Proof of nestedness of subgame perfect equilibria Below is a lemma which I believe to be true and which I would like to use to derive other results

  Take any two games in extensive form (complete information) $\Gamma$ and $\Gamma'$ differing only through their collections of information sets $\mathcal{H}$ and $\mathcal{H'}$. Suppose that for each decision node $x$ in the set of decisions nodes $\mathcal{X} = \mathcal{X}'$, $H(x)$ is a finer partition of the set of actions $c(x) = c'(x)$ than $H'(x)$.

  Then for ever subgame perfect equilibrium outcome of $\Gamma$, there exists a subgame perfect equilibrium of $\Gamma'$ with the same outcome (but the converse does not need to be true).

I could try to write a complete proof but this seems to be basic enough a statement and I don't want to re-invent the wheel (or fail to pay tribute to former proofs). So my question is:

Do you know of any reference where that result is proven (or maybe disproven in case I got something wrong)?

Edit : I am only interested in pure strategies equilibria.

Would this (and why or why not) provide an answer to your question?


Homogeneous of Degree Two Utility Functions and Homothetic Preferences. The understanding that I am not clear is in when do homothetic preferences represent a utility function and vice-versa. My solution to the problem is posted below the problem:
A consumer’s preferences are described by a utility function that is homogeneous
of degree two: For all $\alpha > 0$ and $x \in R^{L}_{+} $ ,
$u(\alpha x) = \alpha^2 u(x)$
The problem that I am not getting clear is:
Q) "Are this consumer’s preferences homothetic? Show that they are or give a counterexample."
My solution:
According to Mas Colell et al. "Microeconomic Theory" (chapter 3, page 50)

Therefore, this given consumer's preferences are not homothetic as it doesn't generate a utility function that is homogeneous of degree 1 (HOD(1)). A counter example would be a utility function that is HOD(1) like the Cobb Douglas Utility Function
$ U(x_1, x_2) = x_{1}^{\alpha} x_{2}^{1-\alpha} $
To conclude, this consumer's preferences are not homothetic as it represents a utility function of HOD(2). While , according to Mas Colell et al. preference $\pmb{\succsim}$  is homothetic $\textbf{if and only if}$ it admits a utility function that is HOD(1).
Could you please help me in understanding where I am going wrong with what Mas-Colell mentioned above "necessary and sufficient condition" and how a utility function that is HOD(2) implies that $\pmb{\succsim}$ is homothetic.
Thanks.

First of all, in order to provide a counterexample, you need to construct a utility function that is homogeneous of degree two, but is not homothetic. Therefore, the counterexample you gave in your solution doesn't work.

To prove the statement directly, let $u(x)$ be a utility representation that is homogeneous of degree two. That is, $u(\alpha x)=\alpha^2 u(x)$. Therefore, if $x\sim y$, which means $u(x)=u(y)$, we have
$$u(\alpha x)= \alpha^2 u(x)=\alpha^2 u(y)=u(\alpha y).$$
This means $\alpha x\sim \alpha y$, and hence the preferences are homothetic.

We can also use the proposition in MWG: A continuous $\succeq$ is homothetic if and only if it admits a utility function $u(x)$ that is homogeneous of degree one. One caveat is that the utility representation is unique up to monotone transformations, so even if one representation $u(x)$ is not homogeneous of degree one, the preferences could still be homothetic if a monotone transformation of the representation, $\phi(u(x))$, is.

In this question, if we consider a monotone transformation $\hat{u} (x)=(u(x))^\frac{1}{2}$, this $\hat{u}(x)$ still represents the preferences $\succeq$. Notice that
$$\hat{u} (\alpha x)=(u(\alpha x))^\frac{1}{2}=(\alpha^2 u(x))^\frac{1}{2}=\alpha (u(x))^\frac{1}{2}=\alpha\hat{u} (x),$$
meaning that this new representation is homogeneous of degree one. Therefore, by the proposition above, the preferences are homothetic.


Ricardian vs Non-Ricardian policy identification I am reading Sala (2004) and I think I have found a mistake in the paper. On page 7 the author argues that one can differentiate between Ricardian and Non-Ricardian policy regimes by considering correlations between primary surpluses and their effect on real debt. See this picture.

Where $s_t$ is current primary surplus, $\alpha_t$ is the discount factor and $b_t$ is the real debt.

He says:

  if the response of $b_t$
  to $s_t$ is negative, the regime is Ricardian; if the response of $b_t$ to $s_t$ is nonnegative,
  the regime is Non Ricardian

While I agree with this, I don't agree with what he wrote in the picture I linked to. I.e that case 1 represents the Ricardian regime and case 2 the non-RIcardian regime.

In case 1 there is no correlation between current primary surplus ($s_t$) and future surpluses ($s_{t+k})$, thus the real value of debt is constant. How is this consistent with the quote above? To me, case 3, i.e the one where $\text{corr}(s_{t},s_{t+k}) < 0$ should be the Ricardian regime because high surpluses today imply low surpluses tomorrow.

Have I misunderstood the author or did he mean to write 'Case 2 and 3 allow for regime identification'?

I think you're misreading what Sala wrote. The first sentence in the image you linked is just saying that in the worlds where either Case 1 or Case 2 occurs, the response of $b_t$ to a shock in $s_t$ allows us to differentiate between Ricardian and non-Ricardian regimes since there are no identification issues. In other words, if either the Case 1 inequalities or the Case 2 inequalities hold, then we can be confident that we have identified a non-Ricardian regime from a Ricardian regime.

According to Sala, it seems that we cannot as easily identify Ricardian regimes from non-Ricardian regimes in Case 3 due to identification issues related to co-movements in real debt.


Difference between social choice function and mechanism outcome function Mas-Colell, Whinston and Green's Microeconomic Theory (3rd edition) defines the social choice function as the following:

Later, the mechanism outcome function is also defined:

The relationship between a social choice function and a mechanism is then stated as:

What is the difference between a social choice function and a mechanism outcome function?

A social choice function presumes the individuals' preference parameters $\theta_i$'s are observable, whereas in a mechanism, such knowledge is not presupposed. Therefore, in a mechanism, the arguments of the outcome function are strategies of the players, which are observable, not their preference parameters, which, although indirectly determine the players' strategies, are not observable.

As an example, suppose $3$ individuals are either rich or pool ($\Theta_i=\{R,P\}$ for $i=1,2,3$) and there are two policies, $X=\{A,B\}$. Assume rich people prefer $A$ and the poor prefer $B$. A social choice function would take a profile of the three people's wealth status and produce a policy outcome, for instance,
\begin{equation}
f(R,R,P)=A,\quad\text{or}\quad f(P,P,R)=B.
\end{equation}
However, if individual wealth status is private information which cannot be directly observed, and the policy must be chosen by a simple majority voting mechanism, then each individual's strategy space would be $S_i=\{A,B\}$ and their strategy $s_i:\Theta_i\to X$ would map from their own type to a policy choice. The mechanism outcome function would turn a profile of the strategies into a policy outcome, e.g.
\begin{equation}
g(A,B,A)=A,\quad\text{or}\quad g(A,B,B)=B.
\end{equation}

There is a special mechanism: when each player's strategy space is also their type space, i.e. $S_i=\Theta_i$, and the mechanism's outcome function is the same as the social choice function $g(\theta)=f(\theta)$, we have what's known as a direct mechanism.


The impact of a devaluation of the national currency under a fixed exchange rate system I would really be thankful if any of you could check my answer to the following question.
Question:
Describe, using the IS-LM-BP model, the impact of a devaluation of the national currency under a fixed exchange rate system?
My answer:
Under a fixed exchange rate system, a devaluation of the national currency by the monetary authority will increase the economy's exports (X) and decrease its imports (M), expanding its net exports (NX) and raising aggregate income (Y) thus shifting, both, the IS and BP curves to the right (IS0 to IS1, BP0 to BP1). At point A, the state of both balance of payments accounts improves due to devaluation of national currency and growth of interest rate. As a result, demand for the national currency increases. In order to maintain a fixed exchange rate, the Central Bank buys up foreign currency, thus increasing money supply and shifting the LM curve to the right (LM0 to LM1). As a result, the interest rate will decrease which will lead to equilibration of the balance of payments and restitution of the external balance at the point B.

This looks good assuming that your country is a small country (i.e., the change in the domestic demand of foreign assets does not change the interest rate in the foreign country). To be clear on the full story, at point A, we have that the foreigners want domestic assets, and so that's why foreigners demand more domestic currency, and that's why (as you said) the Central Bank has to counteract by buying up foreign currency.


What's the (economical) advantage for a company by paying an employee severance payment short before retirement Given following situation
A Company has an employee (Bob) who will retire in 3 years. The company decides to save costs and therefore does downsizing. They offer Bob an severance payment in the amount of 3 annual salaries, if he leaves the company.
  Question
Assuming that Bob is a valuable employee who does a good job - how does it make sense (for a company) to let him go and give him the same amount of money as when he still worked for the company?

If relevant: we assume Bob lives in Germany.

If Bob is actually a valuable employee this probably doesn't make sense.
However it is possible that the things Bob is good at just don't have a market any more. So his work could be good but it is not valuable (any more). Training his to do new things is not considered worthwhile with his upcoming retirement.
If he continues to work he probably also needs an office or similar amenities that are not needed if he is let go.
So one could construct examples where it is worthwhile to pay him his full salary until retirement as severance pay but it wouldn't be a typical situation.


Incentive differences payroll and income tax Do payroll and income tax create different incentives? Is there any difference at all economically speaking?
I suppose different tax deductions and tax rates may or may not apply. If so, what deductions, rates. Are there any books/research on the topic?

Just to add a basic point not mentioned in other answers.  Payroll taxes relate specifically to circumstances involving employers and employees.  Income taxes apply to income from employment, but also to income from other sources which (depending on a country's tax rules) may include self-employment, pensions, savings and investments, property rents, etc.

This makes a significant difference to the incentive effects of the two types of tax. In particular, a payroll tax can create an incentive for workers to become self-employed and/or for their 'employers' to encourage them to do so. As a consequence it makes it important for the authorities to define clearly the criteria under which a worker is deemed to be an employee or self-employed (in the UK for example the criteria are as outlined here).


Negative probabilities - Can we have negative payments in bonds? In Half of a Coin: Negative Probabilities, the author mentions bond duration.

Suppose we have payments at times $t = 1,2,...,n$ denoted respectively by $R_1, R_2, ..., R_n$ and the discount factor is $v = \frac{1}{1+i}$ where $i$ is effective interest rate. Then the bond value today is given by

$$B = \sum_{t=1}^{n} R_tv^t$$

The bond duration is

$$D = \frac{\sum_{t=1}^{n} tR_tv^t}{\sum_{t=1}^{n} R_tv^t}$$

It can be seen that $$D = E[T]$$

where

$T$ is a random variable with range $t = 1,2,...,n$ each having probability $\frac{R_t v^t}{B}$

The author says something like we can have negative probabilities if we have negative $R_t$'s. So this is a kind of bond where instead of making a payment we get a certain amount of money? Is there such a thing? Or is that only in theory?

I heard in a lecture at my university, that measure theory is applied in finance. This field also operates with negative probabilities a lot.

Anyways, I don't see the practical intuition behind using negative probabilities in a bond-pricing model. You can check this article by Burgin and Meissner: Negative Probabilities in Financial Modeling (Wilmott Magazine March 2012).

I think you should migrate your question to Quant SE.


How does Black Friday work? On days like Black Friday, everyone rushes out expecting huge savings on everything they buy. The level of demand seems to reach ludicrous levels, and one would expect smart merchants to react by increasing all of their prices in response to demand.

Yet year after year we see videos of people beating each other up and trampling each other on Black Friday in a display of seemingly mindless consumerism.

Is Black Friday really just a marketing ploy that creates the illusion of savings where really none exist? Has the market just not caught up with consumer behavior? Or is there another mechanism driving Black Friday?

Gary Becker's work on Social Demand probably has something to do with the phenonmena.
Becker basically asked why some popular places consistently seemed to underprice their goods. For example, concerts often sell out very quickly and fancy restaurants in the middle of a busy suburb might be often crowded. These venues could raise their prices, but the basic idea is that the demand for a good may not be independent of other agents' demands.
So demand may be dependent on how much other people also demand the good; you might enjoy going out to eat at somewhere that always seems popular than somewhere that gets less traffic, or you might beg your mom that you just have to go to that popular concert by [insert cool band here], specifically because all your other friends are going. Additionally, social places like restaurants and concerts often have customers who usually or only go in groups, so you could see how that would incentivize fiercer competition among these venues.


How do I quantitatively visualize this situation? Imagine a case where an average of 10% of the income of the people in a certain country is spent on petrol(gas). Now someone comes up with an invention, say a DIY unlimited power source which anyone can make for practically nothing. Obviously the price of oil will fall. But apart from that, how are the other economic indexes going to be affected? Will GDP rise or fall. What kind of parameters of the country will be affected?

Two things will happen:

Firstly, everyone will effectively have had their real incomes rise by 10% (assuming this new energy costs nothing). They will then spend or save this income on other goods besides energy, increasing overall output (note, savings is used for investment as well).

Secondly, energy consumption will likely increase by a large amount now that it is nothing. People who were mindful about their energy consumption due to cost concerns will now not care. Therefore, people will be consuming more energy.


Weierstrass Theorem in Optimization Weierstrass Theorem states that any bounded sequence has a convergent subsequence.

I did that in my maths course and understood it completely. But when I was learning optimization techniques in economics, the definition by the book Sundaram was tweaked slightly to make it fit into the understanding of optimization. It goes like this - (see Figure 1)

If you read it, it is saying just what original theorem said. The only difference is that, instead of starting off with a bounded sequence and reaching the conclusion that it will have convergent subsequence, it started off with a convergent subsequence (by assuming Compact set) and reached the conclusion that it should be bounded. It makes sense right? It did to me too until I found a result on compact set, stated on the same book. (See figure 2)

This redefining of the theorem made it a circular definition - if a set can only be compact if n only if it is bounded then by assuming Compactness in redefinition we implicitly assumed boundedness.

So, my question is please tell me where am I going wrong. Have I understood the redefinition incorrectly or missed so point?

What the book calls the "Weierstrass Theorem" is more commonly known as the Extreme Value Theorem, which states that a continuous function defined on a compact domain attains a maximum and a minimum.

A common proof of this theorem involves the use of the Bolzano–Weierstrass theorem, which you learned in your math course, and which says every bounded sequence has a convergent subsequence.

So the two theorems are actually different, albeit related, statements.


What's good about both exports and imports of a country rising at the same time? I recently came across a question that asks, if exports in a country rises by USD10 billion and imports rises by USD10 billion, what's good about both of these?

To my understanding, the GDP wouldn't change as Net Exports would be constant, so I'm not quite sure how exactly is this good or bad.

There are plenty of issues that can be relevant here, which mean it is hard to give a precise answer. On the one hand, even though GDP is not growing, at least the balance of trade is roughly unchanged. Some countries could experience an equivalent unaffected change in GDP via a trade deficit (e.g. if part of the fall in net imports is compensated with, say, an increase in consumption), which can fuel a currency depreciation and create inflationary pressures, not only on imported goods but on locally produced good which use imported inputs.

On the other hand, it is interesting to compare two countries with the same GDP but different level of exports and imports. The country with greater trade levels is more likely engaged in global value chains, which spur specialisation, and learning for local producers. The literature recognises the role of trade as a mechanism to spur technology transfer (and even transfer of ideas), thereby fostering productivity and growth.


quasi linear utility function if you have a quasi linear utility function, for example $U(l,c)=c-l^{1+γ}/(1+ γ)$ the supply function of l is inelastic right? But can we extend this argument and say that any quasi linear function is going to give you an inelastic function of the non lineal good?
Forgot to mention the production function. But this is the function $y(l)=A(l)^{1-a}$. A is the productivity
So if you take the efficiency condition  you get that $l=(A(1-a))^{1/(a+γ)}$
Thank you.

Thank you.

We solve the utility maximization problem of the individual whose utility function is $u(c, l) = c - \frac{l^{1+\gamma}}{1+\gamma}$ to get the supply function. The problem can be written as:
\begin{eqnarray*} \max_{c,l} & & c - \frac{l^{1+\gamma}}{1+\gamma} \\ \text{s.t.} && c \leq wl\end{eqnarray*}
In this problem, we are assuming that the only source of income of the consumer is his wage income. When we solve the problem we get the labor supply function as:
\begin{eqnarray*} l(w) = w^{1/\gamma}\end{eqnarray*}
The elasticity of labor supply curve is this case is constant and equal to $\frac{1}{\gamma}$. Supply will be elastic if $0 < \gamma < 1$ and inelastic if $\gamma > 1$.


Can Apple use its off-shore cash to do Apple stock buy-backs tax free? It is well established that Apple holds $181B in cash overseas. This appears to be to avoid US Taxes.

Apple has been doing significant stock buy-backs.

My question is: Can Apple use its off-shore cash to do Apple stock buy-backs tax free?

To the best of my knowledge - and I'm not an accountant, so I may very well be wrong: buybacks are not profits, but are instead considered as an 'investment' in Apple in its own company. Since they are not profits, they are not taxed.

Apple using its offshore cash to buy back its own stock is changing the accounting balance rather than actually generating any profits.

Consider the following balance sheet:

        Assets
Cash      100M
   Liabilities
Loans      70M
        Equity
C. Stock   22M
R. Earnings 8M

In this balance sheet, the retained earnings (what is taxed) is 8M.

With a buyback of 12M in common stock:

        Assets
Cash       88M
   Liabilities
Loans      70M
        Equity
C. Stock   10M
R. Earnings 8M

Retained earnings have not changed, the company's taxable income has not changed, and thus the company should not have to pay any taxes.
This should be true regardless of where the money 'physically' is - in the U.S. or elsewhere.


Define structural unemployment I am a bit confused regarding the actual definition of structural unemployment. Some places say that it is the permanent decline of a particular industry, leading to workers being unemployed as they are occupationally immobile.

Other sources say that it is a change in the structure of an economy (e.g. from secondary to tertiary), usually brought about by changes in technology. (Also, just another question, how exactly does improved technology help convert an economy from being mainly secondary to being mainly tertiary?)

So, could you please provide a rock-solid definition of 'structural unemployment'?

Answers would be very much appreciated.

Basically structural unemployment is caused by a mismatch in the skill of the workers available in the labor market and the skill demanded by the "buyers" in the labor market (firms). These workers don't have the skills that the market needs, so no one is willing to hire them.

This happens because the industry in which these workers used to be employed in is in the decline, and I think this is the more correct definition.

Generally, a decline in an industry is caused by a technological change, but not necessary.

Example of tech change -> decline:

The decline in demand for scribes (people who manually write texts in books) when the printing press was invented. This leads to the "decline of the scribe industry" and structural unemployment.

Example of industry decline without tech change:

Lumber industry... after 100 years all trees are gone. This would lead to a decline in demand for lumberjacks and a structural unemployment without technological change.

The second question might be better asked as a separate question per the guideline :)


Are Cobb Douglas goods complements or substitutes? Given
$$U(x,y)= x^\alpha y^{1-\alpha}$$
$\alpha \in (0,1)$,
are Cobb Douglas goods (here $x$ and $y$) complements, substitutes, or neither? Why?

An explanation with mixed partial derivatives would be great. My calculus is better than my economics skills.

Try to think what you mean when you ask whether they're complements or substitutes.

You could mean: "Does my marginal utility in $x$ increase when I get more $y$? That would correspond to the cross derivative $\frac{\partial U^2}{\partial x \partial y}$.

You could (and this is the convention) mean the response to a change in prices. Denote with stars the bundle that maximizes utility given a budget constraint.

$$x^* (p_x, p_y), y^*(p_x, p_y) = \arg\max_{x,y} U(x,y) + \lambda(Y - p_x x - p_y y) $$

Then, the goods are complements if you increase the price of one of the goods, and the demand of the other one decreases:

$$ \frac{\partial x^* (p_x, p_y)}{\partial p_y} < 0 \\
\frac{\partial y^* (p_x, p_y)}{\partial p_x} < 0 $$

And substitutes if that is larger than zero. For the case where that partial is exactly zero, the elasticity of substitution is zero. Try out yourself which case is correct for Cobb-Douglas!


why don't we also pay money to industries that have a negative carbon footprint? I understand that taxes (Pigovian taxes) can be used to steer the economy in a certain way. For example, if you increase the taxes on things related to cigarettes, the price increase will decrease the demand. Or, if you put a carbon tax, the industry will try to produce its products in a carbon-neutral way in order to keep the prices - hence demand - on the same level, which will transform the economy in a more green one.
However, why don't we also pay money to industries that have a negative carbon footprint?
I mean, while producing your product, if you either capture some carbon or product something that can be used to capture carbon, you are directly doing a "good" to the society. Wouldn't this also incentivize companies not just to have a zero-carbon footprint but instead to have a negative footprint?
Are there any examples of such policies?

Are there any examples of such policies?

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

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


If I make an international purchase with a card which contains domestic currency, is this currency converted to the currency of the seller? Let's say that I buy an app from the Play store. The seller quotes in Dollars, and I pay in Rupees (INR) --how does this transaction happen?

Is my ₹ converted into $? Does this transaction also influence the forex markets (of course, negligibly --I'm only asking for understanding's sake).

If I have to purchase a physical good while in the US, I'd have to convert my domestic currency into dollars and that'd push the dollar prices up since there is demand for more dollars.

Does the same happen when I'm at a different country and purchase a good in dollars?

Generally the receiver bank / payment-gateway makes the conversion - except for currency accounts where the transaction is made directly into the account or if the sender chooses to make the conversion.

You can lookup the cutoff times for currency transactions on the different banks.


Employment Volatility and the Relevance of Aggregate Wage Rigidity The Mortensen-Pissarides (MP) framework of search labor is the thing in analyzing (equilibrium) unemployment over the business cycle. Shimer showed that the lack of hires is the big margin that affects the volatility of labor. Since then people tried to analyze potential wage rigidity for new hires.

Is it safe to conclude that - in this context - wage rigidity of old matches does not matter anymore? Is this somewhat depending on the framework (As in: old wages don't matter for hires in MP because of XYZ, but this is a strong assumption)?

Is wage rigidity, conditional on the match being new, the only relevant metric onwards?

Wage rigidity is not the only solution to the Shimer Puzzle (Shimer, AER 2005) that has been proposed in the literature, so I wouldn't say that it is the only relevant metric to consider when thinking about labor market dynamics in this context. However, as I understand the question, it aims at the role of wage rigidity in a Diamond-Mortensen-Pissarides (DMP) model and not on alternative solutions to the Shimer Puzzle.

Thus, here are a few thoughts on the rigidity of wages of newly hired workers:

The baseline DMP model is essentially a model of new hires. The wage formation mechanism as it is described in Pissarides (2000) does not differentiate between newly hired workers and ongoing employment relationships. The Nash bargaining solution dictates a surplus sharing rule that splits up what is being produced in every period, no matter how long the employment spell lasts. The bargaining powers are exogenous. In the baseline model, the elasticity of wages with respect to labor productivity is simply 1. Wages are fully flexible and immediately adjust to changes in labor productivity. This model feature lies at the heart of the Shimer puzzle. The model's inability to generate dynamics consistent with volatilities we observe in the data is due to the fact that wages adjust upwards too much in response to a positive shock, thereby lowering incentives of firms to post additional vacancies.

Since the theoretical model treats every match in every period like a new match, the rigidity of new matches is of primary empirical interest for the calibration and analysis of this class of models.

Haefke et al. (JME, 2013) report empirical evidence for wage rigidity using US labor market time series data.  They find that the wage of new hires (both out of unemployment and after a job-to-job switch) corresponds almost one-to-one to changes in labor productivity. The estimated elasticity is around 0.8 (with quite a large standard error of 0.4). The wage of workers in ongoing employment relationships, on the other hand, shows little flexibility. The authors note that the elasticity of 0.8 is an appropriate calibration target for search and matching models.

Whether focusing on new hires only is too strong an assumption depends mainly on the country one looks at. The US labor market, for example, is driven by huge turnovers. Thus, in every period, a large share of employees can be considered new hires. For some European labor markets, on the other hand, the assumption might be less reasonable because average employment spells tend to be longer and labor market flows smaller.

References:

Haefke, Christian; Sonntag, Marcus; Rens, Thijs van: Wage rigidity and job creation. In: Journal of Monetary Economics 60 (2013), No. 8, pp. 887-899

Pissarides, Christopher A.: Equilibrium Unemployment Theory. 2nd Edition. The MIT Press, 2000

Shimer, Robert: The Cyclical Behavior of Equilibrium Unemployment and Vacancies. In: The American Economic Review 95 (2005), No. 1, pp. 25-49


Matlab: While loop in function I am new to Matlab (& also to stackexchange) and I need to learn it for a dynamic Macro class.
I have trouble using a while loop in a function. The function is supposed to calculate the amount of coins one needs to pay price p. My function, however, just provides a vector displaying which coins I need and not how much of which. I hope, someone jumps in and helps me out of my trouble. Here is my code:
function[c] = achange(p,coins)
s=size(coins);
c=zeros(1,s(2));

while p>0
    for i=1:s(2)
    if coins(i) <= p
        p=p-coins(i);
        c(i)=c(i)+1;
    end
    end
end
end

I thought a little bit about the problem, and I came up with the following quick hack, that seems to work.
Here is the piece of code that should do the job in principle with integers:
function  [exch]=achange(p,coins)
s=size(coins);
c=zeros(1,s(2));
coins=sort(coins,'descend');
it=1:s(2);
isaninteger = @(x)isfinite(x) & x==floor(x);
if p<coins(end)
   return
end
if isaninteger(p)==0
   exch.coins=coins;
   exch.c=inf(1,s(2));
   exch.rest=inf;
   return
elseif any(isaninteger(coins)==0)
   exch.coins=coins;
   exch.c=inf(1,s(2));
   exch.rest=inf;
   return
end
rest=0;
while p>0
    trQ=mod(p,coins)==0;
    idx=it(trQ);
    li=length(idx);
    if isempty(idx)
       rst=1;
       rest=rest+rst;
       p=p-rst;
    elseif li>0 && li<s(2)
      ps=it(trQ)==0;
      idx2=idx;
      idx2(ps)=[];
      for k=1:li
          if p>0
             p=p-coins(idx2(k));
             c(idx2(k))=c(idx2(k))+1;
          end
      end
    elseif li==s(2)
     for k=1:li
         if p>0
            p=p-coins(idx(k));
            c(idx(k))=c(idx(k))+1;
         end
     end
    end
end
exch.coins=coins;
exch.c=c;
exch.rest=rest;
end

At least for the following example it works:
>> exch=achange(57,[10 25])
exch =
struct with fields:
  coins: [25 10]
      c: [1 2]
   rest: 12

>> exch.coins*exch.c' + exch.rest
ans =
57

or for:
>> exch=achange(51,[10 25])
exch =
struct with fields:
    coins: [25 10]
        c: [1 2]
     rest: 6

>> exch.coins*exch.c' + exch.rest
ans =
51

and finally my example from the comments:
>> exch=achange(60,[1 2 5 10 20])
exch =
    struct with fields:
    coins: [20 10 5 2 1]
        c: [1 1 3 4 7]
     rest: 0

>> exch.coins*exch.c'
ans =
60

If any input is not an integer, we obtain
>> exch=achange(57,[5 .10 25])
exch =
    struct with fields:
    coins: [25 5 0.1000]
        c: [Inf Inf Inf]
    rest: Inf

or similar
>> exch=achange(57.8,[5 10 25])
exch =
   struct with fields:
     coins: [25 10 5]
         c: [Inf Inf Inf]
      rest: Inf

UPDATE 21.11.2020
Due to the fact that the allocation of the species is not optimal by the above code, which can be seen, for instance, by first example, where the residual amount can still be allocated to some coins, I provide a small amendment that should produce better results.
The residual amount of the mentioned example is $12$ indicating that the structure of problem is unchanged, which allows us to solve the problem recursively. That is, we should replace the lines of code after the While-loop by the following If-construct to invoke a recursive call whenever it is necessary.
if any(rest>coins)
   exch2=achange(rest,coins);
   exch.coins=coins;
   exch.c=c+exch2.c;
   exch.rest=exch2.rest;
else
   exch.coins=coins;
   exch.c=c;
   exch.rest=rest;
end

Then we can reduce the residual amount of the first example from $12$ to $2$, as we can see through
>> exch=achange(57,[10 25])
exch =
   struct with fields:
     coins: [25 10]
         c: [1 3]
      rest: 2


Divergence of a variable in forward-looking models. Blanchard-Khan conditions (1) This post is, first, regarding the issue from Romer's Advanced Macroeconomics, 4 ed. Chapter 6.4 on nominal rigidity, pp. 264-266 to be precise.

He sets out a simple model with microfounded IS curve, AS curve and MP curve, using standard notation with $\pi$ as an inflation, $y$ as an output and $r$ as an interest rate.

My question is why agents in this model cannot expect $y$ to diverge? Is this due to mathematical and/or economical reasons? Or did I miss some assumption in the text?

Also, does diverge here mean rise ad infinitum or only rise fast enough to offset the convergence of $\phi^n$? [I know, this is a rather math than econ question, but entirely a propos the problem considered].

So here's the model:

(2) Secondly, later in the text a similar issue recurs in chapter 11.5 when analyzing the model of optimal monetary policy in a forward-looking setting. Romer considers cases where self-fulfilling equilibria arise (I guess Blanchard-Khan conditions):

So why do we have to assume that our variable is bounded? Again: is this due to mathematical and/or economical reasons?

(3) Finally, when I elswhere read about Blanchard-Kahn conditions there is stipulated that "Blanchard-Kahn conditions apply to models that add as a requirement that the series do not explode". Why is that? Isn't that possible for an economic system to have such a property? Or why are we ruling out from our analysis models with that property?

Do all these 3 issues touch the same problem and have the same solution or this is just the coincidence that I don't get this assumptions/results(?) in different contexts?

PS
This comment is really helpful claryfing some math related issues, but it does not pertain to the reason for the assumption/result(?) in question.

Edit:
For the clarity reasons I've included more of Romer's solution to the (1) problem.

QUESTION 1
By inserting $(6.28)$ into $(6.29)$, re-arranging and applying direct forward substitution , we obtain

$$y_t = \lim_{n\rightarrow \infty}\left[\left(\frac {\theta}{\theta + b}\right)^nE_t[y_{t+n}]\right] +\frac {\theta}{\theta+b -\theta \rho}u_t \tag{1}$$

Then forwarding $n$ periods and taking the conditional expectation with respect to information available at $t$ we have

$$E_t[y_{t+n}] = E_t\left(\lim_{n\rightarrow \infty}\left[\left(\frac {\theta}{\theta + b}\right)^nE_{t+n}[y_{t+2n}]\right]\right) +E_{t}\left(\frac {\theta}{\theta+b -\theta \rho}u_{t+n} \right)$$

$$\implies E_t[y_{t+n}] = E_t\left(\lim_{n\rightarrow \infty}\left[\left(\frac {\theta}{\theta + b}\right)^nE_{t+n}[y_{t+2n}]\right]\right) \tag{2}$$

The conditional expectation is an integral. Can we interchange integration and limit? To do that Dominated Convergence & Co should hold (they are only sufficient conditions, but we do not have something better). For our case, Dominated Convergence requires that the expression inside the limit is bounded("dominated"), and that the limit is finite. If it is then, using also the Law of Iterated Expectations, and the fact that under the limit $t+2n$ is equivalent to $t+n$ we have

$$E_t[y_{t+n}] = \lim_{n\rightarrow \infty}\left[\left(\frac {\theta}{\theta + b}\right)^nE_t[y_{t+n}]\right] \tag{3}$$

Note carefully that in the left-hand side, $n$ does not go to infinity. Also, remember that we obtained $(3)$ under the assumption that the limit is finite. So $(3)$ tells us that for every finite $n$, the conditional expectation must be equal to the unique limit, i.e. equal to the same number, i.e. it should be a constant.

Can this constant be anything else than zero? Assume the limit is not zero. Then one can verify that the only other finite value that the limit can take is $1$. But for the limit to be $1$ we must have
$E_t[y_{t+n}]\rightarrow \left(\frac {\theta + b}{\theta}\right)^n$, which goes to infinity with $n$. So the left hand side would go to infinity and will not be equal to the limit. Hence we conclude that the limit must be zero, for $(3)$ to hold.
This can happen if we assume that the expectation alone is a non-zero constant, or that it is growing but boundedly (say, it has an asymptote to which it converges from below). But then again, in both cases the left hand side will not be equal to the now zero limit. So we see that the only way that $(3)$ can hold is to assume that the expectation alone is zero.

So I would say that the approach "if we assume that the limit is zero, then we obtain etc" (as presented in the quoted text), is wrong: looking at our solution, which is equation $(1)$, we must first assume/impose that the expectation is zero, to make it all consistent, and finite (note: if the solution $(1)$ included also a constant term in the right-hand side, things would be more flexible).

Sticking with $(1)$, we also see that the only other consistent solution is to assume that the limit goes to infinity -and this can happen only if we assume that the expectation on its own goes to infinity.

QUESTIONS 2 & 3
As I have wrote in another answer, everything in real-world economics is finite -even prices, even expectations. The above mathematical formulations and the mathematical possibility of an infinite solution represent in a colorful way the phenomenon of "bubbles". In real life, bubbles eventually burst -but what we have managed to capture by using the "infinity" concept, is the abnormal inflation of the bubble while it hasn't burst yet. So agents can "expect infinity", in the metaphorical sense just described. But since "bubbles" is not your everyday economic phenomenon, these models usually assume them away in order to study the stable situation.

Marx was the one that argued that capitalism will explode, or rather, implode. So you have an articulated theory that advances the view that a specific economic system possesses the property of (eventual) divergence.


How to calculate price index for natural gas in India? Ministry of commerce and industry of India doesn't provide WPI index for Natural Gas. Is there a way to calculate the same?

Since 2014, this is the official formula to compute the price of NG in India:

The details of this formula, including where the data is taken from can be found here.

To see historical data with this formula (since 2014), see the left panel here. Simply click in the period you want to see. Notice these prices are set for a six-month period.

There is more information about the context of this policy and the different pricing systems regarding natural gas for India here.


Calculating natural rate of unemployment I have sample data on unemployment rate in a market and am looking to calculate the natural unemployment rate. The natural unemployment rate I obtained is constant over a time period, which is not a realistic assumption given the fluctuations we observe in labor force, employment.
As per the keynesian relationship between unemployment and inflation, the natural rate is defined as rate when inflation is stable or change in inflation is 0.
Pandas DataFrame:

import pandas as pd
import numpy as np
import random

df = pd.DataFrame({
                   'Date_Col': pd.date_range(start='1/1/2010', periods=40, freq='3M'),
                   'unemployment': np.random.uniform(5,12,40),
                   'Inflation': np.random.uniform(1,3, 40)
                  })

df['Change_Inflation'] = df['Inflation'].pct_change(periods=1)

# Drop first row
df1 = df[2:len(df)]
df1

I fit the following regression model to obtain estimates and calculate the natural level of unemployment:
change in inflation = b0 + b1 * unemployment + e

Substituting, change in inflation = 0, and solving for unemployment, the natural unemployment rate = b0/b1. The rate I obtained is for entire time period, this isn't realistic as there are significant supply side fluctuations in labor force. Therefore, I'd like to calculate the natural rate for each time period. How would I do so?

The model you fit is simply inadequate to estimate the natural rate of unemployment any results from it will be completely unreliable, so I am not surprised if they make no sense. Furthermore, natural rate of unemployment is not necessary one where inflation is 0, that is Non-Accelerating Inflation Rate of Unemployment (NAIRU). NAIRU is often used as a proxy for natural rate of unemployment but the two are not the same (for some non-technical explanation of differences between natural rate of unemployment and NAIRU see Investopedia).
Estimating NAIRU:
First to estimate NAIRU you typically need multiple equations not just one (see Carnot et al. Economic Forecasting and Policy. 2nd ed. pp 104).
For example, NAIRU can be obtained by combining producer price equation with a Philips curve expressed as a wage setting equation in a wage-price loop. So we would start with a system like:
$$ p^s_t =  w_t - \theta_t +z_t + \alpha \tag{1}$$
$$\Delta w_t = \Delta p_{t-1} - \lambda U_{t-1} + \Delta z'_t + \beta \tag{2}$$
where $p^s_t$ are log of producer prices, $w_t$ are log of wages,  $\theta$ is productivity, $U_{t-1}$ is unemployment and  $z$ and $z$ are some control variables exerting inflationary pressure, alpha and beta are constants. After differencing the first equation we get:
$$ \Delta p^s_t =  \Delta w_t - \Delta \theta_t + \Delta z_t  \tag{3}$$
If we define the wedge between consumer and producer prices, which exists due to influence of imports and taxes, as $\phi_t \implies \Delta p_t = \Delta p^s_t + \Delta \phi_t$ and hence new producer price equation will be given as:
$$ \Delta p^s_t =  \Delta w_t - \Delta \theta_t + \Delta z_t \tag{4}$$
Combining equation (4) and (2) would give us the Philips curve:
$$\Delta p_t - \Delta p_{t-1} =  - \lambda(U_{t-1}-U^*) \tag{5}$$
where finally $U^*$ which is the NAIRU would be given as:
$$U^* = \frac{\beta - \Delta \theta_ t + \Delta z_t + \Delta z'_t + \Delta \phi_t}{\lambda} \tag{6}$$
Normally the whole system above would be estimated in a structural way where you would have separate error correction models (ECM) for producer price equation and wage setting equation  embedded in some structural model that will possibly include more equations (See chapter 3 in the above cited Carnot et al.).
There are also different approaches to estimating the above but even the basic reduced form Philips curve models used to estimate NAIRU will require multiple equations and usually will be estimated not with OLS but with something else like maximum-likelihood with Kalman filter (see this research  by Jacob and  Wong (2018) estimating NAIRU for New Zeeland).
Unfortunately, it is beyond scope of single SE answer to make an exhaustive review of all ways of estimating NAIRU but one thing that should be hopefully clear from the above is that it cannot be done with some simple naïve OLS where you regress inflation on unemployment.

PS:
The following statement is actually not entirely correct statement:

The natural unemployment rate I obtained is constant over a time period, which is not a realistic assumption given the fluctuations we observe in labor force, employment.

Natural rate of unemployment includes only frictional and structural unemployment not cyclical unemployment. Most variation in employment over time is due to cyclical or also seasonal variation. Structural changes or changes in frictions are usually small and relatively trivial compared to cyclical changes. In fact research by Fed shows that in the US natural rate of unemployment over last 100 years was remarkably stable ranging between $4.5$ and $5.5\%$. Consequently, even though there is some variation in natural rate of unemployment, it would not be unrealistic to use flat $5\%$ rate for US as a first approximation.


reference request: models of how racism or sexism affects decision making My background is more in statistics and applied math, so I am not familiar with the breadth of decision making models from economics. However, I am working on a project that involves decision making models, especially with reference to racism and/or sexism in hiring or labor market decisions. I was just wondering if there were any existing economics papers that model decision making where some decision-makers in the decision making process subscribe to differing levels of prejudiced beliefs.

Of course I did search google scholar and looked at the microeconomics section of the American Economic Journal. I found a bunch of statistical papers which demonstrate that there is bias in hiring. But I am really looking for something with a model of the decision making process that includes a racism or sexism component.

Any suggestions would be appreciated.

There is a large literature on this, particularly in the context of labour markets. Some classic references:

Becker (1957) analyses employers who care about making profits
but also seek to avoid interacting with certain groups. One famous
result is employer prejudice need not lead to racial wage gaps as
long as there are enough non-prejudiced employers to hire the
minority group.
Phelps (1972) models employers who use demographic information
(e.g. gender or race) as proxies for unobserved but productivity
relevant variables. Unsurprisingly, it turns out that differences in
means or variances across demographic groups can induce employers to
discriminate in this setting.
Similar models are developed by Arrow (1971) and Aigner and
Cain (1977). I would particularly recommend reading the latter.
Here are some lecture notes which provide a useful overview of
some of the main issues and ideas.


Is there some definition about risk sharing? I was searching for a definition of risk sharing and I have found the following:

$\underline{Definition:}$ Risk Sharing — also known as "risk distribution," risk sharing means that the premiums and losses of each member of a group of policyholders are allocated within the group based on a predetermined formula. Risk is considered to be shared if there is no policyholder-specific correlation between premiums paid into a captive, for example, and losses paid from the captive's reserve pool.

I am confused with the term "captive". What is the exact meaning of this term? Is there any other reference about seome definition of risk sharing?

Captive insurance is an insurance for purpose of insuring the owners of the said insurance. It’s a kind of self-insurance where multiple agents pool their capital together to insure themselves. So the term in that sentence refers to the pool of resources for insurance.

It’s called captive because the modern concept of this kind of insurance was first applied to a company that wanted to create insurance for its subsidiary mines that were referred to as captives and somehow the term catch on.


What exactly is the argument for Free Trade? There's been a lot of talk about Free Trade. People seem to either know nothing about it, or they seem to either support or oppose it with such passion that if you didn't know any better, you would think they were actually at war.

Now, I often don't like so called "Free Trade Agreements" like NAFTA, TPP, RCEP, CETA, etc. but more often than not my aversion to them tends to be based on toxic copyright provisions and a lack of Fair Use protections, not necessarily the actual macroeconomic effects of the trade deal as a whole.

Thus, I have to ask: what exactly is the argument in favor of Free Trade? What exactly is it trying to achieve? And are there ways a nation can address the negative effects of such deals? And what is Free Trade NOT?

The theory behind free trade is denominated comparative advantage, and as mike stated, the advantage is that a country, as a whole, benefits from specializing in the fields at which it is best, as it will get more than it would if it would produce everything alone.

In practice, a big advantage is the ability to operate for a bigger market, reaping economies of scale. This is particularly advantageous for small countries.

The downside is that, although free trade will make the country as a whole richer, it wont make the society necessarily equally richer, so it wont guarantee that an economy will develop. This connects with the concept of exploitative trade and fair trade: by entering international trade, developing countries might leave their economies vulnerable to foreign companies or governments, sometimes in critical sectors such as food and energy.


Income and substitution effect for perfect substitutes I was recently asked about what the income and substitution effects are for perfect substitutes are. Given the rather peicewise nature of the demands for each good in a utility function considering perfect substitutes I'm not sure what the answer is.

That being said, what are the income and substitution effects for a utility function considering goods that are perfect substitutes?

An indifference curve for perfect substitutes is a straight line. In fact it is the line defined by $y=const-x$, for a utility level of $const\in\Bbb R$. We maximize the utility when our budget line is tangent to the IC line. But they are both straight lines, so there are a few cases (considering a situation with only 2 goods):

the prices are not equal ($P_X< P_Y$ for example, then you would always choose good $X$)
$P_X> P_Y$ for example, then you would always choose good $Y$
the prices of the goods are equal $\implies$ our budget line is parallel to the IC line and the utility maximization point is anywhere on the budget line.

For cases 1 and 2:

Let's consider the case where good $Y$ is cheaper and becomes relatively more expensive after a price change.

We can use Hicks' method to determine the SE and the IC by reducing artificially the consumer's income so that he ends up consuming a basket that is on the original IC curve before the price change (I think Slutksy method is impossible to implement, because we would have to reduce the budget so that the original basket is chosen but with the new prices it is impossible, unless the good is an inferior good I guess, but can they are perfect substitutes so they are both inferior, which I'm not sure if it's possible because an inferior good must take up most of your budget)

We go from equilibrium $E$ to $E'$ and the equilibrium $E''$ is the one due to a reduced budget by the method of Hicks.

For the third case, in theory the original equilibrium can be anywhere on the budget line. In practice it is probably in a fixed position and you can use the same method to derive the IE and the SE.


Will banks in the US continue to offer CDs? Earlier this year, the Fed abolished the reserve requirement. My understanding was that the motivation for banks offering CDs was because the Fed didn't impose reserve requirements on CDs, so banks could lend out more of deposits held as CDs than deposits held in other, lower interest forms. Given that CDs no longer provide an advantage to banks over normal accounts in this respect any longer, why do banks have any incentive to keep offering CDs? Is there another reason banks offer CDs?

Demand deposits might be cheaper, but they can disappear due to withdrawals. Banks also need stable sources of longer-term funding to match against their illiquid assets. Holding reserves is only of limited economic importance relative to the need to widen funding sources.
CD’s are cheap relative to other sources of term funding. It would be very hard to imagine that they will be phased out.


How does John Stuart Mill distinguish between "wealth" and "riches"? JS Mill in his Principles (1848):

But though air is not wealth, mankind are much richer by obtaining it gratis, since the time and labour which would otherwise be required for supplying the most pressing of all wants, can be devoted to other purposes.

I am bewildered by the above sentence. Mill seems to be making a distinction between "riches" (or "being rich") and "wealth" (or "being wealthy"). But what is this distinction?

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.)


Does a competitive advantage lead to abnormal profit? Given that organisational capital is specific and difficult to replicate it is considered a competitive advantage (see e.g. here)
According to Wang (2014)

competitive advantage is obtained when an organisation develops or acquires a set of
attributes (or executes actions) that allow it to outperform its
competitors.

Does a competitive advantage allow a firm to achieve abnormal profit?
Or which other advantage would it confer?

I would say yes. For example, consider a perfect competition scenario, with equilibrium price $p$.
Now say (only) one firm acquires some organizational capital that allows them to have lower their marginal cost from $c(=p)$ to $\tilde c < c$.
This firm can charge price $p^-$ and aquire the whole market now, earning abnormal profits $\pi = (p^- - \tilde c)q$.


Who regulates the balancing of the books for commercial banks? How? Is it public information? I've just read Money Creation in the Modern Economy, an article published by the Bank of England. This article brings about a lot of questions in my mind. This article talks about money being created through commercial bank loans, and that central banks only have the authority to set interest rates or to employ quantitative easing in order to stimulate the economy. Loans being repaid should theoretically destroy the money that was created and balance the books, but inflation grows in that economy as banks earn interest (and in this case, the interest is actually the money that never existed, assuming that they destroy the rest of the money paid back). So my questions are:

How is this all regulated? Who regulates the balancing of the books?

This must require a lot of regulation in order to be feasible, because there are many commercial banks, but few central banks, and because central banks lack power. E.g. central banks can only set interest rates thus defining the theoretical inflation rate, or buy assets through quantitative easing.

What's stopping a commercial bank from making a deposit into someone's bank account that isn't on the books or what's stopping them from not destroying the money they get paid back from loans?
Can I find out more about this stuff for each bank? In other words, is this public information or not?

It's public information, and you can take courses, and even university degrees in it.

The double entry book keeping technology used by banks is essentially designed to tackle exactly this problem, and all banks and commercial customers use it. The system itself provides a single error detection/correction mechanism, that guards against human error, and also originally required updates in two separate books, maintained by two separate clerks - which was deliberately done to make fraud more difficult. Essentially if the books don't balance, this is a red flag to find the mistake/fraud that caused this to occur and correct it. These days it's all computerised, but the underlying operations are identical.

The entire accountancy profession's job, is essentially to supervise this process, and periodically audit both banks and companies in order to make sure that the books are balanced, and that nothing illegal is being done.


Bretton Woods vs Gold Standard I've been reading about the history of the IMF recently, and it strikes me as odd that despite the problems that arose with the gold standard (Germany in the 1920s, Fed cutting money supply during the Depression), countries would agree to effectively peg their currencies to gold (via the US dollar).

It doesn't seem to me that there were any substantive differences between the Bretton Woods regime and the gold standard, as seen in the early 1970s, when Richard Nixon was forced to remove the US Dollar from its gold peg. I'd like to know why economists thought Bretton Woods was a good idea.

It doesn't seem to me that there were any substantive differences between the Bretton Woods regime and the gold standard, as seen in the early 1970s

Note that most of what I'm about to write is summarized from Wikipedia.

The gold standard of some form has always existed in the US since the Coinage Act of 1792 with a few interruptions. In 1934, gold was nationalized in the US but the value of the US dollar was still tied to gold reserves. Bretton Woods simply maintained the gold standard. While the rate between the US dollar and gold varied over the years, until 1976, the gold standard was officially kept. In other words, indeed there were no substantive differences because the Bretton Woods era was just a short part of the gold standard history.

  I'd like to know why economists thought Bretton Woods was a good idea.

In the sense that they mostly kept policy that had been in existence for over a century by that point, it wasn't too surprising. The general summarized critique against the gold standard based on my reading of the IGM survey is that gold is too volatile compared to the existing system with the US dollar and the Fed and gold doesn't allow for any counter-cyclical monetary policy. If economists a century ago took the same survey it isn't clear that there would be such a clear consensus against the gold standard. As the St.Louis Fed writes,

  For the pre-Fed period (1790-1913), the average annual inflation was
  0.4 percent with a coefficient of variation of 13.2. During the period 1941-2016, these figures changed to 3.5 percent and 0.8, respectively.
  If we look at the post-Volcker era (1988-2016), annual inflation was
  2.2 percent on average with a coefficient of variation of 0.4.

In other words, we've come a long way in terms of keeping price volatility of everyday goods and services in control. Relative to the past, in developed countries, we are no longer concerned with hyperinflation, which a gold standard makes fairly difficult.

Also from the perspective of the US, it helped solidify the US dollar as a reserve currency. All of the benefits listed in this SE answer apply besides seigniorage.


Difference between no perfect multicollinearity and no multicollinearity Some textbooks (for example, Introductory Econometrics: A Modern Approach by Jeffrey Wooldridge) assume that no perfect multicollinearity for the OLS regression, while others (for example, Econometrics by Fumio Hayashi)  just assume that no multicollinearity. Are there any differences between these two assumptions? and what are the differences?

Thanks in advanced!

Perfect multicolinearity means that two independent variables are perfectly correlated with their $r^2=1$ multicolinearity technically refers to any non zero correlation between two independent variables but when it is mentioned as a problem it usually implies that the correlation is high. So there is a difference between the two terms perfect multicollinearity is a special case of multicolinearity.

Also they have different implications for OLS. Under perfect multicolinearity OLS cannot be identified. Under high muliticolinearity OLS can be identified but standard errors will be inflated.

However, to make the things confusing, I noticed that sometimes people use the terms interchangeably. I only have the Wooldridge book so I can’t check the text of the other one to compare it but I think they actually refer to the same thing.


Discount & Interest rates Small question, is discount rates and interest rates the same/similar thing in economics? A bit confused regarding this.

They are related but they are not same.

An interest rate is broad term for what you pay for the use of assets as a percentage of the value of the asset or principal. See for example definition here.

A discount rate can be the interest rate that Fed charges at its discount window, or it is often in theory used more broadly as the rate at which people discount future cash flows. The latter is also in a sense an interest rate but not interest rate charged by any institution but the one that person would expect to receive to  be compensated for lending/investing their resources and postponed consumption.


What is the monotone hazard rate assumption used for? I was reading this article on advance purchase discounts and pricing in which the author uses the monotone hazard rate assumption. Why does the author use it?

The article is Advance-purchase discounts as a price discrimination device (PDF) by Nocke Peitz and Rosar

Below you can find a screenshot of the part in question.

Thank you very much!

The motivation for this assumption is to have a unique solution. In this article, it is necessary to prove the 1st lemma, i.e. the quasi-concavity of the profit function.  You find a similar motivation in Tirole’s book (Industrial Organization, p. 156).


Taking logarithms of variables It is common to taking logs of variables when perform a regression analysis. But the observations will become negative after logs transformation when it is less than 1. Is this the possible concerns?
(e.g. log(0.5) = -0.6931, but log(5)= 1.6094)

As stated already there is no problem if log(x) is negative. However, you would want to be careful if x=0 or if x<0 because then the logs are undefined. So as long as x>0 then there are no problems at all.


What would be the economic impact of regulating advertising? What I mean by that putting a regulation on businesses that says they can't spend more on advertising than expanding their business.

I know something like this would be very hard to regulate, but I'm just asking what would happen hypothetically.

The first thing we must ask is about which part of advertising are we speaking? Are we talking about advertising on television and other entertainment mediums or are we talking about advertisement via the packaging of the good itself?

One impact either way would be an increase in competition amongst monopolistically competitive firms. These firms are often selling products which accomplish the same ends, however they differentiate their goods in order to give them a competitive edge. The main way which they convey this differentiation to consumers is through advertising. Therefore, if they cannot advertise this differentiation, consumer information may be limited and they may not see a difference between the firm's product and other products in the market. This will lead to parity among products and will move the market closer to a purely competitive market.

Now, sometimes the only differentiation may be the advertising itself (in the form of packaging). For goods such as water bottles (barring whether the water is enhanced somehow) this is the case. There has been much research done to ascertain the best way to package your products in order to draw the consumer to the product. If this was limited, then markets such as these would move towards a purely competitive market.


Purchasing power of currency abroad Say you have two countries A and B. Suppose we have a situation where country A's currency can purchase much more in country B than the other way round. What causes this phenomenen?

Is it possible to have a situation with two equally well off countries, but where one country's currency can purchase more goods abroad?

Well in principle you could. Let's suppose there are two countries that do not trade a lot. Then even if their economic growth is relatively similar, we should not expect their exchange rate to be 1:1.

The exchange rate is a price, so if country A likes more the goods and services from country B than vice-versa, you should expect currency B to have a larger purchasing power than currency A.

However, The demand for goods from abroad is correlated with income, so if both countries have relatively similar economic growths, and they trade a lot with each other, the relative purchasing power of their currencies will tend to be similar.


Why don't prices of USA labor and Mexican labor equalise? That Mexicans workers get paid less US workers is a dynamic which motivates the moving of production to Mexico.  This idea can be abstracted to Developed Markets (DM) labor and Emerging Markets (EM) labor.  This is driving many recent political upsets.

Do the proponents of free globalised trade expect the price of labor to converge?
Is there evidence of convergence?
When will meaningful convergence arrive (example metric EM labor being paid no less than half DM labor)?

So folding in some feedback from commenters about 'why should they?'.  Isn't this case analogous to supernormal profits being competed away?

The underlying reason for persistent wage differences is probably that Mexican workers are less productive than American workers.
It is sufficient that workers in some tradeable sectors are more productive to have persistent wage differences in all sectors. (a good explanation of this effect can be found here: https://en.wikipedia.org/wiki/Balassa%E2%80%93Samuelson_effect#The_effect_in_more_detail)
One would expect that unit labor cost in tradeable sectors converges, not necessarily wages.
Here is a graph that suggests this has already happened: https://fred.stlouisfed.org/series/CCRETT02MXA661N, for an explanation of real effective exchange rates see here: https://en.wikipedia.org/wiki/Effective_exchange_rate


What is meant by credit-based investment? My knowledge of economics is very small so I would be grateful if anyone could answer this question in the style of 'economics for dummies'!

What is meant by the term 'credit-based investment' or 'credit-fuelled investment'? I have come across the term a number of times describing China's fiscal policy.

As the name suggests, credit based investment is investment that takes place based on funds that are themselves borrowed.

An example of credit-based investment is leverage.


Philosophy books for decision theory and economics idea I have learned economics so far, the most astonishing economics' thing is its though which is talkable and visually in the real world or the abstract world that is worth researching and talking. What I see in common is the abstract ideas that are generated from philosophy and economics is the social science study, I am interested in both philosophy and economics but what I only know and read is economics' side, not philosophy's side.

Does anyone recommend any book worth for spending the time to gain both sides of knowledge?

Your question is a little bit unclear. But still, if you wish to delve into the philosophical side of economical topics/question/phenomena, you can check the Stanford Encyclopaedia of Philosophy's article on Philosophy of economics. It might be a good place to start and refine what you are looking for.


Supply curve when the marginal cost is zero The supply curve is built as the average marginal cost (MC), when the MC is equal or higher than the average cost (AC)
The marginal cost increases, as a result of the opposite effect of marginal production
In this case, we get a supply curve that's rising from left to right: higher cost per rising quantity

In the case of marginal cost of zero, I can think of no other case than a supply curve that is equal to AC, and that the AC is dropping, since fixed costs do not change as a result of quantity
And so, we'll receive a curve that's dropping from left to right: lower cost per rising quantity

Real life cases can be broadcast tv, surpluses in production, "internet economy" etc.

Am I wrong in my assumption?
Is there any reference of this type of equilibrium ?
Is it a stable equilibrium ? I mean, since the marginal cost is zero, there is no impact on increasing demand

Took me a bit, but I have figured its out:

The single firm's supply curve is defined as it marginal cost, as long as MC is above it average cost
A firm would not sell below its average cost, since it would loae money, Mathmatically we can define, for the single firm
S = MAX(AC, MC)

Our basic assumption,for this discussion, is that MC = 0

Under the basic assumption and that costs are positive, obviously, then, the supply curve will always equal AC:
S = MAX(AC, 0), AC > 0
S = AC

The other conculsion from the basic assumption is that the production function, under the costs limit, is completely unaffected by quantity
Intuitively: its costs the same to produce 100 products and 1000 products.

If the Total costs function, as a function of quantity, is fixed, then the average function is:
AC = TC/x

In that case, we'll get a supply curve, though a very special one:
It'll decrease price as a result of increasing quantity, and prices will aspire to zero. always

Update:
Allowing myself to add a link to an article I wrote on the topic:

Start-Up economics: the disrupt model


Economies of Scale vs Learning Curve Is there a difference between the meanings of the terms "economies of scale" and "learning curve"?

The term "learning curve" is being used by cost estimators and refers (more or less) to the idea that businesses will have a higher cost per item if they make relatively few products but will have a lower cost per item if they make more products.

I thought this concept sounded similar to decreasing marginal cost within the economies of scale.  Unfortunately, I haven't been able to find information to prove that they mean the same thing.

Can anyone confirm?

Consider a production function

$$y = F(A,K,L)$$

where $A$ represent "technology" (in the broad sense including for example also organizational technology), $K$ is capital and $L$ is labor (again both broadly defined)

"Economies of scale" (a looser synonym of increasing returns to scale), is, in economics, always defined with respect to all arguments in the production function except technology.

We say that the production function exhibits increasing returns to scale if it is homogeneous of degree higher than one... but with respect to capital and labor only:

$$F(A, sK, sL) = s^{\delta}F(A, K, L), \;\; \delta > 1$$

Note that we have not multiplied $A$ by $s$. Note also that economies of scale is a static concept.

Let's turn to the "learning curve" concept: it uses the word "learning", presumably not by accident: but "learning" has to do with efficiency and not with scale.  And efficiency has to do with technology, which is the one aspect left aside when discussing economies of scale.

As a final note, I won't dispute the meaning for the "learning curve" that you report, but I have to say that it sounds strange to me: whenever I have encountered the concept, it was always in a dynamic setting, as a synonym of "learning by doing": as we spend more time with a production process, we become more efficient at implementing it (and even if scale of operations remains the same).

I understand that a falling average cost can of course come as a result of the above process, but the dynamic aspect is crucial, contrasted to a static one.

In fact, in my experience, in a static sense a greater scale of operations always eventually leads to increasing average cost, if we do not allow for time to pass, and so experience and efficiency to be gained, that can more than offset the inefficiencies that accumulate due to the complexity of operations at a larger scale.

The above do not refer to the "easy phase" of decreasing average cost at low initial levels of production due to the inescapable existence of fixed costs.


Information and search Consider a game where a decision maker (DM) has to choose action $l\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$.

The choice set $\mathcal{Y}$ has cardinality $L$. The state of the world is an $L\times 1 $ vector and we denote its $l$-th element by $V_l$.

The state of the world has support $\mathcal{V}$.

When DM chooses action $l\in \mathcal{Y}$, she receives the payoff $V_l$. That is, she receives a payoff equal to the $l$-th element of the vector $V$.

Let $P_V\in \Delta(\mathcal{V})$ be the DM's prior.

The DM may also process some signal (formalised by the concept of information structure) to refine his prior and get a posterior.

Let us define the concept of 1 player Bayesian Correlated Equilibrium provided in Bergemann and Morris (2013,2016,etc.).

$P_{Y,V}\in  \Delta(\mathcal{Y}\times \mathcal{V})$ is a 1 player Bayesian Correlated Equilibrium if

1) $\sum_{l\in \mathcal{Y}}P_{Y,V}(l,v)=P_V(v)$ for each $v\in \mathcal{V}$

2) $\sum_{v\in \mathcal{V}}V_l P_{Y,V}(l,v)\geq \sum_{v\in \mathcal{V}}V_k P_{Y,V}(l,v)$ for each $l$ and $k\neq y$.

Bergemann and Morris show  that the set of Bayesian Correlated Equilibrium is equal to set of optimal optimal behaviours under a range of information structures.

QUESTION: Consider a search model, in which we design a protocol according to which the DM discovers information about the state of the world.

For example, suppose that the DM engages in a sequential search where he discovers the $l$-th element of $V$ if and only if the maximum utility secured up to that moment is lower than a reservation value.

Can this model always be written as prior/information structure/posterior? In other words, does the framework of Bergemann and Morris nest search models?

The solution concept of Bayes Correlated Equilibrium applies to games, viz strategic interactions, between multiple players. Thus, in a single person decision problem its use seems to me inappropriate or at least superfluous. A lot of effort has been spent over the last 70 years (dating back at least to Blackwell 1951, 1953) to explore the notion of information and information structures in decision problems. In that literature lies your answer.

What you have described is a search problem that seems analogous to a Wald-like sequential sampling problem.

Perhaps refer also to the recently burgeoning literature on rational inattention. There, care has been taken in order to explore so-called "posterior separable" cost (of information) functions, which allows one to write the cost of information just as a function of the induced posteriors. See recent work by Caplin, Dean, and others.


What would be the GDP of Algeria without Oil & Gas? Facts :

*Algeria's GDP is 230 B$,
*Oil & Gas account for 30% (70 B$)

My simplistic reasoning would say : Substract 70 from 230 and get a new GDP of 160 B$.

But I know that the concept of GDP is more complex than that: it also includes government spending :

*Government consumption accounts for 30% (70 B$)
*60% of the budget comes from Oil & Gas : 42 B$

So I'll continue substracting: 160 - 42 = 118 B$, the new GDP...

But still, I think it's too high: the household consumption accounts for 35%. Most purchasing power comes from fake jobs created by the government, if there were no Oil & Gas these fake jobs would not exist.

Should I still substract this component from the total GDP?

Is my reasoning correct?

NB: All data come from this website (and I'm not sure if I picked up the right values):

If I interpret your question correctly, you're asking what percentage of Algerian national income is derived from oil and gas extraction. The answer appears to be 30% from the website.

I think the problem is you're assuming that the 30% figure means something like '30% of private spending', and so you're trying to account for government spending as well.

The website says 30% of GDP comes from oil and gas, that means 30% of income in Algeria is derived from oil and gas. It should already include government spending, which is taxed from income. And government spending should already include the fake jobs you mention.


Are there any studies that show that "Affirmative Action" hurts the economy? Are there any studies that show that "Affirmative Action" (an action or policy favoring those who tend to suffer from discrimination, especially in relation to employment or education) hurts the economy?

Based on personal research/reasoning, I believe that "Affirmative Action" could hurt the economy, but I would like to do more research on the subject.  Any links to (credible) studies showing that "Affirmative Action" hurts the economy would be greatly appreciated.

Very interesting question. Those at cafehayek.com seem to dislike it a lot but don't really back it up which is disappointing. At first glance, it is very easy to see how affirmative action could hurt the economy, and construction a model to show this would also be pretty straight forward.

See here(paywalll) (Moro & Norman, 2003). There is pretty strong intuition both ways so I'd think that any valuable study would be empirical.  This article looks pretty light empirically but does support the view you are looking for and provides a useful model.

  We consider a model of endogenous human capital formation with competitively determined wages. Discrimination is sustainable in equilibrium in the presence of two distinguishable, but ex ante identical groups of workers. An affirmative action policy consisting of a quota may ‘fail’ in the sense that there still may be equilibria where groups are treated differently. However, the incentives to invest for agents in the discriminated group are improved by affirmative action if the initial equilibrium is the most discriminatory equilibrium in the model without the policy. The welfare effects are ambiguous. It is possible that the policy makes the intended beneficiaries worse off: even if the starting point is the most discriminatory equilibrium the expected payoff may decrease for all agents in the target group.

Most work in this area suggests that the effects are welfare ambiguous/slightly positive.

This Paper (Leonard, 1990) discusses the idea that affirmative action does not work.

To borrow from the conclusion:

  Direct tests of the impact of affirmative action on productivity find no significant evidence of a productivity decline. However, since the productivty estimates are not measured with great precision, strong policy conclusions based on this particular result should be resisted.

This paper (Long, 2004) looks at the impact of the removal of affirmative action on college applications.

  This paper evaluates the behavioral response of college-bound high school seniors to changes in college affirmative action admissions policies during the late 1990s. After the elimination of affirmative action in California and Texas, the gap between the numbers of SAT score reports sent by non-minority and minority students to in-state, public colleges significantly widened...  predicts a large decrease in the number of reports sent by minority students and a large increase in non-minority score reports sent to top-tier public colleges as a result of changes in the students’ probabilities of acceptance.


How does monopoly affect the informational role of price? It is said in the textbook "Intermediate Microeconomics a Modern Approach" by Hal Varian that monopoly affects the informational role of price. What's the mechanism?

A foundational result from models of perfect competition is that the competitive market equilibrium (i.e. setting price and quantity such that supply = demand) is efficient. By efficiency we mean that the sum of consumer surplus and producer surplus are maximised.

This is actually quite an amazing thing! It means that each individual consumer buys the good if and only if the welfare he receives from doing so is greater than the marginal cost of producing the good. To see that this must be true, suppose that there were a consumer who values a good at more than the cost of production but did not buy it. Then it would be possible to increase welfare by having the consumer buy the good, contradicting the result that the equilibrium is optimal. Similarly, efficiency demands that sellers produce exactly as much as is necessary to sell to the consumers who will ultimately buy.

How could we get to this efficient point? One way would be to have economists calculate what is efficient and then publish this information so that people could look-up whether they are supposed to buy/sell or not. But wait! We know that there aren't economists running round telling consumers whether it would be efficient for them to buy or not. So how do people figure this out for themselves?!

The answer is that the equilibrium price contains all of the information that they need to figure out what is efficient. Since the equilibrium price is equal to marginal cost, and since consumers will buy if their willingness to pay is above the price, a consumer wishes to purchase if amd only if his willngness to pay is bigger than the cost—i.e. exactly when it is efficient for him to do so. Thus, one way to think about the role of a price in a competitive market is that it transmits information to market participants about the efficiency of a trade they are contemplating.

For a monopoly things are different because the monopolist breaks the direct relationship between price and marginal cost by setting $p>MC$. This means that some consumers who have a willingness to pay that satisfied $p>WTP>MC$. The fact that $p>WTP$ means the price is signalling to these consumers that they should not buy, even though it would be efficient for them to do so (because $WTP>MC$). In other words, the price is no longer directly informative about the efficiency of a trade, so one way to think about the effect of monopoly on prices is that it reduces their information content.

ADDENDUM:

It's still possible to calculate cost—and hence the efficient allocation—from the monopoly price, but we need more information. In particular, the monopoly price satisfies $$\frac{p-c}{p}=-\frac{1}{\eta},$$ where $\eta$ is the price elasticity of demand and $c$ is marginal cost. Thus, to figure out marginal cost we need know the price and the elasticity, whereas in a competitive market we only needed to observe the price.


Does scarcity apply only to commodities? I feel like Wikipedia may be misleading me in a subtle or egregious way.

The very first line of Scarcity is:  "Scarcity is the limited availability of a commodity..."

It does, of course, helpfully provide that "a commodity is an economic good or service that has full or substantial fungibility..."

My question, then, is:  Does it really make no sense in economics to discuss the scarcity of non-fungible goods?

(In the interest of full disclosure, my interest in the subject is mostly related to thinking around whether post-scarcity has anything at all to say about non-commodities, but that's quite a different set of questions.)

For completeness, you might want to include the definition of Fungibility as well:  "In economics, fungibility is the property of a good or a commodity whose individual units are essentially interchangeable, and each of its parts is indistinguishable from another part."

If you have a collection of objects, and each object is (in some relevant sense) interchangeable with any of the other objects, then they are fungible and thus a commodity.  If there aren't very many of them, they may be scarce.

However, if you have a collection of objects, none of which are interchangeable with any others in a relevant sense, then they are essentially unique objects.  You could still say that they were scarce (there is only one of each) but not that they are commodities... though in practice, people typically don't refer to unique objects as scarce.


Necessary and sufficient conditions for the existence of a utility function I was reading Jehle and Reny, Advanced Microeconomic Theory, where they discuss in detail, the choice problem of a consumer. The Consumption Set (or Choice Set) $X$ is a subset of $R_+^n$, is closed and convex and contains $0\in R_+^n$. They define a preference relation $\succeq$ on $X$ that satisfies completeness, transitivity and continuity. Then they argue that these conditions are sufficient for the existence of a continuous real-valued utility function that represents the preference relation $\succeq$.
I wondered if there are more general results about the existence of utility functions (continuous or not) to represent rational preferences. The theorem in Jehle and Reny has nothing to say about cases where the choice set does not satisfy the conditions assumed or when we simply do not care about the continuity of the utility function. For example, if $C= \{a, b, c\}$ is the choice set and the preference ordering is simply $a, b, c$ (the preference relation is accordingly defined), then $u: C\rightarrow R$, $u(a)=10, u(b)=2.5, u(c)=\frac{\pi}{100}$ is a legitimate utility function, but the theorem in Jehle and Reny does not say anything about these cases. Again, the famous lexicographic preferences (that satisfy rationality but violate continuity) have no utility functions, but Jehle and Reny's theorem does not tell us anything about it. I wanted to know the most general necessary and sufficient conditions for the existence of utility functions, that also cover these and other possible cases.
Formally, let $C$ be the set of all conceivable choices (no conditions on it assumed so far), and let $\succeq$ be a binary relation on $C$ that satisfies completeness and transitivity.
What are the necessary and sufficient conditions that $C$ and $\succeq$ must satisfy, so that a utility function from $C$ to $R$ that represents $\succeq$ exists?
I would appreciate both proofs and/ or reference materials for this, or even partial solutions.

The following is essentialy due to Debreu. The result is formulated in terms of linear orders, but each complete and transitive relation induces a linear order on the indifference classes:
Theorem: Let $S$ be a set and $\preceq$ be a linear order on $S$. Then $\preceq$ has a utility representation if and only if there exists a countable set $C\subseteq S$ such that whenever $x\prec y$, then there is some $c\in C$ such that $x\preceq c\preceq y$.
Proof: To see that the condition is necessary for the existence of a utility representation, let $u$ be a utility representation of $\preceq$. Call $(x,y)\in S\times S$ a jump if $x\prec y$ and there is no $z$ such that $x\prec z\prec y$. We show that the set of jumps is countable. Clearly, if $(x,y)$ and $(x',y')$ are both jumps, then $\big(u(x),u(y)\big)$ and $\big(u(x'),u(y')\big)$ are disjoint intervals of real numbers. Each such interval contains a rational number, so there is an injective function from jumps to rational numbers and so the set of jumps is countable. Let $J$ be the set of all elements of $S$ that occur as the first or second coordinate of a jump. Clearly, $J$ is countable too. Let $$Q=\Big\{(q_1,q_2)\in\mathbb{Q}\times\mathbb{Q}:q_1<q_2, u^{-^1}\big((q_1,q_2)\big)\neq\emptyset\Big\}.$$ The set $Q$ is countable. For each $(q_1,q_2)\in Q$, choose some $s\in  u^{-^1}\big((q_1,q_2)\big)$ and let $B$ be the set of such $s$. $B$ is also countable and we can choose $C=B\cup J$.
Now we show that the existence of such a set $C$ is sufficient for the existence of a utility representation. Without loss of generality, we can take $C$ to be nonempty and write $C=\{c_0,c_1,\ldots\}$. Now define $u$ by $$u(x)=\sum_{n:c_n\preceq x}\frac{1}{2^n}-\sum_{n:c_n\succeq x}\frac{1}{2^n}.$$
$\square$
A comprehensive source for all things existence of utility functions is the book Representations of Preferences Orderings by Douglas S. Bridges and Ghanshyam B. Mehta.


What Level of Government Debt to GDP Ratio is Sustainable? I was reading that Japan has a debt to gdp ratio of 240pc and I cannot understand why this has not left the country "bankrupt"? From looking at this like an ordinary person this level would be completely unmanageable. Furthermore, considering Greece had problems with its national debt with a debt to gdp ratio of less than 200pc I am not sure how Japan has sustained significantly higher ratio for so long? Therefore my question is what makes a certain level of debt to gdp ratio sustainable? Also who does the government owe the debt to and does it matter who they borrow from? ie domestic vs international.

For interest see the following graph,

As you have pointed out: where it comes from is very important. As to the Japanese situation it is quiet different from the US position from example. In fact most of the Japanese debt is owned by Japanese people (90% of the current debt). More specifically the BoJ plays a big role as a buyer, and puts pressure on Japanese yield, which makes it cheaper for the government to issue bonds !

Another interesting point that is usually left by anlysts: Japan is the biggest creditor in the world. The country holds a net amount of about 3 trillion USD (367 trillion yen) of financial assets through the world, which makes Japan the first creditor worldwide (before China !).

An interesting further reading which gives other information on the Japanese debt under stress tests of the IMF (P.40): https://www.imf.org/external/pubs/ft/scr/2015/cr15197.pdf

You also might want to read this paper of Rogoff and Reinhart called "Growth in a time of debt": http://www.nber.org/papers/w15639 . It was really criticized but is a good first glimpse... Afterwards you might want to go a little bit deeper into the debt sustainability analysis of the IMF...

Edit

The reference of Rogoff is more an introduction to the comprehension of debt dynamic than an argument for the existence of a threshold than would reduce growth. On the controversy of the paper, like pointed out by @dv_bn, you can check this intersting article: http://www.newyorker.com/news/john-cassidy/the-reinhart-and-rogoff-controversy-a-summing-up
Thanks to @denesp: Whenever you see "first creditor" this usually takes public and private assets into account. However, if you want to analyze the public debt you should only take financial assets owned by the government (mostly T-Bills regarding Japan).
I add also an interesting article I have read about it, which was written by economists from the NY FED, check it out: http://libertystreeteconomics.newyorkfed.org/2016/06/the-rapidly-changing-nature-of-japans-public-debt.html#.V2qJW2r2aM8


What are some of the economic arguments for gender-neutral marriage? What are some of the economic arguments for same-sex or gender-neutral marriage (GNM)?

Which arguments have merit, don't have merit or have yet to be decided/tested?

For example, it is hypothesized that 'Legalising gay marriage could give the economy a \$1 billion boost', at least in Australia. Also, apparently, 'Gay marriage boosts NYC's economy by $259 million in first year'. Will such benefits hold elsewhere?

tl,dr: I don't see an economic argument for GN marriage, or marriage in general what-so-ever.

Frictionless environment

All spending on marriage, are nothing more than consumption goods. There is no reason to believe that marriage-related spending have a higher Keynesian multiplier than other consumption categories.

As long as this is the case, as @denesp argues, "money spent on marriage" is money that would instead be spend on different consumption goods. Legalizing marriages would be a boost to the economy, and useful in crises and slumps - but again, by Keynesian logic, the same would be true for burying money in the ground. There is no reason it has to be marriage specifically.

But

However, the real world is no frictionless environment.

To the extent that there are different tax rates for married couples, which set up incentives for working more, increasing the size of the married population may increase total output. But then again, the welfare improving solution is not to increase the share of married couples, but removing tax benefits for married couples.
There may be "efficiency gains" from being married. This is the only possible "real" economic argument: If, being married, and having a state-legalized marriage contract makes people very happy and productive workers, increasing the size of the married population will increase TFP. However, this is a very big if, and I am not aware of research supporting this. In contrast, happiness research seems to indicate that the impact of positive or negative events fades away quickly, and an invididuals "happiness" moves back to average levels quite quickly, even in case of losing a leg (Brickman et al, 1978;   ungated)


demand curve shift in a monopolistic competitive market As more firms enter the market, the quantity demanded at a given price level will thus decline. Therefore, the perceived demand curve for any individual firm will continue to shift leftward until the excess profit dries up.

But my question is, will the slope of the demand curve change as it moves leftward?

Also, there's something that caught my eyes when studying this chapter. I understand that the demand curve won't stop moving to the left until the excess profit disappears. And by that point, the following two statements will be satisfied: (a) the demand curve will be tangent to ATC, and (b) MR=MC.

But I am wondering, is it possible that the demand curve intersects ATC at a point where MR = MC?

But my question is, will the slope of the demand curve change as it moves leftward?
The slope does not change because one assumes that relative prices and consumer preferences do not change. This is a ceteris paribus interpreation you want to see what happens when new competitiors enter the market (keeping everything else as it is). There are the same consumers buying the same productons but simply less (in numbers) for that single firm. Graphically the demand curve makes a parallel shift to the left.
But I am wondering, is it possible that the demand curve intersects ATC at a point where MR = MC?
Since graphs are easier to understand than text i made a little drawing, let $D'$ be the competitive demand and $D$ the demand line that intersects the ATC (your question):

The short answer is no. The longer one is, that it is not an optimal outcome. Remember that $(P_m - ATC(Q_m)) \cdot Q_m$ is the potential profit of the firm (This is simply the difference between the ATC and demand curve, the red lines in the graph). If the demand curve interesects the ATC, there will be opportunity for the firm to change its production plan and make a positive profit. This changes the MR curve, new equilibirum will statisfy MR=MC but it will not be at the intersection point of demand and ATC curve (Points A and B). The optimal monopolistic quantity will always be greater A and smaller B because between those two points profit is greater than at the intersection points itself.


Are corporations essential components of a free market economy? There seems to exist a rarely-stated assumption that somehow corporations are an essential element of a free-market economy, and that they benefit a nation's economy. However, I wonder if this is really true.

Here, I am speaking of the US form of a corporation which allows a small number of people to control capital contributed by a large number and also allows those same people to disavow responsibility for the debts and liabilities of the corporation.

In the Wealth of Nations, Adam Smith deprecated any kind of joint stock companies, writing that a man would be much more careless with other people's money than his own. By this logic one might see corporate law as a way for elites to exploit society parasitically and corporate law as a damage to the economy instead of a benefit.

Is there any theoretical validity to this kind of view?

A classic reference that is somewhat related is Ronald Coase's "The Nature of the Firm". Coase set out to address the following puzzle: since markets are efficient, why do we need to organize into firms? Couldn't we just have each individual acting alone and rely on the market to put the pieces together into complete products? Coases answer to why this wouldn't work well was transaction costs. If there is a (small) cost to engaging in market transactions then the aggregate cost of the many transactions needed to assemble complicated products will be prohibitive. The solution, argues Coase, is to form an organization (a firm) within which all of these transactions can take place without recourse to the market.

Coase's reasoning has been expanded in the 80 years since its publication. Notably, Oliver Williamson did important work to dig into the details of the conditions that make organizing work within a firm especially attractive. He argued that firms should be most likely to form when work is relationship-specific and when there are significant difficulties in writing and enforcing contracts. A great summary of Williamson's work can be found here.

Both Coase and Williamson received the Nobel prize for this work.


Is a hyperlink a kind of informational public good? Links analysis algorithms on the web take the incoming links to a webpage as a sign of its popularity. Given this, can we consider web hyperlinks, in aggregate, as a kind of public good? I am curious if anyone has looked at it from this perspective.

In the Samuelson's definition of public good, the good must be non-excludable and non-rivalrous.

Hyperlinks (if public and pointing to public pages) are non-excludable, and --to the condition of not overloading the hosted content-- non-rivalrous.

The frequency of publication (and other criterions) of hyperlinks pointing to specific pages/domain, is used by ranking algorithms as a proxy of relevance for the users.

Hyperlinks through ranking algorithms create a positive externality (i.e. access to more relevant web-pages).
To the extent that the access to the result of those ranking algorithms is not excludable (you don't need to log in the use google, duckduckgo, etc), you can say that the result of this positive externality is a public good.