Verify Indifference curves of two utility function to be the same I'm being asked to verify that two utility functions, $U(x_1,x_2)$ and $V(x_1,x_2)$ have the same indifference curves and the same MRS.

There is no problem in verifying the MRS to be the same, but how can it be verified that the two utility functions have the same I.C.?
Should I assign a random level of utility and set them equal?

Here is a way to approach the problem:

An indifference curve is a set of consumption bundles all of which yield the same utility (the consumer being, of course, indifferent to which she consumes). Nonetheless, the numerical level of utility is inconsequential, it is just a placeholder for the more fundamental (and ordinal) preference--any monotone transformation of a utility function represents the preferences.

So let $I_U(x_1,x_2)$ denote the indifference curve (of $U$) that contains $(x_1,x_2)$. That is $$I_U(x_1,x_2) = \{(x'_1,x'_2) \in X \mid U(x'_1,x'_2) = U(x_1,x_2)\}$$
Define $I_V$ in an analogous way.

So showing the indifference curves are the same amounts to showing $I_U(x_1,x_2)= I_V(x_1,x_2)$ for all $(x_1,x_2) \in X$.


Verification of understanding of the substitution and income effect of normal, inferior and Giffen goods? My understanding is as follows:

Normal Goods: Income and Substitution effects are both positive.

Inferior Goods: Income effect negative, substitution effect positive. Substitution effect outweighs income effect and so although when the price of an inferior good F decreases (real income increases) and leads to an increase in the quantity of F consumed, this increase is small relative to the decrease in its price due to the substitution effect's magnitude being bigger than that of the income effect.

Giffen Goods:Income effect negative, substitution effect positive. Unlike inferior goods, income effect outweighs the substitution effect.

Please verify whether my understanding, as described above, is accurate.

Additionally, is it correct to assert that the positivity/negativity of the substitution/income effect of a change in price of a good remains the same regardless of whether said good's price increases or a decreases, e.g. regardless of whether the price of a normal good N increases or decreases, its income and substitution effect will always be 'positive'?

[Edited: I think that Theoretical Economist is right in highlighting that I'm perpetuating the confusion between the mathematical formalism, and one way of getting to the intuitive understanding. It also comes down to language referring to the slope of the curve versus effects that are positive or negative depending on moving up or down that negatively-sloped curve. So I clarified the table and text consistently against a price rise and Slutsky.]

I think your intuition is correct, but the derivatives have slopes in the other direction in Slutsky's equation. And it's Slutsky's equation that's ultimately given us this theoretical framework, so let's stick with that here ;)

To be clearer, let's discuss for a Price RISE:

Normal Good:   Demand- = Substitution-- Income-  [Same direction]

Inferior Good: Demand- = Substitution-- Income+  [S > I]

Giffen Good:   Demand+ = Substitution-- Income++ [I > S, weirdly]

I start my understanding of this with the demand curve. Under the “usual” laws of supply and demand, the demand-curve is backward-sloping, so as the price rises, we demand less of it. This is the Ecos101 curve we're familiar with; and it applies both to normal and inferior goods. But for Giffen goods, the demand curve has a positive slope... As the price rises, we actually demand more of it. Usually, examples of luxury goods are given as Giffen goods. The argument runs that as price is an indicator of quality and wealth of the purchaser, people actually by more of these goods as the price rises. The actual empirical evidence for the existence of Giffen goods in the real world, though, is slim and hotly debated... Sorry Apple!

So we understand the demand curves are backwards for normal/inferior, but upwards for Giffens. Why?

It was Slutsky who best disentangled demand curves as comprising an income effect and a substitution effect through a synthesis Marshall and Hicks' respective demand curves. (These are the uncompensated and compensated curves per the comments below.)

Per Slutsky's equation, Theoretical Economist is correct: The substitution effect can only ever be negative / downward-sloping. That leaves only the income effect to explain the differences between the three types of goods.

The link is that as the price of a good rises, in effect income falls. For normal goods, as effective income falls, we demand less of the good. For inferior goods, as income falls, we demand more of the good. Typical examples of inferior goods include staple foods. The idea is that as we get poorer, we cannot afford “rich” foods like meats, exotic fruits, chocolate, and so on; but must "downgrade" to cheaper foods.

Giffen is where things can get counter-intuitive. As the price of a Giffen good rises, even though effectively our income falls, we demand the good so much more that it outweighs the (always-negatively-sloped) substitution effect to yield the total positive demand.

I hope that's both more formal and clearer to understand.

Regarding your final question, the intuitive understanding around the increase/decrease in substitutions based on price rises/falls can be confusing against the fact that the slope of the substitution term in Slutsky is always negative.

From a mathematical perspective, the slope of substitution is always negative, but we can move "up" or "down" that curve to produce "positive" or "negative" changes... More or less substitution of a good.

For the second part of your question about the constancy of these effects; goods can apparently change between being normal/inferior. So if we do as we typically do in economics classes and draw out demand curves and indifference curves as straight lines, it holds.

But in reality, we know that demand curves are not immutable, straight lines, but can (a) curve and (b) change under exogenous variables. Think of the example of an asset bubble. For a while, the asset may actually look like a Giffen good: The price rises, people demand more as they jump on the bandwagon. Suddenly, the bubble bursts, and that asset is “demoted” to being a normal good (just as everyone’s income is decreasing... oops!)


Monthly average rate of discount, 3 month Treasury bills, Sterling Vs 1 Month I have been advised by one of my professors to use UK treasury bills for a risk free rate when calculating expected returns for stocks.

I wanted to know whether I should be using 1 month T-Bills or 3 month T-bills.

Which is better to use and why?
My lecturer mentioned that the risk free rates I download will be annualized percent figures (although % notation may or may not be there), so I would need to convert them to daily rates before I can you use them in regressions. Does anyone know where I can obtain this data? I found the 1 month and 3 month T-bills data on the Bank of England website. I need to know how to get the daily data for these T-bills.

Answer to your first question
Take a look at what Aswath Damadoran uses for his empirical work. He's been teaching applied corporate finance for a little while at NYU. These are his slides.

Answer to your second question
If you have access to any of the following, you should have no problem getting access to any economic and financial time series.

Datastream
Bloomberg

Also try FRED database


Endogeneity and the AR model? an AR(p) process is given by:

$$y_t=\phi_0+\phi_1y_{t-1}+\phi_2y_{t-2}+...+\phi_{t-p}y_{t-p}+u_t$$

In such a model we have endogenous variables. My question is, why is this not an issue when dealing with time series data.

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

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

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

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

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

using the Law of Total Expectations.

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


How do I use a monopsony (product market) graph to show that a firm has more buying power over a supplier? For instance, Tesco has more buying power over British farmers. How would I show this on a monopsony graph where Tesco has a surplus?

I am not sure what you mean by a monopsony graph. If you mean a graph wherein you show that Marginal Factor cost is not equal to the inverse input supply curve, then you do not need the graph at all. The fact that $MFC(x) \neq w_x$ shows that the buyer has market power.

Not sure what you mean by having "more buying power".


Under what conditions does market failure occur? Edit: Is it possible to broadly categorize the ways in which market failures occur into relatively few categories? If so, what are they?

Any situation where markets fail to clear leads to market failure. Some common reasons for this are:

Externalities, or agents not being responsible for costs or benefits of their actions
Information assymetry, or agents operating with different information
Irrationality, or agents doing random things for no reason
Principal agent problems, where someone entrusted with others funds uses them wastefully
Productive inefficiency, or firms failing to produce goods effectively given the allocated capital (think using Gatorade to water plants)
Allocative inefficiency, where firms are not provided the appropriate capital
Economies of scale, or the problem of capitalist firms failing to grow large enough to establish a service
Destructive competition- eg, private militaries blowing each other up
Shortsighted management of natural resources
Monopoly
Moral hazard, adverse selection, and other problems in contract theory


Splittet Value Function and Hamilton-Jacobi-Bellman equation General Problem

Let $k\in\mathbb{R}_+$ be the state variable, $k=k^*$ a fixed point (saddle) and $v(k)$ a value function. The problem is, that the value function has two distinct functional forms, where the switch is at the fixed point.

Do you have any reference for theses kind of problems?
Do you think a solution to the model below can be approximated?
What about a kink in the control/policy function?

Model

Let $t\in[0,\infty)$ and $k\in[0,2]$ is the state. There are two players $i=1,2$ with controls $\tau_i\in[0,1]$. Production is given by $f:[0,2]\to\mathbb{R}_+$. The wages and interests are given by $w_1=f(k)-f'(k)k$, $w_2=f(2-k)-f'(2-k)(2-k)$ and $r_1=f'(k)-\tau_1$, $r_2=f'(2-k)-\tau_2$ respectively. The law of motion for the state is given by
\begin{align}
\dot{k}=r_1-r_2.
\end{align}
There is a saddle at
\begin{align}
k^*=1,~ \tau^*_1=\tau^*_2
\end{align}
where $\tau_i^*$ depens on some parameters. Utility is given by the function
\begin{align}
u(g_i,c_i)=h(g_i)+c_i
\end{align}
where $u_g>0<u_c$. Public good is with $g_i=\tau_i k$ and consumption
\begin{align}
c_1=\begin{cases}
w_1+r_1k+\int^1_k{[r_2-a(\theta)]d\theta},\quad & k\in[0,1)\\
w_1+r_1,& k\in[1,2]
\end{cases}
\end{align}
and
\begin{align}
c_2=\begin{cases}
w_2+r_2,\quad & k\in[0,1)\\
w_2+r_2(2-k)+\int^k_1{[r_1-b(\theta)]d\theta},& k\in[1,2]
\end{cases}
\end{align}
with $a:[0,1]\to\mathbb{R}_+,~b:[1,2]\to\mathbb{R}_+$ representing some cost for $\theta\in[0,2]$.
The payoff functionals are then given by
\begin{align}
j_i(\tau_i,\tau_j)=\int^\infty_0{e^{-\rho t}(h(g_i)+c_i)dt}
\end{align}
with $\rho>0$ time preference rate. And the value functions are
\begin{align}
v_i(k)=\sup_{\tau_i} j_i.
\end{align}
Setting up the Hamilton-Jacobi-Bellman (HJB) equations for each player yields
\begin{align}
\rho v_i(k)=\max_{\tau_i} h(g_i)+c_i + v'_i(k)\dot{k}.
\end{align}
Firstly, I will fix $\tau_2$ at the equilibrium level $\tau^*$. Then the HJB for player 1 reads

\begin{align}
\rho v_1(k) &=\max_{\tau_1} h(g_1)+c_1 + v'_1(k)\dot{k}\\
  &=\begin{cases}\max_{\tau_1} h(g_1) + w_1+r_1k+\int^1_k{[r_2-a(\theta)]d\theta} + v'_1(k)\dot{k},\quad & k\in[0,1)\\
    \max_{\tau_1} h(g_1) + w_1 + r_1 + v'_1(k)\dot{k},& k\in[1,2]
    \end{cases}
\end{align}

The FOCs are
\begin{align}
\tau_1=
\begin{cases}
(v_1'(k)+k)^{-1},\quad & k\in[0,1)\\
(v_1'(k)+1)^{-1},\quad & k\in[1,2]
\end{cases}
\end{align}

First pass implementation

I used the algorithm provided by Benjamin Moll.  For reference: in his optimum growth model the value function converged within 8441 iteration and it took 0.825062 seconds.

I used a CB Production function $f(k)=k^\alpha$ with $Ak$-Technology, that is $f(k)=k$ (for $\alpha<1$ I have a problem) and log preferences a la $u(g,c)=\ln g +c$. A linear cost function with $a:\theta\mapsto (1-\theta)$.
I stopped after 200 iterations which already lasted for 21mins. In the first panel is the guess of the 1st and 200th value function. The second panel shows the difference for between the value function (convergence tendency). And the last panel ist the actual policy function, say, $\tau_1(k)$ (note the kink at $k=1=k^*$). It seems to be right from an intuitive perspective. That is, a country lowers its tax rate on capital if the capital stock is realitively small and vive versa. I'm not quite sure why the procedure is so time consuming.

Update

I was able to increase the speed. Then I increased the range of the grid to the respective endpoints of the state, as well as the number of grid points and ran the VFI (40000 Iterations) until I was out of memory. First panel contains first and final value function. The algorithms is converging with $|v^{40000}-v^{39999}|=0.0077$. The kink in the policy function still remains, but the shape slightly differs now.

I don't think I've seen cases with a kink in continuous time that are solved numerically. Aguiar & Amador (2014) have a kink in their HJB, but they solve their HJB analytically.

Validation

I don't know to what extent Moll et al's algorithm is going to get that right. You will most likely get weird behavior around the kink, but whether it's the real functional form is to be doubted, and you'll have to argue ex-post that "it looks okay alright?".

If you want to get a better grip into whether the kink looks alright, make it more extreme. Without going through your equations, it seems that the first part is convex and the second part is linear. Increase the curvature for the first part so you can "see" more easily whether it still looks correct around the kink.

Also, you definitively should look at the numerical counterparts to the first-order and second-order derivative, the first-order and second-order difference of the approximation divided by the step size. Do they have the correct signs around the kink?

One thing I'd emphasize is having many grid points around the kink. However, since the algorithm gets tougher when you have a nonlinear grid (because the grid step size is now not a constant, but a vector), it might just not be worth it and you could rather jack up overall grid points and keep it linear.

Speed

Finally, you really should look into having sparse matrices for the A and B matrices. 10 iterations per minute is really slow. It takes you perhaps 30 minutes to understand and implement (if you've never worked with sparse systems before), but already after the second time you run the code you've made up that time.

If the problem persists, have a look at profilers for your coding language. For Python, this is a nice solution. Even if you have everything sparse, perhaps you forgot some matrix that you don't even need in the iteration loop. That was the case for me, and with large grid sizes that single reinitialization took up a lot of time. Profiler will tell you what's what.


Meaning of a paragraph related to economics Until early 2016, India’s growth had been accelerating when growth in other countries was decelerating. But then the converse happened. The world economy embarked on a synchronous recovery, but India’s GDP growth—and indeed a number of other indicators such as industrial production, credit, and investment—decelerated. There are five reasons for this:

• First, India’s monetary conditions decoupled from the rest of the world. Until the middle of 2016, real policy interest rates were following the global trend downwards. Since then, the downward drift has continued in most other countries, with rates falling. But in India, for the same period, average real interest rates increased. This tightening of monetary conditions contributed to the divergence in economic activity in two ways. First, it depressed consumption and investment compared to that in other countries. Second, it attracted capital inflows especially into debt instruments, which caused the increase in demand for rupee and consequently rupee appreciates which causes dampening of exports.

Can anyone please explain what is written in bold in layman's terms?

This means that interest rates rose in India at the same time that they stayed relatively low in other areas of the world. The fact that investors could get a higher yield in India led to an increase in demand for their currency (if I can get a 5% yield on Indian bonds, why would I get a 2% yield on US bonds?) This led to an increase in demand for their currency so that investors could buy Indian bonds/Invest in India at higher yields. The appreciation of the rupee (increase in value) led to India’s goods costing more (it took more dollars to buy Indian goods for example due to the currencies rise in value). This led to fewer goods being demanded (higher prices decrease demand). So Indias exports declined.


Intuition Behind the Definition of Prudence? I'm having trouble seeing why an agent is said to exhibit "prudence" when u'''($\cdot$) > 0. How does having a utility function with a strictly positive third derivative make an agent act "prudently"? Thanks in advance.

From the Wikipedia article:

  Economists describe a consumer as "prudent" if he or she saves more when faced with riskier future income. This additional saving is called precautionary saving.

For risk averse consumers with thrice differentiable utility  $u^{\prime\prime\prime}>0$ is a necessary and sufficient condition for consumers to save more for tomorrow when they are really unsure what is going to happen in the future.


Which institutions are in the eurodollar market? My main question is: how much of the eurodollar market is claims issued by depository institutions or Bank Holding Companies?

It's about a $4tn market, but who's in it? Who is funding themselves in eurodollars and who are the dominant players?

I'm trying to figure how much of the market is outside the banking system. Any links/research is greatly appreciated.

Eurodollars are, by definition, held (on the liability side) inside the banking system. They're US dollar deposits held either outside the US or inside the US via an International Banking Facility. On the asset side, eurodollars are typically lent by nonbank financial institutions. This means that the eurodollar market links the two segments of financial markets: it's typically nonbanks providing short-term funding to banks.

For an introduction to nonbank financial intermediation, I'd recommend "Shadow Banking" (Pozsar, et. al., 2010).


What at all justifies income taxes (as opposed to sales taxes only)? For those who do not know, in America, the higher your income, the higher the percent of it is spent on taxes. This means that, whatever tax money is used for, those who are more hardworking (or, at least, those who are more skilled) are essentially punished. And, because we tax low-income citizens less, we are making their life quality nearly the same as everyone else, which encourages unemployment.

If, on the other hand, income taxes were to be eliminated and sales taxes raised significantly, we would be punishing those who spend a lot - essentially, those who abuse their wealth more. (Obviously this is not necessarily always so, but it is more so than if we apply taxes to anything else like income). This, therefore, would encourage philanthropy (and otherwise spending money on things other than buying.)

Note that this can be engineered in such a way that the total tax money the government gains stays the same.

The Question: Why does much of the world still have income taxes? Is there anything (and if so, what?) that makes them better, fairer, or more productive than sales taxes?

*This question is not a copy of the question Are sales taxes regressive? because the linked question is asking specifically whether sales taxes decrease in burden as income increases. My question is explaining that that doesn't matter.

There's a fair amount to unpack in the question, so it might be useful to take it step by step, and consider everything from a more abstract, economic theory perspective.

  ...those who are more hardworking (or, at least, those who are more skilled) are essentially punished....

We should be careful making statements like this for a couple of reasons. First, the assumption may or may not be true, depending on what model of wages you think applies. For example, if wages are largely determined by bargaining, then it isn't clear that wages necessarily directly (or perfectly) correlate with how hard an individual works, or their skill level. Even if we use a non-bargaining wage model, plenty of "unskilled" jobs (for example, auto workers or welders) make more than "skilled" jobs (for example, many teachers). Second, it isn't clear that progressive taxation should be considered "punishing" high income earners. Given that tax brackets are all applied at the margin, earning more only means that (all else equal) your last dollar will be taxed more than your first dollar.

  because we tax low-income citizens less, we are making their life quality nearly the same as everyone else, which encourages unemployment.

While we're flattening the differences between the highest and lowest income earners a bit, I'd hesitate to claim that "we're making the quality of life [of low income earners] nearly the same as high income earners." Given that income still has substantial impacts on quality and duration of life, I'd be hard pressed to agree that we've equalized quality of life.

Beyond that, of course, there's the larger Social Choice problem of "why is somewhat equalizing quality of life a bad thing?" Given that employment and income potential aren't entirely defined by an individual's own effort, but are correlated with many factors that are determined by one's "luck of birth," creating a society that doesn't at least attempt to account for this exogenous "luck" factor seems arbitrary and somewhat cruel.

  ...we would be punishing those who spend a lot - essentially, those who abuse their wealth more.

Again, I'm a bit intrigued by your choice of wording there- why do you consider someone spending income "abusing" it, particularly if we accept your earlier premise that income is tied closely with effort? Isn't spending one's income merely realizing the actual utility potential they earn from doing a job? And if that's the case, why should we discourage spending one's income by substantially raising sales taxes?

  This, therefore, would encourage philanthropy (and otherwise spending money on things other than buying.)

There already exist commonly used mechanisms to encourage philanthropy through taxation: deductions. This method provides a much larger potential incentive to encourage philanthropy, since it effectively makes giving to charity "cheaper" than both spending and holding earned income (since money given isn't counted against your income), as opposed to merely spent income under your proposal. In other words, with an income tax of $\tau$, every dollar I give to charity only costs me $(1-\tau)$, which is the amount I would keep if I took the dollar as opposed to donate it. If there's only a sales tax, then the cost is the full dollar.

So, getting to the crux of the question- there are several reasons the world currently has income taxes. First, there's a distributional concern: the sales tax that would be required to offset income taxes would be quite high, and would cause significant hardship for poorer families. Moreover, only having a sales tax can lead to incentives for wealthier individuals to horde wealth as opposed to spend it, which actually leads to significant economic distortions, and adverse economic outcomes (for example, a fair amount of recent research suggests that too high levels of wealth inequality can lead to slower overall economic growth). As to whether there are fairness implications, I'd point out that the regressive nature of sales taxes are important on this point. Given that a comparatively larger burden of the tax would fall on poorer individuals (since they spend higher proportions of their income), eliminating the income tax in favor of a consumption tax would have distributional consequences.

I don't mean to sound nit-picky or like I'm dismissing your question out of hand, for the record. There is an important debate to be had for any society regarding how its citizens should shoulder the combined tax load. However, I think most of the debate occurs "inside" of your assumptions made in the question, and only by closely examining those can the debate be meaningful.


How do I verify Philips curve empirically for recent years? I wanted to verify the relationship between inflation and unemployment empirically, so I took data from the World Bank and used excel to correlate them.

I got a very, very bad correlation between unemployment and inflation (from 1991 to 2016). Am I doing something wrong here?

I took these two sets of indicators: (1) Unemployment, total (modeled ILO estimate) and (2) Inflation, consumer prices. Here are the links: http://data.worldbank.org/indicator/SL.UEM.TOTL.ZS and http://data.worldbank.org/indicator/FP.CPI.TOTL.ZG

I downloaded the data from here and I studied the data for the United States of America. Is the low correlation because of the fact that the market needs time to react to unemployment rates? If so how did Phillips study it in the first place?

Simple correlation is not a good approach to evaluate the Phillips curve, because you are mixing many periods together. To get a better grasp of what this relationship might have been in the past, use a graphical approach.

I suggest you to do something like this:

So basically, you plot the points, but add a line that connects them temporally. This might give you a better idea of some dynamics. It is clear from that graph that a simple correlation cannot capture the complex dynamics of inflation and unemployment.

For example, this is an animation of the evolution of the Phillip curve for the US:

The author identifies three or four PC over 40 years, reflecting different political/economic periods. A simple correlation analysis however would show none.

Source of images: here.


Persistent changes in relative prices due to productivity differences I read a couple of years ago that in the long run (in centuries) the relative price between, say, schooling and agriculture keeps increasing, since the latter sector gets more and more productive, while there are barely any productivity gains in schooling.

I couldn't find literature that talks about it.  What is the name of this mechanism, or related literature?

When comparing industries it is almost intuitive that a relative productivity increase causes a relative price decrease in the absence of anything else happening. The reason it is intuitive is that all the competitors within the same industry probably benefit from the same productivity increase so together you can all raise prices slowly or not at all or decrease prices.

You might be looking for the Baumol effect. Wikipedia says...

  The rise of wages in jobs without productivity gains is from the
  requirement to compete for employees with jobs that have experienced
  gains and so can naturally pay higher salaries, just as classical
  economics predicts. For instance, if the retail sector pays its
  managers 19th-century-style salaries, the managers may decide to quit
  to get a job at an automobile factory, where salaries are higher
  because of high labor productivity. Thus, managers' salaries are
  increased not by labor productivity increases in the retail sector but
  by productivity and corresponding wage increases in other industries.

According to this, a necessary condition for the Baumol effect is competition between industries for resources.

This is the relevant link.


Monetary Policy and international reserves-- interpretation of the estimated coefficient I have a problem in interpreting a coefficient in my regression below:

I am estimating the following regression in the spirit of an event study analysis with daily data:

$\Delta ER_t = \beta_1 MPS_t +\beta_2 MPS_t \Delta Res_{t'} +\epsilon_t$

in which $\Delta ER_t$ is the exchange rate between day $t$ and day $t-1$, $MPS_t$ is a monetary policy shock at time $t$ and $\Delta Res_{t'}$ is the change in foreign exchange reserve between the $\textbf{month}$ following the monetary policy shock and the $\textbf{month}$ previous to the monetary policy shock (I do not have daily data on international reserves but only monthly data).

How should I interpret $\beta_2$, the interaction term between the monetary policy shock and the change in international reserves? It is clearly not uncovering causation since $\Delta Res_{t'}$ includes a lead variable (the level of reserves one month after the shock), but then can I still argue for an inverse causation effect? For example if I find that the $\beta_2$ is positive and significant, can I claim that larger future international reserves (which increase $\Delta Res$) arise as a consequence of monetary policy shocks that have a larger impact on the exchange rate today?

No, it's a regression model. You can't infer any causality from it.

At best, you can infer that there is correlation between the terms.

But note that even that inference can be hazardous. Without knowing how you got the model terms, what your priors are, and what the data is, it's not possible to say whether or not the correlation is spurious


What is the point of monetary policy if most monetary variables are determined by non-monetary factors? Monetary policy today is largely focused on setting interest rates in order to reach an inflation target / value of the currency. Interest rates are used to affect inflation by changing the demand and supply for saving and borrowing, i.e. demand. It is entirely monetary. However, I get the impression that inflation rates respond primarily to non-monetary factors, such as technological innovation, business growth, and the expansion of international trade. I also feel that this is true of the long-run interest rate, which has apparently fallen due to demographic changes (ageing populations causing a savings glut) and international trade imbalances (funds from trade surpluses in exporting nations being invested in importing nations' financial markets). None of these factors are the responsibility of a central bank to manage yet they seem to be the ultimate determinants of monetary conditions, at least in the long-run. Friedman's quote 'Inflation is always and everywhere a monetary phenomenon' springs to mind as a argument against what I am saying. Is my chain of thought a fair criticism of monetary policy?
These are simply thoughts I have been having so I apologise for the vagueness of the question. I'm looking for someone else's thoughts on the matter and possible ideas to develop the argument further.

I do not know of any serious economist who would think that monetary variables are not to great extent determined by the decisions of central banks.
Monetary quantities depend on what the price level is which is in turn determined by the money market equilibrium. The money market equilibrium, in its simplest form is given by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY$$
Where $M$ is the money supply, $V$ velocity of money, $P$ price level and $Y$ output.
Solving for price level and log-linearizing (so $\%$ changes in right hand side variables give us the $\%$ change in $P$) we get:
$$\ln P = \ln M + \ln V - \ln Y. $$
First observation that you can clearly see from the above is that technology growth or trade do not generally cause inflation. Both trade and technological growth expand production possibilities of our economies and hence they generally lead to higher real output $Y$. This causes deflation not inflation.  Inflation is positive change in price level but increase in output causes decrease in price level.
The velocity depends on what nominal interest rate is so this can be affected by central bank, although velocity can depend also on other factors so it is not fully under its control.
What the money supply is, is completely exogenously given by central bank. Some countries can have institutional restrictions/caps on how and when central bank can increase money supply but these are not economic restrictions and in principle central bank can set $M$ to any value it wants on interval $[0,\infty)$.
Setting the theory aside empirically there is strong relationship between inflation and changes in the money supply. For example, consider the two scatterplot below (from Mankiw Macroeconomics pp 91-92). The first plot shows the relationship between money supply growth in the US and inflation in the US at different points in time (figure 1) and the second one does that internationally for averages for period 1999 to 2007 (figure 2). As you can clearly see data indicate very strong positive relationship. In addition you can see the same strong relationship between nominal interest rates and inflation. These data support also the theory from the above. Of course, correlation does not immediately tells you what the direction of causality is (but these are differenced data so the correlation is definitely not spurious and indicative of some relationship), but there are further academic studies that show that there is without doubt causal relationship between money supply and inflation, and also interest rates and inflation (for example see Maune,  Matanda, Mundonde, 2020;; Barsky, 1987; Mankiw 2019; Romer: Advanced Macroeconomics 4th ed; Grauwe & Polan, 2005; and sources cited therein).
Appendix:
Figure 1:Historical Data on U.S. Inflation and Money Growth

Figure 2: International Data on Inflation and Money Growth

Figure 3: Inflation and Nominal Interest Rates Across Countries


Find Price elasticity of demand in this example ln(Q) = 10-0.7ln(P), where P is price and Q is demand.

What is the price elasticity of demand?

Did you know you can write price elasticity $\varepsilon$ as $\varepsilon \equiv  \frac{d \log Q}{d \log P}$?

(Indeed, $\frac{d \log Q}{d \log P} =\frac{dQ}{dP} \frac{P}{Q}$. Check out wiki on elasticity of a function if you want more detail!)

Using this "log notation" for elasticity, it is easy to see without putting pen to paper that in this example, $\varepsilon = -0.7$.


Does immigration help to sustain welfare in rich European countries? There is a lot of discussions about immigration and its effect on economies lately in Europe, so I'd like to ask a question. Is it true that immigration helps to sustain welfare in rich European countries? For example, in the case of pensions, since life expectation is increasing and natality rates are decreasing in the richest European countries, the ratio of people receiving a pension to that of active workers (who pay those pensions with their taxes) is increasing. Since immigrants usually have a higher natality rate, they should help counteract this effect.

However, often people counter this argument by saying that immigrants receive much more money from welfare, than they return through taxes, for various reasons:

unemployment is much higher among immigrants than among natives
there are many irregular immigrants who still receive healthcare (if they go to an emergency room), but who don't pay taxes
etc.

Especially (but not only) in Denmark, this constant grievance has reached incredible levels. It seems to me baseless racism, but I'm not an economist, so I'd like to know:  are there studies which prove that the contribution to welfare from immigrants is a net positive? Are there studies that indicate that by blocking immigration, rich European countries would risk not being able to pay pensions in the future?

Here is a chart from the OECD, which shows the net fiscal impact of migrants on their recipient country (i.e. by how much to they contribute or withdraw from the welfare state, albeit excluding in-kind benefits such as healthcare). For most Western countries, Denmark included, migrants are modest net positive contributors ("they pay in more than they take out").

This is because migrants tend to be disproportionately working age, whereas the native population contains many retired or young people. Thus, migrants tend to pay a lot of income tax relative to the average native. Luxembourg and Switzerland stand out because both are small economies that attract many high-wage knowledge workers.

On the vertical axis of this chart is the net contribution to the fiscal budget. So a value of 1% means $(\$\text{tax paid}-\$\text{welfare received})/\$\text{GDP}=0.01$. Note that this is different to (and less than) migrants' overall contribution to GDP because, for example, migrants keep much of their contribution to GDP in the form of after-tax wages.

I took the chart from Oxford's migration observatory, which has more information specific to the case of the UK.


Proving or disproving hypothesis? I took statistics class years ago in my college and I don't remember much of it now. I am into public policy research now and I am bit confused about about what conclusion to make from available evidence.

Poverty is the 'root cause' of child labour is what is claimed by International Labour organization (ILO) and thus by lot of other countries. Evidence often cited for this is: most of the child labourers are from poor backgrounds in most of the countries where child labour is prevalent. So there is a correlation and for causality, if we think about it, no money => to earn money => all healthy individuals must work including children => child labourers.

Now I've read few research studies which claim that Poverty is not the root cause of child labour and the evidence they cite is,

There are poor countries where there is hardly any child labourers.
There are children studying in schools who are lot more impoverished than those who are working.
There doesn't exist a poverty line below which a parent is compelled to send their child to school.

So people on this end say, if poverty is the root cause then could we explain this. But this argument could be reversed too. Either way, I'm confused.

How should I go about interpreting and understanding this?

What data is required, and what analysis has to be carried out to settle the question, whether poverty is the cause or not? In other words, I want to set my hypothesis to be "Poverty is not the root cause of child labour", what should I do to either prove or disprove it?

I want to see this to the end. So feel free suggest some readings if you need to.

This is more of a logic question than it is a statistics question. I would say that the first point to address would be to define "root cause." Does that mean it is a sufficient condition? A necessary condition? Line of evidence #1 (there exist poor countries with few child labourers) precludes the possibility that child labour is a necessary condition of poverty as clearly poverty can exist without it. #2 reinforces that conclusion (again, poverty existing without child labour, just at a different scale).

Regarding point of evidence #3, I don't see how that is relevant: whether or not some policy exists compelling parents to act in a certain way doesn't affect the relationship between child labour and poverty.

As you allude to above, correlation is not causality. In this case, it seems from the correlation you can make equally strong arguments going both directions: child labour causing poverty; poverty causing child labour. You can make a logical case for it built on case studies, but making a statistical case for causality would require digging much further into the data.


On a Dalio youtube video The following video https://www.youtube.com/watch?v=PHe0bXAIuk0  argues that credit is the principal force behind the business cycle.

Is this considered to be a established truth within some school of thought and is there a specific school of thought that disagree?

I think this question is too open-ended and unqualified. One can point to two economists in particular who highlight the importance of debt in the cycle - Hyman Minsky and Steve Keen. Both of these economists are not considered to be “mainstream” (although Minsky has been more heavily cited since the Financial Crisis).

If we look at the data, we see that credit (debt outstanding) grows during the cycle, and this can cause financial distress (not always). However, one could argue that the debt growth is a side effect of growth, and not the causal factor. Even though I am highly sympathetic to Minsky’s work, that criticism appears valid. We need to qualify exactly what we mean, but the question has no such qualifications.


Disruption vs economic growth vs inflation On the terms:

Disruption is when new players earn say 1m but take over of a 100m market segment, causing damage to well established but less innovative businesses
economic growth is what we read about growing markets and iverall economy
Inflation is when money gets less worth

Are all these three somehow interconnected, correlated or rather independent? Are there established works on that?

For example, could major diruption outpace economic growth and emphasize inflation?

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

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


How does a CLEC innovate? A CLEC, competitive local exchange carrier, is described...

A competitive local exchange carrier (CLEC), in the United States and
Canada, is a telecommunications provider company (sometimes called a
"carrier") competing with other, already established carriers,
generally the incumbent local exchange carrier (ILEC).

The source for this quote... is a Wikipedia page.
It is my understanding that the ILEC is a former monopoly and that former monopolies usually exist because they were or are natural monopolies. The introduction of a CLEC does not change the fact that the infrastructure of the ILEC has a high cost to create and that cost is an insurmountable obstacle to creating a parallel infrastructure. In fact, the CLEC typically does not create a parallel infrastructure and instead it will rent use of the original electronic or optical fiber infrastructure of the ILEC.
The basis of competition would seem to originate in infrastructure other than the electronic or optical fiber infrastructure. This might take the form of what used to be a call center, although these people can work from home so physical call centers do not even need to exist. Websites can replace call centers for a business that wants to completely avoid talking to people. What remains is the mental effort to create a website to advertise and support customers of the CLEC and perhaps some retail locations to do essentially the same thing that the website does. CLECs exist on what is a small fraction of the infrastructure of the ILEC. If the infrastructure is small there is not a big domain in which to innovate. If the industry is mature there may not be obvious ways to innovate. If there is no innovation then the large scale operation wins; the ILEC wins.
Obviously the CLEC can exist if the ILEC decides not to force the CLEC out of business through competition. The ILEC wants to be popular with politicians and regulators and politicians want to be popular with voters. The CLEC can thrive if politicians want it to thrive and if the ILEC knows what the politicians want. An different way for politicians to be popular with voters is to regulate the profit of the ILEC and voters will pay lower prices. The ILEC profit might be so low that there will be no CLECs.
Edit: The question is "how does a CLEC innovate?" There were comments that suggest CLECs are not innovating and that CLECs are "innovating better ways of getting your money, not better ways of making the Internet work". These comments seem to take a narrow view of innovation being necessarily connected to technological improvement and at the same time seem to allow that "getting your money" is an (ironic?) innovation. I do not subscribe to the narrow view and the irony. I think the word innovative is appropriate to describe any business that can sustain itself in a competitive environment. My broad view is that every form of differentiation is an innovation whether we can prove the individual differentiating choices are beneficial or not. Since there is uncertainty we cannot rule it out. This question recognizes that the status quo shows that the CLEC business model works, but how and why?

Two  types  of  innovation,  namely  innovation  for  new  services  and  innovation  for  alternative  network  infrastructures,  underlie  competition  in  the  telecommunications  industry.  While  innovation  for  new  services  is  provided  mainly  by   telecommunications   operators,   equipment   suppliers   provide   most   of   the   innovation  for  new  network  technologies.  A  network  innovation  in  the  equipment  sector   is   followed   by   an   adoption   process   in   the   telecommunications   sector.   Operators have to decide whether and when to adopt the new technology. Indeed, an immediate   adoption   may   be   costly   and   risky.   Therefore,   adoption   resembles   innovation.   In   the   rest   of   the   paper,   innovation   will   refer   to   both   invention   (endogenous innovation) and adoption (exogenous innovation).

Generally,  regulation  can  affect  these  innovative  activities  via  two  different  channels.    First,    price    regulations    (or    more    specifically,    the    regulation    of    interconnection  charges  and  retail  prices)  alter  industry  profits,  hence  the  incentives  to innovate. Secondly, both price or entry regulations change the terms of entry, and hence innovation decisions regarding new entry.

Regulation and Innovation: M Bourreau and P Doğan 1 Regulation and Innovation in the Telecommunications Industry
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.477.412&rep=rep1&type=pdf
CLECs are given incentives to deploy capital investments that innovate in terms of services and network technology. ILECs are forced to offer competitive services and improve network technology to keep market share away from the CLECs. In the counterfactual world of natural monopoly the ILEC would not have incentives to innovate services or network technology. The ILEC would profit from investments in POTS - Plain Old Telephone Service - for a considerable period of time without any competitive forces making it adopt innovative services or network technology.


How do we explain the difference in average leverage between banks and non-financial firms? I've been reading a little about the capital structure of banks. For example, in this working paper, "Financing as a Supply Chain: The Capital Structure of Banks and Borrowers" by Gornall and Strebulaev (accessed 2014), it mentions this:

There is disagreement on the causes and effects of high bank leverage; however, there is no disagreement that banks and other financial institutions are indeed highly indebted. The average leverage of U.S. banks, measured as the ratio of debt to assets, has been in the range of 87%-95% over the past 80 years. At the same time, the average leverage of public U.S. non-financials, measured in the same way, has been in the range of 20%-30% over a long period, below the predictions of many models. This dramatic difference in financial structure is puzzling at first glance.
In this paper, we explain this gap by modeling the interaction between a bank's debt decisions and the debt decisions of that bank's borrowers....

I am unfamiliar with this literature. I'm wondering, what other explanation exist in the literature to explain the difference in the average leverage between banks and non-financials?

The point @EnergyNumbers raises is correct, and it's easy to understand from an intuitive standpoint: One of the key roles of financial intermediaries is to match the demand for liabilities of a given tenor to the demand for assets of a given tenor.

Financial intermediation allows maturity mismatches to exist in non-finance sectors of the economy by taking the opposite position. To do this, though, financial intermediaries such as banks must have far higher leverage than firms in the rest of the economy.

Consider, for a moment, the tenors of assets that consumers hold: outside of retirement investments (for consumers who are far from retirement age), most consumers have long-dated liabilities (mortgage loans, student loans, etc.), and short-dated assets (bank deposits, money market fund holdings, etc.). This mismatch exists for good reasons. On the liability side, for example, it's not insane for someone to want to own a house and consume housing services before having 100% of the cash necessary to purchase one outright. This sort of consumption smoothing, where one with a long horizon for future earnings brings forward a fraction of their lifetime consumption, is generally considered to be optimal behavior from a utility standpoint.

At the same time, on the asset side, consumers have to be able to smooth shocks to their income, and thus having short-dated, liquid assets, like bank deposits, is also optimal. If you're a consumer who holds all his extra cash in equities, you're going to be really sad when the stock market tanks at the same time that you lose your job and need to cash out of the stock market to cover your expenses for the next few months.

Similarly, non-financial firms have the same sort of demand for assets of particular tenors— they need a certain amount of cash for liquidity management, but at the same time, they want to be able to invest in capital projects (purchase equipment, etc.) that will pay off over a long time horizon.

Of course, in a closed system, the tenor of assets has to equal the tenor of liabilities. So how do we balance this? Financial firms take the other side of these trades, accepting significant maturity mismatches.

Non-financial firms are able to do engage in productive investments by making a deal with financial firms in which the non-financial firms give up a share of their future production in the form of interest payments in exchange for long-dated liabilities. Similarly, consumers are able to engage in consumption smoothing by giving up a share of their future labor income to financial firms in exchange for long-dated liabilities. The financial firms, for their part, end up holding a lot of long-dated assets, while being funded to a great extent by short-dated liabilities (such as bank deposits and money market fund holdings through the wholesale funding market). Financial firms make their money on the spread between maturities (the "carry")— the whole "borrow at 3%, lend at 6%, be at the tee by 3pm" thing.

This has a couple of implications:

The amount of liabilities financial firms must hold relative to assets is a function both of the demand for assets and liabilities of differing tenors in the rest of the economy (i.e., the maturity mismatch in the rest of the economy) and of the size of the financial intermediation sector relative to the rest of the economy. The smaller financial intermediation is relative to the rest of the economy, the higher the leverage necessary in financial firms to rebalance maturity mismatches elsewhere.
The existence of significant maturity mismatches in finance means that liquidity risk is concentrated in financial firms, which could lead to bank runs. This is why deposit insurance is used, and also why banks are given access to the Fed's discount window.


What is meant by an inflation rate spoken in the typical news? The news usually says that inflation for a certain month is say $2.57\%$.  It is never said relative to what.  Should I assume that is relative to the previous month?
If that's so, then the more inflation rises, the more likely the percentage reported will be small and eventually negative --- otherwise, inflation would be rising exponentially.
Wouldn't be more useful if we would look at inflation since the a certain historic mark?  In the US, for example, shouldn't we look every day how much money the dollar has lost its value since 1917 or 1971?

In media the inflation number that you see is generally the Year-on-Year inflation rate, i.e.,
$$\frac{I_t-I_{t-12}}{I_{t-12}}$$
where $I_t$ is the price index (CPI or WPI). For most countries, the index is a fixed base index. So the absolute value of the index gives you the idea of where the prices are relative to the base year.
Inflation rate on the other hand gives you idea of how much the index has increased as compared to same month previous year. The main reason for using YoY over MoM is to prevent seasonality misleading you.
For example, if media reported MoM, every December you'd see high inflation because of holiday season. So inflation of December is not strictly comparable with other months because of inherent seasonality. To prevent this YoY is used.
On your second point: No inflation does not keep decreasing with time. This would be true if price increases with a decreasing slope. There is no economic reason to believe that.
On third point: if we only looked at inflation rate from a historic point then that number would rather be an increasing number. Then again you would not be able to compare it with previous months' or years' numbers as then the difference of inflation would be of interest.


A simple question on a relationship between output growth rate and unemployment rate I'm reading Blanchard's Macroeconomics, and on page 206 of the 5th edition, he writes:
«Let $u_t$ denote the unemployment rate in year t, and $u_{t-1}$ the unemployment rate in year t-1, and $g_{yt}$ the growth rate of output from year t-1 to year t. Then under these two conditions ($Y_t=N_t$ i.e. Output=Employment, and labour force $L_t=L$ constant), the following relation would hold: $$ u_t-u_{t-1}=-g_{yt}$$

But what I get is $\frac{Y_{t-1}-Y_t}{L}=-\frac{Y_t-Y_{t-1}}{Y_{t-1}}$ which is not true... where did I go wrong, or is there a typo?

Any help would be appreciated.

I get the same equation as you do. So you are correct. But tough usually $u_t - u_{t-1} \neq -g_{y_{t}}$, for small values of $g_{y_{t}}$
$$
u_t - u_{t-1} \approx - g_{y_{t}}
$$
does hold. In macroeconomics these kind of (in my opinion annoying) approximations are used every now and then. The author perhaps neglected to mention that he was using an approximation. For example the Fisher equation is sometimes written as $i = r + \pi$, even though it is actually $i \approx r + \pi$ and that only for small values of $r,\pi$.


What are main reasons a typical DSGE model is called non-linear? Why are these non-linearities important? What are main reasons a typical DSGE model is called non-linear? Why are these non-linearities important? Is a non-linear model inherently less stable than a linear model? Why?

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

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

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


Why can high variance help you in Heckman (1998) but not Aigner and Cain (1977)? Heckman (1998) argues that, if the bar for acceptance is high (so most applicants are rejected), then belonging to a group who quality has high variance tends to help you. The argument is something like this: if employers only hire people whose quality exceeds a certain cutoff, but most people fail the cutoff, then if your group's distribution of quality has higher variance it will have more mass above the cutoff.

Aigner and Cain (1977) also discuss variance based discrimination. Assuming that you send a signal equal to your group's mean, the only effect of higher variance is to dissuade risk averse employers to hire you. There is no Heckman style mechanism where high variance can help you if most people get rejected.

I would be very grateful if someone could explain what leads to this contrast.

My (possibly confused) thoughts on this: the Heckman model makes sense if employers decide whether to grant an interview based on whether the probability that someone's quality is above a certain level exceeds a certain cutoff. But that is a crazy hiring rule! Instead, they should just look at whether expected quality exceeds a certain cutoff (to be fair to Heckman, this is supposed to be the hiring rule.)

OK suppose that this is the hiring rule: can high variance still help you (in the context of an audit/correspondence study)? Well, I can see how this works if the researcher perfectly controls on one dimension (e.g. what the auditors say) but doesn't control on another (e.g. attractiveness), and one group has higher variance on that second dimension, which means more of them get over the bar. But that logic totally breaks down in correspondence studies (supposedly also a target). Here the employer does not get to see some realisation from a distribution of quality that is unobserved by the researcher. At best, the employer can say: that group's high variance, so more likely to exceed the cutoff. But that brings us back to the crazy hiring strategy already discussed.

Say you have two distributions, $G$ and $H$ with equal means supported on (say) $[0,1]$ and $H$ is second-order stochastically dominated by $G$. Then, for any concave increasing $u$, we'll have $$\int udG \geq \int udH$$ This would correspond to Aigner and Cain, where the risk averse firm would prefer to hire an agent from distribution G.

However, now suppose that $G$ and $H$ are distributions of talent (with the same stochastic ordering i.e. $H \succ_{C} G$). One equivalent notion to this idea is that distribution $G$ can be obtained by ``fusing" together part of the mass of $H$, i.e. by collapsing part of the mass to its respective barycenter. Given this, it is easy to see that there is always a cutoff $\eta \in [0,1]$ such that $H(\eta) \geq G(\eta)$.

This corresponds to Heckman's result--if the job is sufficiently demanding, then it will be (at least weakly better) to be part of the high variance population. Moreover, note that this by no means depends on the expected quality of the agent. There are simply more of the highest quality people in the group with distribution $H$ than in the group with distribution $G$. They are not just more likely to exceed the cutoff, there are more of them that exceed the cutoff.

Another way to think about the hiring problem is as follows: say a firm wants to hire one person but receives applications from $10$ applicants, $5$ from group $A$ and $5$ from group $B$. A candidate's quality is unknown and it it ranges from $[0,1]$ continuously. Suppose also for the sake of simplicity that the firm may observe the candidate's group (and so knows what distribution he/she is drawn from): the distribution of quality for group $A$ is given by $G$ and the distribution of quality for group $B$ is given by $H$. Interviewing a candidate fully reveals a candidate's type, but the firm has the budget to interview only $4$ candidates. Whom should they interview?

The answer is simple: all four candidates interviewed should be from group $B$ (which has distribution $H$). Why? Because we can think about a candidate's quality as a random variable $X_{i}$ and thus the firm wants to maximize $\mathbb{E}[Z]$ where $$Z:=\max\big\{X_{1},X_{2},X_{3},X_{4}\big\}$$ Since $H \succ_{C} G$, $$\mathbb{E}_{H^{4}}[Z] \geq \mathbb{E}_{G^{4}}[Z]$$

Note also that $H \succ_{C} G$ $\Rightarrow$ $Var(H) \geq Var(G)$ but not $\Leftarrow$. In this sort of thing, I think it is stochastic dominance and not variance that is the apposite metric.


Quickest way to learn about yield management and revenue maximization? I have been asked to determine the optimal ticket prices for live-events. Strictly speaking, I'm working as a data scientist for this company, so this question is a outside my field of expertise. I have a PhD in physics, and I've been trying to learn Micro-econ by watching MIT/Coursera videos.

Separately, from reading articles online, I know that given the inventory (which is similar to airline tickets or hotel rooms) I don't want to find the optimal prices by solving a revenue maximization type problem but rather through yield management. Is this correct?

There are already questions on SE (Where to start learning economics as a mathematician?, Introductory or Primer text on Economics?), about resources for learning intro economics.

But what I would like is a set of books, or online tools that would take someone like me with NO formal training in economics from zero to a firm grasp with the concepts of yield management and revenue maximization.

You should seek for topics under Industrial Economics then. I have these books has reference (see below list). Keep in mind that Industrial Economics is highly focus on competition and market power.

Industrial Organization: Markets and Strategies.
Microeconomic Theory: Basic Principles and Extensions

I find them both easy to read and understand concepts, mainly the first one. When I first had to work with it, my common problem was with the math, but if your background is in Physics, I'm sure you'll have no problems understanding the functions transformations.

Coursera also has some courses that slightly approach Industrial Economics, like this one, but I guess this will not suffice to you.


Burdett and Mortensen (1998), Equation (22), Integral by parts question Suppose $F(x)$ and $H(x)$ are both cumulative prob dist functions on the support of $[b_0,b_1]$ and we know followings:

$$u(x|F)=\int_{b_0}^{x}\frac{m}{1+k[1-F(b)]} dH(b)$$

and from this

$$[1+k(1-F(x))]du(x|F)=mdH(x)$$

We also know that

$$G(w)(m-u(b_1|F))=\frac{k\int_{b_0}^w [F(w)-F(x)]du(x|F)}{1+k(1-F(w))}$$

Then in the paper, authors get following which is equation [22] in the paper

$$\frac{(m-u(b_1|F))dG(w)}{dF(w)}=\frac{kmH(w)}{[1+k[1-F(w)]]^2}$$

I really don't understand how the authors got this. Can somebody help me?

The authors apply in the second step the exact same rules they used in the first step, regarding the calculation of the total differential of an integral, taking also into account that the integral is taken over a function of the integrating variable and not just the integrating variable itself.

The first step is

$$d[u(x|F)]=d\left[\int_{b_0}^{x}\frac{m}{1+k[1-F(b)]} dH(b)\right]$$

$$=\frac{m}{1+k[1-F(x)]}dH(x) \tag{1}$$

and re-arranging we get the first result. Applying the same logic, we have

$$(m-u(b_1|F))\cdot d\big[G(w)\big]=kd\left[\frac{\int_{b_0}^w [F(w)-F(x)]du(x|F)}{1+k(1-F(w))}\right] $$

We are considering the differential with respect to $w$, since this is the argument of the $G$ function. To clearly indicate this we will write $d_w$. To clarify the picture write

$$kd_w\left[\frac{\int_{b_0}^w [F(w)-F(x)]du(x|F)}{1+k(1-F(w))}\right] \equiv k d_w\left(\frac{A(w)}{B(w)}\right) = k\frac{B(w)d_wA(w) - A(w)d_wB(w)}{[B(w)]^2}$$

We see that the denominator is exactly as the final expression of the authors, so it is of no concern. We turn to the numerator.
One by one,

$$ d_wA(w) = d_w\left[\int_{b_0}^w [F(w)-F(x)]du(x|F)\right] $$

$$= [F(w)-F(w)]du(w|F) + \left[\int_{b_0}^w d_w[F(w)-F(x)]du(x|F)\right]$$

$$= 0 + d_wF(w) \int_{b_0}^w du(x|F) + 0$$

We applied here Leibniz rule for differentiation w.r.t. a limit of integration under the integral when the integrand is also a function of the integrating limit. The second zero result comes from the fact that $d_wF(x) = 0$ ($F(x)$ does not include $w$, so as we change $w$ the change in $F(x)$ is zero). So

$$B(w)d_wA(w) = [1+k(1-F(w)]d_wF(w) \int_{b_0}^w du(x|F) $$

$$= d_wF(w)\int_{b_0}^w [1+k(1-F(w))]du(x|F) \tag{2}$$

where we have moved the term inside the integral since it does not depend on the integrating variable which is $x$.

Going to the second term, we have

$$d_wB(w) = -kd_wF(w)$$

So

$$-A(w)d_wB(w) = d_wF(w) \int_{b_0}^w k[F(w)-F(x)]du(x|F) \tag{3}$$

Therefore

$$B(w)d_wA(w) -A(w)d_wB(w) = d_wF(w)\int_{b_0}^w [1+k(1-F(w)]du(x|F) \\+ d_wF(w) \int_{b_0}^w k[F(w)-F(x)]du(x|F)$$

The $d_wF(w)$ is a common factor and the two integrals can be written as one due to linearity, so

$$B(w)d_wA(w) -A(w)d_wB(w)=\\ = d_wF(w)\int_{b_0}^w\Big([1+k(1-F(w)] + k[F(w)-F(x)]\Big)du(x|F)$$

The term $kF(w)$ in the integrand cancels off and we are left with

$$B(w)d_wA(w) -A(w)d_wB(w) = d_wF(w)\int_{b_0}^w[1+k(1-F(x))]du(x|F)$$

But using the re-arranged $(1)$ and substituting we get

$$B(w)d_wA(w) -A(w)d_wB(w) = d_wF(w)\int_{b_0}^wmdH(x)$$

$$= md_wF(w)\cdot \Big(H(x) \big|_{b_0}^w\Big) = md_wF(w)\cdot \Big(H(w) - H(b_0)\Big)$$

But since $H()$ is a CDF in $(b_0, b_1)$, it follows that $H(b_0) =0$.

And we are done. In short, don't be afraid to push through the mathematical calculations.


Divinity for Dummies I understood the general idea of divinity: that it helps to rule out "unreasonable" equilibria.  However, can someone explain it in more details with simple examples so that a senior undergrad student understands it?

Signaling games (games in which an informed "sender" moves first and an uninformed "receiver" second) typically have a plethora of Perfect Bayesian Equilibria which is not really appealing in terms of predictive power.
However, as you already said, some equilibria may be "unreasonable". Refinements serve the purpose to formalize which of these equilibria are unreasonable.

Sequential Equilibrium is not really helpful in eliminating the equilibrium multiplicity, because the multiplicity of equilibria stems from the fact that PBE allows off-path beliefs to be "crazy". That is, we can support many equilibria by assigning "crazy" beliefs when a signal is sent that was not supposed to be sent on equilibrium path.

I take the fact that you ask about divinity as a signal that you dug deeper into signaling so that you know the Spence model and the Beer-Quiche game. Otherwise, look up these examples as they are helpful to illustrate the issue. I provide references below. Back to said issue: For example, we can support a no-education pooling equilibrium in a standard two-type unproductive-costly-education Spence model by imposing that a receiver does not update her beliefs when she observes education - we can even say that education signals a low type, because positive education is an off-path message. As another example, in the Beer-Quiche game, you can support a quiche pooling (sequential) equilibrium where the off-path message (drinking beer) is interpreted as wimpy.

To understand why divinity is helpful, you should understand another refinement first.
Perhaps the most widely used refinement is Cho & Kreps (1987) "Intuitive Criterion"(IC). In a standard two-type Spence signaling model, IC eliminates all but one equilibrium, the least-cost separating one (Riley outcome). Very sloppily saying, IC labels off-path beliefs as "unreasonable" if one type can say:

  "I am going to send this out-of equilibrium message $m$ for which you
  may have a weird belief. I do this to signal that my type is $x$
  although you may believe I am some type $y$. However, notice that if I
  were such a type $y$, I would be better off by staying on equilibrium
  path regardless of what you infer from $m$. Also notice that as a type $x$ I am better off by sending $m$
  IF this speech convinces you that I am really $x$."

Now this is a relatively simple idea to eliminate weird beliefs. Thing is that it does not always work. For example, we can add a third type to the standard Spence model. Now IC does not solve our multiplicity problem. You can verify (or read in one of the references) that IC does not eliminate hybrid equilibria in which the high types send a separating signal while for some education levels low types and medium types are pooled.
The issue here is that possibly more than just one type may benefit from credibly announcing a speech as above. A belief that all such types are equally likely to do this deviation satisfies the IC. However, it might be that some types are more likely to deviate to this off-path message.
Now, enter divinity, an even more powerful refinement.

"More powerful" refinement means that it has even stricter restrictions on off-path beliefs. The D1-criterion restricts the off-path belief upon observing an out-of-equilibrium message to be a point belief with all mass on the type who is most likely to make this deviation: Intuitively, after receiving
message $m$, there are more best responses of the receiver that improve the equilibrium utility of type $x_1$ compared to $x_2$. D1 says Receiver should infer that she deals with a type $x_1$ and put weight zero on type $x_2$. Note that in the two-types Spence model, both criteria coincide. In contrast, in the three-types model D1 eliminates all but the least-cost-separating equilibrium.

D2 is even stricter than D1: It requires the posterior to put weight zero
on a type $x$ upon observing $m$ if for every best response of the Receiver that causes type $x$ to deviate there is some other type $x'$ that strictly benefits from the deviation. Divinity and Universal divinity (after Banks&Sobel 1988) are based on D1 and D2. Divinity weakens D1: Receiver does not have to put belief mass zero on type $x_2$, but his posterior must not increase the likelihood ratio of $x_2$ to $x_1$. Universal divinity is stronger than D2 in that it applies D2 iteratively.

For a more formal treatment, read the original papers. A good summary is provided by Peter Camton. He also discusses the Beer-Quiche-game and in addition covers cheap talk games and the corresponding refinement, neologism-proofness. This guide on refinements may also help (they discuss the 3-types Spence model I refer to).
To stay within the community, see the answers to this well-received question.


Tax Cuts Affect on Economy? If we look at the equation for national Savings = S(priv) + S(pub) = [Y-C+Tran-T]  + [T-G-Tran] = Y - C - G . We see that Tax falls out of the equation. Therefore, does that mean changes in taxation policy don't directly affect the Supply of Loanable funds? If this is the case, and we assume consumption isn't constant, then giving individuals massive tax cuts should influence them to consume and/or save more money. This should increase total savings and shift the supply right and interest rates down, allowing for greater investment in capital, leading to growth in economy. Looking at this, why is it that tax cuts are seen as being bad for economic growth?

Tax falls out of the equation.

Based on your model, tax can still be in the equation, but it is hidden inside of your $C$ and $G$.

First, as you mentioned, if consumption is not constant, then adjusting the tax rate will change $C$ (lower $T$ higher $C$).

But the tax rate is also imbued in your $G$- the government must have some budget. In a balanced budget, $G=T$, which can be a model constraint.

We may not impose $G=T$, but suppose revenue must be a tenth of government spending; $$G = \frac{T}{10}$$

Thus, lower taxes must lower government spending (thus lowering $Y$), or imply higher taxes in the future (See Ricardian equivalence)

  giving individuals massive tax cuts should influence them to consume and/or save more money

This is true, but we must consider the effects on $G$ and a looming future $\tau$ due to massive tax cuts now.


How to operationalize agglomeration economies? How most common way to operationalize the concept of agglomeration economies? I am new in research field. I even don't know what conceptual definition means.

Agglomeration economies is a large concept that includes any effect that increases firms' and workers' income when the size of the local economy grows.
The general idea is to estimate the overall impact of density on a local characteristic, such as the impact of local employment density on local productivity. The density estimate captures the agglomeration effect.
As a naive example to operationalize the concept of agglomeration economies, consider the following specification:
$$Y_c = \alpha Density_c + \beta Skills_c + \epsilon_c$$
where $Y_c$ is a measure of the local outcome in a city $c$, say the logarithm of local wage, $Density_c$ is the logarithm of density, $Skills_c$ captures local skills and $\epsilon_c$ is the error term. If there is no correlation between the random component and explanatory variables, then the ordinary least squares estimate of the elasticity of productivity with respect to density ($\beta$) is a consistent measure of total net agglomeration economies. For instance, a value for the elasticity of the local outcome with respect to density of 0.03 means that a city twice as large (knowing that a factor of 10 is often obtained for the interquartile
of local density in many countries) has $2^{0.03} - 1 = 2.1\%$ greater productivity,
because of either pure local externalities or market agglomeration effects that dominate dispersion effects of any kind.
You will find much more, including a discussion of the mechanisms, in Chapter 5 of the Handbook of Urban and Regional Economics, The Empirics of Agglomeration.


Why are marginal rates of substitution are identical at equilibrium consumption levels? According to wikipedia, "At equilibrium consumption levels (assuming no externalities), marginal rates of substitution are identical". Why is it so?

What does "equilibrium consumption levels" here mean? I thought that equilibrium means that demand equal to supply. How is it applicable for marginal rates of substitution?

One explanation I could think of: MRS (which is equal to $MU_x/MU_y$) is equal to the price ratio $P_x/P_y$. In equilibrium, all consumers will consume where MRS = price ratio, and hence MRS will be "identical" across consumers.

I agree that this might not be a terribly good way of putting it.


Why are CAD, AUD known as commodity currencies Why are some currencies like CAD, AUD known as commodity currencies?

From wikipedia: A commodity currency is a name given to currencies of countries which depend heavily on the export of certain raw materials for income. These countries are typically developing countries, e.g. countries like Burundi, Tanzania, Papua New Guinea; but also include developed countries like Canada and Australia.

In a more practical sense, if the value of a currency is heavily dependent on the value of the natural resources exported, it can be considered a commodity currency. For example, look at the appreciation of the AUD during the recent mining boom. This appreciation was driven primarily by increased Chinese demand raising prices of commodities Australia was endowed with.


What is unknown in Bellman Equation? \begin{align}
 V(W)=\max\limits_{W'\in[0,W]}\qquad& u(W-W')+\beta V(W')\qquad\forall W
\end{align}

$\textbf{My Question}$: Why is the unknown in the Bellman equation $V(W)$ itself? Isn't the choice variable tomorrow's state, $W'$?

The original problem was probably of the form $$\max_{\{W_t\}_{t=1}^\infty}\sum_{t=0}^\infty \beta^t u(W_t-W_{t+1}),$$
$$\mbox{s.t. } W_{t+1}\in[0,W_t] \ \forall \ t,  ~~ W_0 \mbox{ given}$$
When formulated that way there is no need to solve for any function $V$, but the infinite elements of the sequence ${\{W_t\}}_{t=1}^\infty$ are all choice variables. Bellman's main insight is that (under some conditions) the problem can be simplified. Instead of solving for an infinite number of variables, you could solve for a single "policy function" that tells you what to do each period as a function of the current state variables, and a "value function" that summarizes what is the value (in terms of today) of inducing each possible state in the future. Even if there is no uncertainty, it is clear that this value function is an endogenous object, since it must somehow capture the future stream of utility as a single function of the future state. In your case, that function is  $V(W')$. This is why the Bellman equation:
$$V(W)=\max_{W'\in[0,W]} u(W-W')+\beta V(W')$$
has two properties:

1) it lacks the subscripts on the $W$'s, this reflects that you will solve for $W'$ as a function of $W$, i.e. the policy function.

2) has a new object, $V$, that was not in the original problem and it is a function of $W$ (or $W'$) and just by eyeballing the two problems you can see that for them to be equivalent $V$ must be the discounted sum of future payoffs assuming future actions are also optimal. So it is not a choice variable, but definitely, an endogenous object that you need to find when solving the problem.

You can see that the problem of optimally choosing infinitely many objects is transformed into one of choosing a finite number (2) of functions, which are infinite-dimensional objects. Brilliant!


What's is the purpose of "conditional preferences" as specified in Savage's framework? In this paper, "Savages’ Subjective Expected Utility Model" by Edi Karni, he gives a definition of "conditional preferences." See here:

What situation is this supposed to capture? It seems like it might be more useful to define conditional preferences as $f \succeq_E f'$ if $f(s) \succeq f'(s)$ for all $s \in E$. This definition seems like it might be more ... useful? For one, it seems to resemble conditional expectation that way (or does it?). What idea is the definition as given in the paper supposed to capture (this might be a simple question)?

Also, would it be more general to say, in the definition given in the paper, that $f(s) \sim f'(s)$ instead of $f(s) = f'(s)$?

The statement $f\succcurlyeq f^\prime$ and for every $s$ not in $E$, $f(s)=f'(s)$ says that $f$ and $f^\prime$ have the consequences unless $E$ occurs, and $f$ is preferred to $f'$. Loosely, the sure thing principle says that if two acts differ only in their consequence should $E$ occur, their ordering should depend only on their consequences in $E$ and not on states outside of $E$. What the sure thing principle gets you is that if $f\succcurlyeq_E f^\prime$ then $f$ must be conditionally preferred to $f^\prime$ because of the consequences of $f^\prime$ in $E$. Otherwise this would not be known.

Here's a plain English interpretation of conditional preference. Imagine I put together two portfolios, $A$ and $B$. I start both portfolios off with the same asset, let's just say some money in a mutual fund. In portfolio $A$ I put an additional asset that pays a dollar in all states of the world $E$ where a democrat wins the 2016 election. I give you a choice between $A$ and $B$. In action $f$ you choose $A$ and in action $f'$ you choose $B$. Presumably you prefer $f$ to $f'$. But the payoffs of $f$ and $f'$ differ only should a democrat win the 2016 election. So by the definition Karni has given you $f$ is preferred to $f'$ given $E$. With the sure thing principle,  I can separate your preference in $E$ states from your preferences in not $E$ states. So I now know your preference for $f$ must stem from $f$ being in some sense better than $f'$ in $E$ states.

Technically (read: obnoxiously) preferences are defined over the functional space $F$, so the abstruse definitions come from the fact that the notation $f(s)\succcurlyeq f'(s)$ or $f(s)\sim f'(s)$ is not yet defined. Instead Karni has to work with the $f_E$ notation. In this notation you'd write your idea for conditional preference as $f\succcurlyeq_E f'$ iff $f_Eh\succcurlyeq f'_Eh$ (the first part of the sure thing principle). I agree that this is more in line with my notion of what conditional preference should be. Savage mentions both senses in his discussion:

  What technical interpretation can be attached to the idea that $f$ would be preferred to $g$, if $B$ were known to obtain? Under any reasonable interpretation, the matter would seem not to depend on the values $f$ and $g$ assume at states outside of $B$. There is, then, no loss of generality in supposing that $f$ and $g$ agree with each other at states outside of $B$, that is, that $f(s)=g(s)$ for all $s \in \sim B$. Under this unrestrictive assumption, $f$ and $g$ are surely to be regarded as equivalent given $\sim B$, that is, they would be considered equivalent, if it were known that $B$ did not obtain. The first part of the sure-thing principle can now be interpreted thus: If, after being modified so as to agree with one another outside of $B$, $f$ is not preferred to $g$; then $f$ would not be preferred to $g$, if $B$ were known. The notion will be expressed formally by saying that $f\leq g$ given $B$.

(Here $\sim$ is set notation instead of preference ordering.)

The sense that Karni involves two acts that agree with each other outside of $B$. However Savage's definition of conditional preference is exactly $f\succcurlyeq_E f'$ iff $f_Eh\succcurlyeq f'_Eh$.  If there really is no loss of generality in the rest of the proofs it doesn't matter which definition you pick. However Savage's definition is in line with both yours and mine, and the definition of conditional expectation. I'll look to see if that has any real consequences for Karni.

ADDENDUM Using equality instead of $\sim$ is plenty general, simply because if the two acts only differ in consequences that do not have an effect on the preference ordering, you could just redefine the consequence space such that the equality was still maintained. Which is a cop out, but also true.

I believe I've figure it out. The only place Karni seems to use his conditional preference definition is in P7. Savage uses an analogous P7 but with his own definition of conditional preference. P7 says (Savage's wording):

  If $f \leq g(s)$ given $B$ for every $s\in B$, then $f \leq g$ given $B$.

This is a statement of conditional dominance: "a certain consequence $g(s)$ is better than an (uncertain) $f$ for every possible $s$ in $B$, so $g$ should be preferred to $f$ given $B$." Because we have already accepted the sure-thing principle, P7 from Savage and P7 from Karni are equivalent. If we had not accepted the sure-thing principle, Savage's would be more restrictive. So Karni is actually being less restrictive with his definition of conditional preference, and that is presumably the purpose.


Why is elasticity not defined simply as the slope of the graph? It makes more intuitive sense to me: as I increase the quantity, this is how much the price changes. Why is a much more complex formula used that takes into consideration the current quantity and price at a given point on the curve?

A key feature of elasticity is that it is a unit-free measure.  Suppose we are considering the price-elasticity of demand for apples which is $\frac{{\triangle}y/y}{{\triangle}x/x}$ where $y$ is quantity demanded and $x$ is price.  The elasticity will be the same whether apples are measured in pounds (lb) or kilograms (kg) because both $\triangle y$ and $y$ will be in the same units.  Similarly it will not matter in which currency price is measured, because $\triangle x$ and $x$ will be in the same currency units.  This makes comparisons of elasticities, between goods measured in different units, or between countries with different currencies, much more meaningful than comparisons of slopes.


Why aren't we seeing carbon taxes in practice? (See also a version of this question under politics, https://politics.stackexchange.com/questions/48764/why-arent-we-seeing-carbon-taxes-in-practice)

It seems that there are many advantages to carbon taxes, including pricing in the environmental cost and generating revenue (that could offset other taxes).  So why are we not seeing them in practice, at least not very much of them?  I can think of some reasons below, but I don't know which of these if any actually play a significant role in practice and/or are actually well motivated.  Am I missing anything?  Is there any good study of this?

Too difficult to implement / will generate an underground carbon economy. This would be a concern with many taxes, but it seems we should be able to have a pretty good handle on where carbon enters the economy given the necessary physical volumes and processing.
Will hurt economic activity.  But it seems that this can be addressed by using the revenue to stimulate economic activity / reduce distortionary taxes.
Will create too big of a shock to the economy with unpredictable consequences.  But the tax could be gradually introduced according to a schedule.
Unfair to industries that will suffer from this tax.  But we generally don't seem inherently very concerned about disruption of industries (e.g., taxi industry) and it is hard to argue that such action would come as a surprise at this point.  Also, again, the tax could be gradually introduced according to a schedule.
Will economically hurt people who can't afford it.  But this could be addressed by using the revenue intelligently (or by targeting only certain types of carbon, e.g., airline tickets).
Politically hard to sell.  Even if it is in their interest, too many citizens will reflexively complain about, for example, high gasoline prices.  But would they really feel this way when combined with, for example, a check made out from the government distributing the revenue in a basic-income sort of way?  Or is there some other effective way to clearly present it as not just an additional tax from a greedy government?
Industry is politically too powerful.  It will attack/reward politicians based on their actions and launch massive public relations campaigns.  But is it really that powerful or is that exaggerated in people's imagination?
Even though many of the above aren't actually true, citizens and/or politicians are unduly worried that they are true (or simply not well educated about the option), are risk averse, and therefore they don't pursue this route.

I think it’s mainly politics. For example, when France tried to implement increases in tax on  oil (indirect way of taxing carbon) it led to yellow jacket protest.

As you pointed out it’s easy to track who produces the carbon in the economy. Especially on industrial level in developed countries. The reason 1 could be problem in some developing countries though.
As you pointed out the revenue can offset any negative effect as with Pigovian taxes there is no deadweight loss - if set properly
Again you answered yourself plus I would add in a long run it’s better to undergo temporary shock to avoid higher cost down hill.
I don’t think you can say it’s unfair. In fact I would say the fact that the industries create externality in the first place due to lack of property right is unfair (at least if we agree that creating externality is not fair to society which I think most moral thinkers would - although that’s question for philosophy SE).
You again answered yourself.

If you look at the attempts to introduce carbon taxes then you will see 6-8 are the main culprits. In France you get yellow jacket protests in Netherlands farmers protests, in Washington voters refused carbon taxes in referendum last year (see here)etc. - all responses to trying to introduce Pigovian taxes of one kind or another. People of any political affiliations generally don’t like taxes when they are taxes on them as well. I suppose many people also are skeptical the government will make it revenue neutral later by lets say sending check to all people so their income stays the same. In case of redistribution some might not like that and others also don’t believe social spending will increase.


Does Bad Money Drive Good Money Out Of Circulation I have heard the saying, "Bad money drives good money out of circulation," (Gresham's Law) many times.

I'm wondering if it's true, what it really means. What's good money? What's bad money?

And if this is true, what evidence do we have and do we know why this happens?

Gresham's law has to do with commodity money. When several types of commodity money are available (e.g., both gold and silver coins), the one with the lowest quality will drive the rest out of circulation. The underlying idea is that everyone will try to hoard the "good money" while using the "bad money" for payments.

You have a full description of this issue in wikipedia.


What are the most common methods of determining valuation used by economists that claim Bit-Coin is on the verge of being a bubble I have seen many economists saying that bit-coin is highly overvalued and on the verge of a massive corrections.  What are the most popular models being used to determine the proper price for bit coin?

I find it very hard to believe that these economists would base these opinions on this purely on conjecture based on the fact that bitcoin is a new technology, or not backed by a government.

There are two ways to look at the value of a financial instrument. One is the underlying asset base, the other is the yield.

Bitcoin has no underlying asset base and no yield.

Therefore, its only value is whatever people imagine it to be.

In other words, it's completely overvalued. But that does not mean it is on the verge of massive corrections. There is an old saying (attributed, as they often are, to Keynes) that the market can remain irrational for longer than you or I can remain solvent.


If we add up all the income while finding GDP of a country, is income counted multiple times? Suppose 9 others and I are government employees. We get salary which will be counted while calculating GDP. Let's assume that we 10 are the only customers of a shop (for simplicity). The shopkeeper's income is derived from the 10 of us. Now if we calculate the shopkeeper's income while calculating GDP, then the the income will be counted twice since it was counted as our income at first place. So how are situations like this handled?

There is no contradiction here. All these incomes are part of the GDP. In theory all incomes show the value of something. In your example this would be the value of the work done. Since all 10 government employees and the shopkeeper are working they all create value, the size of which is measured by adding up their salaries.

Here you can find an explanation of what GDP exactly is.


What are some theoretical explanations for deviations from the efficient market hypothesis? According (the semi-strong form of) the efficient market hypothesis, the price of an asset should reflect all publicly available information about the 'fundamental value' of that asset. The reasoning is that if there is some public information that suggests the price is below the fundamental value then people will have an incentive to act on this information and buy more of the asset. This increase in demand will cause the price of the asset to rise, closing the original price-value discrepancy.

This reasoning seems intuitively plausible, but significant price-corrections during the recent recession seem to suggest that markets had systematically priced in a manner inconsistent with underlying fundamentals. What academic theories (i.e. published or in working papers) have been advanced (and by whom) to explain why the efficient market hypothesis might fail? Is there much of an empirical consensus on the validity of the efficient market hypothesis in the literature?

I think this piece by John Cochrane represents a typical defense of the efficient market hypothesis from this kind of critique. Here's another. The basic summary is that market efficiency does not imply that expected returns cannot vary or that bubbles will not happen. Bubbles should be unpredictable, and variation in expected returns should be driven by risk or discount factors. Whether that's the case for the financial crisis is definitely a matter of debate.

Do people believe in efficient markets? I think that varies a lot from field to field. It might be more useful to say that efficient markets are usually the null or prior that academics in finance and economics work with when they try to understand something. That is to say if you want to use some data to try to convince them that financial markets aren't efficient, you face an uphill battle, but the struggle isn't impossible.


Values of A,K,N,a in Cobb-Douglas function expressing GDP In many basic macroeconomics textbooks a Cobb-Douglas production function with constant returns to scale is used to express the output of the economy as a function of labor and capital: $Y=AK^aN^{1-a}$.
Question: Given that a is normally assumed to be between 0.3 and 0.5, that the current output of the US economy is around 22T\$/year, and that $N$ (number of worked hours in a year) could be around 0.3TH/year, is there any kind of consensus on what are the values of $K$ and $A$ (at least the current values for the US economy)?
If I assume $a=0.5$, $A=5.4$ and $K=54$, then $Y=A\sqrt{KN}=21.7$, is that an OK choice?
I am puzzled to why I can't seem to find actual values for these parameters. If a book or a paper says that the GDP is expressed with this function, shouldn't it also at least give a realistic example with a range and units for the involved parameters? Maybe I am just looking in the wrong places?
Any thought?
Thank you in advance

K is just a stock of capital. This Fed data show that the stock of US capital is almost 70m at constant prices for the most recent year (2019). But there are other ways of measuring it. You can google papers that estimate multifactor productivity to see what measures for K and N people are using (not everyone uses labor hours too).
A is multifactor productivity. This OECD data show that using 2015 as index year the multifactor productivity in the USA in 2019 was 102. A cannot be measured directly. People estimate it using K and L and using time series/panel regressions. That is why this will be in datasets expressed just as a growth rate or index, we can't see what A is only how it changes.


Completeness from an example I have a set $X = \{1,2,3\}$ and a binary relation $B = \{(1,1),(1,2),(1,3),(2,3),(3,1)\}$.

I am trying to understand if this relation is complete.

The completeness definition I am using is if for each $x,y$ in $X$, either $xBy$ or $yBx$.

At first I thought $B$ was complete but both $(2,2)$ and $(3,3)$ are not in $B$.
In the definition, if I set $x=2,y=2$ then I think we should have $(2,2)$ in $B$.
On the other hand, it seems meaningless to me because isn't $2B2$ related with reflexivity? So for completeness do we actually need $(2,2) \in B$?

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

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


Why the prices for very popular items do not increase? I am always surprised why there are certain services or items which are on high demand, and do not have their prices increased to generate more profit.

As an example, tickets to the very popular EDM festival are always sold out in minutes, but the price each year increases little. Every year the tickets are at around 200-300€, so why not make them 400-500€, since they would still be most likely sold out in a matter of weeks or months, wouldn't they?

Another example, I know a shoemaker who from time to time sells around 20-50 pairs of cordovan shoes, at a price of around 340€/pair. All the shoe stock is ordered (online sales) in around 1 day. Why wouldn't they increase the price by at least 10-20%, and then sell these same shoes over a week or so?

I can see one possible explanation - that getting money immediately has more value, but it seems to me that in the overall a much bigger profit could be obtained if the price was simply increased.

Some online-shop does practice price discrimination.

However, the seller must play the price game carefully to maximize their profits:

Lower price means lower profit per units but may increase revenue and increase overall profits
Higher price is more profitable but hurt sales
Shelter for the rainy day
Competition

In addition, influence factors such as inflation, hot money also come in play.  For example, during economy bubbles, people don't mind paying extra $100. However, once the market shrink, you will face a huge retract of revenue. Worst still, the manufacturers need to served bank debt because they borrow money to expand the business.

Even items like EDM ticket may jack up the price(due to annual scarcity) , it may risk of losing patrons in bad time; too profitable, it will attract competitor enter the market.


Rigorous solution of Stackelberg leader-follower game with N-players? In the classical two-player Stackelberg game (sequential Cournot) we have a linear demand function $P = 1 - Q$ where $Q = \sum_0^2 q_i $, and we assume homogenous production cost $c$. By starting from the "bottom" of the game where player 2 knows player 1's chosen output and best-response reacts to it, and then moving "upwards" assuming player 1 anticipates this response, the game can be shown to have equilibrium solutions:

$$ q_1^\star = \frac{1-c}{2} $$
$$ q_2^\star = \frac{1-c}{4} .$$

We can follow the same procedure with 3, 4 or more players and discover the pattern:
$$ q_n^\star = \frac{1-c}{2^n} .$$

I have been trying to work out a rigorous mathematical proof, say by induction or other methods, to show that this has to be the case, but not managed to find any. Can anybody help please?