How does a mortgage-backed security issued by a bank allows it to borrow cheaper and make more loans? I am currently reading a book called "Austerity, the history of a dangerous idea" by Mike Blythe. I am not an economist, but I am interested to learn more.

Blythe writes (p.24):

  "The old 3-6-3 model presumed that the bank that issued a loan to a
  customer held the loan until it was paid off, with profits accruing
  from the interest payments it received. But what if these loan
  payments could be separated out and sold on to someone else? What if
  many such loans, mortgages for example, could be bundled together as a
  pool of mortgage payments and sold to investors as an
  income-generating contract called a mortgage-backed security? That
  way, the bank that issued the loan could borrow cheaper and make more
  loans because the risk of the loan not being paid back was no longer
  on its books, and the borrower would get better rates. It was win-win,
  as they say."

I don't understand how selling them to investors can borrow money cheaper. Is it the investors' money directly? For example, if I am a bank, can I raise private capital (i.e. from investors) with the agreement of giving them a mortgage-back security?

Thank you for your input!

Here are two ways by which selling mortgage-backed securities (MBS) benefited banks:

The MBS is less costly (or equivalently, more valuable) in the hands of the investor than in the hands of the bank.
The investor is misinformed/misled about the MBS and overpays for it.

Analogy for #1: When you buy car/fire/health/whatever insurance, you transfer the risk to another party (the insurance company) for whom that same risk is less costly (for example because they are able to pool/diversify risk across large numbers). This is the traditional, orthodox "markets are good" view. In this view, MBS's were a good development that further and more efficiently spread out risks and benefited everyone.

Analogy for #2: You suspect you have cancer and go buy some expensive health insurance. So you transfer this toxic asset (or risk) to another party (the insurance company) who, not knowing what you know, incorrectly judges the magnitude of this risk. This is to a large extent what actually happened.

(Note though that #1 and #2 are not mutually exclusive possibilities. Some of both probably did occur and continue to occur. But unfortunately, leading to the financial crisis, more of #2 and less of #1 occurred than was ideal.)


Getting up to Date on Macro I have undergraduate level experience in macroeconomics...but I want to do some further learning to try and acquaint myself with where mainstream macroeconomics is at the moment in the hopes that I can understand the economy better. I understand that most macroeconomics is highly mathematical at this stage and I have no problem with this, but a more intuitive/wordy/theoretical approach would be preferred.

Are there any good online lecture notes, textbooks etc. for this sort of thing?

A good site, with high quality online lectures, is the MIT Open Course Ware.

You will find courses going from Principles of Macroeconomics, Economic Growth, Macroeconomic Theory I, II, III to Advanced Macroeconomics I or II.


Slutsky Decomposition from Indirect Utility Function Given the indirect utility function:
V={M^2}/{4P1P2},
how do we establish the Slutsky Decomposition?
I used Roy's Identity to get the Demand, but I'm stuck with the other components of the Slutsky Equation.

Since you already know the demand correspondences, you can use use the duality principle as follows: $v(\textbf{p},e(\textbf{p},u)) = u.$ Using this we get $\frac{4e(\textbf{p},u)}{p_1p_2}=u$, or $e(\textbf{p},u)) = \frac{up_1p_2}{4}.$ Now, using Shephard's Lemma, we can obtain the Hicksian demands as: $\frac{\partial e(\textbf{p},u)}{\partial p_i} = h_i(\textbf{p},u)).$

However, the job is not yet done. You might get stuck with the $u$ while evaluating the Slutsky's equation. In other words, you need to find the utility function as well. The demand correspondences are(I hope you've obtained the same expressions) $x_1(p_1,p_2,m)=m/2p_1$ and $x_2(p_1,p_2,m)=m/2p_2$. Since the indirect utility function is homogenous of degree zero, you can further write it as $v(p_1,1,m)=v(p,m)=m^2/4p=(m/2).(m/2p).$ From the demand correspondences obtained, you have to represent $m/2$ and $m/2p$ in terms of $x_1$ and $x_2$ ($p_2=1$, as a consequence of homogeneity of $v(p_1,p_2,m)$), and substitue it back into the indirect utility function. Thus, we obtain the the utility function $U(x_1,x_2)=x_1.x_2$(since we obtain the indirect utility function by substituting the walrasian demands into the given utility function, backtracking the same steps gives us back the utility from the indirect utility). I think now one can easily evaluate the Slutsky's Equation.


Is there collaboration between cyber criminals and banks? In disease evolution, one often finds that bacteria and viruses evolve to co-exist with their hosts and become less malevolent. Making an analogy between cybercrime and disease, I am wondering if there can be a symbiotic relationship between banks and cyber criminals?

Here is a more specific example of something I'm wondering about. A cyber criminal with access to a bank's books adds a bunch of car loans in various states of repayment. He then transfers the outstanding amounts of all these loans to himself. Then, at the end of every month, he doctors the bank's books to look like the loan payments have been made. If the bank were to detect such activity, it might be very reluctant to do anything. Doing anything, the result would be default on a large number of authentic looking loans. Doing nothing, the bank would continue to receive for all intents and purposes interest payments on its loans.

To some extent, I have confusion about what is real about any of this money that is changing hands. Can't a cyber criminal increase/decrease a bank's holdings just by changing a number in a computerized ledger book?

The vast majority of cyber crime is fraud. The criminals don't hack the bank directly; rather they hack the customers of the bank and commit fraudulent transactions.

I strongly doubt there is active collaboration. Some criminals may have insider contacts, but that's different to a symbiotic relationship.

There may be an effect somewhat like you mention. Increasing security is expensive for banks, so it is only worth doing if they are experiencing a certain level of losses. In theory it would make sense for criminals to restrict their level of activity, to avoid banks implementing additional security, which would make their job harder. In practice I don't think this happens, because their are multiple cyber gangs and I strongly doubt there is a gentleman's code between then.

It is theoretically possible for someone to hack the bank itself, and directly modify balances - effectively creating money out of thin air. In fact, it is thought that some major nation states (mostly US and China) have penetrated many banks around the word. However, if they started to extract money, this is likely to be noticed, due to internal checks and balances. It is more valuable for these state-sponsored actors to silently remain present, capturing information. And one day, perhaps they will strike, as part of a larger war strategy.


Why can't I find masks for the corona virus? Not an economist by far, just a layman, and that's a layman question.

How is this possible that it's difficult to find mask for the Corona Virus? I have been several times to 7/11, boots, Watson, and other pharmacies, and everytime they did not have it as they ran out. How is it possible that the producers of masks give up on additional earning by not producing more masks, now that it's pretty obvious the demand is going up?

The fact that there are not enough masks is my personal experience in Bangkok - however, some friends of mine have the same experience in Italy, where the Corona Virus outbreak has reached a scary stage.

Generally. I would explain capitalism failure by pointing at government regulations - however in this case I don't see how the government can be involved into mask production.
Any idea?

The supply of masks can't keep up with soaring demand because mask producers have capacity constraints in the short run. See this recent article.


Is there something that does not change its value that can be used to measure currency inflation? Currency is represented as an exchange for something valuable, whether it be an object or work.

Prices for objects can change over time, depending on demand and supply, making objects unreliable to measure inflation. Most countries use precious metals to measure or establish currencies, but the prices for metals can also change over time. The amount of work it takes someone to complete a task depends on their physical and mental abilities, in which no two humans are the same.

Is there something that does not change its value that can be used to measure currency inflation?

TL;DR -- No

Now for the fun part.  No!  No-no-no-no-no!  And here's why...

Conditions change.  Any commodity you can name will change in value over time, as various things happen:

People stop wanting it (I mean, you can buy myrrh these days, but it's not a hot-ticket item)
The availability changes (New mines show up, or old ones shut down)
People start wanting it (use of gallium really spiked when electronics came along)

But wait!  How about gold?  It's been in demand for like evah, right?  Well.  Let's look at the inflation-adjusted price of gold, just for the last century:

Maybe you could try something like "one day's rations", ie enough food to feed the metric standard guy for one day.  Of course, as agriculture gets more efficient...  Hmm.  The US gov't uses a "standard grocery basket" to measure inflation, that works ... okay, though politics occasionally sneak in.

Anyway.  Short story -- nope.


Net Present Value in Nominal Terms I have the following question from my homework:

When calculating the net present value of an investment project, the firm of Henry & Norman expects profit in the first year to be $60,000, and they expect real profits to remain at that level over the next five years.
Since they are using nominal discount rate of 11 percent in their net present value calculation, they want to convert future real profits to nominal profits.  They expect inflation to be 4 percent per year over the next five years.
The nominal profit for year 2 of the investment project is ___________(correct answer, 62,400)
If the investment project has an initial cost of 200,000, the net present value in nominal dollars is _________  (my answer 64,474.50  book answer 38,264.90)

The difference between the book answer and my answer is that I used 60,000 as year 1 profit with no discount.  I realized this was incorrect according to the given methodology in my textbook of $NPV=-C+\pi_1/(1+R)+\pi_2/(1+R)^2+...$
What I don't understand is why we discount the profits in year one but don't consider inflation in year one.  This seems inconsistent to me.  Why do we discount the real profit in the first year and not the nominal profit, or if we assume nominal profits in year one are the same as real profit, why do we discount in year one?

What I don't understand is why we discount the profits in year one but
  don't consider inflation in year one. This seems inconsistent to me.
  Why do we discount the real profit in the first year and not the
  nominal profit, or if we assume nominal profits in year one are the
  same as real profit, why do we discount in year one?

As you said, the firm

  expects profit in the first year to be $60,000, and they expect real profits to remain at that level over the next five years.

They are expecting both real and nominal profits (because they do not explicitly state only one or the other) to be \$60,000 for year one but they need to calculate NPV for $T_0$, thus they need to discount the \$60,000 for a single year (and the others for an additional year).

We're realizing the profit as income starting in $T_1$, and realizing the initial capital expenditure at time $T_0$.

$T_0$----------$T_1$--------$T_2$--------$T_3$--------$T_4$--------$T_5$
-200000 + 60000 + 60000 + 60000 + 60000 + 60000 Real
-200000 + 60000 + 62400 + 64896 + 67492 + 70192 Nominal
-200000 + 54054 + 50645 + 47451 + 47451 + 41655 Nominal Discounted

Calculated in Python:

>>> -200000 + sum(60000 * (1.04**i) / (1.11**(i+1)) for i in range(5))
38264.90224378838

As to the reason the authors of the question gave these conditions, I presume that they want to ensure that you can quickly arrive at the correct calculations based on seemingly trivial but important details. I recall a similar trick in a corporate finance final, where a careful reading of the question indicated that a speedy reading of the question (one that I initially made and expected most of my peers would make) would result in an off-by-one time period mistake.


Obligations of a company Any company may "feel" obligated towards several parties at once:

its shareholders
its employees
its customers
its partner companies (sub-contractors and suppliers)
its country and social environment (if it is based in one country)
(wo)mankind in general (present and/or future)
environment in general (locally and/or globally)

I wonder if this list is kind of complete - or if I've overseen important parties (what about the company itself as an economic subject?) - and more important: If there are schemes to display such obligations (traffic light rating system or pie charts - depending on obligation being an extensive or intensive property) - and where I can find them realized.

A company makes decisions that have positive NPV. No list will ever be completely exhaustive since obligations are not necessarily zero-sum.

How do you increase profits for the shareholders? Mostly by taking care of the customers. How do you win customers? One way is to portray your company as environmentally friendly. This, in turn, helps the (wo)mankind and the nation. Do you see how it all pretty much ties together?

Of course, for a given company, one thing may be more important than the other.


Relationship between the Lagrangian and consumption euler equation? I think that the best way for me to ask my question would be to start with an example.

Suppose that consumers have a two-period horizon and their instantaneous utility is:
$\:$

$U(C_{t})=ln \: C_{t}$

$\:$

Where $C_{t}>0$$\:$ denotes consumption. Assume that agents supply a fixed amount of labour $L$ and have no initial bonds $B$ or capital $K$. Agents discount utility of the second period with the discount factor $1>\beta>0$.
$\:$

The budget constraint is:
$\:$

$C_{1}+\frac{C_{2}}{1+r_{1}}$ =$\:$ $(w/P)_{1}$$L$ $\:$ + $\frac{(w/P)_{2}L}{1+r_{1}}$
$\:$

The Lagrangian is:
$\:$

$\mathcal L = \ln C_1 + \beta \ln C_2 - \mu \left[ C_1 + \frac{C_2}{1+r_1} -(w / P)_{1} L - \frac{(w/P)_{2}L}{1+r_{1}} \right]$

I now have two questions:

Assuming that I compute the correct FOCs, how do I go about deriving the consumption euler equation?
$\:$
Could you guys please help me with the formatting of my lagrangian?
I want to make the square parentheses large enough to encapsulate everything.
$\:$

Thanks.

In this simple problem, using a Lagrangean is an overkill, direct substitution of the constraint is perhaps better.

Anyway, treating the two consumption levels as two distinct decision variables under the budget constraint, the Euler equation emerges from the combination of the two first-order conditions:

$FOC$'s

$$\frac {\partial \mathcal L}{\partial C_1} = 0 \Rightarrow \frac 1{C_1} = \mu$$

$$\frac {\partial \mathcal L}{\partial C_2} = 0 \Rightarrow \frac {\beta}{C_2} = \mu\frac {1}{1+r_1}$$

Substitute the first into the second

$$\frac {\beta}{C_2} = \frac 1{C_1}\frac {1}{1+r_1}$$

re-arrange and you 're done.

I would suggest to also do that with a general utility function, where in the Euler equation the first derivatives of the utility will appear.


Good books to learn social choice theory I wanted to learn Social Choice Theory and have fine mathematical background. I have read about it as a part of advanced microeconomics (Jehle and Rene)- Arrow's Impossibility Theorem etc. and got intrigued by it.

What are some good books to read to know more about Social Choice Theory and in particular, the mathematics of voting systems?

Start with:

A primer in Social Choice Theory, by Wulf Gaertner.

If you want more, have a look at:

Welfare Economics and Social Choice Theory by Allan Feldman and Roberto Serrano

To dig deeper:

Handbook of Social Choice and Welfare
By A. Sen, Kotaro Suzumura
Handbook of Social Choice and Voting by Jac C. Heckelman, Nicholas R. Miller
Handbook of Computational Social Choice by Ariel D. Procaccia, Jérôme Lang, Felix Brandt, Vincent Conitzer, Ulle Endriss
The Handbook of Rational and Social Choice by Clemens Puppe, Prasanta Pattanaik, Paul Anand

For good or bad reasons, there are also entire books dedicated to the specific method of "approval voting" (which tend to discuss other methods as well as a way to enable comparisons):

Approval Voting by Brams and Fishburn
To dig deeper: Handbook of Approval Voting, by M. Remzi Sanver, Jean-François Laslier

To branch out into the neighboring disciplines of mechanism and market design:

Multiagent Systems, Algorithmic, Game-Theoretic, and Logical Foundations, by Yoav Shoham and Kevin Leyton-Brown
Essentials of Game Theory, A Concise, Multidisciplinary Introduction, by Yoav Shoham and Kevin Leyton-Brown (some redundancies with previous reference)
Auction Theory, by Krishna
Market Design, Auction and Matching, by Haeringer


Can we have a Non-Reflexive Preference Relation? I've been thinking about preferences alot recently and have been specifically thinking about the reflexivity requirement.

That is:
$$x \succsim x$$

Though this is apparent and obvious, I have been wondering why this is a required condition for rationality and if its possible to have a preference relation that is complete but non-reflexive.

Is it possible?

Rationality requires the following:

Completeness

For all $x, y \in X$, either $x \succsim y$ or $y \succsim x$ or both.

Transitivity

For all $x, y, z \in X$, if $x \succsim y$ and $y \succsim z$, then $x \succsim z$.

Also note that if $x=y$ then completeness implies that $x\succsim x$. So reflexive preferences follow from completeness. So I would say Completeness and Transitivity are required for rationality. Reflexive preferences just follow from complete preferences.


Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation Why is the partial derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2)$ for $p_1$
$$
\frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2)}{\partial p_1}=\frac{\partial x_1(p_1,p_2,\overline{m})}{\partial p_1} +\frac{\partial x_1(p_1,p_2,\overline{m})}{\partial m}\overline{x}_1
$$
where $(\overline{x}_1,\overline{x}_2)$ is the bundle originally demanded at prices $(\overline{p}_1,\overline{p}_2)$ and income $\overline{m}$ and $x_1^S$ is the Slutsky demand function for good 1 and $x_1$ the Marshallian demand function for good 1?
I understand that $m=p_1\overline{x}_1+p_2\overline{x}_2$ because the pivot ensures that the consumer is still having enough income to purchase his old bundle $(\overline{x}_1,\overline{x}_2)$.
Chapter 8 of Varian shows this to derive the Slutsky equation using calculus. I don't understand the right side of the equation.
I know that $p_1\overline{x}_1+p_2\overline{x}_2=m$ and $\overline{p}_1\overline{x}_1+\overline{p}_2\overline{x}_2=\overline{m}$ where $m$ is the new budget.

This is more of a calculus question. Recall the total differential of a function $f(z_1,z_2,z_3)$:
\begin{equation}
\mathrm df(z_1,z_2,z_3)=\frac{\partial f(z_1,z_2,z_3)}{\partial z_1}\mathrm dz_1 + \frac{\partial f(z_1,z_2,z_3)}{\partial z_2}\mathrm dz_2+\frac{\partial f(z_1,z_2,z_3)}{\partial z_3}\mathrm dz_3.
\end{equation}
Hence,
\begin{equation}
\frac{\mathrm df(z_1,z_2,z_3)}{\mathrm dz_1}=\frac{\partial f(z_1,z_2,z_3)}{\partial z_1}\frac{\mathrm dz_1}{\mathrm dz_1} + \frac{\partial f(z_1,z_2,z_3)}{\partial z_2}\frac{\mathrm dz_2}{\mathrm dz_1} + \frac{\partial f(z_1,z_2,z_3)}{\partial z_3}\frac{\mathrm dz_3}{\mathrm dz_1}
\end{equation}
Applying to your case, we substitute $p_1$ for $z_1$, $p_2$ for $z_2$, and $\overline m$ for $z_3$ (noting that $\overline m(p_1,p_2)$ is a function of the prices):
\begin{align}\require{cancel}
\frac{\mathrm dx_1(p_1,p_2,\overline m)}{\mathrm dp_1}&=\frac{\partial x_1(p_1,p_2,\overline m)}{\partial p_1}\cancelto{1}{\frac{\mathrm dp_1}{\mathrm dp_1}} + \frac{\partial x_1(p_1,p_2,\overline m)}{\partial p_2}\cancelto{0}{\frac{\mathrm dp_2}{\mathrm dp_1}} + \frac{\partial x_1(p_1,p_2,\overline m)}{\partial \overline m}\frac{\mathrm d\overline m}{\mathrm dp_1}\\
&=\frac{\partial x_1(p_1,p_2,\overline m)}{\partial p_1} + \frac{\partial x_1(p_1,p_2,\overline m)}{\partial \overline m}\overline x_1
\end{align}


Choosing the nondominant strategy in a duopoly Would a company ever choose a nondominant strategy in a duopoly?

Let's take this specific example (2007 AP MicroEcon B #2). Two airlines, Airtouch and Windward, are scheduling flights for either morning or evening. There is no collusion, but both airlines know the same profit matrix, as below. (edit: This is also a one-shot game)

                           Windward
           Profit      Morning | Evening
                   ----------------------
           Morning | 1000, 700 | 700, 600
Airtouch           ----------------------
           Evening | 750, 950  | 900, 800

Windward has a dominant strategy of choosing the morning; Airtouch has no dominant strategy.

Airtouch, of course, is dependent on Windward for its decision. If Windward's best decision is morning, Airtouch will choose morning. Same for evening.

If we go with the given solution, Windward would choose the dominant strategy of morning, and Airtouch would then have to go with the morning as well.

But then Windward (and Airtouch, since they have all the same information) realizes that Airtouch is entirely dependent, so if Windward chooses the non-dominant strategy of the evening, it will have a greater profit (800) than it would in the morning (700), even though it is not the dominant strategy.

So then both would go for the evening.

Is there something wrong with this reasoning? Particularly, is Airtouch necessarily dependent if Windward has a sketchy dominant strategy like this? I would think that since Windward begins with the dominant strategy, it holds the initiative, but I'm not certain.

(This, of course, assumes perfect reasoning on both sides, which in real life is definitely not a justifiable thing to presume.)

It seems you interpret the game as a sequential game. If Windward would know that its move was observed by Airtouch it would act as you say. But this is not the case, they move simultaneously, and it is a one-shot game (as defined it is only played once).

Given your reasoning, Windward understands the situation and hence it would choose the evening. Anticipating this Airtouch would do the same. But Windward does not really want to choose the evening. If Airtouch anticipates that Windward will choose the evening that's jolly good for Windward. It is even better if Windward goes on to choose the morning. So what you describe is not an equilibrium outcome and is unlikely to occur in a one-shot situation.

Don't believe me? Let's play. As Windward I understand your reasoning and I make the empty promise of choosing 'Evening'. What will you choose? (And me?)

The situation would be different if the game was repeated, so if reputation was important or if, as I mentioned before, the game was sequential and moves could be observed.


RBC model and indivisible labour First of all, I would like to apologise for the fact that I will include a link in my question rather than a direct question, however, I have no idea how to do it in a different way.

I have been reading this paper recently:
RBC extensions
,

I don't understand one thing completely. On the second page when we are reducing the equation for utility, why cannot we just drop the term:
$$\theta \frac{(1)^{1-\xi}-1}{1-\xi}$$
I was wondering how this could possibly work, because common-sensically:
$$(1)^{1-\xi}=1 \Rightarrow \theta \frac{(1)^{1-\xi}-1}{1-\xi}=0$$
Am I wrong?

Thank you guys!

The only reason I can see right now could possibly be pedagogical. While that term does indeed just equal zero, there could be generalizations where the agent works a high amount with probability $\tau$ and a low, but positive, amount with probability $1-\tau$. In this case, the term would still go through. There are also plenty of functional forms that would result in that term not being zero (taking away the -1, for example, which is often done in applied work). At any rate, this is an idiosyncratic enough case that the professor might have thought it best to show the process of rearranging terms for future reference and to give help with other scenarios. On the other hand, he may just not have noticed it. :)


What are the mathematical constants used in economy formulas? For the calculation of the taxes, the rate is the coefficient of proportionality.
This coefficient is constant because

  It is the value of the ratio between a quantity and another that is constantly repeated in a set of values.
  It is a constant value which is in direct proportional functions or reverse, quadratically proportional or inverse

Other examples of this type in macroeconomic, finance, commercial.. ?

P.S - I refer both type of constants: specific fixed numeric value and as constants in economic theory

Economics is not an exact science and so we don't have Physical Constants i.e. quantities with a universal fixed numerical value.

That said, there are many concepts in economics that predominantly appear as constants in economic models (although in principle they can vary between individuals or across time, and there exists research that explores what happen when they do vary).

Well-known examples include the depreciation rate of capital (usually $\delta$), population growth rate (usually $n$), the rate of pure-time preference (usually $\rho$).

In calibration studies (either purely simulated or combined with empirical data), such constants tend to be assigned widely used "benchmark values" (i.e. quasi- "fixed values") that come from empirical experience usually supported over some decades of data and many countries. For example when calibrated and not estimated we often see $\delta =0.05$, $n=0.01$, $\rho=0.02$.

On another front, Euler's $e$, the base of the natural logarithms, emerges naturally when calculating compound interest rate continuously (and not in discrete intervals). Assume we make a deposit $D$ at yearly interest rate $r$. If interest is calculated once per year, at the end of one year we will get $D(1+r)$. Assume now that we calculate interest monthly, add the interest to principal and then next month calculate interest again. After one year we will get

$$D\left (1+ \frac {r}{12}\right)^{12}$$

In general if we partition the year in $n$ periods we will have

$$D\left (1+ \frac {r}{n}\right)^{n}$$

and if we let $n$ go to infinity we get

$$\lim_{n\to \infty}\left (1+ \frac {r}{n}\right)^{n} = e^r$$

Finally, there are certain "stylized facts" , according to which various economic ratios appear to be "stable" (if not strictly "constant") over time, like the income share of production inputs, or the capital/output ratio. The seminal reference here is

Kaldor, Nicholas, “Capital Accumulation and Economic Growth,” in F.A. Lutz and D.C. Hague, eds., The Theory of Capital, St.Martins Press, 1961, pp. 177–222.

while see

Jones, C. I., & Romer, P. M. (2010). The new Kaldor facts: Ideas, institutions, population, and human capital. American Economic Journal: Macroeconomics, 2(1), 224-245.

for extensions and updates.


Blackwell's Sufficiency Conditions for a Contraction: I wondered if anyone could throw some intuition on Blackwell's sufficiency conditions:
(1) Monotononicty;
(2) Discounting;
Would be genuinely appreciated to hear both terms expressed in plain English.

Let $X$ be a nonempty set, $B(X)$ be the space of bounded functions from $X$ to $\mathbb{R}$, and $\|\cdot\|_\infty$ the sup-norm on $B(X)$. Write $f\leq g$ for $f,g\in B(X)$ if $f(x)\leq g(x)$ for all $x\in X$. Let $\mathbf{1}\in B(x)$ be the function with constant value $1$.
Here is the result of Blackwell:

Theorem: Let $T:B(X)\to B(X)$ be a function such that for some $\beta\in(0,1)$

Whenever $f,g\in B(X)$ satisfy $f\leq g$, then $T(f)\leq T(g)$ (monotonicity).
For all $f\in B(X)$ and $\alpha\geq 0$ one has $T(f+\alpha\mathbf{1})\leq T(f)+\alpha\beta\mathbf{1}$ (discounting).

Then, $\|T(f)-T(g)\|_\infty\leq \beta\|f-g\|_\infty$ for all $f,g\in B(X)$.

The following argument should make things a bit more transparent. Take $\alpha\geq 0$ large enough that both $f\leq g+\alpha\mathbf{1}$ and $g\leq f+\alpha\mathbf{1}$ holds. Since both $f$ and $g$ are bounded, this is certainly possible.
By monotonicity,
$$T(f)\leq T\big(g+\alpha\mathbf{1}\big).$$
By discounting,
$$T(f)\leq T(g)+\beta\alpha\mathbf{1}.$$
Therefore, $$T(f)-T(g)\leq \beta\alpha\mathbf{1}.$$
By switching $f$ and $g$, we get
$$T(g)-T(f)\leq \beta\alpha\mathbf{1}.$$
It follows that
$$|T(g)(x)-T(f)(x)|\leq \beta\alpha$$
for all $x\in X$,
which implies
$$\|T(f)-T(g)\|_\infty\leq \beta\alpha.$$
To finish the proof, simply note that we can choose $\alpha=\|f-g\|_\infty$.
Here, monotonicity guarantees that $T$ preserves the pointwise ordering of functions, and discounting guarantees that if we increase every coordinate of a function by the same amount, the resulting value of $T$ increases at most $\beta$ times this amount.
We want to use discounting even for two functions in which neither equals the other plus a constant amount. Monotonicity guarantees us that if one function is bounded above by another function plus a constant value, a similar bound can be used for the transformed functions under $T$. This makes discounting much more powerful.


How Do Imports Affect GDP Lets say the U.S. imports a brand new Ferrari that costs $600,000. I know that it would take away from the U.S. GDP since it's considered an import. However, if a consumer buys that Ferrari from the U.S., would it also add to the GDP (consumption) and cancel out the imports? What would happen if it just sat in U.S. warehouses unsold? Is it still adding to the GDP (investment) to cancel out with imports?

In the expenditure measure of GDP $$Y = C + I + G + (X – M)$$

imports $M$ appear to reduce GDP.  However, this only offsets the consumption $C$ met by imports; if instead the money had not been spent on a Ferrari but had instead just been saved (and possibly lent abroad so it has no other effect on GDP) then GDP would have the same.

There is a slight effect on GDP if a Ferrari dealership in the US was involved in the transaction: its margin (the final sale price minus the import cost) would count as value added in GDP and would appear in the expenditure measure since the consumption amount would exceed the import amount.


Stata code for linear regression that controls for state effects Someone told me I should put a variable in my regression to see the state effects. (States in the United States) So he wrote this code and said to put in my variables where the ... is.

xi: reg ... i.STATE, robust

(The robust is because the data is heteroskedastic)

So here's what it is with the variables:

sust_all form_type_dum EDUCPAY HAZARDPAY SHIFTPAY SKILLPAY MILPAY COLLBARG RESPAY CHIEFMAX  OPBUDGET OPBUDGEST POPULATION i.STATE, robust

But I'm getting an error in Stata:

invalid syntax

What am I writing wrong? Or is there a better way to see state effects? Can I just leave that out of the regression?

Background

I'm doing a regression on data from 2007 where the dependent variable is number of sustained complaints per 10 officers in a police department. I want to see if any variables about pay or department budget will explain it. The data comes from Law Enforcement Management and Administrative Statistics (LEMAS), 2007. The survey is administered by the US Department of Justice. The STATE variable is the state where the agency is based out of.

Here's a guess about what has gone wrong, since what you wrote down will get you a different error message.

I would bet dollars to donuts that you left out the the reg (short for regress) from:

xi: reg sust_all form_type_dum EDUCPAY HAZARDPAY SHIFTPAY SKILLPAY MILPAY COLLBARG RESPAY CHIEFMAX  OPBUDGET OPBUDGEST POPULATION i.STATE, robust

Also, unless your version of Stata is ancient, you don't need xi:, so just type:

reg sust_all form_type_dum EDUCPAY HAZARDPAY SHIFTPAY SKILLPAY MILPAY COLLBARG RESPAY CHIEFMAX  OPBUDGET OPBUDGEST POPULATION i.STATE, robust

Stata will handle the state FEs for you.


Why is Uber worth almost as much as Boeing? At $68 billion, Uber has a higher valuation than GM, Ford, and Honda.

According to Microaxis, Boeing is currently valued at around $87 billion.

Why is Uber worth so much? I would think that judging the value of companies would be similar to judging the value of employees. People often make the case that your wage/salary should reflect how easily someone else could do your job. (See this question for example on why celebrities are worth so much). Along those lines, it is hard for me to imagine how anyone could replicate the engineering and infrastructure of a behemoth like Boeing, in order to provide equivalent transportation or defense capabilities without taking many years, many talented employees, and billions of dollars to get up and running.

However, I could imagine 1 engineer fresh out of college making an app identical to Uber in only a year. Additionally, there would be no cost for the consumer to download that app, and try using it (there may not be many drivers, but there's also not a large opportunity cost to opening the app, checking for drivers, and closing the app if there are none).

So how could Uber be valued so highly? If it disappeared tomorrow, it could be easily replaced quickly without much start up time, and it could be adopted just as easily by drivers and users (the very same ones working for Uber). If Boeing disappeared tomorrow, everyone would be in trouble.

A big part of the answer to this question must surely be network effects.

Yes, Ford has a lot of engineering talent. But so has GM. This means that Ford has to compete with GM to sell cars, and this competition limits that amount of profit that Ford can make.

Ride sharing is a different story altogether. Suppose you write software that completely replicates the functionality of the technology used by Uber. How many drivers will want to use your software? Probably few or none because all of the people looking for a ride are using the Uber app and drivers want to be where the customers are. How many end customers will use your technology? Probably few or none because all of the drivers are using Uber and consumers want to use the platform where they can easily get a ride. As you say, people can easily open the new competing app to check it out, but if they find nobody else using it then they will just switch back to Uber. The only way to a competitor to overcome this challenge would be if many users simultaneously decided to switch at once, but such coordination is fairly rare in practice, and usually only happens if the new technology is vastly superior to the old one.

This property—that a product's value depends upon how many other people are using it—is known as a network effect, or network externality.

If you think about it, you will see that many products that have this network effect property are monopolised (or at least have relatively little competition). For example,

a social network website is more useful if more of your friends are on there (a network effect)—and Facebook is a pseudo monopolist in this market.
Developers write software for computer operating systems that have many users and users want to use the system with a lot of software available. These netwrok effects helped Microsoft to a position of dominance.
Blu-Ray players are more useful if lots of shops sell blu-ray discs and shops will sell blu-ray discs if many people own a blu-ray player. The network effects here explain why the competing HD-DVD format died out and we were left with a single dominant high-definition media format.

There are many other such examples.

Since people understand that markets with network effects tend to "tip" to monopoly, and since monopolies tend to be extremely profitable, investors think that Uber is a good bet for future profitability.


What has happened in Venezuela? I'd like to ask for the main causes Venezuela has sank economically so abruptly, I mean not too long ago it was considered a rich country (well not a world power but a country that could provide some nice standards for living) and now if it continues this way it's gonna get insanely poor. (That's the look that I get from the news).

I've read some things but I'd like a more global explanation of what has happened and I feel that some of those things were biased, some of them maybe a lot, I think here I'll find a more objective answer.

I'm not asking for a detailed description of what has happened as that would be something that could take an entire thesis, but I'd like to know in a brief manner the principal aspects that have caused that.

Very interesting question, I'll try to summarize some aspects and I probably won't be exhaustive !

Venezuela has long been a country relying on oil (95% of their exports). Certain experts have estimated that Venezuela holds just shy of 25% of worldwide oil reserves, but the oil extracted in Venezuela is very heavy and hard to refine and then sell to other countries, which makes it more expensive than oil coming for example from Saudi Arabia. When prices boomed, the former President Hugo Chávez, who died in 2013, used oil exports to quadruple the foreign debt. He also led a some nationalisations. The main factor for Venezuela's current crisis is therefore the counter-shock on oil prices which lowered exports. This quote comes from an FT article

  If oil prices remain at January’s average levels, exports in 2016 will be less than USD 18bn, while servicing the debt will cost over USD 10bn. This leaves less than USD 8bn of current income to pay for imports, a fraction of the USD 37bn imported in 2015

One of the direct consequences of that is that the country is relying on its dollar reserves to pay its imported goods. The country's foreign reserves are already withering at 12-year lows. Venezuela has even paid Switzerland with gold! But the problem is that on the land the demand was still the same and the supply could not follow, which led to a massive inflation. Inflation will surge to 720 percent in 2016 from 275 percent last year, according to a note published by the IMF.

The huge outstanding debt is also worrying investors.Creditors are now demanding a high premium for their trust in that promise. The yield on Venezeula’s dollar bond that matures in 2020 is 37% (an investment mainly made by hedge fund). This is the more financial aspect of the question: it's hard or costly for Venezuela to get financial help from investors right now. For this aspects, I encourage you to take a look at this article by The Economist:

  About half of Venezuela’s foreign debt is explicitly owed by the sovereign; the rest is owed by PDVSA. There are important differences. Most of the sovereign-debt contracts have collective-action clauses (CACs), under which a restructuring, if accepted by holders of an agreed proportion of debt, can be imposed on all of them. PDVSA, Venezuela’s main source of foreign exchange, would have a harder time restructuring its debt. Its bond contracts do not have CACs


Multiplier effect and GDP The fundamental national income accounting identity is: $Y = C + I + G + X - M$. The multiplier effect tells us that an autonomous injection into the economy will result in a multiplied increase in the real national income due to rounds of induced consumption. My question is, if that is indeed the case, then wouldn't the national income identity need to be modified to include the multiplier? That is to say, wouldn't it become: $Y = k_c C + k_i I + k_g G + k_x X - k_m M$?

You can't apply it to the national income identity directly because its components, namely consumption, investment and imports are functions of national income (output) and hence, they are not autonomous. In fact, in simple undergraduate level model, following Blanchard et al:

$$ Y = C(Y-T) + I(Y,i) + G  + X(Y^*, \epsilon - M(Y, \epsilon)/ \epsilon  $$

Where in addition to variables already described in your post $T$ are taxes, $i$ is interest rate $Y^*$ foreign output and $\epsilon$ is the exchange rate.

So you cant simply apply the multiplayer just to the variables itself as you would apply them to output multiple times. Rather you first need to solve the equation above for output. To do that I will assume two simplifications - $I$ will be fixed (that is $I = \bar{I}$ and consequently $I$ is no longer function of $Y$, and autraky to get rid of $X$ and $M$ - this is to simplify the math as now only $C$ is a function of $Y$ making solution easier (not doing so would only cause multiplier to be more complex and derivations longer). Moreover, assuming that $C$ is given by $C = c_0 + c_1(Y-T)$, the solution to the goods market equilibrium will be given by:

$$Y  = \frac{1}{1-c_1} \left( c_0 + \bar{I} + G - c_1T\right)$$

where the term $\frac{1}{1-c_1}$ is the multiplier (which you denote by $k$). Applying multiplier makes sense only at this step because only now Y was eliminated from the right hand side of the equation. Previously, you were applying the same multiplier to Y over and over again without noticing it.

Also this is completely correct:

  multiplier effect tells us that an autonomous injection into the economy will result in a multiplied increase in the real national income due to rounds of induced consumption.

But no part of the original accounting formula contains autonomous spending aside form $G$. In fact the solution to the goods market equilibrium given by the equation where we eliminate $Y$ from right hand side gives you effect of autonomous injections as in that solution $c_0$ is the autonomous consumption, $I$ was assumed away to be autonomous by assuming its fixed (admittedly that was bit sloppy from me but it simplifies math and shortens the explanations) and $G$ and $T$ are arguably autonomous by themselves.


Developmental studies and industrial policy for the highly developed countries - research trends? Developmental studies usually is field of reasearch whose object is developing countries and industrial policy studies similarly are attributed to the developing countries or the things of the past. But still I feel that issues researched by these branches of economics are becoming more and more relevant to the economics of developed countries:

How to make economic more fair and more distributed when technology developments create technological unemployment, when businesses require and reward exceptional talent but the jobs for least educated or least talented is replaced by automation and artificial intelligence
Automation and artificial intelligence create opportunities to relocate manufacturing from the offshore to the onshore, remove back in developed countries. What policy decision about allocation of education, infrastructure spending promotes such relocation, should this trend be supported by the general or local governments and how?
Industrial landscape is changing in current world, e.g. Artificial Intelligence is emering and completely new factor of production (along capital and labour). How this trend should be supported and how this trend should be guided for the benefit of all. What resources and how should be reallocated to increase competitivenes in all the new fields of technology - robotics, AI, ubiquitous computing, etc. Some of the developed countries rely on the traditional industries and they need modernization as well.
Many more question...

So - my question is - how economics and policy planning is responding to these trend. Are there research trends, topics, journals, important monographs with such perspective?

I feel that the current developments put the developed nations in the situation that is somehow similar to developing countries - in need to increase competitiveness and in need to correct social issues raised by unequal social development. So - these topics should be researched.

I know that I have raised many different topics in my question, but my aim is not to receive separate answer on any of those topics. My aim is to get the name and references to the research trend which answers those questions.

There is a lot of newish research on the adverse consequences of Globalisation and more generally De-industrialization on low skilled workers in developed economies. A good place to start is Autor, Dorn, Hanson in the AER 2013. David Autor has other interesting work on this topic as well as on automation.

Your questions have quite a normative ring to themselves, and it seems to me you already know what kind of answers you want. It is true that discussing the adverse effects of Globalisation or technological progress  on some people in rich countries has become a more active research topic. But I think most people are very still far from questioning free trade or technological progress as Pareto efficient. And I think the overwhelming majority of economists still thinks that industrial policy in a developed country is a silly idea. So I don't think you are going to find this big trend you are looking for.

Also, as a sidenote, even development economics has moved quite far from the kind of research that debated the industrial policy you have in mind. It's mostly about RCTs and institutions now.


What is the Credit-to-GDP gap exactly? I have been hearing a lot about this metric in relation to rising fears of a Chinese financial crisis. I am wondering, what exactly does this mean? I am told it refers to the difference between current credit-to-GDP ratios and long-term trends but I don't fully understand what that would mean. What would be a nice little equation for it? I have looked at some charts and I am seeing that the US has a negative Credit-to-GDP gap, how can it be negative? I just want to know what the inputs into calculating that would be so I can understand for myself what these things signify.
Thanks.

The Credit-to-GDP, say  ratio measures the relative size of the outstanding debt of non-financial private sector, say $D_{p,t}$ with respect to (yearly) Gross Domestic Product, say $Y_t$

$$\text{Credit-to-GDP ratio} =\frac { D_{p,t}}{Y_t}$$

Note that GDP should be measured in nominal terms here, since so is debt. It is a metric related to how much burden WE have placed on our future from our current decisions and activities.

The "Credit-to-GDP" gap is, as the OP notes, "the difference of the Credit-to-GDP ratio from its trend". How do we extract that?

Look for example at the, informative with data and literature, page of the Bank for International Settlements. If you hit the "data" link, you will see that what they do is
a) calculate the Credit-to-GDP ratio (per quarter but always using past-12-months GDP in the denominator), and then decompose the obtained time series by using the HP filter.

The Credit-to-GDP gap is what it remains if from the actual "Credit-to-GDP ratio" series we subtract the (non-linear) trend as calculated by the HP filter. One can understand why then this "gap" can be negative: we are currently below the trend. Finally note that the Credit-to-GDP gap is also measured in GDP percentage units. But sometimes it may be reported as percentage deviation from the trend (i.e. "we are 30% above trend" does not mean that we are "30 percentage points of GDP above trend"). So read carefully any source.

The question is: why use the "gap" and not the ratio itself?

Because we are accepting that the trend likely reflects a sustainable evolution of the economy over time (sustainable by the very ongoing existence of said economy), while the "gap" reflects short-term tendencies that may not be sustainable and may lead to crises if left unchecked and un-managed.

A higher positive gap means that the private sector borrows at a level that is perhaps "not justified" by the current output-producing abilities of the economy. Banks may tend to experience abnormally high rates of loan defaults etc, which can lead to a banking crisis.

A negative gap supposedly implies that there is a "safe" amount of additional borrowing that could be done currently (for consumption or investment purposes), and we are leaving it "unexploited".

But never read too much on a single metric, economic systems are too complex.


Correlation between nominal bond returns and growth I read the following passage and the bolded section has me confused:

  In theory, assets earn a low (or negative) risk
  premium if they tend to perform well when the economy is weak. When growth
  and inflation are primarily driven by aggregate demand, nominal bond returns
  tend to be negatively correlated with growth and a relatively low term premium
  is warranted. Conversely, when growth and inflation are primarily driven by
  aggregate supply, nominal bond returns tend to be positively correlated with
  growth, necessitating a higher term premium.

I thought that growth and nominal bond returns were usually negatively correlated. Why would the growth being supply or demand-driven affect this correlation?

Thank you for any and all answers!

When growth and inflation are primarily driven by aggregate demand, nominal bond returns tend to be negatively correlated with growth

Actually, the above sentence is the explicited version of what you have in mind, i.e. the links between nominal (vs real) returns, (demand-driven) inflation and growth.

  when growth and inflation are primarily driven by aggregate supply, nominal bond returns tend to be positively correlated with growth.

The point is that "supply-driven inflation" is the broad way of saying "weak or no inflation" or even "deflation" (avoided since politically undesirable). Put differently, when growth and inflation are primarily driven by aggregate supply, nominal bond returns tend to be ... real and thus to be positively correlated with growth. Indeed, the traditional (neoclassical) explanation is that non-weak real rates stimulate savings which in turn stimulates technical progress and ultimately, economic growth.

All that being said, the passage you quote is curiously phrased.. and the key words appear to be "tend to be".


Why does a firm make profit in a perfect competition market I'm solving a problem about $n=180$ firms in a perfect competition market, where demand is given by $D(p)=100-5p$. A firm's cost function is $c(q_i) = 2 \cdot (q_i)^2$. Using $p = c'(q_i)$ and the demand function, I was able to derive the equilibrium quantity $q^* = \frac{1}{2}$ and price $p^* = 2$.
When asked about the profit each firm makes, I calculated a positive result for the individual profit in equilibrium $\pi_i^* = p^*\cdot q_i^* - c(q_i^*) = \frac{1}{2}>0$.
How is this possible? Is there not the assumption that a firm does not make profits in a perfect competition market? I know that there can be short term profits, but we assumed the market is in equilibrium here from the start. I'm new to microeconomics, coming from a mathematical background.

The first order condition for profits here (with respect to quantity, since firms are price-takers) is
$$p - 4q_i = 0 \implies q_i^* = \frac 1 4 p,$$
which is the supply function of its firm. So market Supply is
$$nq_i^* = \frac{180}{4} p = 45p,$$
and equilibrium market price
$$45 p = 100 - 5 p \implies p^* = 2$$
and equilibrium market quantity
$$Q* = nq_i^* = 180 \cdot\frac 1 4 (2) = 90$$
Per identical firm we have
$$q^*_i = 0.5$$
The profits are
$$(2)*(0.5) - 2* (0.5)^2 = 0.5$$
...indeed.
So what happens here?
Well "perfectly competitive market" among others things means costless and free entry. But the problem above was solved for a fixed number of firms.
At this number of firms, each firm makes an economic profit. This will induce other firms to enter the market, driving equilibrium price down and economic profits to zero.
I guess the OP can understand how one can compute the number of firms required so as to have zero economic profits (hint: it is not finite).


Could Depreciation of Capital $=\delta(K(t))^{\theta}$ with $\theta<1$ Be a Realistic Assumption? In the context of a long-term growth model with $K$ representing aggregate (man-made) capital, what theoretical or empirical reasons, if any, might be given for assuming that depreciation of capital $D(t)$ could be given by:

$$D(t) = \delta(K(t))^{\theta}$$

where $\delta$ and $\theta$ are fixed parameters both $> 0$ and (this is the key point) $\theta<1$?

[The question is prompted by this paper by Buchholz, Dasgupta & Mitra which considers the feasibility of constant consumption to infinity in a growth model containing a single produced good which can be either consumed or used as capital and a single nonrenewable resource.  It implies (p 553) that constant consumption is impossible when $\theta=1$, reducing the above formula to the familiar $D(t)=\delta K(t)$, but is in some circumstances possible when $\theta<1$. Hence it is of interest to consider whether $\theta<1$ could ever be a realistic assumption.]

For zero investment, $\delta = 0.05$ and $\theta =1 $ and $\theta = 0.9$ we get

We see that it is still a slowing depreciation, which reflects the assumption that capital is more productive in its first years of usage (since depreciation is the mirror image of productive contribution), an assumption good enough for capital equipment with moving parts (and for human capital), and perhaps also for roads, but not necessarily for buildings and things like furniture (here perhaps the Straight-Line method, widely used in Accounting, would be more appropriate -but it creates the need to keep track of capital vintages, since depreciation in that case is a fixed percentage of initial acquisition cost).

So it appears to be a quantitative/empirical matter. With $\theta <1$ capital depreciates slower, but the qualitative behavior is the same, and for smaller values of $\theta$ it can even mimic the Straight Line method, which, as said, is realistic for some forms of capital. So yes, we can have $\theta<1$, it does not appear to contradict any fundamental assumption.


Why are they raising interest rates in Brazil? How does raising interest rates in Brazil (and Russia) help fight inflation and defend their currency?

I understand that the basic model is that raising the rates is meant to encourage banks to lend in brazil to earn on the interest rate differential and it should also reduce local demand for goods and services.

But, both Brazil and Russia are facing recessions and their economies are currently weak. If you raise the interest rates to 14.5 like Brazil has done wont that make the economy even weaker which will make investors flee the country and thus weaken the currency which in turn will increase the price of all imported goods (which for most open economies is a big percentage) and thus make goods more expensive, thereby increasing inflation rather than reducing it.

I would have thought a better way to fight inflation in a recession would be to lower rates to stimulate the economy and thereby stimulate the stock market and attract foreign investment which would strengthen their currency and reduce the price of imported goods. What have I misunderstood?

Brazil raising interest rates probably refers to the central bank raising their interest rate which means that it is more costly for banks to loan money from the government and therefore the amount of money in circulation (as per quantity theory) should go down. It is a policy decision (possibly wrong depending on who you ask) in a difficult economic situation where a country faces both inflation and a downturn.

Your logic about the economy becoming even weaker might very well be true (and I'd agree with lowering rates being a better option). The questions about effects to trade are slightly more complex and not necessarily as straightforward.


Finding distributions of wealth from utility functions Maximize
$$\begin{align}
U_1(x) \qquad & (1)\\
\text{s.t.} \quad U_2(a-x) = c \qquad & (2)\\
\end{align}$$

where we have bundles $x = (x_1, x_2), \quad a = (3,5)$, and want to split our resources between the two users.

$$\begin{align}
U_1(x_1, x_2) & = (x_1 + 1)x_2 \\
U_2(x_1, x_2) & =  36 - (x_1 - 4)^2 - (x_2 - 6)^2
\end{align}$$

The question is

In equations $(1)–(2)$, choosing different $c$ would lead to different $x$. Find all those $x$ with $x_1 ∈ [0, 3]$ and $x_2 ∈ [0, 5]$. Those set of points will comprise those distributions of wealth which are reasonable in the sense that no person’s utility can be improved without hurting someone else.

I don't understand how one can solve $(1)-(2)$, since I think this gives

$(x_1 + 1)x_2 - 36 − (x_1 − 4)^2 − (x_2 − 6)^2 = c$

I can plot this as $c = f(x_1,x_2)$, but I feel this isn't what the question is asking for, since it doesn't define a set of points.  If anyone can give me the direction in which to pursue this question, or let me know if I need to provide more information.  Thanks.

From what it looks like, you are literally trying to subtract $(2)$ from $(1)$, incorrectly as well (You didn't distribute the minus out correctly.) It is saying to use equations 1 through 2 to solve this problem.

You have to set up a Lagrangian with the maximization problem:

$$\max_{x_1, x_2} \ (x_1 + 1)x_2 \\ \text{s.t.} \ 36 - (x_1 - 4)^2 - (x_2 - 6)^2 = c
$$

So we have

$$\mathcal{L} = (x_1 + 1)x_2 - \lambda[36 - (x_1 - 4)^2 - (x_2 - 6)^2 - c]$$

and you should be able to move from there.


Given the supply and demand function what is the difference? Given some unspecified demand and supply functions.

I need to calculate quantity and price after taxation, but what is the difference between having a tax of 20% of total revenue and 20% of profits ($\pi$)? I mean how to calculate this tax in those two cases? And what precisely should be changed when calculating Q and P after tax of those two types is imposed on.

Whether tax of 20% of total revenue creates simply consumer price on a level of $1.2(\text{producerprice})$ or is it something different? In case of profits is it $0.8(\text{supplyfunction})$?
**hope this question now satisfies required format **

Deriving those functions, you can find $p^*$ and $Q^*$, which, multiplying both, should give you equilibrium profits. Now, if you take that tax rate (20%, I reckon?), you can calculate taxes over profits and the tax-free price.

To find the equilibrium price $p^*$, you need to have those two functions in a system and solve for $p$. Then, just replace it on both functions and you should have equilibrium quantities.

Now, I'm assuming demand absorves all quantities produced by companies, no production restrictions and that this market is one in perfect competition. If this last paragraph changes, then my solution will not be correct.
To answer your question - what is the difference -, well, in this case, it is none because we are not considering production costs. If we did, you can see that both values would change.

Nevertheless, to calculate taxes, you need to work around with the system. That will give you total revenues, cost and tax free. Applying 20% leads to net earnings, because you do not have any production costs associated with the problem - something commonly done in Economics. That or consider a variable $c$ of costs.

This kind of exercises are also good to understand what are the effects of  costs on revenues/profits. There's actually a financial term for that but I cannot recall :)


Time Series Analysis - What lag level is appropriate? In my undergraduate econometrics class we were taught the basics of time series analysis. We were basically told to use a model with a one period time lag (lag = 1). However, I wonder that there must be cases where more lags might be appropriate. What would those instances look like? Is there a way to find what might be the optimal number of lags to look at for a particular time series. Could you guide me to appropriate resources that deal with the intuitive Math for this and possibly an implementation of how to find optimal lags in R if possible.
Thanks for your help!

In your course they were likely talking about some specific case. Generally you often see more than one lag across applied work.
For example, one of standard time series models is the Autoregressive Distributed Lag (ARDL) model. In such model you often need to include several lags. The general ARDL(p,q) model looks like:
$$ y_t = \beta_0 + \sum_{i=1}^p \beta_i y_{t-i}+ \sum_{j=0}^q \gamma_jx_{t-j} +e_t$$
where you would typically want to choose the lag order to remove autocorrelation from the model. This is just an example, in many time series models you will want to include multiple lags for example also in VAR, AR, ARIMA and many other models. It is impossible to provide exhaustive overview of these models but you can have look at Verbeek (2008). A Guide to Modern Econometrics. 4th ed chapters 8-9 for an overview.
One way of how to select optimum number or lags is with information criteria such as Akaike or Schwartz Bayesian Information criterion (again just examples there are more of these - see the above mentioned source).
In R there are multiple ways how to implement these. One example is "tsDyn" package - this is mainly used to select optimum number of lags for VAR. For example you could run:
install.packages("tsDyn")
require("tsDyn")
data(barry)
test1 <- lags.select(barry, lag.max = 12)
test1
Best AIC:  lag= 12
Best BIC:  lag= 2
Best HQ :  lag= 2

So in the data above based on Akaike (AIC) we should include 12 lags in VAR model run on these data, according to Schwartz (BIC) and Hannan-Quinn (HQ) only 2 lags. As you can see this criterions do not always agree together so you also have to exercise some discretion but it is beyond scope of this SE answer to fully explain in all cases how to apply these. You can again have a look at the textbook I recommended.


Does consumer theory assume that utility functions are consistent overtime? I'm interested in how we model a consumer with a changing utility function over time.

  Example: an individual's demand for candy/sweets at 10 years of age will be different when he is 20,30 or 40 years old (based on casual observation).This would seem to indicate the utility derived from this "input" in our utility function has changed.

In basic intertemporal models the general assumption is that the objective utility function does not change. mathematically it makes the model simple to compute, however it does not reflect the changes in preferences over time.

However, if we do allow the individuals utility function to change over time in our model, does this not violate the requirements for a rational consumer ?

How do we model an individual with changing preferences over time and is it economically sound to do so?

In The Economic Approach to Human Behavior, Gary Becker said:

  The combined assumptions of maximizing behavior, market equilibrium, and stable preferences, used relentlessly and unflinchingly, form the heart of the economic approach as I see it.

The emphasis is mine. Here "stable preferences" refer to preferences (and by association, the utility functions representing them) that are more or less the same across different periods. The reason for preference stability is obvious. If we allow preference or utility function to change arbitrarily, then we'd be able to explain pretty much anything by attributing the cause to some appropriately chosen change in people's preference.

When it comes to the intertemporal preferences in particular, I agree with @MaartenPunt that, at least in principle, one can incorporate time-dependence into utility function. For instance, in the usual discounted utility framework, we have
\begin{equation}
U(\mathbf x_t)=\sum_{t=0}^\infty D(t)u(\mathbf x_t)
\end{equation}
where $\mathbf x_t$ is a vector of consumption goods at time $t$, $D(\cdot)$  is a discount function (e.g. $D(t)=\delta^t$ as in an exponential discounting model), and $u(\cdot)$ is the time-invariant period utility function. To incorporate time-dependence, we can simply allow $u(\cdot)$ to also be a function of time
\begin{equation}
U(\mathbf x_t)=\sum_{t=0}^\infty D(t)u(\mathbf x_t,\color{red}t).
\end{equation}
To make @MaartenPunt's third comment more explicit, suppose
\begin{equation}
u(\mathbf x,t)=\alpha_t^1v(x^1)+\cdots+\alpha_t^iv(x^i)+\cdots+\alpha_t^nv(x^n)
\end{equation}
where $x^i$ denotes the quantity consumed of good $i$ and $\alpha_t^i$s are the time-dependent weights on the utility derived from each good $i$.
So the same consumption bundle will generate possibly different levels of utility  in different time periods. For example, $\alpha_{10}^\text{candy}>\alpha_{40}^\text{candy}$ would capture the fact that a 10-year-old values a candy more than a 40-year-old does. On the other hand, a time-invariant preference would imply that $\alpha_t^i=\alpha^i$ for all $t=0,1,\dots$.

The above discussion is however distinctly different from the paper you linked to in the comment, which is about dynamic (in)consistency of choices. In the literature on intertemporal choices, the main focus is usually about whether some optimal consumption profile decided at time $t$ will remain optimal when reevaluated at some future time $t+k$.
Usually papers in this literature maintain the assumption of time-invariant period utility function, i.e. $u(\mathbf x,t)=u(\mathbf x)$, but play with various forms of the discount function $D(\cdot)$ (e.g. hyperbolic or quasi-hyperbolic discounting) to generate predictions that match experimental data.


Information Partition and Common Knowledge Person $A$ has information partition $\{\{1,2\},\{3,4\},\{5,6\}\}$
Person $B$ has information partition $\{\{1\},\{2,3\},\{4,5\},\{6\}\}$
$w=3$ has been realized.
I'm confused about what $A$ knows that $B$ knows.
At first I thought of it as $K_aK_b(3)=K_a(\{2,3\})=\{1,2,3,4\}$, but the example I found online says $K_aK_b(3)=\{2,3,4,5\}$. why?

The situation is not described by $K_A(K_B(3))$. $A$ does not know that the draw was 3, and hence does not know that $B$ thinks it is in the set $K_B(3)$. What $A$ does know is that the draw
is in set $K_A(3)$, hence $A$ thinks $B$ should have narrowed it down to $K_B(K_A(3))$.


Deflating GDP using OECD data I would like to know how to find a Euro zone country real quarterly gdp growth, using the OECD database.

We have Quarterly GDP, and CPI.
How should I proceed?

If it's not possible, which database can I use to obtain it?

Any help would be appreciated.

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


Why the Federal Funds rate isn't detrended in a VAR model? In FAVAR (factor augmented VAR) paper (https://faculty.wcas.northwestern.edu/~lchrist/finc520/QJE.pdf), the following transformation code is applied to the data:
1—no transformation; 2—first difference;
4 —logarithm; 5—first difference of logarithm.
There is no transformation for the federal funds rate, among several others. The paper does not say why, but is it because these series are already stationary in levels? Would it hurt to detrend them even if they are stationary in levels?

Yes, if the series is already stationary then there is no need to difference the data to remove a trend. In fact, there is a cost associated with unnecessarily differencing the data such that you are removing / losing relevant information. More generally this is related to the concept of cointegration where even if series are non-stationary, if they are co-trending then you lose more information by differencing than by including the lagged levels in the model specification.
You might also find the following question and answers helpful for thinking about this in a slightly different context: https://stats.stackexchange.com/questions/415914/is-it-a-valid-claim-that-by-differencing-a-time-series-it-loses-its-memory-an


Does quantitative easing appreciate or depreciate the domestic currency? 410 gone says the domestic currency depreciates.

  You've identified the first-order effect: the supply of local currency has increased, so its price (and from the perspective of other currencies, that's its exchange rate) decreases. That's assuming that the move wasn't already (fully) priced-in by the market.

Jess Mehta says depreciates too, but she looks like a mooch for "Crypto Coin Market Expert".

  An increase in the money supply could lead to a depreciation in the exchange rate. This is for two main reasons:

  Inflation: The domestic inflation will make your goods relatively less competitive and export demand will fall. Therefore, there will be less demand for the currency and its value will tend to fall on the exchange rate markets.

  Lower Interest Rates: If you increased the money supply, then this reduces interest rates. Lower interest rates will also tend to reduce the value of the currency.

But Adriaan Slabbert on Quora says it appreciates.

  If there is less demand for something, the price of that thing tends to fall. Since the exchange rate is the price of currency, this means that Country A’s currency should fall, i.e. it will depreciate against other currencies, leading to a higher exchange rate of Currency A/US Dollar.

The exchange rate can be expressed in a simple classroom monetary model as:

$$S = \tilde{m} - \psi \tilde {y} + \lambda (\tilde i)$$

Where $S$ is the exchange rate $m$ is log of money supply, $y$ log of real output $i$, interest rate, $\tilde{}$ denotes differences between variable at home and abroad (i.e. $\tilde{x} = x_{home}-x_{foreign}$), and $\psi$ & $\lambda$ are just model parameters.

So the exchange rate depends both on log of money supply and on interest rate. Furthermore the interest rate itself depends on money supply.

The answer of @410gone focuses on the first order effect of monetary expansion through changes in $m$ whereas the answer on Quora mentions only the effect monetary expansion has on exchange rate through $i$.

However, the Quora answer omits any discussion of other effects, whereas @410gone mentions there are other effects so I would say the @410gone answer is more correct in a sense it mentions that also other effects exist whereas the Quora answer pretends that increase in money supply only affects exchange rate through the interest rate.


Showing existence of a Nash equilibrium in pure strategy Consider a game with $N$ players, each indexed by $i=1,...,N$. Every player $i$ has to choose a $J\times 1$ vector of actions $a_i\equiv (a_{i,1},...,a_{i,J})$ where each $a_{i,j}$ can be zero or one. For each player $i$, let $a_{-i}$ denote the actions of the other players.
The payoff of each player $i$ is
$$
u_i(a_i, a_{-i}; \theta)+v_i(a_i; \delta)
$$
where $u_i$ and $v_i$ are some parametric functions of the parameters $\theta$ and $\delta$. Moreover $v_i$ is monotone decreasing in $\sum_{j=1}^J a_{i,j}$.
A pure strategy Nash equilibrium (PSNE) of the game is $a^*\equiv (a_1^*,...,a_N^*)$ solving
$$
 a_i^*\in \arg\max_{a_i\in \{0,1\}^J} u_i(a_i, a^*_{-i}; \theta)+v_i(a_i; \delta) \quad \forall i=1,...,N
$$
Question: Suppose that I'm able to show that a PSNE exists for $\theta=\theta_0$ and $\delta=\delta_0$ where $\theta_0$ and $\delta_0$ are some specific real values of the parameters $\theta$ and $\delta$. Can I conclude that a PSNE exists for $\theta=\theta_0$ and any value of $\delta$?
In particular, here, I'm wondering whether the claim may follow from the fact that $v_i(a_i; \delta)$ enters additively, does not depend on $a_{-i}$, and it is monotone.

No. Consider the matching pennies game
$$ \begin{array}{c |c}
& H & T  & \\ \hline
H & (1,-1) & (-1,1)\\
T & (-1,1) & (1,-1)\\
\end{array} $$
which we know no PSNE exists.
Define the function
$v_i(\cdot,\cdot)$ by
$$
v_i(H,0) = 5 \\
v_i(x,y) = 0 \quad \forall (x,y) \not = (H,0)
$$
At $\delta = 0$, we have the game
$$ \begin{array}{c |c}
& H & T  & \\ \hline
H & (5,4) & (-4,1)\\
T & (-1,5) & (1,-1)\\
\end{array} $$
which has a PSNE of $(H,H)$.
For any other value of $\delta$, we're back in the original game so no PSNE exists.
Redefine $H = 0, T = 1$ and you have your monotone decreasing requirement.


Why does the European Union give subsidies to farmers? According to neoclassical economics, subsidies are a solution to correct for the existence of externalities in consumption or production.

What is the economic rationale/justification for such subsidies in the EU? Which are the externalities subsidies are correcting for? Or are subsidies justified by other motives, e.g. political?

Markets are extremely poor at pricing events that have very low probability and catastrophic impacts. In part because we're very bad at estimating low-probability events: by definition, they're rare. And in part because the catastrophic impacts fall on pretty much all the population, so any single purchase has very widely-spread potential negative externalities.

And there are strongly asymmetric risks here - if civilisation collapses, it can take centuries to rebuild it. If one country falls under the control of another, it becomes extremely expensive and messy to reverse this.

As such, societies decide - in order to avoid those catastrophic impacts - to pay a kind of insurance premium. A high risk of some market distortion is an acceptable premium to pay, in order to avoid catastrophic loss.

Food is probably the most obvious market where a dramatic loss of supply could lead to catastrophic failure. (the carbon market is another) By subsidising farmers, we ensure the continuity of the domestic supply of food: this helps ensure the availability of food locally, so the population gets fed; and reduces the strategic international risks that would arise from high imports of essential foods.


For stability, is there a limit to the sovereign debt that a Government owes to itself against issued fiat currency? Looking beyond the optical illusion of Governments owing debt to Central Banks, Governments effectively owe themselves the sovereign debt created against issued fiat currency.
By definition, there shouldn't be any limit to the debt that an entity owes itself.
Does this mean that Governments can continue to print a limited amount of fiat currency (say 5% of GDP) annually forever?
In other words, is there a problem even if this debt that the Government owes itself, grows to, say, 1000 times the GDP over centuries?

Does this mean that Governments can continue to print a limited amount of fiat currency (say 5% of GDP) annually forever?

Yes government can 'print' (I use quotation marks because most money is created electronically nowadays) any amount of fiat currency it wants to.

In other words, is there a problem even if this debt that the Government owes itself, grows to, say, 1000 times the GDP?

Depends on your definition of a 'problem'. In terms of affecting probability of default it is not any problem at all. Central bank can scrap all the government debt it owns at a stroke of keyboard.
However, this being said, it is agreed by virtually all conventional economists that increasing amount of money (ceteris paribus) leads to inflation (see Mankiw Macroeconomics 8th ed.). So eventually if government would try to create arbitrary high amount of money it would eventually lead to inflation and at some point even hyperinflation. For this reason it is generally agreed by economists that governments can fund arbitrary amount of spending by creating new money (see this poll among the most prestigious policy economists). This being said there would be some scope for generating seigniorage revenue that way, so monetary financing might not be bad if it is done carefully, but having debt to GDP ratio of 1000:1, completely financed through central bank's high powered money, would likely lead to disastrously high inflation.


Why shouldn't governments use Forex reserve to pay their debts? India has around 470 billion USD in debt and has around 400 billion USD in forex reserves. So why should India or any other nations shouldn't use their forex reserves to pay off their external debt ?

If you had 12,000 dollars owing on a loan, 10,000 dollars cash in the bank and 1000 dollars monthly expenses, but you weren't sure if incoming cash flow could stop for 6 or 12 months, any time, with no notice, would you deplete your entire cash stock to reduce debt?

At that point, if your next paycheque was a week late, you would go hungry. Or, assuming that you had assured your basic subsistence, you might find yourself with no money to buy some other basic things that make your life a lot easier or more efficient.

Otherwise stated, there's a reason that a common measure of forex reserves is "Total reserves in months of imports".

Basically, if India used all of its forex to pay off external debt, then on a moment's notice it could have zero (or at least highly constrained) ability to access critical inputs into production processes. The highly negative impact that autarky or excessive focus on self sufficiency (beyond subsistence needs) could be highlighted in the context of this explanation.

Also (among other things), while a lot of economists disagree that using forex to manage an exchange rate in a situation of short-term crisis is a good idea, it is logically true that if you have no forex then this option simply does not exist.

For a specific example of how this can be a problem, you could refer to the story of the 1997 Asian Financial Crisis. In response to this crisis, most central banks in Asia undertook to substantially increase their forex holdings in order to not suffer a repeat of such a crisis.


Why is the term structure curve of agricultural commodities often downward sloping? I have retrieved the below term structure curve for livestock (lean hogs) from Bloomberg and noticed that it is inverted. I have a vague intuition that this has to do with the storage costs and perishability of agricultural underlyings, but I lack a rigorous explanation. Searching for the solution online has yielded publications and PhD theses on term structure models which slightly exceed my understanding as an undergraduate student.

I would thus greatly appreciate any suggestions for economic explanations.

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

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

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


Is anyone familiar with the following basic resource sharing model? Here is a resource sharing model, I do not remember where I came across it, I am wondering if this is well known in econometrics.

Let $T > 0$ be the total quantity of resources. For example, ad time slot between 6:00 pm to 6:10 pm, hence $T = 10$ minutes.

Two ad companies are competing for time slots by bidding in some nonnegative amount of money. Let company $1$'s bid be $x$, and company $2$'s bid be $y$.

Let $C > 0$ be the cost of entering the bidding process.

Let $r_x$ be the share of ad time slot that $x$ gets, and $r_y$ be the share of ad time slot that $y$ gets.

Then $r_x = \dfrac{Tx}{C+x+y}$, and $r_y = \dfrac{Ty}{C + x+y}$.

The utility for company $1$ is $U_x = m_x r_x - x$

and the utility for company $2$ is $U_y = m_y r_y - y$

where $m_x, m_y$ are the margin utility.

I wonder if anyone has seen this type of model somewhere.

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


What is the state of the art in capital theory? In the first half of the 20th century a great deal was written about capital theory, including writers such as Hayek, Böhm-Bawerk, Sraffa, Knight, Robinson and Fisher. Many of these figures debated and often staked out radically different schools of thought with regards to capital and interest. These debates seem to me some of the most interesting and difficult in all of economic theory. My impression as a non-economist is that there has not been much interest in the 21st century in these debates and it is not taught to students. My question is: is this true, and what is currently the "state of the art" in modern capital theory?
EDIT: Let me elaborate a bit. In the writers I mentioned, some favoured a "pure productivity" theory of interest (Knight), others favoured a "pure time preference" theory (Mises and, I would assume, Hayek), others favour a mixed productivity-time preference theory (Fisher), and other said that the interest rate is simply set by power relations and not by any market equilibrium (Sraffa). Robinson, I would assume, as a Keynesian, favoured a liquidity-preference theory. My impression is that modern economists favour some kind of synthesis between the Fisherian theory and the liquidity preference theory (is this impression of mine accurate?).
With regards to the Romer and Solow growth model mentioned by muflon, as far as I understand these are models with a homogeneous capital stock and so is essentially a "Knightian" theory, the same kind of theory that ignited the Cambridge Capital Controversy. I have seen one economist (Nick Rowe of "Worthwhile Canadian Initiative") say that the whole CCC debate was silly because both sides were trying to explain interest rates without any reference to time preference.
What motivated this question is that when I have tried to understand capital and interest I tend to get drawn to these very old works and very old debates. The various neoclassical growth models certainly use the concept of capital, but I wouldn't say they constitute capital theory in that don't seem to tackle the more fundamental questions associated with capital that got raised in the early 20th century debates.

My impression as a non-economist is that there has not been much interest in the 21st century in these debates and it is not taught to students.

This is misconception but understandable one (I will get to the understandable part at the end). According to The New Palgrave Dictionary of Economics (Becker, 2017) - leading source for economic terminology - capital theory is defined thusly:

Capital theory examines the special role played by time in resource allocation studies. The determination of the interest rate and functional distribution of income as well as how rational agents invest are analysed within single- and multi-sector general equilibrium frameworks. Here, agents exercise perfect foresight over alternative consumption and capital accumulation programs. Efficient programs are characterized. Representative and multi-agent infinitely lived households are studied. Equivalence principles link the equilibrium programs and optimal paths. Heterogeneous agent models with borrowing constraints are reviewed. A behavioural model of intertemporal choice is also compared to its constant discounting counterpart.

Given the above broad definition of capital theory, virtually the whole corpus of modern macroeconomic theory is preoccupied with capital theory. The above broad definition of capital theory as a field would include models of economic growth such as the famous Solow-Swan model or Romer model and virtually any growth model that accounts for capital formation be it endogenous or exogenous. It would also include many overlapping generations models with dynamic capital formation and so on. For an overview of state of the art growth models you might want to look at Barro and Sala-i-Martin Economic Growth 2nd Edition (it is graduate level text so it has state of the art models), but really I can't think of a single macro - or even general economics textbook that would not at least briefly cover these issues (for example Blanchard et al. Macroeconomics: A European Perspective which is prominent macro textbook and deals with these issues).
In addition the above definition easily encompasses general equilibrium business cycle models as well. This is another large area of study in current macroeconomics. Presently this is theoretically covered mainly by the New Keynesian IS-LM models and Real Business Cycle theory. For state of the art examples of such models see Romer (2008) Advanced Macroeconomics 4th ed. For undergraduate treatment you can have look again at Blanchard et al. textbook mentioned earlier.
The areas mentioned above without any doubt the largest areas of research interest in macroeconomics (even throughout presently macroeconomics is becoming more empirical rather than relying on theoretical models as you can see in  Angrist et al. 2017). Consequently, the research interest in capital theory can be presently argued to be quite strong and ubiquitous.
However, In my first paragraph I stated that the misconception you hold is understandable. This is because the term 'Capital Theory' fell out of favor and it is mostly used to describe particular historical sets of theories on capital (especially those you mentioned in your opening question) rather than an area of interest. Hence nowadays when someone publishes theoretical paper that will be about the theory of capital (e.g. Becker, and 1987 - just a random example)  it will be often given different specific name rather than just capital theory (although occasionally I see people still using the term in non-historic context).


Is there any up-to-date list of hours of work needed to buy a Big Mac? Is there any up-to-date list of hours of work needed to buy a Big Mac?

I have found only up to 2018.

I could not find any more recent Big Mac Index in terms of hours worked, and I dont think it is avaiable as wage statistics is usually reported with 1-2 year lag in many countries, but the Economist provides the Big Mac Index in USD, EUR, GBP and few other currencies up to January 2020  and it is being kept up to date with about 1 quarter lag. You can find the index here and raw data for all years here.

Based on their index you can calculate how many hours (or in this case mostly minutes) it takes in some selected countries. For example you can find hourly wages by month in the US for 2020 at the U.S. Bureau of Labor Statistics. You will be able to do this for most rich developed countries but not for all countries around the world.


Devising a model for inflation for a closed points system I am working on a project that involves points. The idea is that users will earn points and redeem them for certain rewards.

The means via which the users earn are fairly limited (They can attend a seminar, a class, etc).

I want to make sure that once the circulation of points increases, we want to employ an inflation model that increases the prices of the items.

I am a complete newbie to economics and have no clue how can this be achieved.

My initial attempts consist of models where the prices increase flatly with respect to the circulation amount - but that wouldn't be fair for people who haven't made any significant contribution to the circulation.

Second thought was to take into consideration the "average" increase in the users' income over a period and increase by that fator. But that is when it hit me - that way, the target prices will keep on increasing and no users will be able to redeem any rewards.

Should I explore per-capita income route? Is there a "text-book" model that I can read about and potentially implement to make a fair system that also motivates people to increase their income?

If your points are exchangable for rewards, the fundamental value of the points is entirely driven by the exchange rate between points and the rewards. (People may value the points more or less than the fundamental value for any number of reasons.)

This means that the inflation rate is entirely driven by the administered exchange rate - up until the point the program runs out of rewards. If you want to prevent the possibility of running out of rewards, the total supply of points must be held less than the redemption value.

This is similar to the operation of a gold standard. In the classical gold standard, a country’s currency (in principle) is exchangeable at a fixed rate against gold. (In practice, the implementation of gold standards changed over time.) You should be able to find a lot of resources on gold standard systems.

If you have a fixed supply of rewards, and you want to keep the exchange rate stable, you would need to find a way to drain points from the system - a tax.

In terms of motivating people, the major question is the value of the rewards. If people don’t want your rewards, your points will have little value.


Stationarity, ADF/KPSS, Autocorrelation and Heteroscedastiy i have a time series which is not stationary due to ADF/KPSS test, but is is in its first difference. So ADF and KPSS tell me it is starionary so it has a constant mean/variance/autocorrelation. But i still need to check for autocorrelation and homoscedastie and i dont get why, since ADF/KPSS told me for example the variance is constant, so why would i check with other tests for homoscedastie?

First, it is actually heteroskedasticity or heteroscedasticity and homoskedasticity or homoscedasticity (depending on whether you prefer to be faithful to the Greek root of the word or prefer the latinized English spelling).
Unit root test only tell you if the dependent variable has constant variance. That is for a dependent variable $y_t$ that is non-stationary (among other things) it will hold that:
$$\operatorname {Var}(y_{t})=\sum _{{j=1}}^{t}\sigma ^{2}=t\sigma ^{2}.$$
However, note this is variance of $y_t$. When you test for presence of presence of heteroskedasticity in subsequent model that uses $y_t$, for example:
$$y_t = a + b x_t + e_t$$
you are testing for constant variance of $e_t$ not $y_t$, since one of the Guass-Markov assumptions behind OLS is that errors should be homoskedastic (although this can be adjusted for by reestimating the errors with different method as it only affects efficiency of OLS estimator).
When it comes to autocorrelation, the same issue as above applies. In addition, unit root tests won't even tell you if $y_t$ is autocorrelated or not. In fact, most unit root tests will be biased in the presence of autocorrelation (e.g. Augmented Dickey-Fuller test) so that is something that you should test separately before you even perform your unit root test.


Does a more even distribution of wealth result in lower taxation? A proportion of government spending is associated with welfare. There are also many factors related to poverty that may result in higher government spending (e.g. poor health, crime, etc.).
Does it follow that a society with a more even distribution of wealth would likely require less government spending and hence lower taxation?

EDIT: The research I found looks at income inequality, not wealth as the question asks.

Specifically with respect to social welfare spending (not necesserily taxation), the following articles from 2003 seem to suggest the opposite is true.
de Mello and Tiongson:

The political economy literature suggests that redistributive spending is higher in unequal societies due to median voter preferences.  Alternatively, it can be argued that unequal societies may spend less on redistribution because of capital  market imperfections.  Based on different  data sources, the cross-country evidence reported in this paper suggests that more unequal societies do spend less  on redistribution.

Moene and Wallerstein:

The empirical relationship between inequality and social-insurance spending as a share of GDP in advanced industrial societies differs across policies. For many policies--pensions, health care, family benefits, poverty alleviation--spending is largely uncorrelated with the inequality of wages and salaries. But for a significant set of policies that constitute roughly 30 percent of the welfare benefit--unemployment insurance, active labor-market policies, sickness pay, disability insurance, and occupational illness and injury--spending is significantly more generous in countries with a relatively egalitarian pretax distribution of wages and salaries.

But your question is framed somewhat more broadly. Inequality may potentially lead to greater spending in other areas like healthcare, police, and so on. I'm not seeing any really comprehensive studies that try to take account of all that. In terms of deficits, Larch (2010) finds that "a  more  unequal distribution of income can weigh on a country's fiscal performance." This does not necessarily show that net taxes are lower in more unequal societies, but Larch does hypothesize that "an  increase  in  the  inequality  of  income  tends  to  soften  the  relative  preference  for  fiscal  discipline". So I would say to answer your broader question, more research may be needed.


Signaling in zero-sum games? The foundation of this question is a bit vague (based on something overheard at a conference) but I'm hoping someone here can provide some clarification.

I overheard a conversation between two people at a conference saying that signaling doesn't really make sense in zero-sum games. Unfortunately, I don't have much more context than that.

I have continued to think about this statement and really can't figure out why it ``doesn't really make sense.'' The zero-sum aspect only talks about the payoffs, where the signaling aspect is concerned with how information is revealed as a function of the players' actions. I don't see why a game being zero-sum should preclude signaling.

Question: Can signaling occur in zero-sum games? Please provide a link to a paper/example if so.

I just taught my students that signalling is useless in Matching Pennies and Rock, Paper, Scissors. You would just lie and be random anyway so why would the other player ever believe any signal at all? That renders signals useless. Perhaps the people you overheard meant just that.


At what rate can a multi-billionaire liquidate his assets without significantly affecting the stock price? Let's consider three different billionaires: Jeff Bezos, Bill Gates and Warren Buffett. Now let's say the three of them (at different times) decided that they want to liquidate all their assets and get as much physical cash as possible. At what rate should they start selling their shares to end up with as much cash as possible?

I understand that this might depend on the stock trading volume but I can't really find the numbers.

I found in this article that Bill Gates sold $1.5 billion worth of Microsoft shares in 2015, so would that be the maximum?
If not, then at what rate can each of those billionaire liquidate his assets without significantly affecting the stock price and thus affecting his own net worth?

One place to start would be to look at the OnBalanceVolume technical indicator.

This is by no means reliable, but it’s a place to start.  It tells you how much of the volume hit the bid vs how much hit the ask.

On a very good day, MSFT on balance volume is 2 million shares out of ~34 million shares traded.

So presumably you could sell some relatively small percentage of the on balance volume, say 5 or 10%, without affecting the price too much.

If you sold 100,000 shares a day at $184 a share, that works out to $18million per day.

If you did that for 200 trading days per year that would be $3.6B per year.

Also note that large blocks are often traded in dark pools which may or may not be recorded in the volume.  More than likely, he sold his shares in dark pools, in large blocks,  to institutions, at the end of day closing price, over a period of months.  If this were the cases, On Balance Volume tells you nothing.  Still, it’s a place to start.