LOC/USD and USD/LOC are currency pairs. Whatever currency comes first is known as the base currency. The currency that comes second is known as quote currency. For major currency pairs, the format of the currency pair is based on established priority. For example, EUR has the highest established priority and thus is almost always shown as the base currency.

Currency pairs quotes work such that one unit of the base currency can be exchanged for quoted amount of the quote currency (hence the name "quote currency"). For example, LOC/USD 6.25 means that one LOC can be exchanged for 6.25 USD. USD/LOC 0.16 means that one USD can be exchanged for 0.16 LOC.

Whenever people say "local currency relative to US dollar", that usually should be parsed as "[base currency] relative to [quote currency]", and thus it would be LOC/USD. A similar interpretation applies for "local currency quoted against the US dollar" (LOC/USD). Another hint is that most "minor currencies" are quoted against the US dollar.


In between eq. $(2.F.2)$ and $(2.F.3)$ we read

  ...Walras's law tells us that $w' = p'\cdot x(p',w')$

Assume now that homogeneity of degree zero does not hold. Then we have, $a>0$

$$x(ap,aw) \neq x(p,w)$$

see definition $2.E.1$

Then we can set $p'=ap,w'=aw$ to examine the case $x(p',w') \neq x(p,w)$.

But then Walras' law would imply

$$w' = p'\cdot x(p',w') \implies aw = ap\cdot x(ap,aw) \implies w = p\cdot x(ap,aw)$$

while also, again by Walras' law we have

$$w = p\cdot x(p,w)$$

So under the assumption that Walras' law holds but that we do not have homogeneity of degree zero we end up saying

$$p\cdot x(ap,aw) = p\cdot x(p,w), \,\,\, x(ap,aw) \neq x(p,w)$$

I believe you can contemplate the situation further from here.


The right term for a market that tends towards consumers switching suppliers freely

If you want a general term, I would suggest frictionless market.

Normally, we would expect customers to reallocate themselves until the waiting time across shops is equalised. Indeed, all else equal, if the waiting time at $A$ is greater than that at $B$ then customers will switch from $A$ to $B$ until the discrepancy is eliminated.

If we do not observe such switching occurring then we say there is some sort of "market friction". Some examples of frictions:

switching costs: switching to a new supplier is costly and the gain in reduced waiting time is not sufficient to compensate consumers for the cost of switching;
informational friction: some consumers don't know of the existence of firm $B$ (or don't know how long its waiting time is). Perhaps they could acquire the missing information, but doing so takes time and effort, which is costly.
principal-agent problems: customers might rationally trust their current supplier because of positive past experiences (formally, reputation can solve moral hazard problems). Or perhaps they just had enough time to learn whether their current supplier is competent or not; something they don't know about the alternatives.
product differentiation: perhaps people like some products more than others. $B$ might be further from their house than $A$ so that visiting $B$ takes longer. Or maybe they know the mechanic at $A$ and like to talk to him/her. This makes them reluctant to switch to $B$.
behavioural factors: if consumers do/can not act rationally then they may fail to take advantage of potential gains from switching.

Here's a neat quote on the issue:

  As recognised by the 2010 Nobel prize, the study of market frictions has generated rich insights in many areas of economics, especially macroeconomics, labour economics and monetary theory.1 In industrial organisation, analysis has focussed on understanding how market frictions can create a source of market power by restricting consumers' ability to change suppliers (Wilson, 2012).


In principle in both positive and negative externality scenario government could just set price to the socially efficient price.
However, outside of static textbook example this is non-starter. The socially efficient price even in presence of externalities (positive or negative) is not constant and it will fluctuate across time. Hence government would have to always change the price it sets. This is problematic since estimating what the socially optimal price is in every instance and in real time is virtually impossible.
Consequently, it is considered more convenient to simply issue subsidy equal to the value of positive externality. In such way no matter how the socially optimal price fluctuates across time as long as the value of positive externality remains constant government does not need to change it across time. Value of positive externality that activity does without doubt fluctuates less frequently than prices so government wound need to reevaluate the subsidy just occasionally.


Economic effects of a Commons Capital Depository

Has anything like his proposed commons capital depository ever been tried in practice?

Sweden had such experiment, but in a much lower scale than it was originally planned and of what Varoufakis is calling for. This was ultimately due to the opposition of employers/capitalists, and the election of a right-wing government.

The idea came from the trade unions in Sweden, and a proposal was presented in 1975 by the economist Rudolf Meidner. According to this article, its goals were:

to counteract the concentration of ownership which, from a general equality perspective, must be regarded as unacceptable;
to increase wage earners’ influence in economic life
through ownership of capital;
to facilitate the continuation of the solidaristic wage policy by a
mechanism to deal with excess profits (which could also be seen as an element in lessening the concentration of capital)

The fund was to be accumulated by holding a proportion of companies’ profits (originally, 20 per cent before tax), which were to be issued as new shares. This was basically an expansion of equity, to be owned commonly by all workers in the economy. After a few decades, this method would leave most of the (equity-based) companies in the hands of workers. So in effect, this was ultimately a socialisation of the ownership of firms. Quite a bold program.

In the end, a reduced version was introduced in 1984, which lasted only for seven years. The fund was privatised by a right-wing government in 1992.

You can read more about this here and here.

More generally, there are plenty of countries with a so called Sovereign Wealth Fund (SWF). Many of these are financed with natural resources like oil (Norway) and minerals (Chile, copper), either coming from special taxation or royalties, or because firms are owned by the state. These funds tend to be invested in a multitude of assets, not only equity. As such, they are not directly attempting to own capital (as in the case of Sweden). I am not aware of any SWF that yields a citizen's dividend though. Many are used as a buffer in case of an economic crisis, or reinvested in other activities like advanced human capital (e.g. Chile).


Real Positive Eigenvalue, but Stable Dynamics

If you have are trying to discretize the continuous time model
$$
\dot{\textbf{x}} = A\textbf{x},
$$
then in discrete time you will have
$$
\textbf{x}_{t+1} = B \textbf{x}_t
$$
but $A\neq B$, since $A$ describes the change in $\textbf{x}$ while $B$ describes the next value of $\textbf{x}$, not just the change. However
$$
\Delta\textbf{x}_t = \textbf{x}_{t+1} - \textbf{x}_t = B \textbf{x}_t - \textbf{x}_t = (B-I) \textbf{x}_t
$$
This new matrix $B-I$ would correspond to $A$.

(From this you can also see why the stability criterion is different.)

Given your equations
\begin{eqnarray*}
\dot{k} & = &  \frac{1}{1+\frac{1}{\rho}} - \frac{1}{1+\lambda} \\
\\
\dot{\lambda} & = &  \rho \lambda - \frac{1}{k}
\end{eqnarray*}
the equations for the discrete modell would be
\begin{eqnarray*}
k_{t+1} & = &  k_t + \frac{1}{1+\frac{1}{\rho}} - \frac{1}{1+\lambda_t} \\
\\
\lambda_{t+1} & = &  \lambda_t + \rho \lambda_t - \frac{1}{k_t}.
\end{eqnarray*}
You will have to calculate the Jacobian of this system to determine stability.


If billionaires stopped spending what would the economic effect be?

If one person decides to reduce his lifetime consumption by (say) \$100, then someone else (or many someone else's) is made richer by \$100.  For example, that $100 might be left to a single heir.  Or at the other extreme, the person might decide to burn a \$100 bill in which case the benefits are spread to everyone who holds money.

When people are richer, they can decide to consume more, or to work less, or some of each.  Because income elasticities of labor supply are empirically quite small, you'd expect most of this to come out in increased consumption.


Creation of Money - Hypothetical Situation II

No or not necessarily because you can't know if the actor will save income or pay down debt, or spend more. The interest rate is not a single factor that determines behaviour.
Nearly all of it is privately created debt money (97%), in circulation. Your 'money' is some bank's liability. You trade their IOUs and they are trusted/licensed to create them. (By all of it I mean in practical terms...there are nominally huge amounts of certain types of security but I don't think their relevance to mainstream social function is useful in the context of this kind of topic)

For more info: https://positivemoney.org/how-money-%20works/how-banks-%20create-money/

Video explanation:https://youtu.be/b6_SLwReMqo

Video from BoE: https://youtu.be/CvRAqR2pAgw

On the influence of the Fed, this is a huge topic. Basically since 2007/8 the Fed creates enough money to compensate for credit contraction in the private sector so that the appearance of growth is maintained. So if in the US nominal GDP growth is 2%, after removing fed stimulus you would see that actual growth is depression level negative. Also the fed sends signals. It could say it would start purchasing corporate bonds directly, which would trigger fund managers into a snowball doing the same. But basically the situation since 2008 is that the Fed is forced to keep monetary policy loose, stimulus ample, to keep lending up and credit growth going.


Central Banks, Large Scale Asset Purchases and Inflation

Here is my question:

  If the federal reserve were to regulate the banking industry so that
  fractional requirements were raised to something like 50% on all
  future deposits, that would have an appreciating effect on the dollar
  since the rate of increase in the supply of dollars needs to keep up
  with the growth of the economy every year. If the Fed offsets this
  appreciation with additional asset purchases by printing money, the
  Fed's revenue/balance sheet would increase...

Reserves are essentially a deposit at the Federal Reserve by banks. Banks have a minimum required level of reserves; anything beyond that are excess reserves. As a result of "Quantitative Easing", American banks already have large amounts of reserves. Raising the reserve requirement would just change the status of the reserves from excess to required, and could easily have little effect on the economy. The precise effects of Quantitative Easing on the economy are debated, but they are certainly not very obvious.

In other words, a policy very similar to raising required reserves was already tried, and had little observable effect.

One thing to keep in mind that reserve creation is distinct from bank money creation. When a bank extends a loan, it creates an asset (the loan) and a liability (the deposit) simultaneously. This step is done independently of existing reserves, or central bank activity.

However, this deposit creation creates a need for extra reserve holdings (during the next reserve accounting period). If excess reserves exist in the banking system, the bank can just go out and borrow the reserves from other banks. That is, lend first, get reserves later. If excess reserves do not exist, the central bank has to create some - if it wants the inter-bank rate to remain under control. Otherwise, some banks will fall short of regulatory requirements, and are effectively illiquid, and will be willing to borrow at extremely high rates to meet regulatory requirements. In other words, reserve creation follows deposit (bank money) creation.

(In case it is not obvious, once the Federal Reserve creates reserves, about the only way they can be destroyed is by currency (notes and coin) withdrawals, or by net tax payments being transmitted to the Treasury. An individual bank can transfer/lend them to another bank, but this does not change the amount outstanding. Therefore, the Fed was able to force an increase of reserves without raising requirements.)

Textbook descriptions of fractional reserve lending tend to be oversimplified. Only some accounts are covered by reserve requirements, and banks have been working techniques to minimise their costs for decades. A lot of "money" is in other money market instruments ("shadow banking") which are not covered by reserve requirements. Raising reserve requirements has the effect of making regulated banks less competitive versus their shadow banking competitors.

Setting a reserve requirement of 50% (for example) would mean that a bank might have to issue a \$50 bond in order to be able to make a loan of \$100 safely. (It has to finance the massive amount of reserves that are imposed on the asset size of its balance sheet.) It would be borrowing in the bond market in order to leave money on deposit at the central bank at the overnight rate.

Balance sheet assets:

\$100 loan; and
\$50 reserves.

Liabilities:

\$100 deposit; and
\$ 50 bond.

The spread on the \$100 loan would have to be increased to make up for the negative spread on the \$50 in reserves (versus the bond). The banking systems ability to lend would be largely crippled, and firms would be forced to switch to alternative sources of financing. If firms cannot get financing, they cannot invest or hire more people, and that makes capitalists and politicians unhappy.

The main economic effect of required reserves is that it is a means of forcing banks to lend to the central bank at a low rate. Until the Fed was given the right to pay interest on reserves in 2008, banks received no interest, and so reserves were an interest-free loan to the government. Even if reserves pay interest, it is at an administered rate set by the central bank (which effectively becomes the short-term risk-free rate). Banks have no choice but to accept that rate of interest, whereas Treasury bill/bond rates are set in auction. (In practice, Treasury bill rates trade close to the policy rate.)

This policy of forcing banks to lend to the government (via the central bank) is often called "financial repression." This matters more for countries with poorly developed bond markets, but the U.S. Treasury can lock in low rates for a very long time without much difficulty.

  and over time that excess profit could start to make up the
  overwhelming portion of the fiscal budget (which could take decades or
  centuries)... Historical issues with the central bank funding the
  budget have always resulted in hyper inflation, but with this work
  around, where the funding of the budget was not coming from the direct
  printing of money but from the profits from security purchases as they
  matured, hyper inflation would be avoided, right?

What percentage of bonds are purchased by the central bank is not an issue. The Bank of Japan has been holding large amounts of Japanese Government Bonds for years, and inflation has not budged. The key is that the deficit is very large (working from memory, some cases were 30+% of GDP), and they were often associated with losses of productive capacity. In other words, the big deficits were the problem behind hyperinflation; a central bank buying existing debt is just a reshuffling of government liabilities.

Attempting to run "too large" deficits and trying to use central bank purchases of bonds reserve requirements to control inflation will not work in the long run. The velocity of money would just increase as people move towards shadow banking. If done for a long enough time, people can just switch over to using a foreign currency, which is usually a critical step towards hyperinflation.

In summary, running a deficit of 1% of GDP and having the central bank buy all the debt (monetising it) is not going to have much of an impact on inflation. (The recent experiments in quantitative easing provide a test case.) Running a deficit of 30% of GDP is probably going to cause serious inflation (unless the country switches over to rationing, such as in World War II), and what the central bank does with its balance sheet is not going to make a big difference.


Endogeneity and Partial effect interpretation of coefficients

I am not sure where the interpretation issue lies. If we look at a relation

$$y = b_0 + b_1x_1 + u \tag{1}$$

and we declare that we would like to estimate $b_0$ and $b_1$ but that $x_1$ is "endogenous", we are essentially revealing that we are interested in the partial effect of $x_1$ on $y$ in the relation

$$y = b_0 + b_1x_1 + \delta'\mathbf x{^*} + e \tag{2}$$

where $\mathbf x{^*}$ contains all the (known or unknown to us) variables that are correlated with $x_1$ (and have something to do with $y$ too), and therefore, $e$ is the conditional expectation function error (not just "any" error term), and as such, by construction uncorrelated with all the variables. Alas, $\mathbf x{^*}$ is unobservable or unavailable to us. Valid IV estimation will nevertheless allow us to estimate consistently $b_1$... which is the partial effect of $x_1$ on $y$ in the above relation $(2)$.

Even if we cannot account for endogeneity, the problem will be that our estimations will converge to someplace unknown. So while we will still be attempting to estimate the partial effect of $x_1$ in relation $(2)$, our numerical estimates will be unacceptable and suspect as regards their value (due to the deficiency of the estimation method) -and not because the desired (but unattainable) research target loses its fundamental interpretation. Our estimates will be "wrongly estimated partial effects". It is not the same as saying "they are not partial effects" (epistemologically speaking).

ADDENDUM
Responding on OP's comments and its enhancement of the question, nothing is stopping us from writing $\partial E(y \mid x, x^*)/\partial x$. At the same time our sample is realized, so is $x^*$ realized, irrespective of whether we know its realized value or not.
Now note that the coefficients/partial effects are assumed constant in this linear setting, irrespective of the variability in the regressors: the partial effect will be the same for all individuals in the sample, irrespective of their actual value for the observable regressor

$$\partial E(y_i \mid x_{1i}, x^*_{1i})/\partial x_{1i} = \partial E(y_j \mid x_{1j}, x^*_{1j})/\partial x_{1j} = \beta_1$$

per assumptions, where $i,j$ are two different observations/individuals in the sample.


Independence of price and wealth in Walras' Law

The answer is that $w$, like $p$, is treated as a parameter in this model. It can only be changed by exogenous external forces that are not part of the mechanism included in the model. In contrast, the demand $a$ is a variable that is entirely determined (endogenously) within the model given the prevailing values of the parameters.

Suppose that $p\cdot a=w$. You are correct to think that if we increase the price, $p$, then we break the budget constraint ($p\cdot a> w$). Within the scope of this particular model, only $a$ is variable and therefore the budget constraint must be restored to equality by a decrease in (some elements of) $a$.

Now, the question why is it so is somewhat philosophical because one could, indeed, build an alternative model that includes some mechanism for determining $w$. For example, we could allow consumers not only to buy goods, but also to supply labour and to negotiate wage rates with their employer. Such models exist within the domain of general equilibrium (a basic treatment of which can also be found in your copy of Mas Collel et al.).

However, there are at least a few reasons to think that the model in question is interesting and relevant despite providing no explanation for the determination of $w$:

Incomes might change in response to the overall price level (i.e. in an inflationary environment salaries are likely to increase). But they are much less likely to change in response to isolated or temporary changes in relative price. For example, the price of fruits changes on an regular cycle depending on when and where they are in season. It would be odd to think that people's income changes in response to this cyclic behaviour. But it would also be odd to think that people's consumption plans did not respond to these price changes. this model allows us to study how people vary demand in the face of such isolated price fluctuations.
At least in the short-run, most consumers are much more able to change their consumption decisions (i.e. to vary $a$) than to change their income. Affecting the latter will often require negotiations, change of job, or even retraining—all of which take time. Thus, the model is likely to be informative about the immediate and short-run effects of a price change. In the data, consumption usually reacts relatively quickly to the economic cycle, whereas wages tend to be "sticky".
In modelling we face a constant trade-off between building a model that is realistic and building one that is tractable/parsimonious. The simple consumer demand model has the virtue of yielding a striking number of sensible predictions from a model that is comparatively straightforward. This has various payoffs (easier to communicate to policy makers, easier to use for empirical work, easier to teach to students, easier to use as the foundation for more applied modelling, etc.)
There are many mechanisms by which $w$ could be determined. For example, it could be union-firm bargaining. Or perhaps firms have all the bargaining power and workers are paid only their marginal product. Or perhaps the consumers are entrepreneurs whose income comes from profits/investments rather than labour. Each alternative would require a different model, whereas this model is agnostic on these points and allows us to focus on another dimension of the problem.


Why is the Stock Market Cap / GDP ratio on FRED well out of date?

This indicator is taken from the World Bank's Global Financial Development dataset, which was "last updated in September 2019 and contains data through 2017".


For the US there is a firm that calculates something from monthly data that the quarterly Bureau of Economic Analysis (BEA) GDP data is also based on: http://www.macroadvisers.com/monthly-gdp/


The evolution of economic thought in the XX century

A reference in this topic is Michel De Vroey. He published a new book on A History of Macroeconomics from Keynes to Lucas and Beyond.

This book retraces the history of macroeconomics from Keynes's General Theory to the present. Central to it is the contrast between a Keynesian era and a Lucasian - or dynamic stochastic general equilibrium (DSGE) - era, each ruled by distinct methodological standards.

See also a paper on The History of Macroeconomics from Keynes’s
General Theory to the Present for the Handbook of the History of Economic
Analysis.


Is this formula for net present value correct?

Q2 : Indeed the correct formulation is for initial investment to appear with a minus sign, since it is an outflow. This reflects the position of somebody who contemplates making the investment. Note also that you shuold check whether there exists some residual value of assets at the end of the operational period examined - this should be added (and discounted) together with the net cash flow of the last future period examined.

Q1 : the logic of the net present value calculation is to notionally compare the returns of the specific investment with some abstract alternative that pays a constant $r$ per period, as a percentage of value left to produce returns. It is as though we have a bank account from which we draw and to which we deposit.

Now think in reverse : in order to "have" amount $F_3$ (three periods in the future), you only need to deposit now in this account $F_3/(1+r)^3$, and leave it there to accrue interest.

Now, if the cash flows are calculated in nominal terms, you would want to deflate them, so as to express them in today's value/purchasing power. The real value of $F_3$ is $F_3/[(1+\pi_1)(1+\pi_2)(1+\pi_3)]$, where $\pi$ is the rate of inflation. So over all we have

$$NPV (F_3) = \frac {F_3}{(1+r)^3 \cdot (1+\pi_1)(1+\pi_2)(1+\pi_3)}$$

Now, if you assume a constant inflation rate (or an average - after all, $r$ is also essentially an average), then you can write

$$NPV (F_3) = \frac {F_3}{(1+r)^3 \cdot (1+\pi)^3} = \frac {F_3}{[(1+r) \cdot (1+\pi)]^3} $$

$$=\frac {F_3}{(1+r +\pi +r\pi)^3}$$

Usually the term $r\pi$ is considered negligible (when we look at "usual" required rate of returns, and when inflation is low, think something like $0.1\cdot 0.02 = 0.002$). So it is common practice to be dropped (both in industry and in academia), arriving at

$$NPV (F_3) = \frac {F_3}{(1+r +\pi)^3}$$

What you were given keeps the inflation rate time variant. This comes from the approximation

$$i_t \approx r_t + \pi_t$$

i.e. that the nominal interest rate equals approximately the real interest rate/rate of return plus inflation. So the nominal rate of return may increase with time solely due to inflation.


How can consumption taxes be made progressive?

This answer simply points out what is, I think, an important part of 1muflon1's answer. There are two ways to think of consumption taxes: One is to tax certain consumption goods with a VAT. Making this progressive is an uphill battle and will cause a lot of distortions that have little to do with distributional concerns. On the other hand, you can simply tax the money spent on consumption, and this can be done in a progressive way. Income equals consumption plus saving. So by making savings tax-exempt, you turn a progressive income tax into a progressive consumption tax.


On trade, What justificaion does the USA have to accuse China of 'selling too much not buying enough from USA'

The US president see’s trade as a zero-sum game, where there is always a winner and a loser, being the winner the one who sells more to the other. This view is not shared by most economists, as the mainstream opinion is that international trade is beneficial for both parties (see Ricardo or Krugman for examples).

In the US’s president mind, “to win the game” they must restrict the sales of Chinese goods, using tarifs or quotas. The US can either produce these goods or import them elsewhere. The Chinese, however, are expected to have no other alternative but to keep importing advanced goods, critical for their economy, such as aeroplanes parts from Boeing.

The expected outcome from this policy is less competition for national producers, potentially resulting in more jobs and higher profits. However, end consumers might end up facing higher prices for several goods, resulting in lower real incomes.


Empirical set-up for measuring elasticity with respect to quality in an environment without price

You might have to create your own set-up for a question like this. Elasticity of quantity with respect to some variable is can generally be measured by

$$\frac{\frac{\partial Q}{Q}}{\frac{\partial x}{x}}$$ where x is the variable you are measuring. In this case, you can do three separate elasticities w.r.t size, speed, resolution. Since you have data on thousands of people, just aggregate it all together and run a regression to measure the quantity of people who buy a tech with such and such size, speed, resolution across your whole time period. So you'll have something like

$$y = \beta_1 x_1 + \beta_2 x_2 + \beta_1 x_1 + \epsilon$$

Where $$x_1 = \frac{\frac{\partial Q}{Q}}{\frac{\partial \text{size}}{\text{size}}}, \quad x_2 = \frac{\frac{\partial Q}{Q}}{\frac{\partial \text{speed}}{\text{speed}}}, \quad x_3 = \frac{\frac{\partial Q}{Q}}{\frac{\partial \text{resolution}}{\text{resolution}}}, y = \text{total techs of all sorts sold}$$

Although you probably want to tweak that a bit, as I'm not sure why you'd want to specifically use elasticity.

If I am fundamentally misunderstanding the model you are trying to do, please let me know.


Using an elasticity to evaluate changes in a dependent variable

why formula #3 may be more appropriate than formula #2?

Actually, #2 is a linear approximation of #3.
Note that
$\partial \log Z$
can be written/seen as
$\log Z_2 - \log Z_1 = \log\frac{Z_2}{Z_1} (\approx 0)$
where the above difference is infinitesimal, hence the use of $\partial$.
In such a case, #1 can be written as
$\epsilon = \frac{\frac{\Delta Y}{Y}}{\frac{\Delta X}{X}}= \frac{\log (Y_2/Y_1)}{\log (X_2/X_1)}$
Equivalently, the above equality is only true because we are dealing with infinitesimal changes. Which means that if, say, $Y_2 >> Y_1$, the above equality implies an approximation, i.e.
$\epsilon = \frac{\log (Y_2/Y_1)}{\log (X_2/X_1)} \approx \frac{\frac{\Delta Y}{Y}}{\frac{\Delta X}{X}}$
Which leads to #2:
$\frac{\Delta Y}{Y} \approx \epsilon \frac{\Delta X}{X}$
Actually, the smaller $\Delta Y$ and $\Delta X$, the better the approximation.

how does one get mathematically from formula #1 to formula #3?

$\epsilon = \frac{\log (Y_2/Y_1)}{\log (X_2/X_1)}$
$\Leftrightarrow \log \frac{Y_2}{Y_1} = \epsilon \log \frac{X_2}{X_1} =$
$\log\left[\left(\frac{X_2}{X_1}\right)^\epsilon\right]$
$\Leftrightarrow \frac{Y_2}{Y_1} = \left(\frac{X_2}{X_1}\right)^\epsilon$
$\Leftrightarrow \frac{Y_2}{Y_1} -1 = \frac{Y_2 - Y_1}{Y_1} = \frac{\Delta Y}{Y}= \left(\frac{X_2}{X_1}\right)^\epsilon -1$


What is the reason of devaluation in Turkish Lira?

The recent shift was likely two major interrelated reasons:

First, there was already relatively high uncertainty regarding the future viability and value of the currency (as @zeta-band noted, they're already incurring high deficits).

Second, Erdogan has made statements suggesting that, if re-elected, he'll take more direct control over the central bank. Given that he'd likely institute policies that would lead to higher inflation (or force haircuts on foreign debt holders), investors see that as a worrying potential future outcome.

Though at the same time, the rising interest rates (which, while lower than rates in Turkey, are higher than they were previously) in other Western countries has made investment in places other than Turkey more alluring, which also can devalue the Lira.

EDIT 2:

Perhaps clarifying that sentence a bit would be helpful (I left off an implied phrase, which is bolded below, which might have led to confusion)

  rising interest rates in other Western countries has made investment in places other than Turkey more alluring than they comparatively used to be.

I'm saying investors consider a variety of different factors when deciding where to invest. If everything about two countries was absolutely equal (both currently and into the future) then we would expect the investor to put more money in the country who has comparatively higher interest rates. However, this all else being equal assumption clearly never holds in the real world- countries have different political risks, economic risks, exchange rate risks, etc. that investors consider.

At the same time, even if every investor evaluates all of these risks identically (meaning everyone looks at the risks in both countries and agrees how likely each event is to occur, and how each one would affect any given investment) we'd still expect to see some variation in investment patterns. Why? Because every investor is optimizing over an entire portfolio, and is considering different specific investments. Additionally, every investor has their own risk preference, a more risk averse investor might be willing to forgo a higher expected return in one country for the comparative "safety" of another.

Which takes us back to the case of Turkey. It's true that the interest rates set by the Turkish government are quite high compared to other countries. However, if you're a US-based long term investor (meaning here the projects you'd be investing in wouldn't allow you to get a return on your investment for a long time) you might be worried about other perceived risks (like future inflation) that would make the high interest rate not enough to overcome the potential risks.

So what do we see? We see that there are some international investors who choose to invest in the US (or Europe, China, India, etc.- just not Turkey), some who choose to invest in Turkey, and some who split their resources between them. Furthermore, we can ask a hypothetical question: for investors in group 1 (non-Turkey investors), all else equal, how high would the interest rate have to be to induce you to invest? Clearly the answer is higher than the current rate, but at the same time, we'd expect at least some of them to shift investment if the Turkish interest rates were 75%. Clearly, as the Turkish interest rate goes up, more and more of those investors would shift resources into Turkey.

What we can then do, however, is consider that second and third group of investors (those who invest at least some of their resources in Turkey) and as them "how would your portfolios change if the US interest rate wasn't 1 or 2%, but 50%?" Obviously, we'd expect those investors to shift at least some of their investments from Turkey to the US.

The critical thing, however, is that there isn't a discontinuity. That means that as one country raises their interest rates a bit, some investors would likely shift some of their resources into that country. What we care about is the marginal investment in each country- the investment that was only just barely worth it given the conditions. These are the investments that we expect to shift.

So in conclusion, what's driving the devaluation is two fold. On one hand, there's a perception of increasing risks inside Turkey. On the other, the return for investing in places like the US are increasing from what it was previously. These two forces (one pushing down the attractiveness of investment in Turkey; one pushing up the attractiveness of investment in the US) are working in the same direction- to push investment out of Turkey, devalue the currency, and push them into other countries.


What do they mean by “bottom line” and why did US IRS turned back 810 millions to IBM? and what do they mean by “unspecified “ layoffs?

As regards your second question,
"Bottom line" is a descriptive term for profits/losses, visualizing that when we calculate whether we had profit or loss,  we start writing revenues then expenses and at the end we have a line that tells us the difference between the two. But since it is the "last line" it is also at the "bottom" of what we have written, hence "bottom line".

Sometimes it is also used figuratively to indicate the "end result" of something other than financial activity, especially with an intent to brush away reasons and excuses why something did not happen or happened inadequately.


Generalization of the Heckscher-Ohlin Model

The HO model has been generalised. Vanek does a good job of it.

Instead of only two countries, there is an index of countries.

There are many industries.
Identical technology
Identical, homothetic tastes.

The HOV theorem states that if a country is abundant in a factor,
its factor content of trade in that factor should be positive, and
negative otherwise.

Empirically, this model is not that successful. Here is a good paper discussing the applications and results.

See below for that extension:
Vanek, Jaroslav, The Factor Proportions Theory: The N-Factor Case,” Kyklos, October 1968, 21, 749-755.


what is the optimum level of production?

Try to think about what the the optimal level of production is supposed to be. What should it maximize? The revenue?

What you have calculated is the revenue maximizing level of production but maybe you wanted to find a level of production that maximizes something different?


The intuition you have is correct. Mathematically you can show it by first deriving the optimal choices with the lump sum income tax. So you will set up the following lagrangian:
$$\mathcal{L} = x^{1/2}_1 x^{1/2}_2 - \lambda [x_1p_1+x_2p_2 - m + T] $$
This gives you 3 FOC's the budget constraint and:
$$ 0.5x_1^{-0.5} x_2^{0.5} = \lambda p_1 \\
0.5x_2^{-0.5} x_2^{0.5} = \lambda p_2$$
Solve for optimal $x_1^*$ and $x_2^*$:
$$ x_1^* =  \frac{m-T}{2p_1} = \frac{32-T}{2} \\
x_2^* =  \frac{m-T}{2p_2} = \frac{32-T}{2}$$
Where here the second equalities take advantage of the assumptions that $p_1 = p_2=1$ and $m=32$.
Now  you can just plug this into the utility function and assuming you made no mistake equate this to the utility with the consumption tax on $p_1$ so you will have:
$$ 8 =  \left( \frac{32-T}{2}\right)^{0.5} \left( \frac{32-T}{2}\right)^{0.5} \\
T =16$$
So under the income tax regime government gets $T=16> t=12$ while consumer still has the same utility as under the consumption tax, meaning the income tax is better. The intuition for that is that income tax does not distort the relative prices only has an income effect whereas consumption tax has both income and substitution effects.


How is the defintion of the mean preserving spread (MPS) not too general?

I realized my mistake whilst writing this, so I will just share the answer as well.

Essentially my mistake was, that I assumed this aspect of the definition ($E[z|x_g] = 0\ \forall\ x_g$) to mean that the expected value of z has to be 0 given, that we are in the lottery that is given by the random variable $x_g$. This reading was however wrong. It actually means, that the expected value of z has to be 0, given that we are at a particular value of $x_g$. This has to be individually true for all values of $x_g$.

Thus, using this definition correctly a negative spreading is not possible anymore, the MPS of the original lottery is therefore always at least as risky as the original lottery. A risk averse decision maker will thus never want to choose an MPS.


Can mixed strategies actually predict behaviour of rational actors in non-constant sum games?

There is a series of papers that address precisely this question. The most famous ones are probably Walker and Wooders (2001) and Chiappori, Levitt, and Groseclose (2002) that deal with penalty kicks and tennis serves. Both papers conclude that the behavior of professional athletes is consistent with them playing g a mixed strategy equilibrium. A more recent working paper by Gauriot, Page, and Wooders (2016) shows that highly ranked tennis players are closer to playing optimal mixed strategies.

One caveat of those papers is that they deal with zero-sum games. As fas as I know, most of the empirical evidence that supports the use of Nash equilibrium over other solution concepts comes from zero-sum games.

People have also tried to justify the predictive power of Nash equilibrium using theoretical arguments. The results for games without pre-play communication are mixed. For a long time, people believed that Nash equilibrium could be deduced from the rationality of the players. It turns out that this is not the case (e.g., Brandenburger, 1992). People also hopped that behavior over time would converge to Nash equilibrium as the players acquire experience. There are some positive results for some specific settings, but not in general (see Nachbar, 2005). In many settings in which behavior converges, it converges to things that are not Nash equilibria (such as rationalizable strategies, or correlated equilibria).

The game that you describe is one of the hardest games to make accurate predictions. I personally do not see why we should expect people playing Meeting in NY to follow pure or mixed Nash equilibria (unless people talk to each other beforehand and agree where to meet).

  I don't understand why this concept is seen as generally useful?

If for no other reason, Nash equilibrium and its refinements are the most important solution concept because they are by far the solution concept most commonly used, at least in the social sciences.

The reason why Nash equilibrium is used so much could be accidental. People often attribute the following quote to Roger Myerson:

  If there is intelligent life on other planets, in a majority of
  them, they would have discovered correlated equilibrium
  before Nash equilibrium.

It is difficult to justify the concept of Nash equilibrium as "the best" solution concept for general games without communication.


Rigorous proof needed: Acemoglu (Intro Growth) Corollary $2.1.2$

The OP correctly identified a mistake here. Since the author claims monotonicity for a general function, let's disprove it for the simple linear case.
Consider

$$x_{t+1} = g(x_t) = -0.5x_t$$

This satisfies all the requirements and conditions stated by the author, and also that the derivative is smaller than unity in absolute values $\forall x$. But it converges with "damped oscillations", and so it is not monotonic since, say,

$$x_0 = -3 < 0 = x^*$$
$$x_1 = 1.5$$
$$x_2 = -0.75$$
etc


How is the utility function with constant relative risk-aversion obtained?

In the slide, we're given the marginal utility (or the derivative of the utility function) as $m(x) = x^{-b}$. The utility function whose derivative is $m(x)$ is

\begin{eqnarray*} u(x) =  \int m(x) dx = \int x^{-b} dx = \begin{cases} \frac{1}{1- b} x^{1-b} & \text{when } b \neq 1 \\  \ln x & \text{when } b = 1 \end{cases} \end{eqnarray*}

Verify that $u'(x) = m(x)$.


Papers on Game Theory and the Housing Market

-Game Theory and Real Options:
Analysis of Land Value and Strategic Decisions
in Real Estate Development- Chun Kit So ( Timothy So )

https://dspace.mit.edu/bitstream/handle/1721.1/84171/867636352-MIT.pdf?sequence=2

-Course blog for INFO 2040/CS 2850/Econ 2040/SOC 2090

Using Game Theory to Understand the Housing Crisis of 2008

https://blogs.cornell.edu/info2040/2017/09/11/using-game-theory-to-understand-the-housing-crisis-of-2008/

-Why housing price in Hong Kong is so high? An explanation in game theory
Ho-Yin Yue1* • King-Tai Leung 2 • Lee-Kei Fung - Economics and Business Letters


Could you recommend a book or lecture notes about time series that is easy to understand?

The book I currently use for my time series class is "Time Series Analysis and Its Applications With R Examples" by Shumway and Stoffer, 4th edition. It's served me fine, and gives lots of example codes that you can plug into R and see what happens with example data.


Utility maximization problem : free product vs priced product?

I think there are some problems with the framing of your question. Some points...

There are some assumptions that need to be added for a meaningful answer.

Diminishing returns, budget constraint, free disposal etc.
In terms of utility maximization, there needs to be a budget constraint. if you add one and seek to maximize utility, the consumer will hold $x_2=\frac{w}{p}$ (spend all their money on good 2, and then hold an infinite amount of good 1.

If you are thinking of something like an app, consider non monetary costs. They operate in the same way. Like the time value of playing a worse app. or movies, if you are given a choice to watch a terrible movie for free or pay to see a good movie, you may elect to pay. In which case time is a factor. You can't consume an infinite amount of terrible movies at time $t$.

In summary, you need to add more to the question. If a good is free, marginal utility has to diminish and $\frac{du}{dx}$ needs to equal $0$ at some point or supply has to be finite. Until at least that is satisfied, the consumer will spend all money on on $x_2$ and hold an infinite amount of $x_1$


Does the introduction of credit card affects Money Velocity?

Credit cards are a way of deferring payment in the form of inter-temporal substitution; it helps reduce the household's liquidity constraint that may prevent it from consumption smoothing as much as they would like if their transitory income was much more spread over the household's lifetime.

You are right that the amount of money doesn't change. Loans require giving away money, but credit cards are a way of creating debt, so banks do not need to hold more cash to give a line of credit like you suggest.


You are right, but to make sure that the odds are really exogenous ("objective") you need to make sure that the subjective uncertainty has no bite here. In other words, you need to assume that the objective lottery played after the horse race is independent of the result of the horse race (in Anscombe-Aumann's terminology).

Let's assume that $Z$ is finite, $Z=\{z_1,\cdots,z_n\}$ and that $L$ is the objective lottery that puts weight $l_i$ on the prize $z_i$, with $l_i \geq 0$ and $\sum_{i=1}^{n}{l_i}=1$.

You can identify the lottery $L$ with the act $f:s \rightarrow \Delta Z$ such that $f(s)=L$ for any $s \in S$. That is, for any $s \in S$, $f(s)$ is the objective lottery that puts weight $l_i$ on the prize $z_i$, exactly as $L$ does.


Where do the rich and poor live in a city? (Calculus)

1. The first question is based on a misreading of the text.
First of all it is quite correct that under the model assumptions stated:
$$(A) \ \ p''(d) = \frac{t(y)H'(y) - t'(y)H(y)}{H(y)^2} y'(d),$$
however there is no problem because the book does not state that
$$(B)\ \ p''(d) = \frac{t(y)H'(y) - t'(y)H(y)}{y'(d)}$$
the book instead states that the second order condition
$$ p''(d) > 0 $$ implies $$(C)\ \ \  \frac{t(y)H'(y) - t'(y)H(y)}{y'(d)} > 0$$
which follows from (A) - the true experssion you have derived for $p''(d)$ - by multiplication of $(H(y))^2$ and division of $(y'(d))^2$.
Nevertheless, I suspect it is a typo even though it is inconsequential.
Obviously, given (C) or [(A) and the second order condition $p''(d)>0$] it follows that $y'(d)>0$ iff
$$t(y)H'(y) - t'(y)H(y) > 0,$$
which again is equivalent to $$\frac{y}{H(y)} H'(y) > \frac{y}{t(y)} t'(y)$$
hence the high income people live in the suburbs ( $y'(d)>0$ income increases in distance from city center) iff and only if the income elasticity of housing is larger than the income elasticity of transport costs $t(y)$.

The second question: How can income be a function of distance $y=y(d)$ when we differentiate the second order condition but not when we consider the first order condition?

The idea is as usual that residents have some income $y$ exogenously given. They cannot decide themselves what income the want nor is their income a product of their location choice. When they choose an optimal location $d^\star$ they choose in such a manner that the first order condition $p'(d) = - t(y)/H(y)$ must hold. However, individuals of different income levels will choose different locations and therefore in equilibrium income will be a function of location $y = y(d)$. Therefore when you want to consider what things are like in equilibrium you can use that income $y$ is a function of $d$.
Glaeser does not proove the existence of such an equilibrium but this type of equilibria with perfect income sorting is known in the literature and the book is a textbook.
The derivation of the first order condition in this simplified model where housing demand is assumed exogenously given as a function of income goes along these lines:
The residents have utility function $U(c,H)$ and income $y - t(y)d$ net transport. They maximize with respect to $c$ so conditonal on $d$ the value function is $U(y - t(y)d - p(d)H(y),H(y))$. In spatial eq. if people with the income $y$ is in the city then they choose some $d^\star$ maximizing the conditional indirect utility function $U(y - t(y)d - p(d)H(y),H(y))$ with respect to $d$ giving the utility $U(y - t(y)d^\star - p(d^\star)H(y),H(y)) = u^\star(y)$. These individuals would only ever consider other locations if they gave the same level of utility (or higher but in that case $u^\star(w)$ would not be maximum). This allows the us to undertake the thought experiment: How would prices have to change as a function of location if other locations gives rise to the same level of utility? This thought experiment is carried out by imposing the condition that $U(y - t(y)d - pH(y),H(y)) = u^\star(y)$ at all locations and solving for the price (giving what is called the bid-function). The derivative of the implied bid-function can be found by differentiating $U(y - t(y)d - pH(y),H(y)) = u^\star(y)$ with respect to $d$ giving the condition $p'(d)H(y) = - t(y)$ which is the wellknown Muth condition.


Why is food less expensive in India than the United States?

I think your intuition is right that food is cheap there. The Economist Big Mac price index suggests that India has some of the cheapest big macs in the world. More generally, the index indicates that there is a strong relationship between GDP per capita (a proxy for labor costs) and Big Mac prices:

Labor is a significant part of the costs of making food (25-35 percent in America). Transportation is a significant part of the cost of food grown far away (world bank data indicates that even exports fees alone can be substantial). But when food is grown locally and prepared locally, the total costs are significantly determined by local labor costs. In addtion, Indian restaurants probably also serves much smaller portions than in rich countries, particularly the United States. They may also make use of less expensive ingredients generally, more stables and seasonal vegetables and less dairy and meat.


According to the logical positivist view of decision theory, utility functions are just descriptions of observable behavior and have no intrinsic meaning absent this vantage. In other words, $u(x) > u(y)$ indicates that $x$ would be chosen in favor of $y$, but the magnitude of the difference carries no addition information. If $u(x) = 1$ and $u(y) = 0$ the decision maker prefers $x$; if $u(x) = 10000$ and $u(y)= 0$ the decision maker prefers $x$. In either case, we can draw the same conclusions.

What does this mean with regard to your question? It tells us what we mean by equality of utility functions: we mean that these two different (so no definitionally equal) functions represent the same observable data. Specifically, exactly when $u_1(x) > u_1(y)$ do we also have $u_2(x) > u_2(y)$. As mentioned in the comments, this is precisely when we can compose $u_1$ with a strictly increasing function and pop out $u_2$. (This is because all we care about is the ordering between objects, and strictly increasing functions preserve order).

So, what might our strictly increasing function look like? Well, we can take the log, so that we get $\frac23 ln(x_1) + \frac13 ln(x_2)$ then multiplying by 6 and adding 3 does the trick. Each of these was strictly increasing so too is the composition:
$$ (x,y) \mapsto 6 (ln(x) + ln(y)) + 3$$
is our desired function.


Where can I find historical (very old) USD printing data?

The Bureau of Engraving and Printing maintains public records on their web site, but that data only goes back to 1980. Therefor your best option might be to write or call them and ask for information for the time period you're interested in. If they are not forthcoming, you can call back and try your luck with a different staff member. If that doesn't work, you can resort of filing a Freedom of Information Act request. According to this page the average turnaround time is 23-31 days depending on the complexity of the request.

There is also this site, which has information on the US money supply from 1959 - present, but I am not sure it is presented in a way you'll find useful for your project. I am also unsure if it meets your definition of "very old."

Good luck!


Econometric analysis of mergers from a company's point of view

A good textbook for this sort of empirical research is Introductory Econometrics for Finance by Chris Brooks. That textbook helped me a lot when I was writing my thesis, which was actually on M&A (if they improve financial ratios for firms). I know writing a thesis is not exactly the same as actual research but reading your question I think you could find it useful.


The best way is taking the index "ingredients" and rebuild it... assuming you manage the index data on a DB or on an excel file, that should not be too difficult

Otherwise, assuming you're index ingredients are averaged equally, then in a sense, the index is calculated as:

Index = (1 + Product1ChangeIn%)^(1/9) * (1 + Product2ChangeIn%)^(1/9) ...

So based on it, without coal, you're index should be:

Index / (1 + CoalChangeIn%)^(1/9)


Will there be any competition amongst cement retailers?

Since they are different retailers, their products are not perfectly homogeneous. The differences might be in delivery times, friendliness of representatives, packaging etc. So, their products are not strictly identical.

For the monopolistic competition, it is mentioned that there are multiple retailers. If we assume they do not collude, there will be a form of competition.

Taking these two characteristics, I would say there is a form of competition, more specifically "Differentiated Bertrand Competition".


GNP, GDP, GNI, GNDI and their relationships?

GNI is simply a new name for GNP.  It is GDP plus net primary income from abroad (i.e. with primary income paid abroad treated as negative). Primary income is described in Chapter 11 of the IMF BOP manual

GNDI is GNI plus net secondary income from abroad (and similarly secondary income paid abroad is treated as negative).  Net secondary income from abroad is the same thing as is meant by net current transfers from abroad: see Chapter 12 of the IMF BOP manual


Hotelling’s Continuous Model - game theory

Pick an arbitrary cdf $F$ that is supported on $[-a,a]$. The median, $m$, must satisfy $$\int_{-a}^{m}dF \geq \frac{1}{2}, \quad \text{and} \quad \int_{m}^{a}dF \geq \frac{1}{2}$$

Note that $m$ is not generally $0$.

The phrase you mention, "the unique NE is where both candidates chooses the policy associated with the median voter," simply means that the unique NE is where both candidates choose a policy located on $m$.

This is easy to show, think of "unraveling toward the center."


You are confusing money supply with GDP. GDP is defined as the total monetary value of all goods and services produced within the economy. For this case,

GDP =  Woman's Earning + Gardeners Earning

Before Marriage = 1000 + 60 = $1060

Even though the woman has $940 she was still compensated $1000 for whatever service she provided. The money supply is 1000 but GDP is not.

Post Marriage = 1000 + 0 = $1000


There are number of reasons to use derivatives. How practical the following are? It, in turn, depends on the costs compared to the importance (utility) of the case. The costs can be substantial.

Hedging purposes, which comes in many forms. E.g. when you buy stocks in foreign currency, you may want to take only the equity risk, not currency risk. Or you buy a fund or etf that comes with country or industry risk that you want to get rid off. Or you believe equity in the long run but don't like the volatility, so you (try to) hedge volatility away.
Limit controlling. E.g., if you are working in asset management industry and take care of funds of customers, the portfolio should have set limits: the derivatives may give you an easy way to comply with limits ("you are happy with the instruments you have chosen to your portfolio and want to keep them but without derivatives, say the minimum amount of equity risk would not be attained").
Leveraging a (sub-)portfolio. "Sometimes you cannot apply loans. But want to have more exposure than is otherwise possible."
Bearing a particular type of risk, e.g., you may believe that volatility is going to increase from the current level. This particular example can work as a hedge to your portfolio at the same time, since usually the increase of volatility means that portfolio performs badly. Moreover, this is an example of risk that is hard to get in to your portfolio without derivatives.
Quick change of allocation for tactical reasons. Say, evolving crisis either forces you to move quickly, e.g., because of limits as in case 2, or because of the capacity to bear risk (economic reason). And this case includes also the panic moves.
Sometimes, there are other motives behind applying derivatives that somehow build upon the first four cases. E.g. you have a complex company structuring case in your hand and you may have to transfer particular types of risk from one party to the other. To the other this is hedging and to the other risk taking: the derivative use could be classified to be "enablers" of transactions.
In the spirit of previous case, derivatives can be used in product design. E.g. some hedge funds promise to apply certain derivatives strategies. These products (hedge funds) may be targeted to professional investors and retail customer. Another example include index loans, typically marketed to retail customers, and may include exotic derivatives like binary options where the underlying is determined e.g. by the month end values of the last 12 months for a basket of securities. The motivation for options reduces to the first one listed above (hedging): the index loan may include a promise ("a guarantee") that, say 95% of nominal will be preserved in every possible scenario to be faced. So hedging appears to be provided to customers.
"Personal characteristics" like willingness to gamble may apply as reason. These may reduce to the third item.


You might call Graeber's theory of money as something emerging from a system of compensation from the harm of others.

The Chartalist's say the state is what makes money, they demand taxes be paid in money, this gives money value, and then the state makes money which it spends on what it wants.

  The Chartalist contribution turns on the recognition that money cannot
  be appropriately studied in isolation from the powers of the state –
  be it modern nation-states or ancient governing bodies. It thus offers
  a view diametrically opposed to that of orthodox theory, where money
  spontaneously emerges as a medium of exchange from the attempts of
  enterprising individuals to minimize the transaction costs of
  barter. The standard story deems money to be neutral – a veil, a simple
  medium of exchange, which lubricates markets and derives its value
  from its metallic content. Chartalism, on the other hand, posits that
  money (broadly speaking) is a unit of account, designated by a public
  authority for the codification of social debt obligations. More
  specifically, in the modern world, this debt relation is between the
  population and the nation-state in the form of a tax liability. Thus
  money is a creature of the state and a tax credit for extinguishing
  this debt. If money is to be considered a veil at all, it is a veil of
  the historically specific nature of these debt relationships.
  Therefore, Chartalism insists on a historically grounded and socially
  embedded analysis of money.

  This chapter distinguishes between several broad Chartalist
  propositions about the origin, nature and role of money, and several
  specific propositions about money in the modern context. It offers
  only a cursory examination of the historical record to illumin- ate
  the essential characteristics of money emphasized in the Chartalist
  tradition. Chartalist ideas are not new, although they are most
  closely associated with the writings of Georg Friedrich Knapp of the
  German Historical School. Thus the chapter briefly surveys instances
  in the history of thought which have emphasized the chartal nature of
  money. The paper then expounds on Chartalism, clarifying aspects of
  the concepts and drawing out the implications for modern currencies.
  It concludes with a discussion of the various applications of this
  approach to policy.

Chartalism and the tax-driven approach to money

Economics (as a profession) generally focuses on another motive for money, solving the problem of the double coincidence of wants. That is, in barter we generally need to both want what the other has or we can't make a deal (unless we have credit, but consider barter among strangers). Money presents an alternative, a good that we don't want per se, but we can use for transactions because everyone else wants it and we can rely upon to want it later as well. Such a thing should be portable, hard to counterfeit, and easily identified. Then when Art wants to buy a Ball and Charlie has a Ball but wants to a Dog, Art can use his money to buy the Ball from Charlie so that later he can use money to buy a Dog from Eric who will then use it to buy Florence's Goat, and so on...

There is an accessible and justifiably famous paper on this sort of money, The Economic Organisation of a P.O.W. Camp,  about how cigarettes emerged as this sort of money in WW II POW camps. Graeber singles this paper out for scorn, saying these people already knew about money and so this is not a good example of a origin story for money, but it is a nice example of money as an emergent phenomenon to solve the double coincidence of wants problem.

I haven't read Ascent of Money, I recall it getting mixed reviews, but I really enjoyed a Ferguson's somewhat related The Cash Nexus,  which might help you understand the national aspect of your question. I also enjoyed The Origins of Value: The Financial Innovations that Created Modern Capital Markets, but that book covers much more than just money.  Famous Myths of Fiat Money has some nice examples of commodity money emerging to solve transactional issues. On Money as a Medium of Exchange is a famous (relatively modern) theory paper that covers the benefits of fiat over commodity money. The book What is Money? in many ways is a long answer to your question, with chapter 7 in particular covering a lot of these issues.


Why do we say the US is in debt to China?

Because, regardless of private debts of Apple, the US government is in debt to China.

  As of September 2014, foreigners owned \$6.06 trillion of U.S. debt, or approximately 47% of the debt held by the public of \$12.8 trillion and 34% of the total debt of $17.8 trillion. As of 2018, the largest holders were China, Japan, Ireland, and Brazil.

https://en.wikipedia.org/wiki/National_debt_of_the_United_States#Foreign_holdings

See also MAJOR FOREIGN HOLDERS OF TREASURY SECURITIES


Are interest included in the computation of government debt

As originally written, parts of the question are unclear. We do not normally calculate the government debt of two countries together, they are calculated independently. Adding up debts across countries can be done, but the debts are quite oftenly in different currencies, so that would need to be taken into account.

The standard for government debt calculations is to add up the face value of all debt emitted. Yes, this does not take into account the differing interest rates, but one can usually find out the average interest rate. So in your example, both countries have debts of \$100.

(As an example, the U.S. Treasury has a webpage on “The Debt to the Penny”, with the total face value of debt; Link to FAQ. Per issue data is found in the reports available here: link to Monthly Statement of the public debt.)

One could look at the market value of government debt, but these data are not usually provided by national statistics offices. Financial data providers (bond indices) have this, but the data often misses out short-term debt, and non-marketable debt.


why don't we also pay money to industries that have a negative carbon footprint?

Are there any examples of such policies?

Yes. Under the 45Q tax credit program, the US pays

\$50 per metric ton of CO2 for projects that sequester carbon and \$35 per ton for projects where carbon is captured and then used for recovering oil underground.


Is anyone familiar with the following basic resource sharing model?

This looks like a Tullock contest. I think in his model the prize from bidding (or putting in effort) is un-divisible, so $r_x$ will represent the probability of winning the price. But other than re-interpreting coefficients, the setting looks identical to me. There are tons of papers on these kinds of models. Hope this helps.


How does one calculate compensating variation for multiple price change?

I think the good way to do that is to introduce the Expenditure function which awesomely solves your problem.

The Expenditure function gives the money one has to spend to achieve a given level of utility, given a utility function $u$ and the vector of prices $p$.

$e(p,u^*)=min_{x \in \mathbb{R}_+^n,u(x) \geq u^*}p \cdot x$

Then you can express your compensating variation in two equivalent ways:

$CV=e(p_1,u_1)-e(p_1,u_0)=e(p_0,u_0)-e(p_1,u_0)$ where $p_0$ and $p_1$ are the old and new prices and $u_0$ and $u_1$ are the old and new utility. One can note that it can be translated as: if given $CV$ in compensation for the change, then the consumer would be indifferent to that change.


Disruption vs economic growth vs inflation

They are interconnected. For example, disruption could lead to deflation, because someone (such as Amazon) can come into the market and sell goods at a lower cost, while increases the quantity of goods. This could grow real GDP (in terms of economic output), while decreasing nominal GDP when adjusting for the deflator (hypothetical scenario).

Economics growth can also lead to nominal price inflation (connection), as more goods and services are sold throughout the economy. Economic growth can also occur with disruption (connection), if the disrupting firms are more efficient in terms of economic output. This would simply increase societies production possibilities frontier.


Is the fundamental analysis also a self-fulfilling prophecy?

If a sufficient fraction of market participants follow technical analysis it can work as self-fulfilling prophecy. If some pattern occurs that technical analysis interprets as signalling an imminent drop in prices these people will sell, which will cause the prices to actually drop.
As is obvious from the above argument, whether an interpretation of the data can become a self-fulfilling prophecy, depends not on the nature of the the interpretation, but on whether a sufficient amount of market participants are prepared to act upon it. For example if fundamental analysis shows that a firm is likely to go bankrupt other firms become hesitant to trade with it because if it fails without settling its bills with them they will have to take the losses. This in turn makes it harder for the threatened firm to survive.


What changes the structural rate of output/unemployment?

Let $L$ now rise. What happens to $u_n$ and $Y_n$?

From the equation, if $L$ rises, everything else equals, then $u_n$ will rise (that is, the fraction will be smaller).

$Y_n$ will also rise and that is a fairly reasonable conclusion - Extra work force will lead to more outputs.
Now, the misleading conclusion is in regard to the markup. Consider now the labour market. When demand (work force) increases and all else remains equal (supply side - firms offering job opportunities), wages will lower and thus that setup will have a new equilibrium - with lower wages and more work force.

This is my interpretation of your question, although the answer may not be 100% accurate, or an answer that actually answers your question.


Understanding the shape of a Marginal Cost Curve

You are missing the average cost curve in the same diagram.
Basic algebra gives us the following.

Let's find the minimum of the $AC = C/Q$. We have

$$\frac {\partial AC}{\partial Q} = \frac {MC\cdot Q - C}{Q^2}$$

For this to be equal to zero, we must have $MC \cdot Q = C \implies MC = AC$. So when $AC$ is at its minimum, it equals $MC$. But we also want the second order condition, and we want the second derivative to be positive, evaluated at the critical point.

$$\frac {\partial^2 AC}{\partial Q^2} <0 \implies ...MC'\cdot Q^3-2MC\cdot Q^2 + 2QC >0$$

At the critical point $MC = AC = C/Q$. Inserting this we get the condition

$$MC'\cdot Q^3-2(C/Q)\cdot Q^2 + 2QC >0 \implies MC'>0$$

So at the point where $MC = AC$ we want MC to be rising. But this implies that it will cross the $AC$ curve from below. In turn this implies that for quantities lower than this point, marginal cost curve will be below the average cost curve, which means that if this left part of $MC$ curve was a supply curve the firm would have losses.

Therefore the supply curve is only an upwards-sloping part of the marginal cost curve. You can now superimpose the $AC$ curve that is consistent with all these.


If governments can accurately do your taxes for you, why would it overwithhold people's income?

This is US specific and more of a political than an economic or technological problem.
In the US, there is a lot of lobbying by tax preparation firms for the antiquated tax system to remain unchanged. See e.g. this 2019 article "Inside TurboTax’s 20-Year Fight to Stop Americans From Filing Their Taxes for Free".
In many other developed countries, the quote from Vice applies: Their governments do simply calculate your taxes correctly (and automatically deduct/credit from/to your bank account the exact amounts). Most taxpayers have to do zero work (all their information on their salaries having already been automatically submitted to the government through their employer). There is also no need to bluntly withhold large and arbitrary sums.


Implications for currencies pegged to USD of Chinese devaluation?

Let's take Lebanon as a country that pegs to the USD and examine the implications of Chinese devaluation on Lebanese imports and exports.

First step is to recognize that what matters for the trade balance is the real exchange rate, not the nominal exchange rate. We need to examine the nominal exchange interrelationships first. The second step is to examine the inflation differential, under different hypothetical scenarios.

Nominal Exchange Rates:

Since the Lebanese pound is pegged to the USD, if China devalues their currency and exchange rate used to be 100 Renminbi for 1 USD, now 120 Renminbi for 1 USD, by definition (of devaluation and peg) the nominal exchange rate between China and USA will change, but the nominal exchange rate between USA and Lebanon will not.

Inflation:

Assuming zero inflation, for simplicity, in all 3 countries, then the
Chinese goods and services will now look cheaper to Americans and
cheaper to Lebanese. In turn, American and Lebanese imports will now
look more expensive to Chinese people.
Assuming China has a 30% inflation rate, while USA and Lebanon have 0
inflation rate, then the fact that the inflation rate differential
between China and USA is 30%, while the Chinese nominal exchange rate
was devalued by only 20%, implies that in real terms, the Chinese currency (relative to both the USD and Lebanese Pound) has
actually appreciated by approximately 10%=30%-20%, leading to Chinese exports looking more
expensive to Americans and Lebanese, and American and Lebanese
imports looking cheaper to the Chinese.
Assuming US inflation rate to be zero, and Chinese inflation rate to be 30% while Lebanese inflation rate to be 5%, we are in a situation where the Chinese currency was devalued, as before, by 20% but the inflation differential (25%=30%-5%) overwhelms the devaluation (25%>20%) hence the Chinese Renminbi has actually appreciated 5% relative to the Lebanese pound, rendering Chinese exports more expensive for Lebanese people. Lebanese exports will now look cheaper to Chinese people.


Is there any reason deflation would reduce profits?

For some models, deflation makes consumers save more, because they expect one unit of money in the future to buy more goods than one unit now. Consumption falls, so revenue and current profits fall.

The fall in demand and profit may have feedback effects: less investment, less innovation.

In general, depends on the model you are using. In a static model with homogeneous firms, the real profits may stay unchanged.


How does buying bonds reduce bond yield?

There are two legs to this question.

How did this action reduce the yields of their government bonds

The price of a bond and its yield are inversely related: if the price goes up, the yield goes down, by definition.
The assumption is that increased purchases by the central bank raises their price, by using supply/demand logic. However, these supply/demand arguments implicitly assume that bond traders are automatons who cannot adjust their selling prices. As such, there can be a debate about how much bond yields fall because of central bank purchases.

and prevent them from having a debt crisis like Greece?

The situations of Greece and Japan are different. The Japanese governments borrows (almost) exclusively in yen, a currency the government controls. (They might have a token amount of foreign currency borrowing, like many other developed countries. Even if they do, the size of the borrowing programme is much smaller than their foreign currency reserves.) The Bank of Japan effectively endures that the Japanese government can issue new bonds near its policy rate.
Conversely, the Greek government (mainly) borrows in euros, but the central bank for the euro is the ECB. The ECB let Greek bonds yields to decouple from other euro bond yields, which forced the Greek government to default.


Business cycle frequency is a frequency that has the length of one business cycle.  Business cycle is:

economy-wide fluctuations in production, trade, and general economic activity. From a conceptual perspective, the business cycle is the upward and downward movements of levels of GDP (gross domestic product) and refers to the period of expansions and contractions in the level of economic activities (business fluctuations) around a long-term growth trend.

The length of the business cycle varies but usually, it is at least a few years.


Why is the term structure curve of agricultural commodities often downward sloping?

In Keynes's Treatise on Money he argued that the phenomenon you describe, known as "normal backwardation", is due to the fact that certain commodities producers hedge their price risk (importantly, they hedge their risk much more than consumers) by selling futures. The intuition for why the producer does this is that it allows the producer to lock in the price of the commodity in advance, allowing them to plan their production based on a guaranteed price.

Now, remember that relatively fewer consumers hedge their risk than producers. Intuitively, this might be because, for example, if the price of pork rises significantly, consumers can easily adapt by substituting away from it; in contrast, if the price of pork falls significantly, pork producers who have been raising pigs for months are unable to adapt easily and may face a significant loss. So the risk is concentrated on producers, and selling futures is essentially just shifting this risk from the producers out into the financial system so that it is (hopefully) more dispersed.

But now the twist: because there aren't a lot of consumers who feel that it's important to lock in today the cost of a ham in the future, there are no natural buyers of these futures. As a result, producers have to sell pork futures at a discount to the expected future spot price, to compensate people for accepting the risk. When this is the case, futures prices in these markets are said to experience normal backwardation.


Why can per share earnings growth only keep up with GDP growth, if no new shares are issued?

The question is really about industry jargon, not economics.

  Wouldn't company B's faster rate of share price increase increase my
  portfolio's value?

What he's referring to is that, at the moment company B went public, shifting your portfolio to company B stocks is simply a re-balancing of your portfolio. There is no profit from re-balancing.

(Of course, once a stock is in your portfolio, there is capital gain if stock price increases, vice versa.)

On the other hand, in the scenario where equity value increases at the moment of IPO, the value of the company increases, which contributes to increase in overall market value (what he calls "GDP growth" and "economic impact").
The difference in value is captured by investors who holds private equity prior to public listing (e.g. venture capital firms).

Each time this occurs, there is capital gain in the economy that's not captured by investor in public markets, simply because they are late to the bandwagon.
This is what he calls "slippage". He claims "over time, the effect of this slippage has been meaningful", which implies the gains of public market investors lag gains
of private equity investors.

(If one compares the historical returns of the public market---e.g. that of stock indices---and the average VC firm, the latter is probably higher. However, it's not clear whether this is still the case after adjusting for  risk. The risk profiles are very different. The typical VC portfolio may have 30 companies, with one eventually turning a profit.)

A rephrasing of the quoted statement might be:

"...per share earnings growth [for investors in public markets] can only keep up with GDP [(market cap)] growth, if no new shares are issued [i.e. no new public listings occur]..."


I think I understand the problem now, your AVC(Q) is wrong. Your fixed costs are 4000, because it's what the firm will pay after it stops production. VC=TC-4=Q^3+2. Thus AVC=Q^2+2/Q. Now you should use your calculus in order to find where AVC has local positive minimum (because it doesn't have global minimum due to its hyperbolic nature).


Must a EU bank pay 500€ to the ECB, if I deposit 100k€ into that bank?

Banks do not make matching deposits into central banks, other than in a hypothetical 100% reserve system. As such, the answer is “no”.
What happens is that the private bank has a liquidity inflow, and it would need to find a corresponding asset, normally a money market instrument. The yield on that instrument is likely negative, but the “negative interest” is flowing to the seller of the instrument.


Income Elasticity of Demand vs. shift in demand curve

Short answer:

Denoting income by $I$, price by $p$, the demand function by $D(I,p)$ and income elasticity of demand by $\eta$, the definition of point elasticity of income is

$$
\eta = \frac{\text{d}D(I,p)}{\text{d}I}\frac{I}{D(I,p)}.
$$

So the change in demand comes from a change in income.

Long answer:

Without specifying your coordinate system the terms "movement along the curve" and "shift of the curve" are meaningless.

Consider the function $f(a,x) = a/x$. Suppose this function determines the value of a variable $y$, that is $y = f(a,x)$. Given $a$ we can plot $f(a,x)$ in the $(x,y)$ coordinate system. If $x$ changes there is movement along the curve in this coordinate system. If $a$ changes the curve shifts in this coordinate system.
However treating $a$ as a variable and given $x$ we could also plot $f(a,x)$ in the $(a,y)$ coordinate system. Then change in $a$ would mean movement along the curve and change in $x$ would shift the curve.

As quantity demanded usually depends on both income and price, you face a similar situation, where $q = D(I,p)$. Income elasticity examines a change in income, but without specifying if your curve is ploted in $(p,q)$ or $(I,q)$ you cannot classify the change in $I$ as either "movement along the curve" or "shift of the curve".


How does the government launch of Tomahawk missiles against Syria affect the economy and governmental budget?

First, we should remember that the government did not particularly spend any money on the air strike, except for incidental stuff like fuel costs.  It already owned those missiles, which were part of a previous government spending program.  Unlike profit-motive organizations that try to be streamlined, the government buys many things it never uses and doesn't necessarily replace things it does use.  This is particularly true of the military.  The US military has enough stockpile to use incredible force in Syria and still not need to change its future spending.

But anyway, let's talk about your question.  Military is, indeed, an example of stimulus-style spending: a government program that employs people and creates demand across the economy, but which does not generate much in the way of goods and services that we would normally count as wealth.  Engaging in war does increase employment and temporarily increase demand.   To be clear, this should not be confused with helping the economy in the long-term.  The Keynsian argument suggests stimulus spending as a way to smooth out short-term trends, but which must be paid for later.  It's not a way to improve the economy overall.

The wealth of a country is measured by the goods and services it produces (or can buy).  Military spending can jump start an economy full of pessimism or in a bad equilibrium, but it clearly shifts resources and people away from wealth-building and is a long-term economic drag.  Think of military spending as similar to hiring people to break rocks or farm weeds, as was done in earlier periods of our history.  It increases employment and but does not add to the nation's overall wealth.  In fact, you can think of military spending as a transfer payment from the wealthy (who pay most of the taxes) to those who benefit from military spending (weapons manufacturers and associated industries).

As you mention, I'm not saying military spending is good, bad, immoral, or moral.  Just saying economically it's a short-term stimulus, long term drag.


(Evolutionary Game Theory) Argue informally there can no longer be an ESS in which only b is played

The "secret handshake" idea was first formalized in economics by Robson (1990).

Suppose initially the equilibrium is $(b,b)$. Since the normal population cannot recognize the mutants, they'd always play $b$.

When the mutants enter the population, because they can recognize their own kind through a secret handshake, they can play $a$ against one of their own (when there is a secret handshake), and play $b$ against the normal population (no secret handshake). This way, the mutants are getting $3$ each time they meet another mutant and $1$ each time they meet a normal. Therefore, the mutant's strategy is a best response to the normal's strategy, but a better response to itself than the normal's strategy is. As a result, the normal's strategy fails to be evolutionarilly stable.


Which think-tanks on economics do you use to keep up with the news?

I like also shorter columns, which are based on good academic papers. So, the VOX, CEPR's policy portal is very good. They occasionally take unsolicited columns, but many are based on CEPR or NBER working papers.

Project Syndicate publishes short and interesting op-ed economics articles.


It think it depends on:

the liquidity and value of government coupons: if you could sell them very easily for cash and with little discount, then there is little difference.
the accessibility/familiarity of the expenditure they are to represent: if they are food coupons to be exchanged in any major supermarket, then beneficiaries could simply using them for their monthly shopping. If they are to be used only in a super-healthy store, not so easily accessible, and valid only to buy children's food, maybe some of the coupons will not be used, or will be resold at a high discount. In that case, they are less like cash, since it is not very rational to destroy cash, or sell cash for less cash.

The two points are surely connected.


Auction with one buyer and multiple sellers

Such a setting is called a "procurement auction" or "reverse auction."
It does not fundamentally change anything. Instead of buyers with privately known valuations, the auctioneer faces sellers with privately known costs. Hence, bidders underbid each other. An efficient auction is then (typically) one where the bidder with lowest costs wins. An optimal auction is one where the winner has the lowest virtual cost, $c + \frac{F(c)}{f(c)}$, the procurement analogue to Myerson's virtual value, $v-\frac{1-F(v)}{f(v)}$, where $F$ is the cdf of the private type (valuation or cost). The first paper on procurement auctions that comes to my mind is Luton & McAfee, JPubE 1986, but I am sure people were aware of reverse auctions as a "mirror image" of standard forward auctions long before that.


Data source for average effective personal income tax rate?

For a lot of things, including average effective (Federal) tax rates, the Urban Institute/Brookings Institution Tax Policy Center is a great place to start. Look at the table that reads "Average Individual Income Tax Rate," as the first one also includes payroll, excise, and corporate taxes.


Regulatory differences between stocks and bonds

Bonds and stocks, and in general all securities related to a firm, are regulated by the SEC in the US. Some other financial instruments are regulated by the CFTC (mainly commodities and derivatives, though some of the latter are regulated by the SEC)
Stocks
Stocks are a share in the firm. Meaning they are actually ownership securities. Hoilding a stock entitle their holder to earn a part of the earnings of the firm - the dividends, and to have a say in the strategy of the firm, through a vote at the Annual General Meeting.
Different kinds of stocks can be found: The difference usually lies in the number of votes that each share carries, or in their seniority in case of bankruptcy (preferred shares get paid before common shares)
A good example is Alphabet's (Google's) shares:

A shares, which have one vote each (NASDAQ:GOOGL)
B shares, which have 1 vote each (not publicly traded)
C shares, which are capital-only (no votes attached) (NASDAQ:GOOG)

This allows the founders to maintain ownership of the company while raising additional funds. As you can guess, Sergei Brin, Larry Page and then Eric Schmidt own a minority of the total stock, but secure more than 70% of the voting right through their holding of B shares.
Bonds
Bonds are debt securities: they do not represent ownership but they represent a claim. In opposite to stocks, there are plenty of different types of bonds. There is a huge diversity, and the main characteristics that can change are the following:

Maturity (When do you get paid back the nominal amount): it can go to a few months to 30 years or more (the UK still has outstanding debt with no maturity)
Interest rate (How much do you get, and at which frequency?): It can go from zero to any other amount. It can be fixed, or variable, for example indexed on inflation.
The seniority (who gets paid first in case of bankruptcy)
The collateral (Are you entitled to receive a particular asset in case of default?)
Other options, such as convertibility (some bonds can be converted to shares, for example if the firm defaults on these bonds, or if the bondholders asks for the conversion.)

To put everything together, what happens in case of a bankruptcy is that direct creditors are paid first: the government (taxes), the employees, the suppliers, etc. Then, the other creditors are paid, if there is anything less, in order of seniority: either because some debt are embedded with particular seniority level, such as First Lien Debt, or in order of maturity (short term debt first). Some debt have a collateral, which the holders of the debt have a claim on in case of default. For example, ABS and MBS are 'guaranteed' by assets which the lender will get if they aren't paid. The governments can also extend guarantees on private firms lending.
This explains why the two types of security have different risk profile.
For a firm, the rules/regulations on each type of security have a very deep impact. Namely, it is less costly to raise debt: first, debt costs less (interest rates are typically lower than equity yield), and also because the interest rates are tax-deductible. This can cause problems as it incite firms to take on more debt than they otherwise would, as underlined by this article from The Economist.


WAPM and CRS across all production plans

Sure it can, because the maximal profit is 0, and that level is attained at all output levels.

A similar problem is a profit maximizing firm with constant returns to scale. If such a firm has a maximal profit it can attain then that profit level is 0. If the maximal profit level was something else, it could be increased by doubling or halving production.


Why do currencies cover orders of magnitude?

No matter where you live in the world, there is sort of a minimum value that your currency needs to practically be able to represent somehow.  If your standard unit of currency is more than that minimum value, you need to subdivide your currency to be able to represent smaller values.  In the U.S., we subdivide our U.S. Dollar into 100 cents, meaning that the smallest value that you can spend is $0.01.  (My parents talk about being able to go to the store when they were kids and buy candy for 1 cent, but that is no longer the case.)

If your standard unit of currency is small enough, you don't need to subdivide it any further.  This is the case with Japanese yen; 1 yen is roughly equivalent in value to 1 U.S. cent, and you won't find anything for sale in Japan for a fraction of a yen.

I visited the Czech Republic last summer.  One Czech koruna is roughly equal to 4 U.S. cents, and I didn't see anything for sale there for fractions of a koruna.

There really isn't anything more to it than that.  If we, in the U.S., decided that we didn't like the decimal point anymore and valued everything in cents, nothing would change, except that what we know today as the one-dollar bill would have the number 100 on it, and a price tag that had $4.95 on it today would look like 495¢ instead.

Currencies change in value with respect to each other from time to time.  You can read about some of the events in the past that affected the value of the Japanese yen on the yen Wikipedia article, but none of that history is really relevant if you are concerned about the value today.  If a currency goes up in value, it will just have to be subdivided more so that the smallest values can still be represented.  If on the other hand, the value of the currency goes down (much more common), some of the smallest subdivisions will be eliminated.  Canada has already stopped production of their penny, and there is discussion in the U.S. about doing the same here.

When the Euro was created (about 20 years ago), they had to pick some value to begin with, and they chose to make the Euro equal in value to the U.S. dollar at the time.  It has since changed in value with respect to the dollar, and today 1 euro = $1.11 USD.


Demand Curve Price not perfectly elastic

Counting your quantity in ounces makes sense, I wouldn't change that (I assume each point is a total sales/price combination at a given time?).

If you want to look at the impact of a percentage change in your price, you should take the logarithm of price. A .3 change in log(price) is roughly equivalent to a 30% change in price.

That said, you do in fact see a downward slope on your demand curve, which indicates that a drop in price is correlated with an increase in sales, although it's a general negative relationship and there's nothing special about 30% in particular (I wouldn't expect there to be!). So you're pretty much showing what you want (discounting issues about statistical significance, or causal identification - if these prices aren't set randomly this isn't technically showing you a demand curve).


Difference between Negotiable Instrument and Financial Asset

CDs are money market instruments and hence are financial asset. There are traditional and negotiable CDs.

Traditional CDs are like term deposits in banks, and are not tradable. Liquidation before maturity entails penalty charges.

Negotiable CDs can be traded in the secondary market (referred to as money market). The original holder can 'liquidate' them at prices below the face value in the market. At maturity, the holder of the negotiable CD receives the face value of the security from the issuing bank.


Effect of positive inflation shock on the exchange rate

Before intuition. let's determine the outcome. By the Uncovered Interest Rate Parity

$$ i_t  = i^*_t - [s^e_{t+1 | t} - s_t] \tag{1}$$

where $i_t$ is domestic nominal interest rate, $i^*_t$ is "foreign" nominal interest rate, and $[s^e_{t+1} - s_t]$ is expected appreciation of domestic currency in percentage terms ($s$ is the natural logarithm of "foreign currency per unit of domestic currency" exchange rate).

The "Fisher equation" for the relation between real and nominal interest rate in expected inflation is

$$i_t = r_t + \pi^e_{t+1|t} \tag{2}$$

where  $r_t$ is domestic real interest rate, and $\pi^e_{t+1}$ is expected domestic inflation. Putting $(1)$ and $(2)$ side-by side we have

$$r_t + \pi^e_{t+1|t} = i^*_t - [s^e_{t+1|t} - s_t]$$

Assuming that there are no real effects by an inflation shock, and that the international economy couldn't care less (so also $i^*_t$ remains unaffected), using the change operator we have

$$\Delta \pi^e_{t+1|t} = \Delta (s_t-s^e_{t+1|t}) \tag{3}$$

where now the right-hand side represents "change in expected depreciation" of the domestic currency (note that the right hand side may be algebraically negative in which case it is "negative depreciation" = appreciation).

Now, it is reasonable to argue that expectations for tomorrow will take into account what happens today. Moreover, usually current inflation shocks either affect in the same direction expectations about future inflation, or not at all.

So an inflation shock happens in period $t$ which increases the left-hand side of $(3)$. Then so must also increase its right-hand: a domestic positive inflation shock increases expected depreciation of the domestic currency. In other words it creates expectation of currency devaluation. The currency may still be expected to appreciate, but less than before the inflation shock.

Mathematically this can come about in different ways but realistically one should expect that what will happen is that $s^e_{t+1|t}$ will go down, i.e. that the domestic currency will be expected to devalue.

The main intuition behind this comes if one realizes that, for the people abroad, domestic currency is just another product, that has a price. If due to inflation this "product" is worth less (because now it can buy less of utility-enhancing or productive goods), this should be reflected in its price, which is the domestic exchange rate $s$ (price of domestic currency measured in units of foreign currency), which should get lower.

This is the rationale also behind the closely linked "purchasing power parity". Of course, this is a highly stylized analysis and all sorts of real-world imperfections and rigidities will affect what will actually happen. But the tendency is the one described above.


How and on what basis the inflation target is determined?

Recently, at the 2017 Money and Banking Conference at Buenos Aires, the Governors of the Central Bank of Peru and Paraguay talked about this same thing. Those two countries successfully brought inflation from double-digits to ~2% in recent times and they said the changes were opportunistic: if they were sure they'd be able to meet the IT, they changed it.

Also, Peru has a constitutional amendment that allows for Peruvians to have a savings account in any currency they want and indeed around ~70% of deposits were in dollars which implies they aimed at something close to US' inflation.

This is in stark contrast to the host's (Argentina's) strategy, mainly to reach a 1-digit inflation around mid-2019, just before the presidential elections. The bands are:

14.5% ±2.5 for 2017 (they already failed, it will end up around 20%)
10.0% ±2.0 for 2018
5.0% ±1.5 for 2019.

While the targets are aggressive and they already surpassed this year's band, market's inflation expectations consistently have a downwards trend.

Finally, what's so special about 2%? An unexpected deflation has a negative short-term effect on growth. High inflation also has a negative effect on growth. So, being stable around 2% is a nice "Goldilocks" zone.


Do there exist 'comparative statics' for fixed points?

"Comparative statics" may refer to two closely related but not identical exercises:

a) Regarding a specific equilibrium point, we examine how the properties, associated values etc of it change as we vary the value of an exogenous parameter.

b) But also, we can put under "comparative statics" the case where the model has multiple equilibria. Inherently, when more than one equilibria exist, it means that they are dependent on the value of (or inter-relation between) some of the model parameters. Assessing this situation, i.e. contrasting the two solutions, the sets of parameter values for which we obtain the one equilibrium or the other ("values" do not necessarily mean numerical ones -they may be bounds expressed in terms of other parameters etc), understanding the economic essence behind the differences, is a comparison of two static situations.

So @Oliv comment below the question is valid, indeed, the initial condition structurally is just one more exogenous parameter of the model.

That said, in most cases, dependence (or not) on initial conditions (or "history-dependence" more generally) usually falls under stability analysis:

if a fixed point is globally asymptotically stable, it means that there is no dependence on the initial value, whatever it is (in the feasible space).
if a fixed point is asymptotically stable, it means that it has a basin of attraction, but which may be only a subset of the feasible space.

Proving global asymptotic stability is usually difficult (in most cases, one has to find an associated Liapunov function), and it becomes harder the more non-linear is the differential/difference equation/system under study. So computationally showing that it is indeed globally asymptotically stable, is useful.


Quantity theory of money: microfoundations

In the chapter 4 of the graduate textbook  Lectures on Macroeconomics there is "The Overlapping Generation with Money". In that case we have a model which is microfounded (i.e. accounts for how our consumers interact with money on the microeconomic level). This is essentially an explanation of Paul Samuelson's 1958 "consumption loan model".

You can find a useful set of videos on this model here:
https://www.youtube.com/playlist?list=PL10zuK3j9SNl15Xy-EGteGDTd74j4uE_n