Is the price-quantity diagram fundamentally wrong?

The graph you've depicted is just very generic supply and demand intersection, under the generic/introductory assumption that an equilibrium price exists.

Even at this level of abstraction, the demand curve is perfectly flat for a price taker, so it's not always the case that those two functions (supply or demand) are always a bijection between price and quantity. That should address some of your confusion/question (1).

Furthermore, some introductory econ texts are bad at explaining that even a this level of abstraction, the market and an individual firm may have completely different price-quantity graphs; the graph you've shown is valid for a competitive market as a whole, but not for individual producers in it. Here's standard textbook slide of the better variety, which does make this distinction.

  Demand curve faced by an individual firm
  is a horizontal line

  Each firm is so small that its sales have no
  effect on market price. As a result, each
  regards market price as given.

  Demand curve faced by whole market is
  downward sloping

  Shows amount of goods all consumers will
  purchase at different prices

Your main question (2) involves a production cost, which does not appear depicted anywhere on that graph. The production cost isn't necessarily the same thing as the producers' price-output curve.

Even in the case where the market consists of only one supplier (a monopoly), so when the (producer) firm and industry graphs coincide, one needs to plot additional functions for the marginal return and marginal cost to start talking about profits. Even in this case, the discussion isn't trivial, e.g. it depends whether the monopoly can engage in price discrimination (sell to different consumers at different prices).

As for your specific scenario in (2):

  If someone is willing to buy 1 billion "Goods", and my production cost is lower than what he offers - I will produce 1 billion "Goods" for them (assuming that I can) after I tried to get a better price - since I will make a profit after all.

This is closer to a how a price-taking producer (aka perfect-competition producer) optimizes output. Remember from the first diagram, that the demand from its perspective is flat, so that entails a linear total revenue (or, equivalently, a constant marginal revenue):

Note that the demand isn't even included in this graph except implicitly as the slope of the total revenue. However, since it follows that in order to maximize profits MC = MR = P (again under the perfect competition assumption), then the marginal cost is equal to the externally set price (for a price-taking producer), so the intersection of the price (demand) and MC gives the quantity:


As @denesp has pointed out making real precise predictions with game theory is difficult because it is hard to gather data on payoffs and behavior under uncertainty, not to mention the fact that game theory typically assumes individual rationality (although the behavioral game theory referenced by @HerrK above loosens some of those requirements)
Of course that has never stopped people from trying. At least in environmental and resource economics there are plenty of papers looking into dynamic games that are calibrated to make some general (but perhaps not very accurate) predictions. This overview paper from Hannesson includes a lot of references to such papers in fisheries, a similar but older overview paper on transboundary polution was written by Finus.
Given what you're interested in, I'd look into repeated games with sequential moves. In a very simple set-up it could work out like this: each period the employers make an offer, and the unions then decide to either go on strike (hurting the employers and employees and moving to another round) or accept (which ends the game). As said, I don't think it will give you an accurate prediction, but it would perhaps give you some insights in the motives at work.
The problem with such a game set-up is that

I'd expect both the employers and unions to fall for sunk cost arguments (can't quit now, we've gone so far...), which a rational player wouldn't do
Repeated games in the presence of uncertainty often have multiple equilibria that can be supported by trigger strategies. Although these trigger strategies are subgame perfect, they are also non-renegotiation proof, and that is probably exactly what you're interested in.

Hope that helps.


How does the taylor rule make the MP curve upward sloping?

In effect, the desired real interest rate $R_t$ is chosen by the government (via changes in the nominal interest rate). But it is chosen based in the Taylor rule. The "standard" IS-MP-PC model (as in Jones's Macroeconomics textbook), is as follows:

IS:

$$\tilde{Y}_t = \bar{a} - \bar{b}\left(R_t - \bar{r}\right)$$

PC:

$$\Delta \pi_t = \bar{v}\tilde{Y}_t + \bar{o}$$

MP (Taylor rule):

$$R_t = \bar{r} + \bar{m}(\pi_t - \bar{\pi})$$

In the latter equation, the central bank/government choses $R_t$ according to deviations in inflation from the target. As inflation increases, the real interest rate increases.

Now, according to the Phillips Curve, inflation responds positively to demand shocks ($\tilde{Y}_t$). In consequence, the real interest rate responds positively to $\tilde{Y}_t$. This is why, in the IS-MP diagram (with axis $R_t$ and $\tilde{Y}_t$), the MP has a positive slope.


Why does the price and wealth derivatives, weighted by the price and wealth, sum to 0?

As mentioned by Mas-Colell, Whinston and Green, the equality is true "for all $p$ and $w$". It is a consequence of the budget constraint, which is satisfied for any prices and income values:
$$
\Sigma_{k=1}^{L} p_k x_k (p,w) = w.
$$
As you mention, the equality
$$ \Sigma_{k=1}^{L} \frac{\partial x_l (p,w)}{\partial p_k} p_k + \frac{\partial x_l (p,w)}{\partial w} w = 0 $$
arises when applying the Euler-theorem to the budget constrained demand functions. As demand functions are homogeneous of degree zero in $(p,w)$, they are left unchanged when prices and income are up- or downscaled by any number $\kappa>0$:
$$
x_l (\kappa p,\kappa w) = x_l ( p, w) ,
$$
and this equality holds for any value of $p$ and $w$. This implies the former equality and also explains why it is not only true for the upscaled new prices and income $(p,w)=(\kappa p_0,\kappa w_0)$ but actually for any prices and income because both $\kappa$ and $(p_0,w_0)$ can be arbitrary.

What about the economic interpretation? Hmm... I would say that any simultaneous (marginal and arbitrary) change in $p$ and $w$ triggers changes in the values of demands such that the (own- and cross-) price reactions and the income response compensate. It is equivalent saying that all price elasticities and income elasticity add to zero for any demand function $x_l$.


Natural resources and gravity determines trade. How the balance of payments is settled is not really important. But there are a few possibilities

a country has a lot of debt and defaults or refis it down to a very low rate to go negative indefinitely;
foreign aid;
moneyprinting that isn't adequately adjusted in foreign exchange;
selling overpriced domestic assets that are not properly accounted in the bop records;
stealing things

An example of 1 would be any debt crisis.

For 3 for example, Zimbabwe was trade deficit during it's episode

For 4, US startup equity is boosting it's balance of payments. It is not fdi or portfolio investment and includes travel expenses and things not adequately tracked;

For 5, any sort of anti western government expropriating assets, like Zimbabwe, uses that to fund it's balance of payments.


Extensive Labor Margin and Full Insurance

I'm not very well versed in macro-labor, but I'm aware of a few papers that might be close to what you mean. One could make unemployment uninsurable, and instead let agents partially self-insure by saving capital, like in Chang & Kim (2007) AER paper. Also Krusell & coauthors have some papers (like 2010 ReStud) where they combine uninsurable unemployment with search/matching framework.

The obvious problem is that dealing with heterogeneity is painful, because one must keep track of distribution of variables across agents (e.g. employment status and savings). If you're interested in computation and what can go wrong with it, check out comment on Chang & Kim paper by Takahashi (as well as reply by original authors in the same issue).


Compensating variation versus change in value of goods consumed?

It wouldn't.  The value of consumer's endowments and the value after they trade should be the same.  i.e. Neither consumer becomes richer in terms of money.  They just allocate their money towards buying goods they value more.

Additionally, prices are a function of both consumers' demands while CV only depends on the demands of one consumer.  Consider the following example

In autarky consumer 1 has endowment, $e_1=(1,1)$ and utility
$$u_1(x,y) = x + 2y $$
so $u_1(1,1)=3$
Now there is trade where consumer 2 has endowment, $e_2=(1,1)$ and utility
$$u_2(x,y) = 2x + y $$
When the consumers trade the equilibrium price is $p_x = p_y$  and equilibrium consumption bundles are that consumer 1 gets $(0,2)$ and consumer 2 gets $(2,0)$.  The value of both consumers' endowments and equilibrium allocations is $2p_x$.  But in terms of compensating variation (with $x$ as the nominal good) consumer 1 would require 2 units of $x$ to move from free trade to autarky while consumer 2 would require 1 unit of $x$.


What would happen if a country bans the trading of its currency against foreign currency?

This is quite a common response to an exchange rate crisis (which normally also suggests broader economic problems).  The consequences depend on how diligently the government applies the ban, the relationship between government and businesses that trade internationally and how far the official rate strays from the true (black market) rate.

First, it is almost always possible to buy and sell currency on the black market, and perhaps legally in neighbouring countries.  The black market rate is likely to follow the downward trajectory of the currency prior to the ban.  Exchange controls create risk for currency traders, so buying and selling on the black market tends to be expensive (i.e. the rates for buying and selling move further apart).

Second, lots of businesses urgently need foreign currency to import inputs and goods for retail sale.  They will try and find a strategy for obtaining that currency.  They may be able to buy it on the black market.  If the government is able to sell some local currency at the official (overvalued) rate, it may also sell foreign currency at the official rate to firms it sees as a priority (e.g. oil importers or friends of the regime).  For instance, tourists entering East Germany were forced to buy a certain quantity of local currency per day of their visit at the official rate, giving the government a source of forex.  If these strategies are not possible, companies may try to create symmetry in their import/export businesses, so that they can use the foreign exchange they earn themselves to cover their imports.  Government may or may not intervene to prevent this.  Importing firms without a viable strategy are likely to fail.

All in all it makes international trade more difficult and expensive, so prices of imported goods are likely to rise even more quickly than they were under the sliding exchange rate.

The most reasonable motivation for this type of exchange control is to prevent people and companies from shifting their savings into another currency, which could cause a general banking collapse.  If you see the exchange rate falling continuously, you would be tempted to convert your savings from local currency to dollars, which hold their value.  If everyone does this, the exchange rate slide accelerates, banks can't cover their liabilities, loans are called in, and banks and businesses may fold.

The Soviet bloc is a common example of the use of official exchange rates but they've been used by governments in trouble all over the world, recently in various African countries, a few in South America and less recently in Asia.


Your reasoning is not entirely rigorous, Even for a rational agent there can be a small gap between WTA and WTP due to the wealth effect. However, empirically this effect accounts for a very small fraction of the WTA/WTP gap, which is why other explanations are generally preferred.


Price elasticity when relationship between sales, price and other factors is not linear

There is a confusion between a "linear relationship between two variables" and an "econometric equation that is linear in the unknown parameters to be estimated".

The first has to do with what happens in reality, and it implies that the marginal relation is constant. The second may be obtained even if the actual relation is not linear, but non-linear in specific ways that permit to obtain it by a suitable transformation of the data.

To illustrate this, for the OP's case, the actual (deterministic part of the) relation may be

$$X_d = AR^aP^{-b} \tag{1}$$

Demand $X_d$ for the product is a positive non-linear function of social ratings $R$ and a negative non-linear function of its own price $P$. The marginal effect of price for this relation is not-constant

$$ \frac {\partial X_d}{\partial P} = -\frac{b}{P}X_d <0$$

By assuming $(1)$ we have already made a series of assumptions about the interplay of the variables involved. This specification permits us to obtain "an econometric equation that is linear in the unknown parameters to be estimated" since by taking logs we have

$$\ln X_d =\ln A +a\ln R +(-b)\ln P \tag{2}$$

So while the marginal effect of price on demand is not linear and not constant, the elasticity of demand with respect to price is constant, and equal to $-b$ (the sign indicating direction of influence).

But is $(1)$ an adequate way to represent the actual relation?

So the proper way to proceed here is to

1) To the best of our knowledge, using evidence and logical arguments, we determine the qualitative interrelations between the variables involved: is the effect positive/negative? Is the relation of their levels linear/non-linear? Is it monotonic or, say "inverted-U", etc.

2) We construct a mathematical form that reflects qualitatively the conclusions/assumptions arrived at in step 1. For example, if we believe that an "inverted-U" relationship exists between levels of $Y$ and $Z$, this could be modeled by $Y = a + bZ + cZ^2$ with $c<0$

3) If the mathematical expression we obtain in step 2 is not linear in the unknown parameters of interest, we check whether it can be transformed into one that it is. Of course, there are estimation methods for non-linear relationships, non-linear least-squares being the easy example. But experience has taught us that our estimation techniques are better when they estimate equations linear in the unknown parameters, this is why we always try to arrive at such a specification, even if we may accept in the process certain approximating steps to what we have obtained in step 2 (and not just exact transformations).


Why do companies launch products at much higher prices, only to reduce the price drastically after a few months?

Two very general reasons are:

1) High prices at the beginning target "early adopters" - people that have a higher "willingness to pay" for a new product just to have it first. Early adopters know that they pay more, and they 're ok with it.

2) As regards consumer reaction, it is much better to reduce prices than to increase prices. So sometimes prices are set high to "feel" the market response and then adjust accordingly.

Note: these are very general and "universal" reasons for the phenomenon. The degree to which are qualified in each special case, market, country, etc its a matter of examination. Also, in some circumstances other strategic considerations may lead to the opposite action: start very low to "sweep the market" (price self-subsidy) in order to drive competitors out/increase market share, and then start increasing prices when market has become "captive" to a degree.


Who is the first person/paper to introduce "mixed strategy"?

Although I don't have the book here, I am quite certain that mixed strategies are already present in the book from 1944. I believe that I have read somewhere the claim that "mixed strategies" where actually introduced in an earlier version of the book (published in German in 1928, says Wikipedia). However, what I have read mostly is the claim that Emile Borel (yes, THE Borel) first wrote down this idea in a note in 1921.
I guess here is a man with enough authority to state that:

E. Borel was the first author to evolve the concept of a strategy, pure as well as mixed, although he did not go beyond the case of the symmetric two-person game.

says von Neumann here: "Communication on the Borel Notes", J. von Neumann and M. Fréchet, Econometrica 1953.


Real world example of using difference quotient vs. derivative

You can see the applications in microeconomics. A tiny example could be on elasticity of demand.

Let's say

$$ D = \frac{tC}{P+t} $$

where $P, t, C$ are respectively price, tax and constant. If you like to see the effect of tax change on demand you can use the difference quotient ;

$$\Delta D = \frac{(t + \Delta t C)}{P + t + \Delta t} - \frac{tC}{P + t}$$

I skip the intermediary calculations. This one yields ;

$$\frac{\Delta P}{\Delta t} = \frac{P.C}{(P+t)^{2}+\Delta t.(P+t)}$$

Hope that it helps.


I restrict myself to credit rating for Banks only.

There are different solutions, in bold are my preferred one.

To have just an idea about single banks register a free user account to rating agencies as S&P, Fitch, Moody's and type the bank of interest. Also history in some cases is available. (this solution is just per bank and slow)

Database Compuststat via Wharton (WRDS subscription), not free. Only S&P historical ratings, but with a complete database after you insert the correct tags of interest. Download via web, or with external software R, Matlab, etc.
Bankscope (new Orbis bank), not free via web or WRDS subscription. Fitch ratings but they are not able to be saved to file due to restrictions (just to that manually). Very user-friednly database and historical data too.
Thomson one banker, not free. A complete overview of ratings can be seen bank for bank with historical view. But it is not possible to get it in batch for historical ratings for all the banks in one shot. Slow but complete.

Other databases can be Datastream (not free and partially historical data ), Bloomberg (current and historical ratings data but one company at time).

There are also other database but after some research I managed to get them.


Why are allocation and distribution important consequences of the second welfare theorem?

The First Welfare Theorem essentially says

  price equilibrium with transfers => Pareto optimal

The FWT hence solves the "problem of efficiency" i.e. If we let the market work through prices, we will achieve Pareto efficiency.

The SWT, on the other hand, states

  Pareto optimal => price quasi-equilibrium with transfers*

It assures us that any Pareto optimal point can be achieved via the market.

Note that distribution and inequality are normative problems which must be addressed through say, the political process, rather than economics. The concept of Pareto efficiency does not tell us anything about distribution. Oftentimes in a 2x2 model, giving Agent 1 all the resources and Agent 2 none of the resources counts as Pareto optimal.

Therefore the SWT addresses the "problem of distribution" by saying that "Ok, society has decided that a certain Pareto optimum is the most desirable outcome. We know that we can achieve this by redistributing endowments/incomes and then letting the market work."

*PQWT is a weaker definition of PEWT


Why does the price for a prescription drug fluctuate?

Prescription drug prices, like those of most other retail products, fail to satisfy the law of one price routinely. The most obvious observation is that prices differ across pharmacies at a given point in time (http://www.nber.org/papers/w8548.pdf) but just like supermarkets give discounts, so do pharmacies. If you always buy from the same shop, you are bound to end up paying different amounts.

The reasons for this are manifold. Different consumers have different abilities or willingness to store and buy large chunks when it is cheap and stochastic prices allows for price discrimination (see Sobel 84 for an early reference). The idea is simple. Myopic consumers arrive in each period and buy if $p<V$, then leave the market. Otherwise, they die. Strategic consumers have a valuation of $v<V$ but can wait if the price is above $v$. Firms compete in prices. In equilibrium, firms charge often $p=V$ to extract rents from myopic consumers but every now and then they offer $p<v$ to attract all strategic consumers looking for prices.

Competition between stores may also result in random prices in a standard consumer search framework. Finally, retail prices may change because manufacturers prices are also random as a way to discipline pharmacies by encouraging consumers to shop.


cournot competition with strategic consumers

Studying a situation where consumers and producers interact to set price is precisely the study of bargaining. Any game theory text you pick up will almost certainly cover bargaining. The text I learned from, which I enjoyed thoroughly was Osborne's an introduction to Game Theory.

A first example of a bargaining game would be Rubinstein's game of alternating offers

I don't think adding consumer strategic behaviour to Cournot directly would be particularly more enlightening than studying bargaining separately, since Cournot already abstracts from the price setting mechanism.


In GDP growth studies, are factors of production measured as stock or flows?

In Nicholas Stern (1991)'s The Determinants of Growth first equation (I a), without preconceived ideas, one reads

$\frac{\dot{K}}{K}
= \frac{d K}{d t} \frac{1}{K}$

Which means explicitly (in discret values)

$= \frac{K_{t+dt}-K_{t}}{dt} \frac{1}{K_{t}}$

If $t$ is in years, and that we are interested in the variation of $K$ over $1$ year (i.e. $dt=1$), one obtains

$= -1 +\frac{K_{t+1}}{K_{t}}$

Even if the above equality could represent either the variation of a stock or the variation of a flow, the story behind this is about stocks. To summarize

$K_{t}$ is the stock of capital in the economy at year $t$
$dK = K_{t+dt}-K_{t}$ is a flow of capital occuring at year $t$, differently put an investment in capital.
$\dot{K}=\frac{d K}{d t}$ is the absolute dynamic of investments in capital in economy $\forall t$
$\frac{\dot{K}}{K}$ is the relative dynamic of investments in capital in economy $\forall t$

Depending on the object you are looking at, it can be both measured in flow or in stock. To know with what you are dealing with, you must understand the story behind equations.

To the practice side of the issue, you cannot make realistic analogy between Solow's capital and, say, tractors. The least abusive perception of $K$ would be cumulated flows of investment in terms of money since, for example in micro-based CGE modelling, it is conceived as representative of the shareholding structure of the economy, and is thus linked to income formation via dividends (see the zero profit condition). In this non-realistic framework, although non-abusively linked to the everyday-life object, $L$ is very similar to $K$, is a self owned stock, and gives right to wages, that are flow objects, as dividends are. Still on the practice side of the issue, the difference between $L$ and labor force is the fact that the former is effectively employed, while the latter is not. Put differently, the link between the two is the labor market, $L$ is a demand, while labor force is a supply, and both form jointly a labor market whose equilibrium is reached via deflation/inflation of wages.

Finally, to my knowledge, the fact that  the same factor of production (stock) is employed in more than one activity over a given period (flow). is not really a neoclassic native notion, I would say, once again when one refers to CGE modelling, because of the capital market clearing condition. It is more a monetary-macro-financial object, and is, e.g. all what debt is about when dealing with capital. However I do not see any analogy with $L$ in this case.


This paper:https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2712957

Is exactly what you need.


Prove that the profits of the firm weakly decreases with input prices

From FOC, we know that:
\begin{align}
\nabla_x\pi(\mathbf{x},\mathbf{w})=p\nabla f(\mathbf{x})-\mathbf{w}=\mathbf{0} \tag{1}
\end{align}
This will be true at equilibrium, i.e. for any given $\mathbf{w}$, the input vector $\mathbf{x}$ will adjust so that the above holds.
Now consider $d\pi(\mathbf{x},\mathbf{w})/d w_i$ (and using $(1)$):
\begin{align}
\frac{d\pi(\mathbf{x},\mathbf{w})}{d w_i} &=\nabla_x\pi\cdot\nabla_{w_i} \mathbf{x} \, + \nabla_w\pi\cdot\nabla_{w_i} \mathbf{w} \\
&=0 +\nabla_w\pi\cdot\nabla_{w_i} \mathbf{w} \tag{*}\\
&=\nabla_w(pf(\mathbf{x})-\mathbf{w}\cdot \mathbf{x)} \cdot \nabla_{w_i} \mathbf{w} \\
&= \Big(p\nabla_wf(\mathbf{x})-\nabla_w(\mathbf{w}\cdot \mathbf{x)}\Big)\cdot \nabla_{w_i} \mathbf{w} \\
&= \Big(p \frac{\partial\mathbf{x}}{\partial\mathbf{w}}\nabla f(\mathbf{x})-\frac{\partial\mathbf{x}}{\partial\mathbf{w}}\mathbf{w} - \mathbf{x}\Big)\cdot \nabla_{w_i} \mathbf{w}\\
&= \mathbf{J}(p\nabla f(\mathbf{x})-\mathbf{w})\cdot \nabla_{w_i} \mathbf{w}  -\mathbf{x} \cdot \nabla_{w_i} \mathbf{w} \\
&= \mathbf{J} \nabla_x\pi(\mathbf{x},\mathbf{w})\cdot \nabla_{w_i} \mathbf{w}-\mathbf{x} \cdot \nabla_{w_i} \mathbf{w} \tag{**}\\
&= -\mathbf{x} \cdot \nabla_{w_i} \mathbf{w} \\
&= -x_i
\end{align}
where, in steps $(*), (**)$, FOC is used and $\mathbf{J}$ is the Jacobian matrix.
Since, $x_i \geq0$, we have:
$$\frac{d\pi(\mathbf{x},\mathbf{w})}{d w_i} \leq0$$


What does it mean to have a strictly increasing transformation in consumer theory?

If I'm understanding your question correctly, you are referring to increasing transformations of a utility function. Suppose I have a set of alternatives $X$, a rational preference relation $\succsim$ on $X$, and a function $u:X \rightarrow \mathbb{R}$ which represents this preference relation. Then it can be shown that for any $v:\mathbb{R} \rightarrow \mathbb{R}$ which is monotonically increasing, $v \circ u:X \rightarrow \mathbb{R}$ also represents these preferences. Try to prove this; it's a good exercise.

So in classical economic theory, we never have a "unique" utility function which represents preferences. This is because we can always take an increasing transformation of the function and get something else which contains all the relevant information with respect to our preferences.


How are low/middle/high classes defined mathematicaly?

Actually there is no single agreed upon definition of low middle and high class. For example, Pew research center uses the following definitions:

  “Pew Research defines middle-income Americans as those whose annual household income is two-thirds to double the national median. For a family of three, that ranges from \$42,000 to \$126,000 in 2014 dollars.
  The lowest-income group earned \$31,000 or less for a family of three while the lower-middle group earned between \$31,000 and \$42,000 in 2014, according to Pew Research. At the most affluent levels, upper-middle-income, three-person households earned between \$126,000 and \$188,000, with the highest-income households topping \$188,000 in 2014 earnings.”

In economics research on income distributions usually people don’t explicitly define what low middle or high class is but rather they calculate deciles of income distribution and then also 99percentile and 99.9 percentile (that is the very rich and ultra rich).

But really you could define it in multiple ways splitting it by quartiles where the lowest quartile is lower class two quartiles in middle are middle class and upper quartile is upper class would also make sense. Saying lower class is just lowest 10% and upper class highest 1% and everything in between is middle and upper middle class could also make sense etc. So the ‘best’ way how to measure it is to certain degree arbitrary and different measures could be appropriate in different settings.


Why does the Federal Reserve seem to hold so much weight on the unemployment rate, relative to labor participation?

As mentioned in the press conference, other data is taken into consideration, such as the Employment - Population Ratio, especially when filtered/line series graphed to detail trends in demographics.

This blog post provides a bit more insight on the data.

It seems relatively, the U.S. is climbing to employment-pop levels we haven't seen since the mid 80's, which seems to suggest the outlook isn't as terrible as initially thought.


What's the best reference for rigorous study of mixed-strategy nash equilibrium?

The book by Gibbons that Tobias mentions is titled "A Primer in Game Theory" in Europe. It is excellent, especially in its coverage of more advanced games of imperfect/incomplete information. But it is quite concise in its treatment of games of complete information like the ones you are studying. The book by Osborne might therefore be a better choice. Both of these books are aimed at the introductory graduate level and are therefore quite rigorous.*

However, I feel compelled to say that it sounds like you are taking a first course in game theory, so I would be inclined to suggest also the book "Strategies and Games: Theory and Practice" bu Dutta. It is more verbose, but I think also provides a more gentle introduction to topics like Nash equilibrium and mixed strategies. Game theory, like much of economics is often best learnt by first obtaining a firm grasp of the intuition, and later supplementing it with sufficient rigor.

(*) There is also "Game Thoery" by Fudenberg and Tirole, which is less of a textbook and more of a reference. But it is, perhaps, even more rigorous as a result.


Material capital is any durable good that is used as a factor of production and, by virtue of being durable, it is gradually consumed in production over a maximum possible duration of a length that is determined by (i) how much a unit of capital is used and (ii) the depreciation rate of a unit of capital. Capital forms by labor and savings (which is in accordance with the labor theory of value) and/or capital forms by chance (which is in accordance with the marginal theory of value).

Imagine, for example, a solitary person that is stranded on a tropical island. To stay alive, that person must eat and, on the particular island, imagine that virtually every bit of edible biomass is a coconut. In order to be able to consume any coconuts, coconuts must be produced. Without any tools, this person must climb a palm tree to obtain a coconut and, once back on the ground, then must find a way to crack it open. If the person has obtained enough coconuts to last long enough for the person to take a day off from climbing trees then the person, by virtue of their coconut savings, can afford to leisure. Yet, perhaps the person decides not to leisure and, rather, decides to produce tools (i.e. to labor) to make coconut production easier. Perhaps the person fashions a pole out of bamboo to knock coconuts from the tree so that the person doesn't have to keep climbing trees, which reduces the amount of work required to produce coconuts and, therein, makes coconut production that much more productive by virtue of the bamboo tool, which is a form of material capital (as it can be used repeatedly to produce coconuts, which cannot be used repeatedly). As Abraham Lincoln (1861) once said, "Labor is prior to, and independent of, capital. Capital is only the fruit of labor, and could never have existed if labor had not first existed." Yet, capital also forms by chance. To break open the coconuts, the person might use a rock and, perhaps, if there were no rocks on the island that could be used to crack open coconuts then, thanks to misfortune, the person might starve.

Capital cannot be discussed without also discussing tools and technology; they are inseparable. A tool is when capital and a technology coalesce. For example, a makeshift wooden spear is a hunting tool. It is a coalescence of wooden material (capital) and a hunting technology. The wooden object of which the spear is made is material capital, which depreciates at a rate at which the wooden material’s maximum strength decreases. Knowledge about how a wooden object can be used as a spear is a hunting technology. Such technical knowhow is cognitively embodied (in some form or another) in the living body of the tool user, and it is expressed in the body’s behavior, which is behavior that determines how the material object is used (and effectively renders it a tool). This theory has support in the life sciences. (Alfred Marshall [1922] once wrote, “Economics [is] biology broadly interpreted.”)

The phenotype of an organism extends beyond the individual organism, as expressions of an individuated organism’s genes are not contained within that individual organism. Gene expression can be manifest in the behavior of its kith and even in the behavior of another species entirely. “Genes in orchids express themselves phenotypically [as] changes in bee behavior, which result in [a] transference of pollen grains containing those same genes” (Dawkins 1984). The extended phenotype of any individuated organism is the gene expression that extends beyond the embodied physiology of that individual, and it is “less purely biochemical than . . . the conventional local phenotype” (Dawkins 1984).  Among the many kinds of phenomena that can be considered to be of an extended phenotype are artifacts like fabricated shelters and tools. “Caddis larvae live in houses which they themselves build out of stones [or] other material. The form of the house is determined by the behavior of the builder, which is presumably influenced by the builder’s genes” (Dawkins 1984). The genome of a builder is the energetic scaffolding of the behavior of the builder (Hoffmeyer 2014), and such behavior, which is gene expression, determines the form of what the builder builds.

The coalescence of capital and a technology as a tool is a process of semiosis.  A tool is a sign of capital signifying a technology, which is a notion that comes to be more clear in reference to Ferdinand de Saussure’s semiological conception of the (dyadic) sign. The makeshift wooden spear is a sign of capital signifying a technology. The wooden spear is a hunting tool, and a tool is a sign. The wood of which the spear is made is material capital, and capital is a signifier. The knowledge about how the wooden object can be used as a spear is a hunting technology, and a technology is a signified. The wooden spear, which is a hunting tool, is a sign of wooden material capital signifying a hunting technology, and the arbitrariness of the signifier speaks to the old adage that anything can be used as a weapon. Tools are to technology are to capital as signs are to signifieds are to signifiers.

Returning to the topic of capital, material capital extends from human capital (e.g. knowledge, skills, & innovation) and financial capital extends from material capital. Financial capital is part of financial infrastructure, which is a tool by which other tools (and material capital commodities) can be obtained by supplying one's saved income (or positive profit in production) rather than one's labor. Human capital is phenotypic, which means there is a genetic component. As Ronald A. Fisher once wrote, "In organisms of all kinds the young are launched upon their careers endowed with a certain amount of biological capital derived from their parents." (Fisher 1930). Fisher considered the inheriting of household wealth by offspring from their parents to be an extension of a more generalized inheritance process stemming from the inheriting of genes by the offspring from the parents, which is a notion that foreshadowed the Dawkinsian theory of the extended phenotype. Fisher was a protégé of the political economist Leonard Darwin, a son of Charles Robert Darwin. Charles Robert Darwin notably employed the Malthusian population principle from classical political economics (see Malthus 1798) as the architecture for designing his theory of natural selection (see C. Darwin 1860) and, as Karl Marx (1867) once remarked, "Darwin has interested us in the history of nature's technology, i.e., in the formation of the organs [that] serve as instruments of production for sustaining life." Indeed, Charles Robert Darwin's grandfather, Erasmus Darwin, had written of an "Economy of Vegetation" (1791) and, prior to that, Carolus Linnaeus described all life as an "Economy of Nature" (1749). Indeed, "The ultimate subject matter of biology and economics is
one, viz., the life process" (Daly 1968).

NOTE: In answering this question, I've borrowed heavily from two draft works of mine that are on my Academia.edu page (i.e. I have not plagiarized whatsoever): https://independent.academia.edu/AaronHRubin
The following two links are to the two works of mine from which I'd borrowed:

https://www.academia.edu/28416634/A_Brief_Historical_Survey_of_Economic_Thought_and_the_Life_Sciences

https://www.academia.edu/29823064/LifeEconomyEnergyandSemiosis_-_working_paper.pdf


Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?

Yes, there is such an interpretation in Section 3 of the original paper by Pratt:

  Pratt, J. (1964). Risk Aversion in the Small and in the Large.
  Econometrica, 32(1/2), 122-136.

Under some regularity conditions, the coefficient of absolute risk aversion approximates the risk premium divided by half the variance for a small actuarily fair gamble. In Pratt's words, "$r(x)$ is twice the risk premium per unit of variance for infinitesimal risks". A similar interpretation holds for relative risk aversion, see Section 10.


How exactly does elasticity relate to slope?

The two demand functions $D_1(p),D_2(p)$ cross at the point $(Q,p)$. Their respective elasticities at price $p$ are
\begin{align*}
\epsilon_1(p) & = \frac{\text{d}D_1(p)}{\text{d}p}\frac{p}{D_1(p)} \\
\\
\epsilon_2(p) & = \frac{\text{d}D_2(p)}{\text{d}p}\frac{p}{D_2(p)}.
\end{align*}
However since both function cross at the point $(Q,p)$ we know that
$$
D_1(p) = D_2(p) = Q.
$$
But then
$$
\frac{p}{D_1(p)} = \frac{p}{Q} = \frac{p}{D_2(p)}.
$$
Meaning the only difference between their elasticities is $\text{d}D_i(p)/\text{d}p$, which is their slopes.

As for your 1. question, the conditions are not clear. Is the 'flatter' curve only 'flatter' locally, or for every price $p$? If you only mean locally, then no, the statement is only valid in the intersection point $(Q,p)$.


I there an established correlation between Federal Reserve balance sheet and MB( monetary base)?

The two series are linked by an accounting identity, which is why they tend to move together closely. There’s no theoretical limit to how much larger assets can be than the monetary base, though. If you look at the two tables in the H.4.1 Release, you’ll see that the first table is basically the Fed’s assets (what you refer to as its “balance sheet,” but in reality one side of the balance sheet). The second table effectively shows the other side of the balance sheet, its liabilities. Two lines in the second table add up to the monetary base: “currency in circulation,” and “Reserve balances with Federal Reserve Banks.” The sum of all the other lines in the second table is the gap between the two series. These other balances serve a number of different purposes, and as of the moment I am answering this, the biggest contributor is something known as the Treasury General Account, which you can basically think of as the Treasury’s own checking account held directly at the Fed.


Prove that if a good is inferior, it is also a Giffen good

As pointed out in one of the comments, a descriptive answer to the question is available here. However, here OP has asked for a rigorous proof. It is not true that if a good is inferior, it is also Giffen. On the contrary, if a good is Giffen, it is inferior. Here's a proof for this. Note that I am using some of the properties directly as including their proofs will make the answer undesirably long.
First some definitions:
Let $h_i(\mathbf p,u)$ and $x_i(\mathbf p, m)$ be the compensated (or Hicksian) demand function and Marshallian demand function for good $i$, respectively. Here, $\mathbf p$ is the price vector, $u: \mathbb R^n \to \mathbb R$ be the utility function meeting all the regularity conditions (quasi-concavity, continuity, etc.), and $m$ is the income.
Formally,
\begin{align}
\mathbf h(\mathbf p,u) = \arg \min\limits_{\mathbf x} \, \mathbf {p \cdot x} \\
\text{such that } u(\mathbf x) \geq u
\end{align}
Further, let $e(\mathbf p, u)$ be the expenditure minimizing function for a given minimum utility level $u$. So, $e(\mathbf p, u) = \mathbf{p\cdot h}(\mathbf p,u)$.
For Marshallian demand function:
\begin{align}
\mathbf x(\mathbf p,m) = \arg \max\limits_{\mathbf x} \, u(\mathbf x) \\
\text{such that } \mathbf {p \cdot x} \leq m
\end{align}
Now, from duality we have:
\begin{align}
h_i(\mathbf p,u) \equiv x_i(\mathbf p,e(\mathbf p, u))  \\
\end{align}
Differentiating this equation w.r.t $p_i$:
\begin{align}
\frac{\partial h_i(\mathbf p,u)}{\partial p_i} & = \frac{\partial x_i(\mathbf p,e(\mathbf p, u))}{\partial p_i} + \frac{\partial x_i(\mathbf p,e(\mathbf p, u))}{\partial e}\frac{\partial e(\mathbf p, u)}{\partial p_i}  \\
\end{align}
In the terms, $ \frac{\partial x_i(\mathbf p,e(\mathbf p, u))}{\partial p_i}, \frac{x_i(\mathbf p,e(\mathbf p, u))}{\partial e}$, $e$ is not really being treated as a function, so we replace with $m$, giving:
\begin{align}
\frac{\partial h_i(\mathbf p,u)}{\partial p_i} & = \frac{\partial x_i(\mathbf p,m)}{\partial p_i} + \frac{\partial x_i(\mathbf p,m)}{\partial m}\frac{\partial e(\mathbf p, u)}{\partial p_i}  \\
\end{align}
Rearranging gives:
\begin{align}
\frac{\partial x_i(\mathbf p,m)}{\partial p_i} & =  \frac{\partial h_i(\mathbf p,u)}{\partial p_i} - \frac{\partial x_i(\mathbf p,m)}{\partial m}\frac{\partial e(\mathbf p, u)}{\partial p_i}  \tag1
\end{align}
Now, note the following properties:
(1) From convexity of preferences (or quasi-concavity of utility function), $h_i(\mathbf p, u)$ is non-increasing in $\mathbf p$. Therefore, we have that:
$$\frac{\partial h_i(\mathbf p,u)}{\partial p_i} \leq 0$$
(2) $e(\mathbf p, u)$ is non-decreasing in $\mathbf p$. So we have:
$$\frac{\partial e(\mathbf p, u)}{\partial p_i} \geq 0$$
Using these in $(1)$, we can say:
$$\frac{\partial x_i(\mathbf p,m)}{\partial p_i} > 0 \text{     only if}\,\, \,\, \frac{\partial x_i(\mathbf p,m)}{\partial m} < 0$$

A side note: it seems that at some places (in some comments and the descriptive answer sited above) that a Giffen good is the one that does not follow Law of demand. This is not strictly speaking true. The law of demand pertains to Hicksian demand not the Marshallian demand. As it can be seen in the proof, $h_i(\mathbf p, u)$ is always non-increasing in $p_i$, but $x_i(\mathbf p, m)$ may not necessarily be. So the law of demand always hold under the regularity conditions on preferences.


Deriving Simple Tax Multiplier with Calculus (Macro Ugrad)

So here $C$ is a function with the argument $Y-T$, like $C=f(Y-T)$

So differentiate the equation: $dY=C' * (dY-dT)$

The result immediately follows like in the book.

The reason you don't do the partial derivative is that C has only one argument - while Y and T are in there, it only takes in 1 input.


Market economy status that World Trade Organization (WTO) uses is not really an economic status per se. Rather its a 'legal' status that determines how other WTO members are allowed to treat country with regards to imposing tariffs or other protective measures. The reason why this status exist is that in past non-market economies such as
Union of Soviet Socialist Republics (USSR) were considered to be engaged in dumping since they heavily subsidized their economically nonviable industries.
WTO has created some special provisions made in case such economy would want to join WTO, and such economies with non-market status could be subject to some extra protectionists policies (in this case especially anti-dumping policies) in contrary to original WTO mission of promoting the free trade.
Such status has nothing to do in principle with whether the country is actually predominantly based on market economy or not. Its rather just a term WTO uses in its policy. A legalistic language does not need to conform to economic reality, for example often many taxes from economic perspective are legally not considered taxes but have different status such as social contributions in many countries.
According to professor Li Jinshan:

The term “non-market economy state” originally appeared in the 1930 Tariff Act of the United States, as opposed to “state-controlled economy”. For the US, socialist countries totally monopolized the national economy and controlled prices of all merchandises. Hence, the prices of exported goods were untrue, and importing countries needed to seek a third country’s data to be a reference to calculate the market price for anti-dumping investigations and for determining anti-dumping duties on goods from the socialist countries. .... In accordance with these criteria, all socialist countries were listed as “non-market economy states”. The EU, Canada and other WTO members followed the US in defining the concept of “non-market economy” and relevant criteria in their anti-dumping laws.

Also yes the WTO can decide whether economy has market economy status or not as its a legalistic term that does not need to correspond to whether economy is actually a market economy or not. In fact until recently countries could choose themselves how to treat China. As further argued by Li Jinshan:

In its WTO accession agreement, China agreed that other WTO members could treat it as a non-market economy until 2015. This classification was agreed in the US-China 1999 bilateral agreement and was multilateralized as part of China’s WTO entry protocol. This classification is vital to one area of trade policy: dealing with dumping allegations against Chinese firms.

So not only WTO can give the economy such status it can even let some countries decide whether they will treat an economy under such status or not. In fact as the article you link mentioned this is all about EU treating China as non-market economy. Of course, countries might dispute this at WTO (it’s in some ways similar procedure to having dispute at a court), but in this case China lost the dispute.


How much revenue could an 100% land value tax be able to generate for the Indian government?

In Australia, Prosper compiled a survey of all economic rents and came to the conclusion that the Australian government could effectively be funded with rents alone.
This is without taking into account that abolishing taxes will further increase the value of economic rents, i.e. in the absence of taxation firms and households will have more net income to pay for economic rents (land, carbon, licences, fees) which further increases government revenues.
Mason Gaffney (2009) argues that all taxes come out of rents (ATCOR). According to this a tax reduction would increase rents by at least the same amount. This would imply that a government funded with taxes could just as well be funded with rents. See my question about ATCOR here.


mean variance utility function for risk loving person

For a risk lover, r is negative. Making the term $-\frac{r}{2}Var(X)$ positive. Thus, as variance increases, $E(x)-\frac{r}{2}Var(X)$ increases, which means their utility increases.


How to calculate the spending multiplier from a given set of equations?

Your friend is right. If you look at the initial investment equation, and comparing it to your definition, you have:
$$I=900+(0)Y-50i$$
So $d_{1}=0$ and $c_{1}=0.8(0.75)$ and thats why you get the spending multiplier as $\frac{1}{0.4}$


Why Should Expenditure Equal Income in Computable General Equilibrium (CGE) models?

It is because saving is investment expenditure, they must be  equivalent in standard macro models. To explain this forget about CGE models for a second, they are set up in this way because all macroeconomics is set up in this way.
In macroeconomics by definition income = expenditure. This is definitional. For closed economy by definition income (Y):
$$Y \equiv C+ I + G \tag{1}$$
where $C$ is expenditure on consumption (which is what you likely confused with expenditure in general), $I$ is expenditure on investment (public plus private saving), and $G$ is government expenditure (see more details in Blanchard et al Macroeconomics a European Perspective).
Now $I$ will by definition be equal to public and private saving since private saving $S_p$ is by definition income not consumed after taxes: $S_{p} = Y-T-C$. Public saving $S_G$ is by definition any difference between taxes and government spending $S_G = T-G$. Together then all saving must be:
$$S= S_p+S_G = Y-T-C+T-G=Y-C-G$$
Now this must be equal to investment since just by rearranging equation 1 we find that investment is:
$$Y-C-G =I \implies S=I$$
Hence the reason why the CGE imposes restriction that income is equal to expenditure is not that there should be no saving (although there might be simplified models where saving will be 'turned off' to make it easier for students). It is because expenditure and income are macroeconomically equivalent even in presence of saving (which is just investment spending).


How to address PPP when doing price comparison across countries?

As you are interested in very specific items, using an aggregate PPP measure like the ones provided by the World Bank (which are as aggregate as the GDP or private consumption), or the Big Mac index is not very good idea. This answer explains in some detail how PPPs are calculated ((the bottom line is that aggregate PPPs include a whole range of products; see here for more details).

If you are interested in just a few products, or maybe a single product (steel), as one of your comments suggest, you have to look into a more dissagregate PPP. You can find it here. These PPPs are still quite aggregate (for example, in the Classification tab you can find the full list). In your case, you might be interested in the Gross Fixed Capital Formation: Construction index. See here for more details on what this index includes. Notice that this is still quite an aggregate measure of PPP. Another drawback is that this is only available for either 2011 or 2005.

A final note is that you are normally one adjusts for PPP when the interest is in comparing cost of living or wellbeing across countries. Adjusting for PPP makes less sense when the comparison is for example about the cost of sourcing a material from different countries. Here, exchange rates is what you need, as this reflects the actual cost for firms of selling/buying a product in different markets. As you do not provide the context of your question, it is not possible to tell whether PPP is pertinent or not to you.


Construct a game with only pure strategy nash equilibrium

This was cross-posted. See my answer to this question here:

https://math.stackexchange.com/questions/1650075/construct-a-game-with-only-pure-strategy-nash-equilibrium


Are Parameter Estimates Unbiased If the Dependent Variable is a Per Capita Rate Based on Approximate Population Data?

What about assuming a multiplicative error process and then using logs?

Say the data generating process were a little different:
$Y_i  =  \beta_0 \cdot  X_i^{\beta_1}\cdot E_i$

If $Y_i  =  Z_i / P_i$ in truth but all we could really observe was:

$\hat{P}_i = P_i \cdot \Gamma_i$, where $P_i$ was the true value and $\Gamma_i$ was a strictly positive measurement error.

We' be estimating the following equation in practice:

$\hat{Y}_i  = Z_i / \hat{P}_i =  \beta_0 \cdot  X_i^{\beta_1}\cdot E_i$

take the logs of both sides (lower case letters are logs of individual variables):

$y_i  = \beta_0 + \beta_1 \cdot x_i + \epsilon_i - \gamma_i$

If we define a variable $\xi_i = \epsilon_i - \gamma_i$ then we can have an equation $y_i  = \beta_0 + \beta_1 \cdot x_i + \xi_i$ that looks very much like the one you wrote above.

If $\xi_i$ satisfies the same relationships with the log variables that $\epsilon_i$ does with the level variables it seems like everything should still work.


Predicting Shifts in Supply and Demand for Loanable Funds

The best way to think about this in terms of an intro course is to break down “total savings” into “private savings” plus “public savings.”

Private savings: Y-T-C

Public savings: T-G

If you sum these, taxes drop out, so changes in the level of taxation do not affect the supply of loanable funds.

However, this tax change specifically affects the taxation of savings. It’s a decrease in the tax on interest income, which should spur households to save more and consume less. Thus, the result of the change is an increase in private savings.

Not to confuse the issue too much, as I don’t know how you’re being taught, but I will note that the notion that government “savings” contribute to loanable funds is disputed, as it involves an implicit assumption that government spending does not result in productive investments.

From a practical standpoint, it’s often better to think of government borrowing as contributing to the demand for loanable funds instead, though many intro courses do not teach it this way.

Most governments (outside of typically oil-producing nations that have sovereign wealth funds) are net debtors, so even if they run a surplus, that shows up primarily as a decrease in government bonds outstanding (i.e., lower demand for funds).

If you think about it this way, then you can let changes in the level of taxation be neutral with respect to the supply of loanable funds, but you’ll still see “crowding out” effects as a result of deficits, as the increased demand for funds results in a higher equilibrium interest rate.


Money is, in essence, debt. More broadly, it's a system of clearing and credit. That entry in the computer means that the bank owes you \$1000, which is worth whatever others are willing to exchange for that sum— one way of thinking about it is that if you have \$1000, you have a general claim on the rest of society for \$1000 worth of whatever society produces.

The fact is that most money is in the form of loans (debt), not currency. This is well-explained in a recent Bank of England paper.


How exactly does removing labor market rigidities reduce structural unemployment and increase potential output in an economy?

Potential benefits of labor market reforms such as a reduction in job security and trade union power:

To find the answer to a reduction in job security, just apply it to your personal life(assuming you are employed). If labor market reform comes in and puts my job at risk, I would become more competitive and work harder in order to keep my job. This reaction would apply to most people.

As for a reduction in union power, this is more macro scale oriented. What unions don't realize is that financially they are hurting themselves & their company, albeit ethically/morally/quality of life at work they are gaining. So to keep things short and not go too far into controversial topics regarding unions, if union power is reduced, then market efficiency would increase from a financial standpoint not only for the firm, but for the macro economy and thus the employees.

As for structural unemployment, if there are market reforms structural unemployment will almost always rise in the beginning, but usually fall back down and most times dip even lower than previous levels due to efficiency gains from adapting to the reforms.

Hope this helps, I know it's not as detailed as you probably want it to be, but for that level of detail one must get into the controversial topics and pick a bias.


Are my conclusions correct in context of these examples of forceful extraction of money?

Well this is trivially true because GDP measures output. Here the only producer in the whole economy is the teacher, if the bandit or government can make teacher work more then of course GDP increases.

Note the GDP increase here because the teacher actually produces 200\$ worth of services not because money ‘circulate’. You can calculate GDP even for barter economy where there is no money. What matters is that this bandit or government managed to ‘convince’ the teacher to produce 200\$ of services.

Even in a totalitarian society where everyone is forced to do things at the end of the barrel of a gun GDP won’t be necessary zero.

However, this being said it is not realistic to assume that if government set taxes to 100% people will still provide goods and services assuming government can’t use forced labor.


Would you consider airport parking to be a monopoly or a monopolistic market?

If there are different companies offering with different prices, but not so many companies that it is perfect competition, then it is monopolistic and not a monopoly.


Why consumption is defined as $ C_t:= \left(\int^1_0C_t(i)^{\frac{\epsilon-1}{\epsilon}}di\right)^{\frac{\epsilon}{\epsilon-1}} $

For some reason Ubiquitous edited this information into the question, rather posting it as an answer:

  $i$ indexes the goods available for consumption

Integrals are just sums with a lot of components (technically infinite). Here the space of goods is assumed to have large dimension, rather than just consisting of two or three types of goods.


Is this supply and demand reasoning in Picketty's book circular?

The quote describes a very specific situation, which is not the general description through which the "law of supply and demand" is presented in non-technical terms.

It says

  If the supply of any good is insufficient

The correct term would be "quantity supplied at a specific point in time". Then the "insufficient" part, supposedly means "quantity supplied is less then quantity demanded". Ok. Then it says

  and its price is too high

So not only suppliers bring in the market a lower quantity that the quantity demanded by the consumers, they also "charge" a "too high" price... "too high" with respect to what? Presumably the consumers' "willingness to pay"?

So the first part of the quote describes consumers that have a priori specified both quantity desired and maximum acceptable unit price: "I want to buy 4 kgr of bread but at a price of no more than 0.5 euro/ Kgr." I understand that this sounds familiar: we tend to determine our needs/wants both in terms of quantity and we have some idea about what a "reasonable price" could be, by our past experience.

But once a consumer has specified two aspects distinctly, it must also decide on priority, if any: if the price is above 0.5 euros/Kgr, will he buy nothing? if this is case, then this consumer has "lexicographic preferences" over the unit price: he cares first for the unit price, and then for satisfying his needs through the consumption of bread. If the unit price is not right, he won't buy at all. This is a special situation, not just theoretically, but as to the degree it represents the "majority" of consumer behavior as observed in practice.

But ok, let's analyze the special situation presented in the quote.

The bakery has only 2 kgr and sells for 1 euro/Kgr. I won't buy at all, because the unit price is not right. I don't care whether the baker brings in 2 more Kgr to reach 4 - as long as "the price is not right", I am not buying. So for this special case, "supply responses" are irrelevant. Now if the baker lowers the price to 0.5 euro per Kgr, I will buy his 2 kgrs, (Piketty's quote ends here)
and I will tell him that I am willing to buy 2 more Kgrs as long as he will sell these 2 additional Kgrs also for 0.5 euros. If the baker agrees, "supply responds" and the price is not raised back. If he brings in the 2 additional Kgrs but raises the price above 0.5 euro/Kgr, they will be left unsold, and we will have excess quantity supplied, not excess quantity demanded.

What would be a more  general framework?

"I will spend 2 euros for bread. if the price is 0.5 euros/Kgr, I will buy 4 kgr. If it is 1 euro/Kgr, I will buy 2 Kgr. Etc". In other words, through its utility maximization, the consumer will determine the budget share that he will allocate to bread, and quantity demanded will be determined by the price.
Assume that there exists also a second consumer, that he has decided to allocate 4 euros for bread.
The baker appears with 4 Kgrs charging 1 euro each.
The first consumer asks 2 kgrs and the second asks for 4 kgrs, for a total of 6 Kgrs. We have excess quantity demanded, but not "too high a price".
Now, the baker is not in our heads, he does not know the budget shares we have allocated for bread: he thinks "hey, these guys ask for more than I have, so it may be the case that I can still sell my 4 Kgrs for a higher unit price, -they seem to really want that bread so maybe they are willing to pay a higher unit price".
He then declares that the price of bread is now 2 euros/Kgr. The first consumer then asks for 1 kgr, the second asks 2 kgr, for a total of 3 Kgrs. Now we have excess quantity supplied. This is how the "cobweb" theorem works bringing market equilibrium.

Of course the baker could conceivably think "hey, let's make 2 more Kgrs, since these guys ask for 6 Kgrs in total, keeping the price at 1 euro/Kgr". Whether he will choose to sell his 4 Kgrs for 1.5 euro/Kgr, or 6 Kgrs for 1 euro/Kgr, I will leave for the OP to contemplate.


Does this explanation pertaining to the Supply Curve and Law of Supply make sense?

The figure from your study material looks very much like the one you found via Google. In particular, it shows a leftward shift in supply and a corresponding reduction in quantity supplied for any price. We can confirm this with a minor edit to the figure:


Is there any formal definition of a relationship between resource availability and demand?

I'm going to take a stab at providing the information that I think that you want, but I won't be answering the question that you asked. If this doesn't help you, consider changing the question as I don't think that we are necessarily understanding it.

TL;DR:  Resource availability and demand are mostly unrelated.  If anything, low resource availability will reduce demand (in the long term, not the short term).

Resource availability has no direct effect on the demand curve.  The demand curve reflects how people value the resource.

Availability determines the supply curve, which measures the cost of production.  I.e. at a specific quantity supplied, the supply curve will give a specific price.  That is often a marginal price.  That is to say, it is the price at which the last unit can be produced.

In general, in a market economy, the quantity supplied and the quantity demanded are the same.  And that value occurs when the demand and supply curves intersect.

I've been using a term, quantity demanded, with which you may not be familiar.  It may be that what I call quantity demanded is what you are thinking about when you say demand.  That happens sometimes.  Demand in economics is generally a graph of how the quantity demanded will change based on price.

In general, if a resource is constrained, this moves the supply curve (and may change its shape).  A constraint will move the supply curve to the left.  Since supply curves generally slope up and demand curves slope down (the higher the price, the more people will find a way to supply; the higher the price, less people will demand at that price), moving supply to the left will reduce the quantity supplied/demanded.

Meanwhile, there will be a bunch of people who would like to buy the resource but not at that price.  These also may be the people you think of as "increased demand."  From an economic perspective, this unmet demand is not measured beyond that.  It is the portion of the demand curve to the right of the quantity demanded.  That area will increase if the demand curve stays the same while the quantity demanded shifts left.  Most economists would not refer to this as increased demand, but you may be.

Now all that's the short term reaction.  In the long term, lack of a resource may cause demand for the resource to drop.

Consider gasoline.  Let's assume that it becomes constrained.  Initially, in the short term, my only real options are to pay more or drive less.  But in the long term, I can get a different car.  My new car may run on natural gas or electricity.  But if I do that, then the gasoline demand curve changes.  Not by a lot, as I'm only one person.  But if many other people do the same thing, collectively we shift the demand curve.  It would be reasonable then to say that lack of availability reduced demand in the long term.


How are economic principles applied to non-financial models, such as a democratic election?

Long story short: Preferences orderings are over more abstract outcomes instead of money. It's still a story of maximizing expected utility.

Agents are usually assumed to have preferences over outcomes. This is assuming something like consequentialism. In financial models, the outcomes are dollar amounts and so there is a natural preference ordering. In something like a political model, outcomes are policies. So, people have indirect preferences over political candidates based on beliefs and seek to influence the outcome by voting. This is probably a bad model of voting, as most people don't honestly believe their vote matters I'm guessing.

Beyond voting to influence current decision-making, here is a good paper about voting as communicating: Piketty (2000)


Literature on factors affecting number of houses built

It won't help much with the high frequency variation of interest to you but this is a famous and important paper on this topic:

  I process satellite-generated data on terrain elevation and presence
  of water bodies to precisely estimate the amount of developable land
  in U.S. metropolitan areas. The data show that residential development
  is effectively curtailed by the presence of steep-sloped terrain. I
  also find that most areas in which housing supply is regarded as
  inelastic are severely land-constrained by their geography.
  Econometrically, supply elasticities can be well characterized as
  functions of both physical and regulatory constraints, which in turn
  are endogenous to prices and demographic growth. Geography is a key
  factor in the contemporaneous urban development of the United States.

The Geographic Determinants of Housing Supply (Saiz (2010))

This paper may also be useful:

  The long-run price elasticity for alternative specifications of new
  housing supply is estimated using U.S. annual data for 1950 through
  1994. The basic model expresses residential construction as a linear function of new housing price and the prices of construction inputs.
  Long-run elasticities range from 1.6 to 3.7, suggesting that new
  housing supply is price elastic. Residential construction responds to
  both the real interest and expected inflation rates, but other
  construction cost variables perform poorly. However, the results are
  sensitive to the time-series processes underlying the variables. A
  modified model that expresses residential construction as a function
  of changes in input prices, rather than their levels, produces a
  long-run elasticity of about 0.8 and a significant inverse
  relationship between new housing supply and the construction wage
  rate.

The Long-Run Elasticity of New Housing Supply in the United States: Empirical Evidence for 1950 to 1994 (Blackley (1999))


Estimates for 'inflation expectations': the 'breakeven' rates. What are they?

Intuitively, this is the story: The interest rate on inflation-linked bonds (which means that the coupon payments are adjusted for inflation) can be seen as a real interest rate, because one is always exactly compensated for the realized inflation. Subtracting this real interest rate ($r$) from a nominal interest rate ($i$) gives the average inflation expectaction ($\pi^e$) over the period remaining before maturity. Just use the fisher-equation to see this: $r=i−π^e$.


Can anyone recommend a resource for monthly trade data for Mexico from before 2010?

I had a look for a few places. Looks like the WTO have something relevant. I haven't looked at the dataset but hopefully it is useful. This only has annual trade. The World Bank also has some data also covers annual data.

http://imts.wto.org/CDS/gp/tsselection.aspx

I think this one has your answer. It has monthly data. Only 1000 records at a time but up to 5000 if you sign up. You will probably have to be a bit clever with your queries and then merge a few spreadsheets as well. Clunky interface but the data looks vast.

http://comtrade.un.org/monthly/Main/Data.aspx


What did the Swiss National Bank use to purchase EUR while pegging the Franc to the Euro?

This quotation by Michael Bordo, Owen F Humpage, and Anna J Schwartz (2012) was the richest description I could find on how the SNB achieved the floor:

  In March 2008, the Swiss National Bank eased monetary policy in
  response to expectations of deflation, deteriorating economic
  conditions, financial-market distress, and a Swiss franc appreciation
  that resulted from the global financial crisis. In conjunction with
  this action, the Bank aggressively bought euros in the
  foreign-exchange market in 2009. Throughout March and April 2009, the
  Swiss National Bank did not seem to sterilise its substantial
  foreign-exchange purchases; the Swiss monetary base rose by more than
  the value of foreign assets on the Bank’s books. In response, the
  Swiss franc depreciated. By April 2009, however, the Swiss monetary
  base had more than doubled from a year earlier, and the Bank – now
  concerned about latent inflation – began to sterilise the liquidity
  resulting from its huge interventions. The Swiss interventions
  continued through June 2010, but the Swiss monetary base either grew
  by less than the Swiss National Bank’s holdings of foreign assets, or
  the monetary base actually declined. The Bank was clearly sterilising
  the operations, and the franc appreciated by nearly 10% between April
  2009 and June 2010. On balance, from May 2010 to August 2011, the
  Swiss monetary base contracted and the franc appreciated, reaching an
  historic high on a real trade-weighted basis.

  In early August 2011, the Swiss National Bank announced a series of
  new measures to inject liquidity into financial markets with the
  objective of stemming the Swiss franc’s appreciation. The operations
  included foreign-exchange swaps in which the Bank sold francs spot and
  repurchased them forward. The franc depreciated sharply, but undertook
  a stunning reversal late in the month. The Swiss National Bank then
  announced that it was prepared to buy foreign exchange in unlimited
  quantities to maintain a floor of SF 1.20 vis-à-vis the euro. The
  Bank’s holdings of foreign exchange increased substantially, but the
  Swiss monetary base increased by even more. Since September, the Swiss
  National Bank has maintained an exchange-rate floor, by giving up
  control of its monetary base in conformity to the fundamental
  trilemma.

Foreign-exchange intervention and the fundamental trilemma of international finance: Notes for currency wars

If they are not controlling their monetary base they probably be doing standard currency interventions. That is, they credit their own accounts at banks with CHF, then using those credited accounts to purchase Euro denominated assets. Or perhaps, they enter into spot Euro-CHF FX transactions and use the proceeds to buy Euro denominated assets. If they were selling gold then they'd sell gold for dollars and buy euros with dollars. That might modestly move the Euro-USD  exchange rate but would affect the Euro-CHF rate only indirectly. But the Swiss monetary base shouldn't be increasing.


How to maximize revenue by changing price?

Your question does not provide enough information for me to walk you through the process step-by-step using your information, but hopefully I can point you in the right direction.

You question about Price Elasticity of Demand (usually just called Elasticity of Demand). Elasticity of Demand is used to show how responsive demand is to a change in price. For example, if a $1\%$ increase in price leads to a massive drop in the quantity demanded, say 75%, then we would say that the demand is relatively elastic. If an increase in price does not really cause a drop in the quantity demanded then demand is relatively inelastic. The concept of elasticity of demand translates to your question because $price\ multiplied\ by\ quantity\ equals\ revenue$.

You mention that if you increase $(C)$, you reduce $(B)$. Yes, this is (usually) correct because the relationship between price and quantity is negative-- the higher the price, the fewer items sold. As for reducing $(D)$, this depends on the elasticity of demand. For example,

Assume the price for each subscription is $\$2$. Assume that at a price of $\$2$, you sell $1,000$ subscriptions. This gives you a revenue of $\$2,000$: $$\$2( 1,000)=$2,000$$

Elasticity demand can be calculated a few ways, I'm going to use: $$Elascitity\ of\ Demand = {\frac  {{\mathrm  {Percent\ Change\ in\ }}Q}{{\mathrm  {Percent\ Change\ in\ }}P}}$$ Where $Q$ is quantity demanded and $P$ is price.

Lets consider the following two examples:

Scenario 1:

Assume that you increase the subscription price from $\$2$ to $\$3$. Now assume that an increase in price from $\$2$ to $\$3$ decreases the total number of subscriptions sold from $1,000$ to $960$. Notice that the number of subscriptions decreased, but revenue increased from $\$2,000$ to $\$2,880$: $$\$3(960)=$2,880$$ This happened because the demand for subscriptions is considered inelastic. Price by 50% [$(3-2)/2$], and your quantity decreased by 4% [$(960-1000)/1000$]. Since the percent of the price increase increased by more than the quantity demanded decreased, you increased your revenue. Your elasticity of demand in this scenario is, $$\frac {\mathrm -0.04}{\mathrm 0.50}=-0.08$$

Scenario 2:

Assume that you apply the same price increase from $\$2$ to $\$3$ per subscription, but this time the quantity sold drops from $1,000$ to $400$. Your revenue is now, $\$1,200$ $$\$3(400)=$1,200$$ In this case an increase in price caused your revenue to decrease. What happened? In this case subscriptions are considered elastic. The price increased by 50% [$(3-2)/2$], and your subscriptions demanded decreased by 60% [$(960-1000)/1000$].Your elasticity of demand in this scenario is, $$\frac {\mathrm -0.6}{\mathrm 0.50}=-1.5$$

To answer your question, you are looking for the place on your demand curve where the % change in price is the same as the percent change in quantity demanded. This is point is called Unit Elastic. In order to calculate this for yourself, you will need to know the relationship between the price of subscriptions and the quantity demanded.

Consider reading more about elasticity of demand as there are a couple of ways to calculate it. When you do the calculations you will get an elasticity of demand number that ranges from $0$ to $-∞$. (Some people will convert these numbers to absolute value... $0$ to $∞$, means the same thing.) The number you get from calculating your elasticity of demand will tell you what to do with your price. For example, if you get an elasticity of demand number that is greater than $-1$ (or less than $1$ if you use absolute value), then increase your price because revenue should increase. If you get back an elasticity of demand number less than $-1$ (or greater than $1$ if you use absolute value) then decrease your price and your revenue should increase. You want to adjust your price until your elasticity of demand number is $-1$ (or $1$ if you use absolute value). $-1$ is the point of unit elastic.


Does migration exacerbate (albeit delay) the problem of aging, economically-inactive populations in Western societies?

I don’t really see the connection you are drawing. As @Fizz has pointed out, immigration usually happens over time and maybe when immigrants grow old there will be more immigrants to support all of the new old. Likewise, in many countries immigrants tend to have more children than non-immigrants, so that will attenuate the aging problem.

If anything it should be something to check case-by-case, but I don’t see any causal relationship between immigration and the “aging problem”. I see how just mechanically these two are related, but I don’t expect the relationship to have any particular systematic pattern.

It feels to me like you are saying that taking more exams is bound to lower your average grade. Of course more exams will impact your average grade, but it really can go up or down depending on many other factors.


Why does the European Central Bank use the 5y5y rate to measure inflation

In an interest rate swap, two parties swap with each other the obligation to pay a fixed rate for the obligation to pay a floating rate. Because it concerns a simple swap of obligations, the rates must have equal present value for both parties. The market quotes the fixed rate, so this is the variable of interest.

Draghi may have been referring to one of two types of swap contracts: the 5-year/5-year interest swap or the 5-year/5-year inflation rate swap. The case of the 5-year/5-year inflation rate swap is simplest. Because the contracts trade at equal present values, a lower fixed rate implies lower expected inflation.

The case for the interest swap requires an additional assumption. Consider that interest rates consist of two components: a compensation for inflation rate risk, and a compensation for default (and possibly other) risks. This latter part is called the risk premium, and it also affects the quoted fixed rates. So in order to draw any conclusions about market inflation expectations on the basis of interest rate swaps, it is simplest to assume that the risk premium is constant. Of course this is not necessarily the case, and this assumption could be investigated by looking at the difference between the two different swap contracts.

Finally, I cannot be certain about why the ECB prefers this measure to any other measure of inflation expectations. But besides the fact that it is a market measure, the timing adds up: the 5 year swap starts in 5 years, so it is an indicator of inflation 5-10 years in the future.


$\beta$ is the measure of the sensitivity of stock returns to market returns. This has nothing to do with the value of $R^2$.

Your results appear to be fine, you can get significant beta estimates but low $R^2$. Why?

As measured by $R^2$, 24.56% of variation in Apple returns is accounted for by the variation in the market index, $S$&$P 500$. Clearly, there must be other factors that determine the remaining 75.44$% of variation in the Apple returns. Other factors that you could include in the model are copmany size and market to book value (Fama and French Three-Factor Model). By including these omitted variables in your new model, you may achieve higher r-squared value.


How Does Production Possibility Curve Shift (Partially)?

Perhaps in order to produce 80 pizzas you don't need 10 workers but just 8 and the extra 2 workers can now produce wings.


In a trade imbalance does the importing country's currency become more valuable?

No. In fact the opposite happens. The value of a currency (or the exchange rate) is determined by supply and demand of the currency on the currency market. If country A imports more, the supply of country A's currency will increase more, therefore losing its value.

Suppose B's goods are priced in B's currency. Then, the supply of A's currency increases in your example, because it needs to sell its own currency to purchase more of B's currency to be able to buy B's goods. Therefore more of A's currency comes on the market, while more of B's is demanded. If priced in A's currency, the exporters in B will still want to have B's currency as they need it because they live in B. Then they will want to exchange the amounts of A currency obtained for B currency.

Hence, in both cases on the markets for currency, demand for B's currency increases, while supply for A's currency increases, therefore reducing the value of A's currency.

The currency would not (necessarily) "stockpile" however, as import tariffs in B do not influence the exchange of currency.


What is an example of a choice which is not necessitated by scarcity?

The basic idea behind scarcity and opportunity cost is fundamental to economics. Basically, if resources are infinite, you have everything.

In my opinion, there are no infinite resources because a lifetime is finite. In one way or another, it can be argued all choices are necessitated by scarcity.

Eating chips means at that time, you cant be eating a burger. That is your opportunity cost.

This may be the point of your homework question, to make you realise that scarcity is a key driving force behind decision making.


I have used gambit (python) in the past and could recommend it. It also includes a small GUI which makes things very intuitive.

R also has GameTheory if you prefer this platform instead


What do game theorists think of behavioural economics?

Disclaimer: My academic coming of age was in an environment where behavioral economics played only a minor role. My research is theoretical, both "behavioral and non-behavioral", economics.
I believe it is incorrect to say that game theorists (or economists) in general are not convinced by behavioral economics. You can easily see it is considered to be quite relevant by finding Thaler, Shiller, Kahneman and Selten (yes!) in this list. I also do not feel like young economists stay away from behavioral economics.
That being said, there are some (not necessarily good) reasons why many economists have a certain dislike for behavioral elements. One is that students often criticize standard models, taking a "behavioral approach" that in the end simply breaks down to "why should I study Bayesian Nash equilibrium if people are not clever enough to make such calculations anyway" -- this is a fair point, but if you want to have game-theoretic analysis or predictions you should base these on some closed system. I don't find "people are stupid and hence anything can happen" particularly illuminating. Luckily, this is not what modern behavioral economics does although some critics of "standard economics" seem to think this. Adding behavioral aspects often makes a model more complicated to analyze, which the same kind of critics then complain about again.
Behavioral economics often simply incorporates systematic "errors" (?) such as time inconsistency, loss aversion, social preferences, overconfidence, probability weighting and so on. This is reasonable because there is almost undeniable evidence of such biases.
An issue that I sometimes have with such models is that they don't deliver surprising insights. For instance, if you assume that a decision maker is overconfident and then find that this decision maker has a preference for riskier prospects than a "rational" decision maker without this bias, I am not very moved. The result just reflects the assumption. When I see the magician putting the rabbit in the hat, I don't clap when he pulls it out. I am not saying that every publishable result needs to be surprising, but it needs to add to our current knowledge. Serious economists know the limits of their models and are aware that changing the beliefs in some direction alters behavior.
By far not every behavioral paper is like that: many, in fact, expand our current knowledge and our theoretical toolbox tremendously. However, we then have many little toy models that are applicable in only some environments and not so much in others. In contrast, the rational benchmark is always applicable and usually comes with a normative touch: this is how utility maximizing agents are supposed to behave. Maybe it is just me, but I sometimes feel that this is also a point that many critics of "standard assumptions" actually mean: people should be more social and less egoistic and firms must not only maximize profits. That is, this normative aspect gets mixed with the analysis. However, you cannot blame behavioral economics for people having wrong perceptions about it.
Moreover, you usually cannot exploit homo oeconomicus. In contrast, the behavioral agents have systematic flaws by design and therefore they will be exploited. Behavioral agents often introduce a Dutch book. As a result, behavioral assumptions often only make sense in decision theory (i.e., individual decisions without interaction), but not so much in game theory (i.e, strategic interaction) because no equilibrium exists when a money pump is present. I guess what I am trying to say is that while some behavioral biases are reasonable and hard to deny, they -- if all their logical consequences are taken into account -- can still produce unreasonable predictions.A nice paper making such a point is the AER paper "Until the Bitter End" by Ebert & Strack discussed here.


"My difficulty is to reconcile the fact that humans do not think in
  real terms: we observe and value everything via its nominal value."

Those who do that, suffer from what is called the "money illusion".

  "In the hypothetical case of comparing two objects that have the same use (let's say, oranges from X country and orange from Y), we always
  use its nominal value to determine what to buy."

Indeed, because this is a comparison of two distinct (even if comparable) products, at a single point in time.

Now just answer the following question:

  Your wage today is 100 and the price of oranges today is
  100/kgr. Tomorrow, the price of oranges will be 200/Kgr and your wage
  will still be 100. Will your wage tomorrow be the same, as regards
  what matters, with your wage today?

Certainly, its nominal value will be the same. But what about its real value, i.e. the value in terms of what matters? (how much you can consume, is what matters).


How did the Plaza Accord revalue the Japanese Yen?

The Plaza Accord was implemented through market mechanisms. According to Wikipedia Central banks of the signatory nations spent $10 billion dollars. They exchanged these dollars for other currencies. This increases the supply of dollars and may even decrease demand if so far the central banks have been purchasing dollars. Due to the higher supply and not higher demand the 'price' or exchange rate of the dollar fell. At the same time the countries also implemented policy changes. This would effect the mid to long term exchange rates.

The Japanese interest rate did indeed fall.
http://www.tradingeconomics.com/japan/interest-rate
 Mind though that the US interest rate also fell
http://www.tradingeconomics.com/united-states/interest-rate


This should help you figure out how to compute RSS for the different models.

Let's begin with what we have:

We know that

$y$ is an $n \times 1$ vector that has observations of the endogenous variable
$x$ is an $n \times 2$ matrix of observations of the exogenous variables
$\beta$ is a $2 \times 1$ matrix of coefficients

Unfortunately (or fortunately depending on how you look at it), we don't know what $x$ and $y$ look like in this equation. Instead we are given $(x' x)$, $(x' y)$, and $(y' y)$.

Using your comment about what RSS actually is -- Namely, that

$$\text{RSS} = (y_{\text{observed}} - y_{\text{estimated}})' (y_{\text{observed}} - y_{\text{estimated}})$$

First notice that $y_{\text{estimated}}$ is simply $x \beta$. Then replacing this in the previous formula gives us

\begin{align*}
  \text{RSS} &= (y_{\text{observed}} - y_{\text{estimated}})' (y_{\text{observed}} - y_{\text{estimated}}) \\
  &= (y_{\text{observed}} - x \beta)' (y_{\text{observed}} - x \beta) \\
  &= y'y - 2y'x\beta + x \beta \beta' x'
\end{align*}

Now this is almost what we want. We want things to ultimately be in terms of $(y'y)$, $(x'x)$, $(x' y)$, and $\beta$. The first term is exactly $y'y$, but other terms look like they have pieces we want and we just have to find a way to get them.

Now, notice that each of the elements in our equation above is simply a scalar (aka sizes are such that they are $1 \times 1$). The determinant of a scalar is itself, then by using properties of determinants we can say:

\begin{align*}
  2y'x \beta &= \det(2y'x\beta) = \det(2 \beta' x' y) \\
  x \beta \beta' x' &= \det(x \beta \beta' x') = \det(\beta' x' x \beta)
\end{align*}

I will leave the linear algebra itself as an exercise.


How to find the long-run relationship using this regression (3rd time posted)

INITIAL ANSWER March 24

Ok. Let's answer this without answering. Your moral obligation to this community, in case it matters to you, is to report back with your work and your answer.

1) In Economics we use the difference of natural logarithms to express (approximately) something specific. It is essentially stated in the body of the exercise.

2) An estimated relation through regression is essentially an estimation of the expected value, which in turn can be thought of as some long-term average. So don't you think it should validate the assumed long-run values given in the exercise?

3)  Given the assumed long-run values in the exercise what is the relation between $C_{t-1}/Y_{t-1}$ ,  $C_{t}/Y_{t}$, and of $C/Y$, in the long-run? Or between $\Delta \log Y_{t-1}$ and $\Delta \log Y_{t}$ (in light of your answer in 1) above).

4) Given the assumed long-run values in the exercise, do you think that the answer will be of the form $C = a + bY$, or of the form $C = bY$?

The final step will require remembering your answer in 1).

ADDENDUM April 7th
Now that the question came to its proper home, and a two-weeks interval has passed, let's complete this:

Given the estimated relationship, in order to be consistent with our model, we accept that this relationship will also hold in the long-run. In the long-run some magnitudes are constant. Which ones, in our case? We are told that the long-run growth rate of Consumption and of Income are the same, constant, and equal to $0.25$. This means that in the long-run we will have the equalities

$$C_{t-1}/Y_{t-1}= C_{t}/Y_{t}=C_{LR}/Y_{LR}$$

$$\Delta \log Y_{t-1}=\Delta \log Y_{t} = \Delta \log C_{t} \equiv g =0.25$$

...since the difference of natural logs approximates the growth rate.
Given these, and given the estimated long-run inflation that is given and equal to
$$\Delta \log P_{t} \equiv \pi = 0.1$$
 the long-run relationship is transformed into an equation with a single unknown, $C_t/Y_t$. Specifically, we have, making first symbolic and then numerical substitution:

$$g = 0.8g+0.7g+0.1\ln(C_{LR}/Y_{LR}) -0.15\pi$$

$$\implies g(1-0.8-0.7) + 0.15\pi = 0.1\ln(C_{LR}/Y_{LR})$$

$$\implies  0.25\cdot (-0.5) + 0.15\cdot 0.1 = 0.1\ln(C_{LR}/Y_{LR})$$

$$\implies -0.11 = 0.1\ln(C_{LR}/Y_{LR})$$

At this point, it appears that the "old exam question" made a mistake, because the choices given for answering seem to "ignore" the existence of the coefficient $0.1$ attached to $\ln(C_{LR}/Y_{LR})$.

If the relation was $-0.11 = \ln(C_{LR}/Y_{LR})$, we would obtain by taking the exponential $e^{-0.11} = C_{LR}/Y_{LR} \implies 0.896 = C_{LR}/Y_{LR} \implies C_{LR} \approx 0.9Y_{LR}$, which is one of the choices given.

But with the coefficient $0.1$ present we obtain

$$... \frac {-0.11}{0.1} = -1.1 =\ln(C_{LR}/Y_{LR}) \implies e^{-1.1} = C_{LR}/Y_{LR} \implies C_{LR}\approx \frac 13Y_{LR}$$

which is not given as an option.

PS: The standard errors of the estimates are not involved in the above calculations. One could comment that their magnitude compared to the magnitude of the estimates indicates that the estimates are "statistically significant" for confidence $>95$%.


Yes, the earlier answer about currency value gives some links, including a link to an IMF publication that presents models (methods) with some notes on how to calibrate them and further links to literature. There they describe among others also the macroeconomic balance framework that takes into account the internal and external balance at the same time.


Bellman Equation with Two Discount Factors

No. Consider the following problem: Each period, one total unit of consumption falls from the sky that can be distributed between the two agents in any way. Their per-period utility is simply how much they consume. We let $\alpha=1/2$. Assume that $\beta_1>\beta_2$; the first agent is more patient. All optimal allocations have a very simple form: The consumption unit is arbitrarily distributed in the first period, in all subsequent periods, agent 1 gets everything. This implies that the value function for continuations is completely independent of $\beta_2$, which it clearly is not in your suggested form.


Can corporate tax loss carryforward function like a sort of insurance policy?

The structure of the tax ladder is such that the marginal tax rates keep increasing. The upshot is that if you earn more, your net earning (after taxes) will never be lower. So a company with a good year will always be better off compared to a company with a bad year, holding everything else equal. In this sense, tax does not provide advantage to companies with a bad year.

Your idea of "insurance policy" would be most closely related to the concept of automatic stabilizer. But this concept talks about the macro picture of the entire economy, so I'm not sure if it's wise to link the two together.


Why will these steps NOT fix the problems with LIBOR?

Rather than answer regarding your specific proposal, as that would be of less use generally than providing the current state of thought about interest rate benchmarks, I will provide a quick review of the literature, allowing you to think more generally about the issue.

Regarding LIBOR specifically, the Wheatley Review of LIBOR was the foundational document outlining the general issues with LIBOR and setting a path for reform. After this review, the International Organization of Securities Commissions (IOSCO) published a report, "Principles for Financial Benchmarks" that addresses general issues surrounding benchmark governance, quality, methodology, and accountability. You will find that this report is particularly important in thinking about benchmark calculation approaches, as it provides a framework for evaluation of benchmark proposals, yours included.

Since then, the Financial Stability Board's Official Sector Steering Group has issued specific recommendations relating to LIBOR reform; this document relates the general IOSCO principles to the specific issues that arise in interest rate benchmarks.

Finally, two academic articles may prove of interest to you.

Duffie and Dworczak's "Robust Benchmark Design" discusses the design of robust estimators in situations where a benchmark is based on transactions and agents attempt to manipulate these transactions to profit on derivatives based on the benchmark.

Finally, Duffie and Stein discuss LIBOR reform and alternative reference rates in "Reforming LIBOR and Other Financial-Market Benchmarks."


Best formula for price depending on amount

I think your expectation that a "best" formula exists is very unreasonable.

There is no "best" car design, there isn't a formula to design the fastest airplane with total weight $x$ and there is no easy formula that will give you the best price in general situations.

Sciences have a lot of unsolved optimization problems. Economics, psychology and most sciences involving humans have a lot of seemingly unknown variables, further complicating things. So while there are some principles which you can base your pricing strategy on I have never heard any reasonable person claim that a general best price mechanism exists and I don't think it does.


How do I choose the correct model for a regression?

Plot things. Do the raw data look like they have cycles? (I assume so, given that you are talking about economic data and want to use an autoregressive model.) Next, try to get the order of the autoregressive model by taking differences until the cycles disappear. This can also be tested formally using (a version of) the Durbin-Watson test. There will likely be further patterns. What do you see? Does the variability stay constant over time (likely when you have percentages) or is there a tendency for the variability to grow? What smooth (and simple) function follows the general distribution of the data? Fit it, assess the fit, repeat with different functions, until you have something reasonable.

Model selection is far more of an art than a science, and there often are several reasonable models that you can use.


Trade in services between the US and China

Table 2.2 of https://www.bea.gov/scb/pdf/2017/10-October/1017-international-services-tables.pdf suggests

US exports of services to China in 2016 worth $\$54$bn and
US imports of services from China in 2016 worth $\$16$bn

Later parts of table 2.2 give a breakdown of types of services.  Travel (for all purposes including education) - which should not include transport - seems to be a large part of US exports of services to China


Why has QE produced hyper-inflation in other countries, but not US and China?

That is because inflation is a change in price level and price level can be expressed using the basic monetary model as:

$$P=\frac{MV}{Y}$$

Where M is money supply, V is velocity of money and Y is output.

Hence, while it is true that the price level is increasing in money supply (M) it is also decreasing in (Y). Hence if your money supply grows for example by 5% but also your output grows by 5% and velocity stays the same your country will experience 0 inflation.

Countries that experience high levels of inflation such as Venezuela have a double problem of increasing money supply while their output is plummeting making their inflation very bad, while other nations get less inflation than you would normally see given change in M due to growth in output.

Furthermore, in certain types of recessions when there is a liquidity trap all increase in M can be offset by decrease in V. This is the reason why for example US or Euro-Area experienced low inflation even though they had large recessions and large expansion in money supply in the recent recession.

In more complex models expectations play role as well but I don’t want to go too much into technicalities as the main lessons carry from them to the above mentioned simple model.