currency as reserves, and conversely when it reduces the foreign currency reserves it will get the previously created money back and thus reducing money supply). Even if a central bank has no control directly over money supply of other countries this allows central banks to also to certain degree control value of other currencies. For example, in past China’s central bank was partially keeping dollar overvalued and yuan undervalued by keeping large USD reserves.


Your first response to the trade deficit would seem to increase imports and not exports, unless I'm misunderstanding and you are writing from the perspective of Malaysia. In that case, the policy might be otherwise flawed due to the lower amount a fisher would supply given a lower price for exportation. While you may reach an agreement with other countries to import fish, your fishers must still, as private individuals, be incentivized to supply fish for this trade. I believe a better solution would just be the opposite of that in your first trade surplus answer, raising tariffs.


Deriving formulas from Gali's book on the New Keynesian model

Mathematically speaking, we are not sure. The infinite sums mentioned is of the form

$$E_t\sum_{k=0}^{\infty}\gamma^kX_{t+k},\;\; 0<\gamma<1$$

The fact that there is the declining factor, $\gamma^k$, provides some comfort that the sum converges, but from examples like the harmonic series we know that even if $\lim_{k\rightarrow \infty}\gamma^kE_tX_{t+k} =0$, the sum may not converge.

Some times authors provide rigorous conditions for convergence, but I believe it is more important not to be trapped by our own tools: the use of infinite horizon is, of course, non-realistic. The only reason we use it is that it makes the mathematics more tractable. So in reality we model a problem with possibly long but finite horizon. In such a case, there is no issue of convergence. By extending the problem to the infinite horizon we silently assume that this won't destroy convergence, since it is an artificial extension.

The ultimate economic argument for convergence, is that it is meaningless to talk about economic magnitudes going to infinity. Even for prices, where it is tempting to think that they do not have an upper bound per se, we must remember that prices as a component of an economic system do have ultimate bounds.

With prices flying to heaven, the economy goes to hell (if you excuse the christian iconography), because the price system stops functioning as a signal mechanism to co-ordinate decisions in a decentralized framework. But in the real world, when such explosions "start to happen", the society that encloses the economy in question, will intervene in one way or the other, in order to end the phenomenon. The historical experience from war-time hyperinflations and from other price-bubbles verifies this.

Ideally, we would want a single model to encompass both possibilities and also model the possible "extraordinary reaction" to the explosive case: herein infinite PhDs lie.

Returning to the specific situation from the link, note that the price in eq. $(3.7)$ is determined by the ratio of two such infinite sums. Even from a mathematical point of view, this is a bit more favorable, because even if each sum separately diverges, their ratio may converge. But again, my point is, "don't let the mathematics make you forget the economics" of the situation.


Reverse of broken window fallacy for file sharing/piracy

If I understand correctly, the claim is is:

  Proposition: Take a budget as given, and consider a world with two goods, $A$ and $B$. In the first scenario, the price of $A$ is positive, and the household spends $E_A$ on $A$, and nothing on $B$. In a second scenario, the price of $A$ is zero.The household will now spend the same amount $E_A$ on $B$.

How did this abstraction work? A represents the copyrighted work, B contains all other consumption goods. I don't think there is strong empirical evidence for or against the claim. So then, what does the theory say?

Neoclassical Theory

The rational agent under a general class of preferences does first decide his optimal consumption level given (permanent) income, and then decides how to allocate that consumption expenditure between different goods. For him, the answer would be Yes.

Caveats

However, what happens if we depart from the rationality assumption? Many weird things can happen. For example, instead of optimally choosing how much to save, the consumer could first decide, what he wants to consume, and then save the remainder. In this case, since he already has A "for free" he might be contempt with that, think that "having some B" is sufficient, and then save the remainder. In that case, it may very well be that the answer is No (or at least, not necessarily). Not all the money not spend on copyrighted material will be used for consumption on other goods.

There are many reasons to believe why the rationality assumption is not always giving us the full story, especially when you look at life-cycle consumption, saving rates and divergence of savings at retirement ages.


How does the central bank changing interest rates change interest rates in the commerical banking sector?

The federal fund rate is a cost for the commercial banks. They borrow at the federal fund rate and then they lend to the consumers.
The federal fund rate variation impacts the lending cost of the banks directly.
It's how it changes the interest rate charged by commercial banks.


You are never going to be able to fill in the gaps exactly, so the best approach may depend on what you want to use the data for.

One reasonable approach might be to use an average offset from the 10-year rate, e.g. adding about $0.3$ to it.  If you did that, then you would get the red data on the chart below, which compares reasonably well with the actual blue data for the 15-year rate, though not perfectly.  So you might use the red line as a proxy for the earlier missing blue data.  This might not be such a good idea if the purpose of your analysis was precisely considering the changing gap between the 10-year and 15-year rates


Practical examples of fair division algorithms being used

The easiest generalization, of envy free sharing of a heterogeneous cake between two cake eaters is quite common. My family growing up frequently used the you divide and I choose method for sharing a lone piece of dessert. Depending on what you'd accept for "concrete example", Abraham and Lot use this method to divide the land of Canaan.  A  two-stage fair division problem was used in the partitioning of Germany after World War II. The Talmud has examples of fair division rules, which though are only thought experiments, are thought to have been applied in the Jewish diaspora over inheritance matters.

I would also argue that the marriage / matching problems of Lloyd Shapley and Alvin Roth are a form of fair division, and one that scales to very large numbers of players and applies only to multiple, indivisible "cakes. Their methods have been used extensively in real world problems of school, job, and kidney assignment.


Relation between Inflation and Bank deposit interest rate?

The US doesn't have a long time series of deposit interest rates available for free. However, they do have one month CD data from 1966 to 2013. This is a short term loan to a bank, that pays a slightly higher interest rate than a savings account. It is widely available across banks and FDIC insured for smaller balances. The following figure compares those one month CD interest rates with the rate of inflation:

The correlation coefficient between these two series is 0.72. So they do move together (which is not surprising). However, you can see that there are long periods where there are large differences between the two series. Sometimes these differences are positive and other times they are negative.


If the (direct) utility is concave in all goods, is the indirect utility necessarily concave in wealth?

Your statement does not seem to be true for normal goods either. A counterexample:
$$
U(x_1,x_2) = (x_1x_2)^{\frac{2}{3}}
$$
By the Cobb-Douglas property the optimum bundle given $w,p$ is
$$
(x_1,x_2) = \left(\frac{w}{2p_1}, \frac{w}{2p_2}\right),
$$
so both goods are normal. The indirect utility is
$$
U(w,p) = \left(\frac{1}{4p_1p_2}\right)^{\frac{2}{3}}w^{\frac{4}{3}}.
$$
Here $w$ is raised to a power higher than 1 so $U(w,p)$ is convex in $w$.


Additional components in utility functions (behavioral economics)

Your formulas contain an undefined $p^*$, and the Fehr-Schmidt utility function is wrong. The brackets should be $\max\{p^*-p,0\}$ and $\max\{p-p^*,0\}$, respectively. Apart form that, the two additional terms are usually called the disutility from advantageous inequity and the disutility from disadvantageous inequity, respectively. Calling them "transactional (dis)utility" would not fit in this context.


Can the theory of the second best mathematically justify labor unions in some scenarios?

Quoting your quote, emphasis altered by me:

The “theory of the second best” clearly argues that once markets depart at all from perfect competition, efficiency may well be increased by further departures. For example, in the case of monopsony power in low-wage labor markets, legislated minimum wage increases can potentially move wages closer to efficient levels and increase employment.

It seems to me the quoted Economist summary misrepresents this quite a bit! No one is claiming that unions or state intervention will yield the second best (which is a somewhat vague concept - what are the exact information constraints here?), merely that they may be welfare increasing.
To expand on this a bit: if we don't know where "the competitive equilibrium" wage would be, but people agree that it is in the [8,40] dollar range, then instituting an 8 dollar minimum wage policy would not have a detrimental effect and would be welfare improving in cases when the current wage is below \$8. But there is no claim of optimum, not even in expected value.
Mathing it up:
$$
\begin{align*}
S(p) & = p \\
D(p) & = a - p \ \text{ where } \ a \sim \text{U}[16,80]
\end{align*}
$$
so
$$
p^* = \frac{a}{2} \sim \text{U}[8,40].
$$

The paragraphs above are the gist of the answer, but I can also produce a hiperbole on par with the Economist. Suppose that I told you that due to variance in quality some lollipops manufactured by a certain company are detrimental to one's health. The Economist seems to argue, that someone proposing the idea of quality control is promising not that they will catch some of these poisonous lollipops but all of them. And since this is clearly not possible, as quality control itself has varying quality, it is pointless to even try to improve the situation. But quality control may be justified even if some of the subpar lollipops are discovered. In fact quality control may be justified even if it supervised by a nonexpert and hence only catches half as many subpar lollipops as possible, as stopping some bad effects are preferential to stopping none.
It occurs to me that given the difference between the marital ideal and the status of the average marriage it is rather fortunate The Economist does not give marital advice.


What are the costs of requiring banks to have more equity?

If banks are forced to hold 20-30% of their assets as common equity, their cost of capital is much higher. This is because the expected return on equity needs to be close to other industries, and that generally is much higher than interest rates. Typical targets for return on equity are around 20%, even in the modern low interest rate environment.

The result is that banks are much less competitive versus non-bank finance, and so would lose market share. Since non-bank financial entities are less well regulated, the risk to the system would rise if they take over lending.

So the immediate question is: how exactly can regulators stop all risk migrating to non-bank finance? Considering the flexibility of contract law, that is not easy, since financing arrangements can be embedded into almost any commercial contract (e.g., accounts receivable). You cannot just look at existing non-bank financial practices, you need to deal with any new structures that pop up to take advantage of the situation.

Once that question is answered, we would then need to figure out how to get borrowing rates to be a relatively reasonable spread over government bonds, since the lending spreads have to cover the return on equity for 20-30% of the balance sheet.


That Quarterly GDP chart looks as if it is already the percentage change in real GDP (for example put "Time" on "Annual" and note that the effects of the 1973 and 1979 oil price shocks are negative rather than positive)


Papers on International Trade and Environment

I have to disagree with the previous answer. There is quite a large literature on international trade and the effect of environmental regulations. To start off there is the whole race to the bottom literature and the environmental Kuznet's curve. A good start of trade versus the environment is given in Esty's 2001 Bridging the Trade-Environment Divide (found a.o. here). Copeland and Scott Taylor have a 2004 article on international trade, growth and the environment in the journal of economic literature.

As for trade in natural resources and related trade policies Ruta and Venables have an overview paper here.

For a more general equilibrium model on differences in environmental regulations and how that affects trade you could start at Chichilnisky's 1993 North-South trade and the dynamics of renewable resources (here).


Intertemporal consumption smoothing is using savings or borrowing to make consumption less volatile than income (or sometimes wealth). The intertemporal consumption smoothing  motive can arise in many settings, but an early and famous example is the Milton Friedman’s permanent income hypothesis. The idea is that if income contains permanent and temporary shocks then maximizing the NPV of lifetime utility will make you ignore temporary shocks and consume a fixed fraction of your permanent income.

Essentially, you know temporary shocks are temporary. If you cut back on consumption in the face of these temporary shocks you'd end up with consumption that is higher than average in better times. Because of declining marginal utility of consumption this is a worse consumption plan than keeping your consumption fixed in good times and bad.

In contrast, if you experience a permanent negative shock to consumption there won't (in expectation) be a good time to make up for the lost income. Leaving your consumption unchanged in the present would therefore require even larger cutbacks in the future. This is a worse consumption plan than cutting your consumption immediately and using that new and lower plan going forward.


Is it possible to have transferable utility in non-cooperative games?

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


How can I write a conditional expectation of finite state markov process in matrix notation

Let the $n$ states of the finite-state markov chain be denoted
by $\{x_1,...,x_n\}$ and let $\vec e = [e(x_1), ..., e(x_n)]'$.
Now,
first note that because $X_{t+1} \mid X_t$ is independent of $W_{t+1}$, we can write
\begin{align*}
\exp(\eta) e(x) &= E[\exp(D'x + x' F W_{t+1})] E[ e(X_{t+1}) \mid X_t = x] \\
  &= \exp(D'x + x' F F' x)\, E[ e(X_{t+1}) \mid X_t = x] .
\end{align*}
Then, because this must hold for all values $x= x_1, ..., x_n$, we
can assemble the following vector equation,
\begin{align*}
\vec e \, \exp(\eta)
  &=
\begin{bmatrix}
\exp(D'x_1 + x_1' F F' x_1)\, E[ e(X_{t+1}) \mid X_t = x_1] \\
... \\
\exp(D'x_n + x_n' F F' x_n)\, E[ e(X_{t+1}) \mid X_t = x_n]  \\
\end{bmatrix}\\
  &=
\text{diag} \begin{bmatrix}
\exp(D'x_1 + x_1' F F' x_1) \\
... \\
\exp(D'x_n + x_n' F F' x_n) \\
\end{bmatrix}
\, \mathbb P \, \vec e \\
  &=
\text{diag}(f)\, \mathbb P \, \vec e \\
\end{align*}
where $f = [ \exp(D'x_1 + x_1' F F' x_1),  ..., \exp(D'x_n + x_n' F F' x_n) ]'$
and $\text{diag}$ is the operator that takes a vector and places
it on the diagonal of a matrix where the off-diagonal elements are zero.
So, we can express the equation as a linear operator $\mathbb M$ on $\vec e$
with
\begin{align*}
\text{diag}(f)\, \mathbb P \, \vec e
  &= \vec e \, \exp(\eta) \\
\mathbb M \vec e &= \vec e \, \exp(\eta).
\end{align*}


Quarterly industry-level productivity growth?

Here is exactly what you are looking for, at the finest level of NAICS disagregation.

Example for aircraft manufacturing:

Example for Software publishers:


Can one prove Pareto efficiency in an n-party system by showing all Pareto improvements between any two given parties are made?

@HerrK. got it right in his comment (he should have deleted the somewhat confusing "yes" from the beginning and then posted it as an answer) It is possible that no pairwise improvements are possible but general Pareto-improvements are still possible. A simple counterexample for three actors and three goods is as follows. Let the utility functions be the same for all actors, that is
$$
U_A(x,y,z) = U_B(x,y,z) = U_C(x,y,z) = \min(x,y,z).
$$
Let actor $A$ have 3 units of good $x$, and 0 units of the other goods, whereas actor $B$ has 3 units of good $y$, and 0 units of the other goods, and actor $C$ has 3 units of good $z$, and 0 units of the other goods. No pairwise exchange can increase utilities above zero. But the goods could be distributed so that everyone has a unit of each. This would increase all utilities to one, making the original distribution not Pareto-efficient.


Can stock exchange workers go on strike?

The Stock Exchange workers in US could strike if they wanted. The right to strike in US is enshrined in the US National Labor Relations Act of 1935. See also explanation of the law by the National Labor Relations Board  to see conditions under which strike can occur. None of the conditions seem to exclude stock exchange workers.

However, as @BrianRomanchuk points in his +1 comment, strikes are normally called by unions. According to the statistics published by U.S. Bureau of Labor Statistics in 2019 by occupation only $4.2\%$ workers were members of union and only $5.1\%$ represented by unions in the "Business and financial operations occupations" and if we look more narrowly only at finance as industry (which is arguably more appropriate for this question) the figures become $1.4\%$ and $2\%$. This being said I could not find any statistics specifically for only stock exchanges, but I would expect that unionization rates there would be lower than the aggregate for whole industry.

At the same time statistics show that people in the US working in finance and insurance industry were in 2018 ranked 4th in terms of average salary (see here).

So to sum up, people in US working in financial industry are not generally members of unions or even represented by unions. This would presumably make organizing any meaningful strike difficult.  At the same time people working in finance industry in US are already in one of the highest paying professions meaning that there is most likely not much incentive to strike.


Increase in the price of skateboard wheels cause a decrease/no change in the demand of skateboards? (2 separate markets w/ 2 separate buyers)

Since there is no change in consumer preferences, the demand function will not change.
The firms supplying skateboards face increased costs due to the wheels being more expensive. This will alter their supply function and thus the equilibrium price in the skateboard market may change, and hence the equilibrium quantity demanded may also change.


The Econometrics of the Stone Geary Production function

Stone-Geary production functions attempt to reflect the real-world observation that for production to be feasible, there exist minimum thresholds in the quantities of inputs employed. This is not about initial investment but that one cannot use miniscule levels of inputs and obtain "very little" output -for production to even begin, one needs input amounts above a certain threshold, dictated usually by technology. At the aggregate (market or macro level), perhaps this effect practically vanishes, but for firm-level data, this may be an important feature of actual production.

Assume that we have data for $i=1,...,n$ firms and we postulate the existence of a Stone-Geary production function

$$q_i=f_i(\mathbf x_i;\mathbf a_i) = A\prod_{j=1}^K(x_{ji}-a_{j})^{\gamma_j}$$

The model is non-linear in the parameters, and It will remain non-linear in the parameters even if we take the natural logarithms. So one could in principle consider Non-linear Least Squares (NLS) estimation using the above specification without taking logs, but it is advisable to do take logarithms, because it lends a "degree of linearity" in  the model which will only do good  to the NLS estimator and the iterative estimation algorithm that it will be used by the software, since no closed form solution exists. So we specify, for $K$ non-constant regressors,

$$\ln q_i =\ln A + \gamma_1\ln(x_{1i}-a_{1})+...+\gamma_K\ln(x_{Ki}-a_{K}) +u_i,\;\;\; i=1,...,n$$

where we want to estimate the gammas and the alphas plus the constant term... Note that the above specification assumes that the "thresholds" (the alphas) are the same for all firms, per regressor (they are not indexed by $i$). So in all we are estimating $2K+1$ parameters with a cross-sectional sample of size $n$ and we must have $2K+1 < n$.

Also, note that $A$ is the level of of output when all inputs exceed their threshold by one unit.

The NLS estimator requires starting values for the coefficients. For the gammas, one could run OLS by setting the alphas equal to zero and use the OLS estimates as starting values. For the alphas, one could start by setting them equal to zero, except if one has some idea about what they could be approximately.

A good thing of such an approach is that the estimated thresholds can be checked for plausibility, using existing knowledge about production processes, which provides a non-statistical test for the validity of the specification.

An open access paper discussing the approach with empirical applications can be found here.


Why did non-seasonally adjusted gdp usually drops on Q4 and Q1?

Output usually falls during certain quarters/months and for many countries it is in the winter. Tourists usually travel for vacations in summer when kids also get long summer holiday. Farm work is highly seasonal and there is more of it in summer than winter (as pointed out by @dismalscience in an excellent comment construction is seasonal too) etc. As a result GDP will fluctuate seasonally and this is in fact the reason why we seasonally adjust series for many research purposes. Although usually these fluctuations are not big enough to cause recessions.
Depending on geography and in which industries country specializes it will be affected differently by seasonal variation in output. There is no a priori reason why it should happen in Q1 and Q4 but for most countries it will be either during winter or summer.  Since you do not mention which country you talk about there is not much what can be said about that.
If real GDP dropped in two consecutive quarters then usually it would qualify as a recession (for example that is definition given by Blanchard et al. Macroeconomics in glossary on pp 569), but that is not the only definition used in literature - there simply is no single agreed upon definition by all. Research on calling recessions  often uses seasonally adjusted real GDP in order to identify recessions (e.g. Hamilton, 2011), but most definitions do not specify whether it should be seasonally adjusted or not.


A question about Lagrange multiplier(when $\lambda=0$)

A $\lambda = 0$ means that the objetive function's derivative with respect to the restriction is zero. In more intuitive terms, one cannot change the expected utility of consumption by relaxing or tightening the budget restriction. This is a weird case, for sure, I think you're missing something here. Maybe telling us what the variables mean can help?


Hayek's defense of competition regulation

This article states:

  In  both  of  his  seminal  works  in  political  theory,
  The  Constitution  of  Liberty  and Law, Legislation and Liberty, Hayek endorsed as a legitimate function of the state the  power  to  regulate  monopolies  and  curtail  industry  practices  in  restraint  of  trade.

For example, in the first book, in Chapter 15, Hayek declares the importance of the nature of government intervention:

Notice that Hayek considered trade unions as workers' monopolistic institutions that damaged free market. Hence, in his view, these are undesirable. In Chapter 18 of the above books it says:

More on monopoly is in Chapter 17:


Indifference curves and equivalence classes

Yes, indifference is an equivalent relation.

That was covered in other answers and comments. I'm here to point out that preference relations are not partial orders. A partial order has the property that

$$a\leq b, b\leq a \implies a=b$$

This not true precisely because of indifference. Rather, preference is typically assumed to be complete and transitive which means it is a total order on the quotient $X/\sim$


The simplest method would be to watch how quickly your inventory is depleted.  If your baseline is that you sell 1000 widgets a day at a dollar per widget and suddenly you're selling 1250 widgets a day (or selling out of the 1000 widgets your factory can produce a day by early afternoon), it is reasonable to believe that the demand curve has shifted to the right (there demand at a price of $1/ widget has risen by 25%) and to respond by raising prices.  From that same baseline, if you're suddenly only selling 750 widgets a day, it is reasonable to assume that the demand curve has shifted to the left and that you need to respond by lowering prices.

In the real world, think of the hot toy every Christmas.  If your supply of Tickle Me Elmo dolls fly off the shelves minutes after you get them and grown adults are fighting each other in the store to get their hands on one, it's a pretty safe bet that you're selling them at below equilibrium prices.  If the Furbies on the same shelf sit there for months without selling, you've probably priced them above the equilibrium price.

Of course, in reality, stores may have additional methods.  They can look around at what other people are selling items for.  They can do market research to survey customers and potential customers to determine the demand.  Online, they can show people different prices for the same product and see how that impacts purchase decisions.


Can 10% of the population provide super-abundance for the entire world?

Listen to the 30 seconds leading up to that claim. To me it is clear that he is talking of factory jobs. And there he is right. The top countries have no trouble producing more than 10 times the per capita consumption of industry goods per worker.

What he is saying is that production of goods is very efficent. He then goes on and mentions Germany and the US. I looked up the numbers of my home country, Sweden. In Sweden, the number of factory workers has decreased by more than a third since 1970, but production is way up. His point is that lack of production capacity isn't the reason why not everyone has a car, tv, washing machine, etc. We have the technology to produce the same material wealth (things, not services) for the entire world using just 10% of the population.


Relationship between government expenditure and exchange rate?

The relationship between government expenditure and exchange rate is an important one. The key question in current policy and academic debates is What are the effects of fiscal policy on aggregate economic activity in a globalized world?
The central challenge in this debate is how to identify fiscal shocks in the data. Auerbach and Gorodnichenko (2015) address this challenge by using daily data on US government spending. Exploiting this high-frequency data, they find that unexpected government spending instantly affects exchange rates and the dollar appreciate, which if I understand correctly supports your intuition.
The direction of the response of the exchange rate is consistent with basic macroeconomic theory; in an economy with a flexible exchange rate, government spending shocks should lead to appreciation of the domestic currency.