How is price elasticity determined in practice?

In many practical instances, price elasticity of demand (PED) is calculated in a back of the envelope fashion, just as taught in the textbooks! Firms can adjust their price by some small amount and observe the demand response. For relatively small changes in price and quantity, little accuracy is lost by assuming that the demand function is locally linear, so that the change in price and demand jointly give an estimate for $$\frac{dQ}{dp}.$$ Since $p$ and $Q$ are already known, this is enough to calculate the PED:
$$\eta=\frac{dQ}{dp}\frac{p}{Q}.$$

This method yields only a point estimate of elasticity at the current price. However, one can get an incredibly long way with just this estimate thanks to the so-called Lerner condition: that a firm with marginal cost $c$ facing a price elasticity of $\eta$ maximises profit when $$\frac{p-c}{p}=-\frac{1}{\eta}.$$ Once the price elasticity of demand is estimated in the above fashion, this formula can be used to infer if the firm's price is above or below its profit-maximising level (allowing a firm to correct towards that level). Alternatively, this kind of analysis is often used as a heuristic in competition policy (antitrust) because, by estimating the right hand side of the Lerner formula, competition authorities can get an estimate for the left hand side (i.e. for how much power the firm has to price above marginal cost).

One drawback of this approach is that, at least in its simplest implementation, it does not control for factors such as how a change in the price of a product affects the demand of other products sold by the same firm (and thus overall profit).

You can see a nice informal discussion of Amazon's book pricing based on this kind of back of the envelope work here.

For more formal purposes, and when data is readily available, the process is often similar but slightly more careful in the estimation of demand. An excellent example of this kind of work can be found in Ellison & Ellison's 2009 Econometrica Paper, Search, Obfuscation, and Price Elasticities on the Internet. They proceed by estimating the firm's demand function econometrically (rather than via the heuristic method described above), and then calculate the implied PED from this estimated demand. Using an equation analogous to the Lerner condition, they are able to infer how far from the competitive case the market is, and attribute this discrepancy to search obfuscation.

In practice, for economists working outside of a firm, the main difficulty is often obtaining the data necessary to estimate the PED (Ellison & Ellison had excellent data thanks to collaboration with a firm in the market).


What effect would removing the lowest denomination currency have?

The practice of rounding to the smallest currency unit is called Swedish rounding. I know of a few papers that discuss likely economic concequences.

Eliminating the Penny from the U. S. Coinage System: An Economic Analysis Lombra (2001)

Time to Eliminate the Penny from the U.S. Coinage System: New Evidence Whaples (2007)

Pennies, Pricing, and Rounding: Is All the Relevant Analysis in? Lombra (2007)


How to compute Walrasian equilibrium in the case of logarithmic utility?

let $u \equiv xy^2$, then we have:
$$U=lnx+2lny=ln(xy^2)=ln(u)$$
Since $U'(u)>0 \: \forall u>0$ it follows that the $(x,y)$ that maximizes $U$ also maximizes $u$; $\max \{U\}=\max\{ln(u)\}=ln(\max\{u\})$. $u$ represents the same preferences as $U$.

Clearly, $u(x,y)=x^a y^b$ with $a=1$, $b=2$.


Critiques to Mankiw, Romer, Weil (1992) paper on Economic Growth

Here are three:

Klenow, P., & Rodriguez-Clare, A. (1997). The neoclassical revival in growth economics: Has it gone too far?. In NBER Macroeconomics Annual 1997, Volume 12 (pp. 73-114). MIT Press.

Klenow, P. J., & Rodriguez-Clare,A. (1997). Economic growth: A review essay. Journal of monetary economics, 40(3), 597-617.

They pose certain conceptual issues as regards entangled causalities (in the economics' sense, not in the econometrics' sense).

All are freely downloadable.

Bernanke, B. S., & Gürkaynak, R. S. (2002). Is growth exogenous? taking Mankiw, Romer, and Weil seriously. In NBER Macroeconomics Annual 2001, Volume 16 (pp. 11-72). MIT Press.

This paper argues that one of the most important implications of any Solow framework is that long-run growth depends only on exogenous technological progress, and that MRW do not test in the right way this implication (the authors do it their way and reject this implication).

But I don't think you will find papers with deep statistical-econometric testing/validation of the model.


At forecasting, should I calculate inflation rate daily, monthly or annualy?

Inflation is the percent change in a price index per unit time. You should compound at the same frequency as the units in the inflation measure. Many reported measures of inflation are year over year measures, which means that even though they may be reported monthly or quarterly they overlap substantially between observations. You want to be sure to handle this properly by choosing non-overlapping intervals.


How will London's role as a financial center be affected after the Brexit and what are possible alternatives?

London remained for long as a key financial centre for Europe due to several reasons:

Historic: several universities and authors dedicated to the study of wealth (Smith, Ricardo, Malthus, Keynes
Combination of privileged international positions with US (language + colonization) and commonwealth countries, as well as an average sized internal market
Looser regulation than most countries in EU, providing lower barriers to entrepreneurship
Fairly efficient justice system
Management and investor attitude: social class or country of origin is less of an obstacle than in France, investors not as conservative as in Germany

Comparing these factors to other large cities in Europe, it will be hard to match it.

In Germany, Munich or Berlin could be more attractive for investors than Frankfurt. Paris would be the favorite in France, but regulation doesn't attract investors nor entrepreneurs - so Amsterdam or Luxemburg would be much more inviting in this regard.


Price Elasticity of Demand - elastic demand and impact of price reductions on total revenue

Like anything derived from calculus, the statement is guaranteed to hold true only for infinitesimal change. Unfortunately, since I don't know the entire demand function, I can't say much more than this.

A clear example of why this wouldn't work: starting at the same point \$100 and Q = 1000, we can decrease price to zero and total revenue would go down.


Why must the rate of GDP growth be positive?

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


How bad is piracy hurting the entertainment industrie's economy? Are they going bankrupt or have a good outlook?

Economic evidence on the effects of piracy is mixed. Most of the evidence focuses on the music industry, where piracy has been especially prevalent and where data is often more readily available.

Some papers find evidence that piracy has little or no effect of industry profits (here is one prominent example).

Other studies (example) find that piracy displaces sales and reduces profits. The estimates there imply that each song pirated costs the industry about 30 US cents.

Most surveys of the literature seem to conclude that the overall effect is negative.

Some messages that emerge from the literature:

piracy especially harms large, well-established content creators, but may benefit small/independent creators who otherwise find it harder to reach an audience;
for music: the industry has somewhat pivoted away from recorded music sales in favour or live performances as a source of revenue;
the revenue cost of piracy is offset by the benefit consumers get from consuming free music. Putting aside the competing interests of firms and creators, the main social problem associated with piracy is its potential to reduce the number of creative works produced in the first place (by reducing the rewards to creating new works).
evidence on the incentives to create new works is also mixed (see, e.g., here);
thanks to political lobbying, creators probably enjoy 'too much' copyright protection (see here and here). Piracy may be helping to offset this somewhat;
there are other things going on in the industry that may may more important than piracy. In particular, (i) search technologies give rise to 'long-tail' effects where a small number of works (e.g. Harry Potter) become incredibly successful but the majority not (a reference is here), and (ii) platforms such as Spotify, iTunes and Netflix are emerging as very powerful actors who are able to appropriate much of the industry revenue.

In summary, piracy probably does seem to be hurting the entertainment industry to some extent, but not critically so.


Budget constraint in Radner Sequential Trade Equilibria

In Radner's model each actor starts with an initial endowment, an asset vector $\omega$. You can trade this to any asset portfolio $x$ that has lower or equal value, so
$$x * q \leq \omega * q.$$
Denoting asset trades by $\theta = x - \omega$, you can also express this as
$$
\theta * q \leq 0.
$$


From a mathematical point of view, a function of the form

$$Q_d = \left( \frac {A-p}{B}\right)^{1/\gamma},\;\; \gamma > 1$$

will have a negative second derivative and so it will be strictly concave (for $\gamma =1$ we get a linear demand function). The function hits the (vertical) $p$-axis for $(Q_d=0,p=A)$, and the horizontal $Q$-axis for $(Q_d = (A/B)^{1/\gamma}, p=0$). Namely this is "concave all the way", not just concave in the middle which eventually becomes convex. Typically, we expect  $A>B$.

Inverting, we obtain

$$p=A-BQ_d^{\gamma}$$

Let's now go down to the individual level, and assume quasi-linear preferences in income, an appropriate formulation when we look at one good "against all others":

$$v(q,y) = u(q) + y,\;\;\; s.t. \;\;pq+y = M$$

The first-order conditions will give

$$u'(q) = \lambda p,\;\;\;\ \lambda =1$$

Combining with the inverse demand function we get

$$u'(q) = A-BQ_d^{\gamma}$$

where $Q_d = \sum q$.

Integrating we have

$$\int u'(q) dq = A\int dq - B\int \left (\sum q\right)^{\gamma}dq$$

from which we arrive at (setting the arbitrary constants of integration to zero)

$$u(q) = Aq-\frac{B}{1+\gamma}Q_d^{1+\gamma}$$

We obtained this result by assuming that the  individual believes that its own demand does not affect any other individual demand. So we have a negative externality: the more "massive" is a good (the more massively demanded), the less utility we obtain from it (so any individual demand does not affect any other individual demand, but their sum, does affect the individual elements). So such a specification would be appropriate for goods that are not characterized by the "safety of the flock" aspect, but appeal to our quest for individualism and personal uniqueness.

Assume now that we do not want to have this negative externality in the individual utility. Then, we assume that all consumers are identical, and we start with the utility specification,

$$u(q) =  aq-\frac{b}{1+\gamma}q^{1+\gamma}$$

This utility specification does imply that there exists a maximum utility level from the good and then utility declines, so it belongs to the general family of "quadratic" preferences.

Indicatively, for $a=100, b=10, \gamma=1.3$ we have

The indifference map is constructed by calculating

$$y = \bar v - \left[aq-\frac{b}{1+\gamma}q^{1+\gamma}\right]$$

for arbitrary values for $\bar v$ (which, in quasi-linear preferences, correspond to the income constraint).For $\bar v = M=400,450,500,550,600$ the map looks like

Such an individual utility specification will give the optimal relation

$$a - bq^{\gamma} = p$$

and the individual demand

$$q = \left( \frac {a-p}{b}\right)^{1/\gamma}$$

Summing over all $N$ consumers we get

$$Q_d = N\left( \frac {a-p}{b}\right)^{1/\gamma}$$

and we want to arrive at the market demand function

$$Q_d = \left( \frac {A-p}{B}\right)^{1/\gamma}$$

This can happen if we identify $A=a$ and $B = b/N^{\gamma}$.


Yes, you can run diff-in-diff with aggreggate treatment in this case.
Yes, standard errors should be clustered at the treatment (here=state) level.
No, the number of clusters is not an issue, as the relevant number is the total number of clusters and 50 should reasonably avoid the small cluster problem.
The way you can think about this is to forget states exits. You simply have some (US) observations (firms?) that are treated and others that are not. In principle, that gives you diff-in-diff if you can satisfy all the assumptions on the control group (similar behavior in absence of treatment).
However, three other general problems arise.

Ideally, in this case you'd also want to show results at the aggregated treatment level, which you can't do because of small sample bias, since that gives you only 50 observations in each time period, but that's fine.

Finding the right control units/states (satisfying assumptions, e.g. parallel trends) is hard. The fact that only one state is treated may mean that state is very unique in the context of your research question. Maybe you want to use propensity score matching or synthetic control in addition to diff-in-diff.

Treatments at state level can be very general and you need to ensure other diverging policies also aren't happening etc.

That being said, these types of analyses can be performed and are often done. I recommend finding a paper that does diff-in-diff with treatment at the state level and follow their steps to get you started.


Why did John Keynes believe that monetary policy to be less effective than fiscal policy?

This was due to the idea of liquidity trap, and due to Keynes thinking that in economic recession it is easy for an economy to slip into the liquidity trap. Liquidity trap is a situation where preference for holding cash becomes virtually infinite. Keynes (1936) in the 'General Theory' states:

There is the possibility...that, after the rate of interest has fallen to a certain level, liquidity-preference may become virtually absolute in the sense that almost everyone prefers cash to holding a debt which yields so low a rate of interest. In this event the monetary authority would have lost effective control over the rate of interest.

Infinite preference for holding money means that more savings will not necessary lead to more investment but rather reduced income (see Blanchard et al. Macroeconomics a European Perspective - box on the 'paradox of savings' on pp 55). Keynes called this the 'paradox of thrift' and in his own words (again quoting from the General Theory):

For although the amount of his own saving is unlikely to have any significant influence on his own income, the reactions of the amount of his consumption on the incomes of others makes it impossible for all individuals simultaneously to save any given sums. Every such attempt to save more by reducing consumption will so affect incomes that the attempt necessarily defeats itself.

Consequently, if an economy is in a liquidity trap monetary policy becomes impotent because monetary policy stimulates economy by lowering interest rate which encourages investment and borrowing and thus spending, as well as putting upward pressure on prices, which in turn helps to 'grease' the wheels of economy by reducing the frictions caused by sticky prices and wages (e.g. wages are very slow to adjust nominally so inflation can force real adjustment even when nominal ones would require long negotiations). These links break in liquidity trap as in such situation changes in money supply tend to just affect holding of money rather than encouraging investment or other spending.
However, government spending can still stimulate economy even in such situation. In fact, paradoxically in such situation government spending becomes extra potent because monetary policy that follows Taylor rule (or similar rule) usually works against government spending, because in normal situation such central bank would raise interest rates when government would pursue expansionary fiscal policy. Nonetheless, in situations as liquidity trap they reinforce each other because in such situations such central bank will keep its interest rate on the minimum possible level even if government pursues fiscal expansion  (see discussion in Blanchard et al reference mentioned above, the Burda and Wyplosz in Macroeconomics ch. 10 have nice discussion of this or if you look for some more nuance then models in texts such as Romer Advanced Macroeconomics - although this is all contemporary treatment).


If a respective sector’s foreign direct investment (FDI) is not stable  then this will create uncertainty which is a general deterrent  to international investment.   Because a recipient country can affect investment decisions policies may need to change for a particular industry/sector.

Investment requires a stable economic environment and changes in the economic cycle, currency fluctuations, and changes in business confidence creates uncertainty, which is a general deterrent to international investment.

Possible Problems:

Transport costs would be increased as less firms having factories (manufacturing plants) overseas within consuming industries.   This is especially important for bulk increasing products, such as motor vehicles.
Investors will have a difficult time accessing to a countries markets thereby spending less on FDI resulting in  decrease in GDP for an industry resulting in decrease aggregate GDP.
more trading blocks forcing firms to deal with more barriers to trade such as tariffs.

Developments:

Less production growth and less productivity for a sector.

In a working paper by Robert Lensink and Oliver Morrissey (2001) titled "FOREIGN DIRECT INVESTMENT: FLOWS, VOLATILITY AND GROWTH IN DEVELOPING COUNTRIES"

When unstable FDI is introduced into their model the results have a negative effect on growth.

They stated that there are a number of reasons why volatility of FDI inflows may be negatively associated with growth.

One of them are that the volatility of FDI undermines investment (R&D [ If FDI inflows are uncertain, costs of R&D are uncertain, which negatively affects incentives to innovate.]), and thus has an adverse effect on growth and productivity.

Another finding, stated in their paper, is that they found increases in the volatility of FDI negatively affects growth as it decreases the certainty equivalent value of FDI and consequently increases set-up costs and decreases the rate of return on assets (page 10).


What exactly is certainty equivalence in the context of DSGE models?

Intuitively, it means that the model has such characteristics that "the best we can say" about remaining uncertainty, is that it will be zero. From general experience, we know that it won't be zero, but the information we possess does not permit us to say anything else than that it will be zero. The even deeper assumption here is that the information and knowledge we possess make all things that remain unpredictable to average to zero.

In such a case, of course the actual realized path of the model is affected by these totally unpredictable shocks, but the decisions we take are based on a rule "as if" the future shocks will be zero (it is implied that we have to take decisions prior to observe the realization of the shock).

More technically, quoting from Lungqvist & Sargent's "Recursive Macroeconomic Theory" 2004, 2nd ed:

  a) p.113: "CERTAINTY EQUIVALENCE PRINCIPLE: The decision rule that
  solves the stochastic optimal linear regulator problem is identical
  with the decision rule for the corresponding nonstochastic linear
  optimal regulator problem.

  b) p.115: The certainty equivalence principle is a special property of
  the optimal linear regulator problem, and comes from the quadratic
  objective function. the linear transition equation, and the property
  that (future disturbances have zero mean conditional on the current
  state). Certainty equivalence does not characterize stochastic control
  problems generally.

Please read also this post, so that if you do further search, to make sure that you look for "certainty equivalence in macroeconomics".


Are slacks the same as mix-inefficiency?

If by "slack" we mean that part of the quantity used from an input does not result in an increase in output, then it is evident that this is an inefficient mix of inputs. It is not even about re-allocating inputs to reduce/minimize costs, we are clearly totally wasting some input quantity.


What was the "free Coynage" referred to in Dudley North's (1691) Discourses Upon Trade?

It seems to refer to the free coinage act of 1666 introduced by British Parliament under the rule of Charles II.

The name of the act was:

  An Act for encourageing of Coynage.

But it is often referred to as free coinage act. The full text of the act can be read in this source.

According to the act:

  Gold and Silver to be coined gratis. For every Pound Troy of Gold or Silver brought, there is to be delivered a Pound Troy of Current Coin.; For every Pound Troy of Gold and Silver finer than Standard so much more than a Pound Troy delivered; and for baser Gold or Silver so much less.

So the act basically abolished seigneurage and allowed people to bring their silver/gold to the royal mint and having it minted into coins. Hence here the free literary means people did not had to pay for coinage of the coins.


Is the money market model based on assumption of no interest rate targeting on the part of the central bank?

I remember making myself the same question when studying those models in Mankiw's book. The answer I arrived is that from the point of view of the model, the Central Bank's policy is reflected in the money supply variable, and the interest rate variable is an abstraction that represents the main interests rates in an economy that are given by the equilibrium.
Think about this, in the model when there's an increase in money supply, what happens with the equilibrium interest rate ceteris paribus? It goes down. And the opposite is also true. But, who controls the money supply variable? The Central Bank.
So if you look at what happens in reality is somehow like that, the Central Bank cuts rates so the money supply decreases. Obviously the mechanism by which this happens in reality is different compared to the model, even they're like the 'opposite', but remember that models simplify reality in order for it to be more understandable, and in this case the CB intervention is modeled this way.


What does a stock market index stand for?

Indexes don't have units. They're indexes.

An index is a ratio of two numbers. The two numbers have the same dimension. So their ratio is unit-less.

The compilers of each stock market index set a denominator which represents a base set of conditions, and they then may adjust that denominator to ensure that events that change market cap, but which should not change the index, do not change the index. The sum of the market capitalisations of all of the index members forms the numerator. These are both expressed in the domestic currency (so for the FTSE 100, the currency is GBP; for the S&P 500, the currency is USD)

For more, see https://www.investopedia.com/ask/answers/040215/what-does-sp-500-index-measure-and-how-it-calculated.asp

Stock market indices are still exposed to currency variations, because the denominator is not adjusted for currency variations, and the numerator is exposed to them: the index members' market caps are all in the same currency, and their profitability will almost always have some exposure to the currency too.

For a multi-currency index, a standard currency is chosen, and then each company's market cap is converted to that currency. Again, the numerator and denominator are expressed in the same currency, so the index has no unit.

The one freak in all this is the Dow Jones Industrial Average, which doesn't behave like other indexes (it's an index, but it's a straight price average, not weighted by market cap), and should, broadly speaking, just be ignored.


It would be really tough to find papers (other than structural models) that empirically determine a particular utility function. Because of their subjective nature, it is incredibly tough to obtain observable data to estimate them. So researchers study the primitive preference relations that utility functions represent. Arguably, the preference relation is what you want to study when talking about rationality and choice. Utility functions are useful insofar as it opens up a tool-box of real analysis tools which a binary relation doesnt typically allow.
So you should rather look for papers that test rationality from observable choice data. I have elaborated a bit on this in an answer to a related question: Click Here


Spatial Durbin model in Stata - How it is estimated?

I'm assuming you know how to do spatial weights matrices and such, so I will just skip that and throw out a disclaimer that I use R as my primary statistical programming language, not STATA, so let's first observe a generic spatial model:

spatreg $ylist $xlist, weights(W) eigenvalues(E) model(lag)

The lag in that function can be replaced with an error option if you want the SEM. To do a spatial durbin model (SDM) in R I find that using mixed or a durbin option does the job. Try and see if that works in place of lag in model(), for future reference. Sometimes the option is there but not many people use it because they don't usually care about estimating the model.

Next, try out the spmlreg function which appears to have the spatial durbin option:

spmlreg $ylist $xlist, weights(W) wfrom(Stata) eigenvar(E) model(durbin)

For a better understanding of the function, check out P. Wilner Jeanty's documentation of spmlreg.

Maybe both of them work fine, and that'd be cool. The more options the better.


This is not a structural paper. The authors are not "deriving" a log-linear relationship from a model, which they then proceed to estimate. They rather start by postulat the relationship:

  Let $C^J_{it}$ be the number of citations made by the patent
  applications Japanese firm i filed in year t to the cumulated stock of
  bindigenousQ U.S.-invented patents granted as of year $t$. I can then
  write the log of $C^J_{it}$ as a simple log-linear function of several
  other observables

  $$ c^J_{it} = \beta_0 + \beta_1 p_{it} + \beta_2 FDI_{it} + \gamma_i +
> \alpha_t + \epsilon_{it}$$

which is their equation (1).


A non-mainstream answer...

As Steve Keen is fond of pointing out, mainstream economists (incorrectly) think that the level of private debt has no macroeconomic effects so nobody was looking out for any unusual build up.

Keep in mind the following two facts:

Most private debt is in fact loans from banks - in other words
demand deposits - which are money. So when private debt rises,
the money supply grows.
House prices are not properly reflected in standard measures of inflation.

In the years running up to the crash of 2007/8, central banks were monitoring the level of inflation and adjusting interest rates so as to keep inflation low. There was a housing bubble which meant that house prices were rising relative to the price of everything else (i.e. stuff recorded in inflation measures). The housing boom meant that private debt (i.e. the money supply) was rising at around ten percent a year whilst inflation was running at around only two or three percent. Almost no mainstream economists thought that this was dangerous.


Converting word definitions of Pareto-Optimal into math symbols

Let $\Omega$ be the set of all feasible allocations with an element $\omega \in \Omega$.  Consider $I$ agents such that the utility of agent $i$ is described by $u_i(\omega)$.

Definition 1: $\omega \in \Omega$ is weakly Pareto-optimal if $\nexists \omega' \in \Omega$ such that $\forall i$ $u_i(\omega') > u_i(\omega)$.  Weak Pareto-optimality is basically just saying that for any other allocation, $\omega'$, in the set of feasible allocations that not everyone can strictly prefer the alternative.

Definition 2: $\omega \in \Omega$ is strongly Pareto-optimal if $\nexists \omega' \in \Omega$ such that $\forall i$ $u_i(\omega') \geq u_i(\omega)$ with strict inequality for at least one $i$.  Strong Pareto-optimality is a little stronger in the sense that your allocation must be strictly preferred by some to all other allocations and everyone else can be indifferent.

I hope that is helpful.


How does John Stuart Mill distinguish between "wealth" and "riches"?

I can only speculate on what Mill meant, but it seems to me that

This is mostly a figure of speech. People sometimes say things like "I have no money, but I am wealthy in other ways", meaning they have something they would not trade for money, i.e. monetary wealth.
If there is a distinction, it is in the concept of ownership. Air is not wealth because I do not own it. There are several things that are beneficial to have (that enrich us) that we do not own and could not easily trade. Health, loved ones, air, etc. One can have, but not own these things, so they are not wealth.
(Except in Spaceballs.)


Utility function in Ramsey-Cass-Koopmans model

Recall that in the RCK model households choose their consumption and savings so as to maximise current and future utility (i.e. future generations). Then the objective function is given by
$$ U = \int_{0}^{\infty} u[c(t)]e^{nt}e^{-\rho t}dt$$
The RCK model assumes the functional form of utility
$$ u[c(t)] = \frac{c(t)^{1-\theta}-1}{1 - \theta} $$
Note that this function is increasing and concave, and that assuming that $\rho > n$, it ensures that lifetime utility does not diverge. This is a very practical assumption as it ensures that households would not have infinite lifetime utility and therefore allows for a well defined solution.
This is is called constant intertemporal elasticity of substitution (CIES) or constant relative risk aversion (CRRA) utility function (note that this isoelastic utility function is the only class of utility functions with constant relative risk aversion).
You can check for this by computing the risk aversion coefficient, $\frac{1}{\sigma}$, where $\sigma$ is the intertemporal elasticity of substitution (measures the willingness on the part of the consumer to substitute future consumption for present consumption) and is defined as
$$ \sigma =  \frac{1}{u''(c)} \frac{u'(c)}{c}$$
From the functional form of utility you obtain
$$ \sigma = \frac{1}{\theta} $$
And therefore the risk aversion coefficient equals $\frac{1}{\sigma} = \theta$, which is constant and independent of consumption.
Note that the intertemporal elasticity of substitution is analytically derived as the inverse of risk aversion. This follows from considering fluctuation in the marginal utility of consumption over time as a form of risk. For example, a risk-averse individual would choose to smooth their consumption path to avoid such risk (fluctuations).


Yes, the relation $B$ over $X$ is not complete since $3 \in X$ but $(3,3) \notin B$.

The variables $x$ and $y$ in the completeness definition "$\forall x,y \in X, xBy \lor yBx$" are treated as placeholders and thus are not necessarily distinct. In fact, completeness implies reflexivity when you let $y = x$ in the definition.


Does a tighter spread between occupancy and stabilized occupancy
  indicate higher demand?

Not necessarily. Demand is not the only factor that determines occupancy rates. A tight spread by itself only indicates market steadiness (that is, uniformity over time).

Using your example, Market 2 could have experienced a significant increase of demand in the past two years and yet present a lower occupancy rate if cost at new facilities outweighs the demand increase. The new bedrooms are available but only few consumers can afford them.

Government intervention and/or expectations about the future might also discourage suppliers from effectively releasing to the market much of the new facilities. This certainly amounts to a reduction of supply (and a higher Occupancy Rate, accordingly), but metrics might fail to capture that reduction in a market that would otherwise reflect the same demand and Occupancy Rate as Market 1.


Difference between Maximum Output and Potential Output

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


First, note that both firms have constant returns to scale. This implies that firms must make zero profit in equilibrium. If they could make a positive profit, they could make even more profit by scaling up production and no profit-maximizing production plan would exist. So who owns which firm does not really matter. We know from the first welfare theorem that every equilibrium must be Pareto efficient. With the given utility functions, this means that both firms have to produce a positive amount. But this pins down the relative prices of $x$ and $z$, and of $y$ and $w$, respectively. So this reduces the problem to one in which you have to find two prices. You can set one of the remaining prices to be $1$, and then calculate the excess demand for one good. FInd the price that makes this excess demand zero. As a consequence of Walras' law, this price will clear all markets.


How to test for invertibility in ARCH family models?

It's not clear what you mean by "invertibility of the mean equation". Invertibility, in the Box-Jenkins context, is a property of ARMA processes. A characterization of invertibility is that an ARMA process is invertible if and only if the MA polynomial has no roots inside the unit disk in the complex plane. Empirically speaking, invertibility means the current (unobservable) innovation is a weighted sum of what has been observed, although the weights in the sum are unknown ex ante. An ARCH type model usually do not assume any type of ARMA specification for the mean.
As for the variance $\sigma_t^2$ term in, say, GARCH, by assumption it follows an ARMA process, and its invertibility can be checked like any ARMA model.
For "X"-GARCH extensions that leaves the ARMA linear process framework, it's not clear how you would define invertibility.


Buying stocks in company merging/acquisitions

Stocks/shares are equity (a share is 'a part of' something) and are thus essential to ownership of a company. Owning shares means that you own part nof a company. The ownership, as a side effect, gives voting rights on the C-suite and dividends.

Acquiring a company requires you to buy all of the shares of that company (so that you own it).


In this paper, page 8, it says

  Quarterly seasonally adjusted nominal GDP and its deflator
  are constructed by Higgins and Zha (2015).

That paper can be found here (google did not help to find this paper. I had to look for the personal website of one of the authors, here).

This document states in section II.1, Step 1:

  Annual
  real GDP-va –
  RGDP_va_A
  – is set to
  NGDP_va_A
  in 2008 ...

This is confirmed later in the next page, when they say:

  Except for the base year (chosen to be 2008) ...

So it seems to be 2008.


Can I normalise the Dixit-Stiglitz price index to 1?

To me it depends. If you are dealing with price indexes that are somehow distributed spatially, i.e. you have $P_i \ \text{for} \ i=\text{NY},...,\text{CH}$ it would make no sense to normalize only one of them. I say "only" because it would be a priori impossible to normalize them all since, say, transport costs would ineluctably force them to be different.

If you are dealing with a unique price-index, I see no reason of why you could not do so. Indeed, note that you have

$ p_m = P(p_m)^{1-\varepsilon} \bigg[ \frac{I}{Y_m} \bigg]^{1/\varepsilon}$

which underlies an under-identified system. So, yes you can include the $P-1=0$ equation in your solver.

Regarding the contradiction it creates with your (over-identifying) wages and rental rates, to me it looks like you should take things upside-down. Under Dixit-Stiglitz monopolistic market, firms set their price by assuming a constant elasticity of substitution (CES), $\varepsilon > 1$, and profit maximization leads to a constant mark-up on variable cost

$p_m = \frac{\varepsilon}{\varepsilon - 1} c_m(w_m)$

where $c_m(w_m)$ is the unitary labor cost of producer $m$, function of wages $w_m$. So there are a priori nothing to guess freely at that level, just use the relation you have between prices and wages.

Also, the level of capital, $K_m$, should be set before any king of GE-resolution. Indeed this is a "calibrating" characteristic and I do not see why -- at least given the content of your question -- you want its obtention to be melt with that of the general-equilibrium (GE) vector of prices.

I would not calibrate $\varepsilon$ if I were you, since there is a big narrative behind the choice of its value: this is somehow representative of the "market depth", see Rivera-Batiz (1988) for an intuition about the level of elasticity that might be chosen. Do you want your narrative to be chosen by your solver?

Finally, you say that we can think of $I_m$ as $\sum_m p_m Y_m$, which is (only) true at equilibrium... But how is your $I_m$ formed ? It looks like each consumer also possesses her own firm (given that $I$ is indexed by $m$)? Is it $I_m = w_m + K_mr_m$, where $r_m$ is the rate of return of the firm $m$ ?

Need more precisions from you to go further.


Why do exports include only hard products?

Found a fairly nice one from OECD. It includes combined trade in goods and services as a percentage of GDP. It is also possible to drill into goods only (which seems most commonly presented in the public domain) or services only data.


Would an $8 National Minimum Wage Work in the US?

The labor market is missing one of the criteria of a free market, the ability of participants to decline a transaction if they only receive disadvantageous offers.

This is not a problem as long as there are more open jobs than applicants; market forces provide sensible price points (different for different skill sets) here. If there are more applicants than jobs however, prices fall quickly as there is no supply elasticity, and the gradient is basically given by the cost of the commute.

The two major ideas to counteract this market failure are a minimum wage, and a Universal Basic Income (UBI).

The minimum wage approach tries to change as little as possible. Competition for low-skilled jobs is still fierce, but at least the holders of these jobs are able to live in houses, get proper nutrition and possibly also have free time in which to improve their skill set, which will enable them to enter a different market segment, reducing pressure at the bottom. Upward mobility is greater when there is a bigger surplus in workers' wages after cost of living, because it allows for better learning conditions.

From a government perspective, we want everyone to be upwardly mobile, as we can expect that low-skilled building and manufacturing jobs to become even more scarce in the future, while at the same time, we need lots of specialists (to the extent that the US still has special visa for skilled workers).

The \$15 figure is pretty much arbitrary, but a full time (40h/wk) worker should come out at roughly \$28,000 before taxes, which is not great, but should be sufficient for rent, transportation, food and further education; at the same time the number isn't so high that it leads to competition with skilled jobs.

Going with \$8.26 would still avoid the "race to the bottom" in wages, but leaves workers nothing above subsistence level, diminishing their education opportunities and thus worsening the situation as more low-skilled workers enter the market than leave it, so unemployment remains long term and workers remain low-skilled until retirement, which is not sustainable especially in light of technological advance.

For completeness, the UBI approach simply corrects the missing part of the free market by allowing everyone to reject bad offers. This would be easier to police than a minimum wage as it removes the requirement to look at individual contracts, and just goes with equilibrium prices.


What's the difference between gross fixed capital formation and gross private domestic investment?

The term gross private domestic investment (GPDI) seems to be used only by the US. The term gross fixed capital formation (GFCF) is used by the rest of the world (but not by the US). (This is thus simply the US being exceptional as usual by using its own terminology and methodology.)

Roughly, the difference is this: Ignoring inventories, GFCF includes government investment, while GPDI does. More precisely, the difference is this: $$\begin{alignat*}{1}
\text{GFCF} & =\text{Gross private domestic fixed investment}+\text{Gross government fixed investment}\\
 & =\text{GPDI}-\text{Change in private inventories}+\text{Gross government fixed investment}.
\end{alignat*}$$

To elaborate just a little, the rest of the world follows the UN System of National Accounts (SNA, 2008), while the US does not. In the usual identity $Y=C+I+G+NX$, we have the following differences between the UN SNA and the US:

If you are looking at countries other than the US, then you may not be able to find data for GPDI so easily. In which case, you may want to use GFCF.

Conversely, if you're looking at only the US, then you'll probably want to use GPDI.

Of course, in your analysis, you should be clear about what precisely your statistic, be it GFCF or GPDI, is supposed to measure.


What does n stand for in the taylor rule?

As you mentioned before, $\bar{n}$ is the sensitivity parameter of the interest rate to changes in short run output in a monetary policy rule. What is the relationship of $\bar{m}$ and $\bar{n}$ within the Taylor rule? It heavily depends on the given economic climate.

Assuming the basic Canonical New Keynesian DSGE Model the equations of our economy are the following:

IS (investment/saving) curve:
$$   y_t = E_t [y_{t+1}] - \theta r_t +u_t^{y} $$
AD (aggregate demand) curve:
$$ \pi_t = \beta E_t [\pi_{t+1}] +\kappa y_t + u_t^{\pi}$$
Taylor rule:
$$   r_t = m E_t [\pi_{t+1}] + n E_t [y_{t+1}] +  u_t^{r} $$

If you estimate the Taylor rule empirically with some kind of economic techniques, there should be considered 4 scenarios (shocks) .

Demand shock ($m, n > 0$)
Supply shock ($m > 0, n < 0$)
Monetary policy shock ($m, n < 0$)
Technology shock ($m > 0, n < 0$)


When was the supply and demand model first used?

The Wikipedia page about the supply and demand model has a History section.

According to Hamid S. Hosseini, the power of supply and demand was understood to some extent by several early Muslim scholars, such as fourteenth-century Syrian scholar Ibn Taymiyyah, who wrote:

  "If desire for goods increases while its availability decreases, its
  price rises. On the other hand, if availability of the good increases
  and the desire for it decreases, the price comes down."

Antoine Augustin Cournot first developed a mathematical model of supply and demand in his 1838 Researches into the Mathematical Principles of Wealth, including diagrams. However, John Locke (1691), Adam Smith (1776) and David Ricardo (1817) also used this model.


Yes. Note that in the paper the authors assume that the action space is continuous, so it is possible to bid in arbitrarily small fractions of a dollar.

Suppose players $i\in\{1,2,3\}$ have bids $b_i$ that, without loss of generality, are ordered $b_1<b_2<b_3$. Write $p$ for the actual price.

If we forget about player four for a moment, then players' probability of winning are

$$\Pr(1\text{ wins})=\Pr(b_1\leq p< b_2)\equiv \pi_1$$
$$\Pr(2\text{ wins})=\Pr(b_2\leq p< b_3)\equiv \pi_2$$
$$\Pr(3\text{ wins})=\Pr(b_3\leq p)\equiv \pi_3.$$

Suppose $\pi_1>\pi_2,\pi_3$. Then the optimal thing for 4 to do is to bid $b_4=b_1+\epsilon$ ($\epsilon$ positive and small). This bis would result in
$$\Pr(1\text{ wins})=0$$
$$\Pr(2\text{ wins})=\Pr(b_2\leq p< b_3)$$
$$\Pr(3\text{ wins})=\Pr(b_3< p)$$
$$\Pr(4\text{ wins})=\Pr(b_1\leq p< b_2).$$

One can easilly check that $\pi_1>\pi_2,\pi_3$ implies that $\Pr(4\text{ wins})$ is bigger than any rival winning probability. Likewise, if we had $\pi_2>\pi_1,\pi_3$ then the optimal thing for $4$ to do would be to bid $b_4=b_2+\epsilon$.

edit: The above reasoning works if we take $\pi_1>\pi_2,\pi_3$ (with strict inequality). But what if the inequality is not strict?

Suppose that $b_1<b_2<b_3$, and that $\pi_1=\pi_2>\pi_3,\Pr(p<b_1)$. Then it seems like $b_4=b_1+\epsilon$ must yield a lower winning probability than that enjoyed by player 2 for any positive $\epsilon$. indeed we would have
$$\Pr(b_1+\epsilon\leq p<b_2)<\Pr(b_1\leq p<b_2)=\Pr(b_2\leq p<b_3).$$
Similarly, $b_4=b_2+\epsilon$ will yield a lower winning probability than that enjoyed by player 1 for any positive $\epsilon$.

I think that, in equilibrium, this won't happen so I guess the result is fine. But it makes the proof seem a bit hand-wavey.


The fisher hypothesis, as well as related aspects of the neutrality of money hypothesis, are typically argued only to operate in the long-run, with changes in money supply having short-run effects which are modeled with monetary disequilibrium theories.

So, a nation sells bonds in exchange for liquid assets denominated in its currency and then holds onto those assets, reducing the liquidity in their economy. As a result, at short-run levels of demand, that currency will be more highly valued than it would have been otherwise (lowered inflation). However, in the long run potential investors are presented with an incentive to lend in the currency, increasing the savings rate and lowering spending until their nominal interest rate (dependent on the amount of currency available and the spending rate) is low enough that the real interest rate is the same as it was before (assuming a constant level of expected future returns in the economy over this period).

This relies on investors only considering the real economy to be of significance in their long-run deliberations "Will future demand in this industry justify my investment and provide me with a good real rate of return down the line? If I think future inflation will be very low or negative it might just be more appropriate to hang onto my money." This is, like any model, a huge simplification, but in terms of a perfectly rational investment community (it's ok, you're allowed to laugh) it seems as though it should hold fairly well.

However, to bring this into the real world somewhat. Short-run levels of inflation and short-run levels of the spending and savings rates do not seem to be especially short run. Ordinary consumers who make up the majority of the economy take a long time to change their behaviour to bring these into an equilibrium, and shocks and government interventions and technology changes are sufficiently frequent that in effect everything stays more dynamic than monetarists would imply. Does this make the hypothesis useless? Not entirely, as an investor with no means of predicting the future accurately you could do worse than trusting it and just trying to keep your margins high in case of unpleasant surprises.

As a concise answer to your question: You're right in the short-run, the fisher hypothesis is supposed to apply to the long-run, but whether it does so accurately is virtually impossible to tease out of chaotic real world data.


Extracting group effects from individual fixed effects

Good question.

You observe $y_{ijt}$ ($i$: firm, $j$: country, $t$: time). Let us not consider time effects as they are irrelevant to our discussion. You are considering identifying "country effects" using two approaches.

In short, the two are as different as RE vs FE in standard 2D panel models, with the main difference being in what you assume about the correlation of the explanatory variables and the firm effects within country groups. (i) Dropping firm-effects and using country dummies gives consistency if firms within the same country have no fixed effects [1]. (ii) Defining country effects by the averages of firm fixed-effects allows for firm-level fixed effects [1] correlated with the regressor levels.

More detailed discussions follow.

Your first approach (of having country dummies and no firm effects) is represented by the model $y_{ijt} = c_j + X_{ijt}\beta + v_{ijt}$, with $E(v_{ijt})=0$ and $X_{ijt}$ being uncorrelated with $v_{ijt}$. If there is no firm-level correlation of $X$ and $v$ within country groups (that is, if $X_{ijt}$ is exogenous to the error $v_{ijt}$), the random-effects regression (POLS or FGLS or whatever) of this model gives consistent estimators. However, if $v_{ijt}$ contains firm-level fixed effects (say, $\mu_{ij}$) that are correlated with the level of $X_{ijt}$, this approach leads to inconsistency.

The model corresponding to your second approach is $y_{it} = c_j + \mu_{ij} + X_{ijt}\beta + e_{ijt}$, where $E(e_{ijt} | X_{ij1}, \ldots, X_{ijT})=0$ for all $t$. What is important here is that $c_j$ and $\mu_{ij}$ are not separately identified without further restrictions even under this strict exogeneity of $X_{ijt}$ (because you can add a constant to $\mu_j$ and subtract the same constant from $\mu_{ij}$). You are proposing to define $c_j$ by the further restriction that $n_j^{-1} \sum_{i=1}^{n_j} \mu_{ij}=0$, which is fine.

What is the real difference between the two approaches? For the model $y_{it} = c_j + \mu_{ij} + X_{ijt}\beta + e_{ijt}$, the difference is that the first assumes that $X_{ijt}$ is exogenous to $\mu_{ij} + e_{ijt}$ while the second assumes that $X_{ijt}$ is exogenous to $e_{ijt}$. Under the assumption that $X_{ijt}$ is strictly exogenous to $e_{ijt}$, the difference is reduced to whether $X_{ijt}$ is correlated with $\mu_{ij}$. If, within a country, a firm with high $X_{ijt}$ level has higher $\mu_{ij}$, then only the second approach gives a consistent estimator. It is all the same as any RE vs FE considerations in standard (2D) panel data models.

[1] "Fixed effects" above mean time-invariant effects that are possibly correlated with the levels of the explanatory variables.


Roughly speaking, $X_1$ and $X_2$ are affiliated because they have the common component $T$. That is, if $X_1$ is large, $X_2$ tends to be large as well, because a large $X_1$ makes a large $T$ likelier than without this information.
The variables are affiliated if for the joint density $f_{X_1,X_2}$
$$f_{X_1,X_2} (x',y)  f_{X_1,X_2} (x,y') \geq f_{X_1,X_2} (x,y) f_{X_1,X_2} (x',y') \quad \forall x'\geq y, y'\geq y,$$
which here holds with equality. That is, they are weakly affiliated. See below.
In Krishna's book $G$ (resp. $g$) is usually the CDF (resp. density) of the highest value among the other bidders, $Y_1$. Here, there is only one other bidder such that $Y_1=X_2$ and $g(y|x) = f_{X_2|X_1=x}(y |x)$.

Now, my answers only help you if you know how to find the joint density.
Here is what we want to find:

 So, how to get there?

$S_1,S_2, T$ are i.i.d. draws from the uniform distribution.
Let us first consider the joint CDF of $X_1, X_2$ conditional on $T=t$. That is easy, because they are independent now! Once we have this conditional CDF, we use that
$$F_{X_1,X_2} (x,y) = \int_0^1 F_{X_1,X_2|T=t}(x,y|t) f_T (t) dt,$$
where $f_T(t)= 1$ if $t\in [0,1]$ and $f_T(t)= 0$ otherwise.
Then, we take derivatives with respect to $x$ and $y$ to find $f_{X_1,X_2}(x,y)$. This should look like what Krishna has in his picture or alternatively, like the function in the appendix of Avery (ReStud 1998), where the example is from (I guess).
These calculations are cumbersome work with a bunch of case distinctions and thus it is easy to mess up, but you start with
$$F_{X_1,X_2|T=t}(x,y|t) = \mbox{Pr}(X_1<x,X_2<y|T=t) = \mbox{Pr}(S_1<x-t,S_2<y-t)$$
and then pay attention to the support of the uniform distribution. The CDF is $F_{S_1}(s)=s$ for $s\in [0,1]$ and zero for smaller $s$ and one for larger $s$.

Let us take an exemplary region, $y>x>1$:
$$F_{X_1,X_2}(x,y) = \int_0^{x-1} 1 dt + \int_{x-1}^{y-1}(x-t)dt+ \int_{y-1}^1 (x-t)(y-t)dt,$$
which gives us something of which Mathematica says it has a derivateive $\partial x \partial y$ equal to $2-y$. Now, we can verify one of the regions of Krishna's graphic.
One more for fun, if $x<y<1$,
$$f_{X_1,X_2}(x,y) = \frac{\partial^2}{\partial x \partial y} \left( \int_0^x (x-t)(y-t) dt + \int^1_x 0 dt \right) = x.$$
And so on. Now, you can go back to my reply 1.

The conditional density of is given by the equation
$$f_{X_1,X_2} (x,y) = f_{X_1|X_2=y} (x|y) f_{X_2} (y),$$
where
$$f_{X_2}(y) = \begin{cases} y &\mbox{if } y \in [0,1] \\
2-y &\mbox{if } y \in [1,2],
\end{cases} $$
which follows from the fact that $X_2 =S_2+T$, and $S_2$ and $T$ are independently uniformly distributed. You get there with convolution. What you get should look like this plot from the Avery paper

Then, you integrate to find $G(y|x)$ and go back to my reply 2.


It is not necessarily true that lagged $y$ are endogenous. That depends entirely on the structure you assume for $u_t$. If $u_t$ is white noise, there is no endogeneity, in the sense that

$$ E(u_t|\mathbf{y}) = 0 $$

where $\mathbf{y}=\{y_{t-1}, \cdots , y_{t-p}\}$.

This is trivial to prove, once you realise that the above equality can also be expressed as

$$E(u_t y_{t-i})=0 \,\,\quad, i=\{1, \cdots, p\} $$

using the Law of Total Expectations.

Conversely, it is trivial to show that if $u_t$ follows an autoregressive process, the above conditions does not hold anymore, in which case there is endogeneity, and OLS estimates are inconsistent.


Remember that utility function only matters ordinally... that is, you only care if $u(A) > u(B)$, and $u(A) = 100$ with $u(B) = 10$ is the same thing as $u(A) = -1000$ and $u(B) = -1000.0001$ (both have $u(A) > u(B)$.)


I have uploaded all the videos on YouTube as two separate playlists which cover asset pricing part 1 & 2 courses.

Asset Pricing part 1:  https://www.youtube.com/playlist?list=PLpccx1MwQZb7t7HJ6lBo4L3DXhknCD0K7&disable_polymer=true

Asset Pricing part 2:  https://www.youtube.com/playlist?list=PLpccx1MwQZb6XsKU3O81GrpqaxyyGoHpH

Regarding the class, I think Coursera moved to the new platform and thats why these courses and some others have disappeared. I heard that they are preparing the courses based on the new platform.


In a penny auction, each bid raises the going price of an object by just one penny. However, placing such a bid is costly whether or not you win. Usually it costs one dollar to place a bid -- sometimes this is obfuscated by making you purchase bids (or bidding credits) before you participate. In any case, if the opening bid of an auction for something is 0.01, and the auction ends with the price at just 10, then one thousand bids have been placed and therefore the site has made 1,000 on top of what the item actually sells for (10). So if the item has a value of 500, then they would represent that as 98% discount even though they actually made a profit of 510, simply because they ignore the bidding costs (their primary source of profit).

Now, if you happen to be the person who makes the winning bid, and you have not bid previously, then obviously you would be getting a very good deal -- in the example above, you would be paying 11 for an item that might be worth 100 or more. However, it is difficult (and out of your control) to be the winning bidder. After every bid, time is allowed for other bidders to outbid you, in which case you lose the money you spent on the bid.

With all of this in mind, participating in penny auctions is essentially gambling. Sites that market these discounts and obfuscate the cost of bidding are highly misleading. I personally believe they should be banned. Note that these penny auction sites should not be confused with standard auction sites like Ebay. In standard auction sites, you pay only if you win -- you do not pay simply to make a bid.


Have there been any true "communist" nations as Marx envisioned?

(I am not certain of whether I use established English terminology here).

The answer is no, because in a communist state (as described by Marx), there are no markets, especially, markets for production factors. And in none of the countries that implemented a socialistic socio-economic system, was labor "directly socialized" -it continued to be considered as owned by each worker individually, and it was priced, bought and sold. And it doesn't matter how this was done, i.e. of whether the wages were determined through some market mechanism or decreed by the state. All it matters is that labor was still private property.


If public roads are public goods, in what way are they non-rivalrous?

The property of rivalry is a continuous (rather than binary) variable.*

A good is rivalrous if my consumption of it reduces the amount that can be consumed by others.

So, a particular Big Mac is fully rivalrous, because each bite I take from it reduces (by that exact same amount I've bitten) the amount left for you.

The degree to which roads are rivalrous is lower: My driving on a deserted road at night does not reduce at all the amount that can be driven on the same road by others.

But your doubt is correct—it is not generally $0$: My driving at peak hour at a city center does reduce the amount that can be driven by others.

Ideas are a good (and possibly sole) example of a good that's perfectly non-rivalrous. (My "consumption" of the Pythagorean Theorem leaves no less for anyone else.) Side point: But with the right laws and accompanying enforcement—e.g. patents, copyright—even ideas can be made excludable.

Defense is often given as a classic example of non-rivalry. But I would argue that although defense exhibits a very high degree of non-rivalry, it is less than perfectly non-rivalrous. (The resources used to defend John in New York from a nuclear attack does reduce the US Department of Defense's ability to defend Jane in Hawaii. The resources used to defend a nation with over 1B people are greater than the resources used to defend a nation with less than 1M people.)

*Likewise, the properties of excludability and being a public good are continuous (rather than binary) variables. (Many introductory textbooks tend not to emphasize this important point sufficiently.)


Real option effect of uncertainty - irreversiblity vs fixed cost

There exists a post on capital adjustment costs, which gives a good overview of the different types of capital adjustment costs.

http://economictheoryblog.com/2015/08/20/capital-adjustment-costs

However, ultimately the post summarizes Cooper, R. W., & Haltiwanger, J. C. (2006). On the nature of capital adjustment costs. The Review of Economic Studies, 73(3), 611-633.

Regarding your question, I guess as long as there are any sunk costs associated to investment you destroy future option, regardless the nature of these costs. Consequently the nature of capital adjustment cost should not really change the way uncertainty affect investment through real option effects.


Why Need a Numeraire Good in Dynamic Analysis

Is there any reason not to make $P_0 = 1$?
In microeconomics (which your problem seems to be about, rather than macro) consumer's demand is homogeneous of degree zero in prices & income. That is if all parameters measured in money change by the same ratio (say they are all multiplied by 10) consumer decisions are unchanged. The root of this is that what usually matters is the price ratio between two goods. But
$$
\frac{p_1}{p_2} = \frac{r \cdot p_1}{r \cdot p_2}
$$
for all $r > 0$, so any proportional price change does not change the price ratio between two goods.
As a result of this, we are usually left with a degree of freedom when solving these models. To do away with it and simplify equations it is best to just arbitrarily select a good and appoint it numeraire.
In macroeconomics you have similar issues if you assume the neutrality of money.


The most famous perpetual bonds are UK Government Bonds known as consols. They weren't issued to avoid the rollover risk you highlight. Rather, their key benefit was liquidity. They could sell new consuls on the same terms as the old consuls and they have enhanced liquidity because it made the new and old issue more liquid.
They turned out to be a pretty horrible investment in real terms for early investors. Inflation ate away most of their value.
Despite their seemingly infinite life, because they pay out coupons and we discount the future geometrically their interest rate sensitivity behavior is similar to existing long dated bonds.
Unless the bond is callable, you generally can't make money by repurchasing your own bond at market prices. If interest rates drop, making you want to replace old bonds, the price of the old bonds goes up until the yield of old and new bonds are equated. Things are a bit different with changes in credit risk but even in that case it can be tricky.
The product you describe also sounds a lot like preferred stock. The Wikipedia article on perpetuities gives consuls and preferred stock as two examples.


What are main reasons a typical DSGE model is called non-linear? Why are these non-linearities important?

They are called non-linear because they often consist of non linear equations (although linearized approximations exist).

No matter what kind of empirical research you are doing it is important to avoid misspecification. If relationships are non-linear it’s not appropriate to try to fit an linear model which identifying assumption requires linearity. If you would do so your parameter estimates would be biased.

There is nothing inherently unstable about non linear processes. In the context of DSGE models dynamic stability implies there should be no unit root in the modeled series. There is no reason why non-linear series would be more prone to have unit root than linear one.


If you draw the corresponding game tree, you will see that "equivalent to simultaneous move game" implies that the game has no proper subgame and the only subgame is the whole game.
This is because the information set of the second player covers every move of the first player.
Therefore, every Nash equilibrium is trivially also subgame perfect.


Is there any way to sufficiently cover the cost of a UBI?

Since you say that you want to ignore social benefits etc. then answer is trivial. As long as the cost of UBI is not so high that taxes would cross the peak of Laffer curve then answer is always yes, after the peak always no (peak of Laffer curve is a point of maximum possible revenue government can extract from economy through taxation).

On left side of Laffer curve just raise taxes high enough and you can pay for it. On right side the program would be too expensive to pay for it as simply it’s cost would outstrip the maximum resources government can extract from economy. So the candidate can decide to raise VAT taxes higher or to increase federal income tax etc as long as the candidate does not cross that point.

You can also cover any slack by government borrowing - there a maximum sustainable point would be where the growth rate of debt just matches the growth rate of economy. If you consistently borrow more than that you put economy on a path where in the limit debt to GDP goes to infinity- which is not good. If you consistently borrow equal to growth rate or less than that then you are on either stable path or path where Debt to GDP goes to 0 in limit.

I am also not aware of a study that would say that UBI reduces healthcare costs, however my feeling is that the point that candidate was trying to make is that thanks to UBI gov. can reduce some healthcare welfare spending as every person already gets subsidy that can be spend on medical care.

Also there can be no profit. UBI is a transfer of resources from one point in the economy to other. It does not create any profit. You could argue that compared to some other transfer it can create less distortions and less deadweight loss, but I would not call that profit. A profit is a difference between total revenues and total costs of some activity UBI has no revenue side only cost side as it’s a welfare-transfer measure.

However, as always question is if the value of UBI to society outweighs the costs they have to bear for it, but that is ultimately just a value judgement. So thats a problem for moral philosophers to worry about and answer not for economists.


Economic Impact of A Student Loan Bubble Popping?

If, as you say, 15% of student loan borrowers were to default and the government were to forgive their loans, that would simply be a transfer of wealth from the government to those borrowers (on the order of about 15% of \$1.3 trillion, or about \$200 billion). What happened from there would depend first on whether the government funded that transfer by cutting other spending or by issuing debt. Inflation is a basically unrelated issue— the monetary authority (the Federal Reserve) is independent of the fiscal authority (Congress and the Treasury), and as they say, the monetary authority acts last.

Student loan payments are generally not due until some time after a student leaves school, so as a practical matter, forgiveness on defaulted loans would not generally affect whether students remained in school versus being in the workforce, unless you assumed that students started borrowing more with the intent of defaulting (a "moral hazard" scenario). I'll ignore this possibility just to keep things simple and to keep the focus on the fiscal and monetary impact.

In all scenarios, borrowers who received loan forgiveness would be better off, as their wealth would increase by the amount of the forgiven debt. They would, as noted, likely already be working or seeking work. Because they had already stopped paying their debt, we would not assume that they would experience improved cash flows. Work on structuring modifications to defaulted mortgages suggests that households are more sensitive to changes in cash flows than changes in net wealth, so we would only expect these individuals to increase their consumption modestly, but we would in fact expect this side of the ledger to result in increased consumption and economic growth.

However, if the government financed this debt forgiveness by reducing its consumption, it would probably be a net negative to GDP in the short run, as it would remove \$200 billion in government spending, which would not be made up by the slight increase in consumption by borrowers. Government consumption expenditures are currently equal to about \$3.2 trillion annually, which equaled about 18% of GDP in the most recent quarter, so... the direct impact would be a reduction of about 1% of GDP. You can make assumptions about consumption multipliers for government consumption and come up with different results, but this is the direct impact in that scenario.

If the government financed the debt forgiveness by issuing its own debt, it would increase the stock of outstanding US government debt by \$200 billion, or about %1. This would have little impact on debt markets, so there would be no concern about "crowding out" private borrowing, and because it was debt-financed, there would be no reduction of government consumption. As a result, the only real effect on GDP would be the small net positive contribution from increased private consumption.

With respect to inflation, even if the monetary authority bought all the additional debt issuance, it'd only increase the amount of money in the financial system by a negligible amount. For comparison, the Federal Reserve's aggregate increase in holdings of Treasury securities in response to the financial crisis and through its quantitative easing program was close to about \$2 trillion, or ten times the size of this hypothetical debt issuance. Inflation during that period has generally remained below the Fed's 2% target. So currently, the effect on inflation would likely be negligible.


Are there any Sovereign Debt Guarantees, apart from those issued by the US?

Has any other state done anything like this before? Who, when, where?

Yes, one (relatively) recent example from 2010 is EU member states guaranteeing portion of Greek debt see the Guardian article about it (although technically the countries are all in loose (con)federation).
Another example could be UK guaranteeing Irish land bonds in between 1920–1938 (see Foley-Fisher & McLaughlin 2016).
It is also commonly done by supranational organizations such as World Bank (of course World Bank is not a state but it gets its funds from donor states so you can view it as donor states running the program through the World Bank).

Is this an efficient form of foreign aid?

Well this is extremely broad question because efficiency could be examined from multiple angles, and as always an important question in public economics is compared to what?
The abovementioned research by Foley-Fisher & McLaughlin (2016) shows that such guarantees can reduce but not eliminate the risk premium. So they have a positive effect on reducing country's servicing costs. However, I am not aware of literature that would compare and contrast efficacy of this foreign aid program relative to some other programs that might perhaps use the same resources more efficiently. This being said debt guarantee is likely to be much less costly for donor country, so it would not be unreasonable to conjecture that it could be part of efficient foreign aid policy mix.


Market Value Changing in Response to News

There are likely two major (and closely related) reasons for this:

First- stock prices aren't purely reflective of what a company is worth today, instead, stock prices reflect the expected future prices as well. Events like this, which increase uncertainty and instability, might change expectations about future stock prices. This is then incorporated into current stock prices, which leads to a fall.

Second- a lot of automated trading algorithms incorporate news keywords into their pricing structures (for example), which can lead to reactions based on the headlines themselves. These can then create a feedback loop with other funds, like ETFs, which trade based on volatility indexes.

I'm sure there are other reasons as well, (perhaps the breakdown in the summit led some traders to reevaluate the relative bargaining power of the US and China in their upcoming summit, which in their mind might lead to an increased likelihood of a trade war, as a hypothetical), though those two can explain many large fluctuations!


Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?

Yes.
I have to include at least 30 characters in an answer, so let me repeat: Yes.


Consumer optimum in an economy with a continuum of commodities

As the OP noted in a comment, Theorem 1 in section 12 of Kolomogorov and Fomin's Calculus of Variations seems to provide some comfort that we can indeed use the Langrange Multiplier method when the number of our variables is infinite. Still, the authors do that in a footnote, writing "the reader will easily recognize the analogy with Langrange multipliers". So no, this does not rigorously show what we want.

I think that what we need is a paper like Craven, B. D. (1970). A generalization of Lagrange multipliers. Bulletin of the Australian Mathematical Society, 3(03), 353-362. which in its summary writes:

  The method of Lagrange multipliers for solving a constrained
  stationary-value problem is generalized to allow the functions to take
  values in arbitrary Banach spaces (over the real field). The set of
  Lagrange multipliers in a finite-dimensional problem is shown to be
  replaced by a continuous linear mapping between the relevant Banach
  spaces.

This is math-speak but it says what we wanted to hear (one can also find a short exposition in wikipedia to the degree that it trusts the content).

Then, we can form the Lagrangean of the problem

$$\Lambda = \int_0^1 c_i^\theta\,\text{d}i +\lambda\left(M - \int_0^1 p_i c_i\,\text{d}i\right)$$

and calculate the first-order condition(s) by , informally speaking, "looking at the integral and seeing a sum",

$$\frac{\partial \Lambda}{\partial c_i} = 0 \Rightarrow  \theta c_i^{\theta-1} = \lambda p_i, \;\; i \in [0,1] \tag{1}$$

...a continuum of conditions. For later use we  define

$$\sigma \equiv 1/(1-\theta), \Rightarrow 1-\theta = 1/\sigma, \;\; \theta = \frac {\sigma-1}{\sigma}$$

The constant $\sigma$ can be shown to be the elasticity of substitution between any two goods.

Writing $(1)$ for commodity $j$ and equating through the common lagrange multiplier we arrive at

$$c_i = \left(\frac {p_i}{p_j}\right)^{-\sigma}c_j
 \tag{2}$$

Multiply both sides by $p_i$ and take the integral over the commmodity space with respect to $i$:

$$\int_0^1 p_i c_i\,\text{d}i = \int_0^1 p_i^{1-\sigma}p_j^{-\sigma}c_j\,\text{d}i$$

$$\Rightarrow M = p_j^{\sigma}c_j\int_0^1 p_i^{1-\sigma}\,\text{d}i$$

$$\Rightarrow c_j = p_j^{-\sigma} \cdot M \cdot \left(\int_0^1 p_i^{1-\sigma}\,\text{d}i\right)^{-1} \tag{3}$$

which is Marshallian demand for commodity $j$.


Preference over lotteries without independence axiom

No, not necessarily. Without the independence axiom (or something else to replace it) there is not much you can infer about preferences over (non-degenerate) lotteries from knowing preferences over outcomes only.

For instance, let $p^L_n$ be the probability of outcomes $n \in \{1, 2, 3\}$. Then preferences  over lotteries $\succeq^*$ represented by the utility function

$$U(L) = p^L_1 + \beta [p^L_2p^L_3],$$

are continuous  and rational, but do not satisfy the independence axiom. For $\beta$ large enough, it is not even the case that $(1,0,0)$ is the best lottery, although $(1,0,0) \succ^* (0,1,0)$ and $(1,0,0) \succ^* (0,0,1)$.

To see why, observe that

$$ U(1,0,0) = 1, $$
$$ U(0,1,0) = 0, $$
$$ U(0,0,1) = 0, $$

However, for $\beta > 4$,

$$ U\left(0,\frac{1}{2},\frac{1}{2}\right) > 1 .$$

Violation of the independence axiom can be seen from the fact that, when $\beta > 4$,

$$ [1,0,0] \succ [0,1,0]  ,$$

although

$$ \left[0,\frac{1}{2},\frac{1}{2}\right] \succ \left[ \frac{1}{2}, 0, \frac{1}{2}\right]. $$


Profit Function: Just revenue maximization subject to constraint? if so where is $\lambda$?

The problem
$$\max py(x) $$
$$s.t. wx \leq \bar{C} $$
could be interpreted as revenue maximization subject to an operational budget contraint. However the solution of this can differ from the solution of the profit maximization problem, as costs do not appear in the goal function. $\lambda$ here would show by how much an additional dollar spent on operational costs would increase profits. If $y$ is strictly increasing in $x$ the entire budget would be spent even when $\lambda < 1$. However with such a low $\lambda$ a dollar spent earns less than a dollar, so it should not be spent if the goal is to maximize profits.

In fact, if the goal is profit maximization then and there are diminishing returns then dollars should be spent exactly if they earn at least one dollar.

If $y(x)$ is strictly increasing and strictly concave in $x$ and you set $\bar{C}$ at such a level that the Lagrangian's solution yields $\lambda = 1$, then the solution of the above problem would also solve the profit maximization problem.

The Lagrangian is

$$L=py(x) - \lambda(wx - \bar{C})$$

The equation system solving the Lagrangian is

$$
\begin{align*}
pMP(x) -\lambda w & = 0 \\
wx - \bar{C} & = 0
\end{align*}
$$

Getting $x = \bar{C}/w$ from the second equation one and plugging it into the second equation one has

$$
\frac{p}{w}MP\left( \bar{C}/w \right) = \lambda.
$$

So $\bar{C}$ determines $\lambda$. If $\bar{C}$ is set at such a level that $\lambda = 1$ then the first order condition

$$
pMP(x) -\lambda w = 0
$$

becomes

$$pMP(x) - w = 0$$

which is also what you would get by solving the unconstrained profit maximization problem.


how to test endogeneity in a cross section data?

Endogeneity can rarely, if ever, be tested.  It can certainly exist in cross-sectional data.

Running a presumably OLS regression without a theoretical model will just give you a measure of the co-movement of the two variables. Since no other variables are included, what you are estimating is $E(C \mid S)$, i.e. the conditional expected value of Consumption if no other information is used except for the environmental index. Including the square attempts to capture the case of a non-linear conditional expectation.

This is more of a "prediction" framework (although not forecasting), rather than an analytical / causal framework.

Informally, you can argue for the existence of endogeneity if either there exists other variables that are correlated both with consumption and the environmental index and/or if their relation is an equilibirum one of co-determination.

Accepting that endogeneity exists, does not invalidate your regression specification. It just says that the coefficients you are estimating may not be what you would want to estimate:
Here for example

$$\beta_1 + 2\beta_2 = \frac {\partial  E(C \mid S)}{\partial S}$$

But maybe you are interested in how "consumption changes" when the environmental index changes when other influences on consumption are taken structurally into account. This essentially implies that you would want a more rich right-hand side in your specification.

Note: "Take structurally into account" is not the same as saying "all else held constant". If you estimated a regression with more explanatory variables, the betas themselves would change, so the marginal effect of the index in that alternative scenario would be different even if we examined under the "all else held constant" assumption.


Is undervaluing environmental impact a subsidy?

Yes, undervaluing environmental impact is a subsidy, within the context of the IMF report that you are referring to.

Here's what that report says in its abstract (my emphasis):

  it focuses on the broad notion of post-tax energy subsidies, which arise when
  consumer prices are below supply costs plus a tax to reflect environmental damage and an additional tax applied to all consumption goods to raise government revenues.

It goes on further on pages 10-11 to define some aspects of the subsidy in more detail.

In particular:

  post-tax consumer subsidies represent the amount by which the cost borne by the consumer falls short of the total economic cost of consumption. This excess cost (or subsidy) is either covered by governments in the form of budgetary support or foregone revenues or passed to the society in the form of environmental damage.

and

  Producer subsidies exist when producers receive either direct or indirect support that increases profitability above what it otherwise would be (that is, the support is not passed forward in the form of lower consumer prices). This support can take many forms, including receiving a price for the output above the supply cost, paying a price for inputs below supply costs, receiving preferential tax treatment, or receiving a direct transfer from the budget

This makes it clear that within the context of that report, undervaluing environmental impact is a subsidy. And that is entirely consistent with how "subsidy" is used within the field of environmental economics generally.

See, for example: The Economic Cost of Global Fuel Subsidies, Davis (2014):

  Fuel  subsidies  are  different  from  subsidies in  most  other  markets  because  of  the  substantial  external  costs  of  driving.

And Energy subsidies: How large are they and how can they be reformed?, Clements et al 2014:

  The subsidy estimates capture both those that are explicitly recorded in the budget and those that are implicit and off budget ... Tax subsidies
  arise when energy taxation, which includes a corrective component for externalities and a component for revenue consideration, is below the efficient level. The efficient taxation of energy requires corrective taxes to capture negative environmental and other externalities owing to energy use.

And Fossil fuel subsidies in the Pacific island context: Analysis of the case of Kiribati, Peltovuori (2017)

  Subsidy in this report is defined according to the definition of World Trade Organisation's (WTO) Agreement on Countervailing Measures (ASCM) (Uruguay Round Agreements, 1994). This definition has been recommended to G-20 by the Global Subsidies Initiative (The Global Subsidies Initiative, 2010). The methodology for quantifying fuel subsidies in this study is the price gap approach. In the price gap approach, a cost recovery price for fuels is first estimated based on the world free on board (FOB) market prices. All additional monetary and non-monetary costs such as transport, storage, distribution costs, and corrective taxes to account for externalities are then added on top of the FOB price. This cost recovery price is then compared to the actual price. The gap between the two prices is the amount of subsidy per price unit.

These pollution costs are included within the broader definition of subsidy as used by the IMF, because these negative production externalities are costs incurred by production, that the producer itself does not directly bear. Thus, those costs are not reflected in prices, leading to market failure and an unfair competitive advantage, of the same kind and market impact as if they'd received a cash subsidy on their directly-incurred costs.

The "Economics Help" site explains the issue

The deadweight loss from coal pollution is the red striped triangle: this comes about because coal producers do not have to pay for their pollution, leading to a competitive advantage, and an artificially high quantity sold Q1 at price P1.


What is a good way to generate realistic utility curves?

It's somewhat simple, actually. You can just use a Cobb-Douglas with $m+1$ goods available, the last one being leisure. So, you should have something like:

$$U(x_1,x_2,...,x_m,x_{m+1}) = \prod_{i=1}^{m+1} x_i^{\alpha_i}$$

Subject to $\sum_{i=1}^{m+1} \alpha_i = k$, where $k$ is the degree of homogeneity of the utility function. Usually, $k=1$ is considered reasonable.


Financing U.S. government budget deficits, and their impact on interest rates

The treasury can issue more bonds and the central bank buys it up, prints more currency and gives it to the government. This is called monetizing the deficit.
Although this practice may be challenged by the central bank itself depending upon the situation.
The treasury can sell new bonds to commercial banks and other financial institutions. Commercial banks use these to be kept as statutory reserve requirements with the central bank and also as safe assets because these are, of course, most highly rated securities. The demand could be more or less but there is always a demand for safe assets. Think of a countries like China and Japan which invest heavily in U.S treasury bonds and other assets. Theoretically speaking, government can finance any amount of deficits via the central bank route.

Crowding out will happen when the government is borrowing huge loans from the commercial banks and dries up the sources of funds for the private investors. It also depends on the purpose and timing of the spending. Whether the government is spending on non-productive programs or productive programs which are in turn helping the overall health and investment environment of the nation and whether it is spending counter-cyclically or cyclically. Also, if there is an upward pressure on the interest rates due to possible crowding out, we can expect central bank to make necessary adjustments.
Moreover, the mechanism is not so simple. It is complex as hell. The flow of savings in the economy is not fixed and hence the pressure may or may not build up. It largely depends on the investor sentiments and expectations also.


The endowment effect is the hypothesis that people ascribe more value to things merely because they own them.


How is hyperinflation categorized, and how is it fixed?

So hyperinflation should be demand-pull right?

The Weimar Republic in the 1920s is the classic example of hyperinflation. An oversimplified summary is that the Weimar Republic had to pay reparations that was way beyond what its economy could support: to put it differently, forced exports led to a heavily increased AD. And so this is a case of primarily demand-pull. In general, many hyperinflations start because of expenditure increases due to war, reparations, or poor government spending. I couldn't find a clear cut primarily cost-push hyperinflation trigger but it is theoretically possible to construct such an situation: stop all production of goods and services by raising the minimum wage to infinity and taxing inputs to infinity. Of course, probably a black market will just result. Once hyperinflation sets in, supply can often collapse as people stop investing in productive assets, so both demand-pull and cost-push apply.

  strong credible fiscal policy can hyperinflation be fixed, but I don’t understand what it means. Does it mean that monetary policy is useless when it comes to hyperinflation? And does it mean that the solution to hyperinflation is “contractionary fiscal policy” or “expansionary fiscal policy?”

You could trivially create hyperinflation by just unnecessarily printing increasing quantities of money. In this case, trivially adjusting your monetary policy to simply stop printing money is the solution. But it is important to remember that states almost never just print money for the sake of printing money: it is often a last choice that are forced to do to make some kind of payment (reparations, war, etc). And so the ideal solution is to stop the cause behind those payments, which is usually impossible. This would indeed be technically under the definition of contractionary fiscal policy. But to use the phrasing "contractionary fiscal policy is the solution" probably doesn't convey the severity of the situation: for example, case by case descriptions such as diplomacy (begging reparations to be reduced as in the case of the Weimar Republic) or ending the Second Congo War and self-dealing (in the case of Zimbabwe) will probably be more appropriate.


No, the primary purpose of options is not to provide insurance against changes in the price of the underlying instrument: options don't have a primary purpose, they don't have an agenda, and they don't have a plan. They're just another tradeable instrument.

Some people buy them as means of insuring a position. Some people write them as a means of insuring a position.

And as Aurigae notes, in a crisis all correlations tend to one; so even if, in theory, your options insure the rest of your position, in reality, in a crisis, the counterparty risk can become very high, so the insurance is least available when it's most needed.


Would a Federal Job Guarantee hurt the economy?

Conventional economics research is not very kind to the idea of job guarantee (see discussion in highly cited works of  Palley, 2001;  Sawyer, 2003 and Seccarecia 2004). In general most of the profession agrees that job guarantee program (i.e. program where government is some sort of employer of last resort/provides employment) is generally not efficient from either macroeconomic or microeconomic perspective, with emphasis on the macroeconomic perspective.
The problem is not that it would destroy jobs on a net basis. The whole aim of such program is to create government jobs for anyone that is unemployed so on net basis it would increase the number of jobs. The problem is that especially if the wage for these jobs is set at above minimum wage, or more specifically market wage at each individual sub-market it would crowd out productive jobs from the economy and instead create less productive government jobs (see the papers cited above).
Next unless this is founded by debt or high powered money it will not increase consumer spending on net basis. This is just elementary macroeconomics, if government runs balanced budget government spending multiplier will be exactly equal to 1 meaning it will not create any additional stimulus for the economy and even that assumes government funds itself with non-distortionary lump sum taxes so in reality it would likely depress demand (see Blanchard et al. Macroeconomics: a European Perspective).
Now, in principle there is nothing wrong with government running deficit or financing projects with high powered money but both are not suitable for some large permanent program. When it comes to financing projects with high powered money there is virtually unanimous agreement in the profession that only limited amount of real spending can be financed in such way (see this poll among top US economists). There is also issue that amount of real spending that government can finance with high powered money depends on macroeconomic situation (e.g. more of it can be financed when interest rates are zero and less otherwise). When it comes to deficit it is generally considered desirable to run budget deficits in recessions, but in the end government needs to respect its intertemporal budget constraint so in expansion it also should run surplus (technically thanks to economic growth there is some leeway as if we assume there are no 'end times' when debt has to be repaid, government could run deficit equal to rate of growth and keep its debt-to-GDP ratio stable - but with GDP growth rates most developed nations have this would only give extra leeway of about $1-2\%$ hardly enough to fund some ambitious program).
Lastly, issue with job guarantee program is that anything it promises to do can be done better in some other way. If you want to raise welfare of the poor then there is a plethora of relatively more efficient redistribution policies. If your aim is solely boosting employment then there are many other policy instruments such as earned income tax credit, which in combination with minimum wage can boost employment while creating also some floor below which peoples' earnings can't fall. If your goal is to stimulate economy then simple fiscal stimulus to households would be more efficient etc (you can see overview of this in the above cited literature). Hence, most conventional economists would reject job guarantee on the grounds that there are more efficient alternatives.


Relation between foreign currency reserve and exchange rate and others

Quick and easy way is to think of a foreign currency (let's call this USD) as another good with its own demand and supply.

Imports and exports

When a country imports a lot (assuming it imports from the US or the invoice is in USD), the importers will need to pay for these goods in USD. To do this, they go to a bank (roughly speaking) and buy USD, pay for USD with the local currency. This drives up the demand of USD, and hence the price of USD goes up... the local currency depreciates against the USD.

When a country exports a lot, the reverse happens. Importers in other countries will need to pay local currency, so they sell the USD they have in order to get the local currency. The supply of the USD goes up (or you can think of it as demand of USD goes down)... price of USD goes down, and the local currency appreciates against the USD.

FX reserve

Now to go back to your original question... FX reserve is just a place for a country to hold foreign currencies (since USD can't be used locally). It's like a warehouse for USD, controlled by the central bank.

When a country can export a lot there will be a lot of people who wants to sell USD. The rapid appreciation of the local currency could affect firms (profits, etc.) so the central bank might "intervene" to stabilize the rate in the short run. They do this by buying up USD... in a sense create additional demand for USD so the price of USD doesn't fall down too fast. They then put this USD they bought in the reserve.

This is why the change in FX reserve could be used as a proxy to see how much central bank has intervened in the FX market.

In buying USD, they could print new local currency and buy USD outright, resulting in higher supply of local currency and higher inflation, or they could "sterilize" the action by selling bonds just as they would do when they want to reduce money supply by the same amount that they used to buy USD.

On the other hand, if the local currency is depreciating too fast (price of USD going up), the central bank could help by selling USD in the reserve to increase USD supply.

The problem, though, is that the reserve could run out. This is what happened in the Asian Financial Crisis in 1997.

Hope this helps!


Investment is the value of machinery, plants, and buildings (capital) that are bought by firms for production purposes.

Investment contributes to many macroeconomic situations to include:

A.  Contributes to current demand of capital goods, increasing domestic spending

B.  Modernizes production processes and improving cost effectiveness

C.  Allows for the production of new and improved products, increasing value added in production

D.  Increases production capacity

The Investment types (machinery, plants, buildings) are directly linked to current and future sales (sales of final goods) of the firm.

An intermediate good is defined as the goods and services (including energy, raw materials, semi-finished goods, and services that are purchased from all sources) that are used in the production process to produce other goods or services rather than for final consumption.