What is the long run equilibrium in layman's terms? My textbook states
An economy's long-run equilibrium is the position it would eventually reach if no new economic shocks occurred during the adjustment to full employment. You can think of long- run equilibrium as the equilibrium that would be maintained after all wages and prices had had enough time to adjust to their market-clearing levels. An equivalent way of thinking of it is as the equilibrium that would occur if prices were perfectly flexible and always adjusted immediately to preserve full employment.
Does this mean that, in the long run, ordinary people like me have already found jobs with our wages already adjusted to price levels affected by inflation and monetary policy by the Fed? In comparison to the short run, is the transition period where the price of money fluctuates with increasing/decreasing money supply by the Fed non-existent? What is the long-run equilibrium for the average Joe and how does this affect me personally?

Long-run equilibrium is a theoretical construct. One may argue that an economy never really gets a chance to actually reach it. So it is best to explain it in a hypothetical setting:
Imagine an economy with fixed population and all markets in equilibrium. By all markets I mean the money market (no excess money, no shortage of money), goods market (no pilling of goods in factories, no shortage either - producers' plans for production are unchanging) and labor market (whoever wants to be employed at the going wage-rates is employed). Now, strictly speaking, one more market, bonds market, is left, but by the famous Walras law, when $n-1$ out of $n$ markets are in equilibrium, so will be the $n^{th}$ one.
You can say that the economy is currently in long-term equilibrium. It is producing at full capacity. So let's give it a demand-side shock. It could be a monetary shock by the central bank, or by government by increasing/decreasing spending, external shock due change in export demand, etc. Basically, a shock which shifts the aggregate demand curve.
Now we have a disequilibrium. Not all goods that are produced could be sold (or not enough are produced). There is more money circulating in the economy than required (or not enough money to meet the need of increasing transactions). What do we do now?
Usual option: In the immediate aftermath, we should produce less (or more) to meet the new demand. To do this workers are fired (or more are hired at higher wages) changing the labor market equilibrium as well.
Alternatively, we could also just slash (or increase) prices so that demand is balanced again. But there are problems with this. It is almost impossible to do this in a synchronized way everywhere. On the top of if, producers would also want to simultaneously cut wages (or workers will demand higher wages due to higher prices - that producers may not be immediately agree to). This alternative option, as per macroeconomic literature, is not smooth. It faces rigidities and happens slowly. As your book points out, if, hypothetically, it did happen then there would be no change in employment or output levels.
This is what distinguishes short-run and long-run equilibrium in macroeconomics. The usual option is the one that creates a short-run equilibrium where the prices and wages are yet to be adjusted to reach the long-run equilibrium.


Interpretation of the Cross Partials of the Cobb-Douglas Consider a Cobb-Douglas Prod. Function $$Y=AL^{a}K^{1-\alpha}$$
This has the cross-partial:
$$\frac{\partial^2 Y}{\partial K\partial L}=(1-\alpha)\alpha AL^{\alpha-1}K^{-\alpha}$$

Is the interpretation of this the change in the return to labour, with a change in capital (and by Schwarz's theorem, also the change in the return the capital, with a change in labour)?

Then, is it correct to say that the return to labour increases as $\frac{1}{K^a}$ with capital?

The interpretation of the cross partial here is the change in the return (or marginal productivity) of labor when capital increases marginally. Similarly, it can be interpreted as the change in the return of capital, when labor increases marginally.

We often only want to interpret the sign of the cross-partial and not the exact value. Here we see that the productivity of one factor increases with the other factor. Interpreting the exact value is more difficult, but also not really interesting for most economic applications.

Furthermore, it is not correct to say that the return to labour increases as $\frac{1}{K^a}$ with capital. How did you arrive at this conclusion?


Providing subsidies affects Marginal Private cost but not Marginal Social Cost? According to the theory that I'm seeing on the internet and in textbooks, when a government wants to correct underproduction due to a positive externality of production, they can decide to subsidize the good.

The subsidy would reduce the costs of production for the firm, and hence shift their Marginal Private Cost to the right towards the Marginal Social Cost curve. In an ideal situation, the curve could be made to actually lie on the MSC curve, and the underproduction would be completely solved.

The problem I have with this is that nobody talks about why it's possible for the MPC to ever get closer to the MSC curve. The formula for Social Cost is Private cost + external cost (which is negative in the case of positive externalites of production). So if I were to reduce the private cost of the good, then it's social cost would also reduce. In other words, if I move the MPC curve forward, the MSC curve should also move forward by the same amount.

Doesn't that mean the only way to get the MPC curve to actually get closer to the MSC curve is to reduce the positive externality itself (which obviously isn't done)? Or is it that people already know that the MSC curve will move, so when they're talking about the MPC curve touching the MSC curve, they're talking about the old MSC curve and not the new one?

The amount of external cost is determined by the level of production in this framework.

If the producers receive a subsidy the MPC shift to the right as you point out. That also means that for each level of cost production increases and therefore the external benefits are less, that is, they are internalizised. If the subsidy is enough the external benefits of production are zero and the MPC=MSC.


Calculating the Competitive Equilibrium in a pure exchange economy with 3 comodities and 2 agents Consider a pure exchange economy with three commodities and two households with individual endowments
$e_{1}=(1,2,3) \text { and } e_{2}=(3,2,1)$
respectively, and utility functions
$u_{1}\left(x_{11}, x_{12}, x_{13}\right)=x_{11}+2 x_{12}+3 x_{13} \text { and } u_{2}\left(x_{21}, x_{22}, x_{23}\right)=3 x_{21}+2 x_{22}+x_{23} $
respectively.
Which of the following is the competitive equilibrium price vector?
Options:
(A) (3,2,3)
(B) (1,1,1)
(C) (1,2,1)
(D) None of the above
My attempt:
First I tried solving the optimization problem of the first agent
$ max \hspace{0.5 cm} u_{1}\left(x_{11}, x_{12}, x_{13}\right)=x_{11}+2 x_{12}+3 x_{13} \\ \text{subject to} \hspace{0.5 cm} p_{1}x_{1} + p_{2}x_{2} + p_{3}x_{3} = 3p_{1} + 2p_{2} + p_{3}\\
 $
I took three cases:
Case 1:
$
\frac{p_{1}}{1} > \frac{p_{3}}{3} > \frac{p_{2}}{2} \hspace{0.5 cm}  \text{or} \hspace{0.5 cm}  \frac{p_{1}}{1} > \frac{p_{2}}{2} > \frac{p_{3}}{3} \\  \text{Here I took the price level of a good i and divided it with the marginal utility of that } \\ \text{good. From this I concluded that the optimal bundle in this case should be:}   \hspace{0.5 cm} (0,\frac{p_{1}}{p_{2}} + 2 + 3\frac{p_{3}}{p_{2}},0) \hspace{0.5 cm} \\ \text{Now I took other cases as well where I took  the price relation as follows:} \hspace{0.5 cm}  $
$ \frac{p_{3}}{3} > \frac{p_{2}}{2} > \frac{p_{1}}{1} $
But the problem becomes very complicated and difficult to solve. Can somebody guide

First, there is no such thing as the competitive equilibrium price vector. If $(p_1,p_2,p_3)$ is a competitive equilibrium price vector, so is every positive multiple of this vector.
Second, to find the demand you also have to look at the cases where some inequalities are not strict, where they are actually equalities.
Here is how you can simplify the problem: The equilibrium consumption must be at least as good as keeping the endowment for both consumers. You can check that this means that if one of the consumers consumes the total endowment of a single good and nothing else, they are worse off. So in equilibrium, everyone must consume a positive quantity of at least two commodities. It is also easy to check that for no price system would both consumers consume positive amounts of all three commodities. There is no relative price $p_1/p_3$ under which both consumers consume positive amounts of both good $1$ and $3$. Togehter, this should help you pin down the (here unique) relative equilibrium prices.


How digital currency (like Bitcoin) proponents solve the problem of its high volatility to make it a good candidate to replace fiat? I have recently read an article about a family living with no fiat currency for several years. Indeed there are lots of advantages of using a digital currency.
I am wondering if having an important fraction of transactions relying on a digital currency is possible (basically replacing fiat with digital currency for an important part of the economy). The first counter-argument for this being possible is the high volatility of the digital currencies.
I have very little economical knowledge, but almost everything from small businesses to the entire country economy seems to rely on currency stability (e.g. inflation rate should be small enough and EU actually forces a maximum value, business plans require relative currency stability, people expect a rather uniform or at least predictable monthly income).
How digital currency proponents solve the problem of its high volatility to make it a good candidate to replace fiat?

tl;dr:
fiat money can be fully digital money as noted in the +1 comment of Jasper so it does not make much sense to talk about replacing fiat money with digital money as fiat money can be fully digital - those are two separate categories.
But I understand that your question is  about bitcoin/cryptocurrency not just any digital money. There are several proposals on how to make bitcoin competitive (as there are not many economists who think it could replace fiat money). These proposals address the biggest weakness of the cryptocurrencies which is inflexible money supply and range from pegging cryptocurrency value to some other currency to inflation targeting.
Full Answer:
Part 1: Clearing out Misconceptions
I think this question is based on confusion about what fiat money and digital money is so I will clear that misconception first. By definition, following Mankiw Principles of Economics pp 606:

fiat money:
money without intrinsic
value that is used as
money by government
decree

Fiat money can be both physical (for example paper notes, coins etc.) and can also be digital (money on you debit card). Also note, not all physical paper notes would be fiat money. Under gold standard where paper notes are backed by gold there would no longer be any fiat money because then the value of money is not created by government decree anymore. So whether money is fiat or not has no relationship to what medium is used as money (paper/bits etc.).
If you want a comparable term that distinguishes bitcoin from fiat digital currency, the term would be "fiduciary money". Fiduciary money is basically a 'version' of fiat money where the value is not created by government decree but solely by trust (again fiduciary money can be both in form of physical paper and digital). In fact this is also how economists categorize bitcoin. According to Velde (2013):

Bitcoin is a fiduciary currency
Fiduciary currencies—in contrast with
commodity-based currencies (such as
gold coins or bank notes redeemable in
gold)—have no intrinsic value, and derive their value in exchange either from
government fiat or from the belief that they may be accepted by someone else.
They are inherently fragile; government
orders can be ignored or doubted, and
a currency that has value only because
of the belief that it will have value may
have no value at all (for instance, if I
believe that no one will accept it, I will
not accept it either).
The term “mining” may lead one to
think that bitcoin is not fiduciary. It
is true that real resources (computing
hardware and energy) are expended
in creating bitcoins. Since entry to mining is free, the value of these resources
will be the market value of bitcoins produced (whose number per day does
not depend on the size of the network).
But once created, the bitcoin has no
value other than in exchange, contrary
to a gold coin.

Part 2: How to Solve the Problem of Volatility
First, it is important to understand little bit about what determines the price level in terms of some money, where 'value' of money is inversely related to the price level. For example, the US-bitcoin exchange rate ($S$) should be given by $S=\frac{P_{US}}{P_{Bc}}$, where $P_{US}$ is price level (aggregate prices) in terms of USD and $P_{Bc}$ in terms of bitcoin. This needs to hold otherwise if the equality would be violated one could just buy bundle of goods in bitcoin sell it for US dollars and then exchange dollars back to bitcoin for riskless profit (or vice versa depending on how the equality is violated). If there would exist such opportunity it would quickly disappear because as people would take advantage of the exchange the demand for dollars or bitcoin would change until it would reach equilibrium where the above would hold. So there is an inverse relationship between value of bitcoin and its price level.
Broadly speaking the price level for any money is determined by money market equilibrium.  In its simplest form this can be described 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 (this is oversimplification, expectations of these quantities matter as well but since you are not an economist I wanted to only use most basic models to provide structure). Solving for price level and log-linearizing we get:
$$\ln P = \ln M + \ln V - \ln Y $$
So if money supply would increase by $1\%$ you would expect price level (decrease in value) to increase by $1\%$, holding all else equal, the same for velocity and for real output you would expect decrease in price level (of course in real life there might not be 1:1 proportionality but again this is just to provide some structure for our thinking - in addition with bitcoin which is in some sense close to commodity money the production costs of mining new bitcoin would play a role as well, but lets assume that away for now for simplicity).
Here you can nicely see what the problem with cryptocurrencies vis-à-vis standard fiat money is. Most of cryptocurrencies  have a very inflexible money supply. For example, money supply of bitcoin cannot normally decrease - there is no way how you can 'un-mine' properly mined bitcoins, and there is hard cap on what maximum number of bitcoins ever will be. This means that for bitcoin $M$ will eventually become fixed. This means that its value (inverse of the price level) will be always at mercy to the shocks to velocity or real output (and in more complex models expectations of those). In fact according to the Iwamura et al (2019), the inflexibility of money supply is precisely the main reason what causes the price instability of crypto currencies.
Fiat money monetary system does not have such problem as central bank can, at least in principle, always choose what sort of $M$ it wants, and those central banks that have mandate for stable prices try to do so in a way that keeps prices stable (although usually this is done in indirect way through interest rates as opposed to directly choosing some $M$ - but in principle they could choose any $M$ if they  would want to).
Now finally we can turn to your main question:

How digital currency proponents solve the problem of its high volatility to make it a good candidate to replace fiat?

Well coincidentally there is whole paper that tries to address this question, namely:
Iwamura,  Kitamura, Matsumoto,  & Saito (2019). Can we stabilize the price of a cryptocurrency?: Understanding the design of Bitcoin and its potential to compete with Central Bank money
They basically argue that in order to make bitcoin or other cryptocurrencies competitive there must be some way how to make supply of money flexible both upward and downward. Their potential fixes include:

Currency Peg/Currency rule: The cryptocurrency could be pegged to some  real life currency, where there would be some rule that would adjust money supply in a way to always keep exchange rate between lets say USD and Bitcoin or euro and Bitcoin fixed. Alternatively, there could be some less restrictive rule where bitcoin would have to follow other currency within some band.

Monetary Policy without a Central Bank:  you can simply have some monetary rule (some argue central banks follow monetary rules such as the Taylor rule) that affects money supply by making it easier or harder to mine bitcoins that depends on some parameters in economy (for example, real output).

Inflation Target in Cryptocurrency: crypto currency money supply could be set up in a way that it always targets lets say $2\%$ inflation (or zero inflation - which would be perfect price stability, but most economists argue small positive inflation is vital for economy (see more on that here).

However, the above being said I do not know of any conventional economist who would think that cryptocurrencies should replace fiat money. Most macroeconomist believe that state should manage business cycle using, among other tools, monetary policy. In addition to that cryptocurrencies have further problems as mentioned in the paper cited above:

First, cryptocurrencies are more expensive to produce, and the production costs are hard to retrieve. Bank notes issued by the central banks require some printing and material costs. These costs are negligible compared with the face (nominal) value.
Second, bank notes are reversible between new issues and absorption because the central bank basically buys and sells securities with bank notes. A cryptocurrency cannot be absorbed, but if equipped with a built‐in value stabilization mechanism, this shortfall of irreversibility can be softened (but not eliminated) in practice.
Third, Bitcoin‐type cryptocurrencies use a delayed finality confirmation structure to avoid double spending. Consequently it typically takes hours to use obtained money. Bank notes can be used  immediately as obtained. Fourth, Bitcoin type cryptocurrencies face security risks, such as Denial of Service attacks, more widely than bank notes.

Some of the above can be aleviated further, as authors explain:

The third and fourth points are relative problems, and also intrinsic to Bitcoin‐type currencies. They are not general problems with cryptocurrency. The third point considers a problem directly compared with bank notes for direct transactions. Considering transactions with Bitcoin‐type currency may occur over a remote distance, finality confirmation may be quicker and much cheaper with a Bitcoin‐type currency than that through a bank. The fourth point is closely related to the protocol design of a Bitcoin‐type currency, and is not a general cryptocurrency issue. The instability associated with mining pools due to strategic behaviors between and within pools can be reduced substantially if the valuation system is improved in line with our suggestions.

However, the first and second point are inherent problems of cryptocurrencies, as authors further explain:

The first and second points are fundamental shortfalls of cryptocurrency. As currently described, cryptocurrency values are based on associated production costs. This mechanism is similar to commodity money, notably gold and silver coins. Historically gold and silver coins have been replaced by credit (or fiat) money basically because of the above‐mentioned first and second points.

Consequently, at best it is reasonable to aim to make crypto currencies competitive vis-à-vis fiat currency, rather than as their replacement.


Should I include country dummies when I combine datasets of 3 countries? I am currently doing the analysis using firm-level data of three countries combining together.
Also, it is a cross-sectional analysis. Therefore, in the regression, I control for industry dummies to account for differential effects in industry level.

I think I don't need to control for country dummies due to some reasons:
(1) The countries that I use in my analysis share similar characteristics including development level, political, and socio-economic conditions.
(2) There are only three countries in my analysis.

In this case, I expect that the results will not be affected even though I don't control for country specifics.

However, I am not sure if my idea is appropriate since I cannot find any reference to support it yet.
Therefore, I would like to ask everybody here if you have any idea whether or not country dummies is necessary in my case.

Thank you!

I would advise you to think deeper about your research question first, as this will guide the decision to use country fixed effects. If you would like to exploit cross country variation, for example by studying how the same industry functions differently across countries, then do not use country dummies because it will absorb the variation you want.

If you want to study a causal relation that is independent of country, then using "within-country" variation (i.e. include country dummies) is the most restrictive approach and will sweep out all fixed country characteristics. Your coefficient will then be identified off deviations from within country means.

Are you sure that countries are similar across most characteristics in order to defend not using country dummies? It may be hard to defend solving omitted variable bias on those grounds. If you really want to go this route, then include several country covariates as controls.


what is $b(p)$ in the Almost Ideal Demand System? In Hal Varian's Microeconomic analysis (page 213) he discusses the Almost Ideal demand system. There he describes the AIDS system as follows:

  The almost ideal demand system (AIDS) has an expenditure function of the following form:
  $$e(\boldsymbol{p},u)=a(p)+b(p)u$$
  where
  $$a(p)=a_0+\sum_ia_i\log p_i+\frac{1}{2}\sum_i\sum_j\gamma^*_{ij}\log p_i\log p_j $$
  $$b(p)=\beta_0\prod p_i^{\beta_i}$$
  $$...$$

So I know $a(p)$ is a second order approximation of $p$ on our expenditure function, however i am having difficulty understanding what exactly $b(p)$ is.

What is $b(p)$?

In the original article by Deaton and Muellbauer (1980), An Almost Ideal Demand System, they characterize the expenditure (cost) function for the class of PIGLOG preferences as:

$$\log c(u, p) = (1-u) \log \{a(p)\} + u \log \{b(p)\}\tag{1}$$

Where they go on to describe in intuitive terms:

  " With some exceptions (see the Appendix), $u$ lies between $0$ (subsistence) and $1$ (bliss) so that the positive linearly homogeneous functions $a(p)$ and $b(p)$ can be regarded as the costs of subsistence and bliss, respectively. " (p. 313)

Some algebra gets you equations $(2)$ and $(3)$ in the paper, which are analogous forms of the equations you have above.


Need Advice Debugging MLE Code to Estimate an ARMA(p,q) I'm trying to estimate an unknown ARMA(p,q) series via a Kalman Filter & QMLE.

The issue is most of my optimized likelihood values end up around -350, except one or two which are hugely positive! It doesn't seem likely that adding a single AR or MA lag would cause such a drastic jump in my likelihood function.

I've tried messing around with optimization parameters in Matlab such as MaxFunEval, and MaxIter but I am still finding this issue.

If this is the wrong place for a question like this I apologize in advanced.

If anyone per chance runs into the same issue,

The reason the MLE is exploding is that a system with explosive roots (eigenvalues outside the unit circle), might make the Kalman-filter predictions explode at a point, and thus creating a few very large MLE values.

The solution is to rig the MLE function s.t. if any of the eigenvalues lie outside the unit circle, return an MLE >=0. Thus the optimization algorithm will be forced to find a stationary local minimum.


Why does having a single market price maximize quantity traded? From what I have heard, the exchange of goods defined by the intersection of supply and demand generally maximize quantity traded, although this doesn't apply in cases of monopolies, imperfect information etc. I am trying to understand why this is true, and came across what appears to be a counter example:

There are 4 people in a market for eggs, 2 buyers and 2 sellers. The buyers are each willing to pay up to \$10 and \$3 for 1 egg each. The sellers are willing to sell an egg each at \$9 and \$2. The most productively efficient trades are when one egg is bought for some price between \$9 and \$10 and another is bought for some price between \$2 and \$3. What happens according to supply and demand is that one egg is traded for a price between \$3 and \$9.

The fact that there is one price seems, in this case, to reduce the total traded quantity. What am I missing?

The competitive equilibrium price does not necessarily maximize the amount of goods produced. (The answer to your actual question ends here.)

What the competitive equilibrium price does is reach an efficient level of production. Any situation where the production level differs from the equilibrium level is Pareto-inferior to the equilibrium. This means that starting from the competitive equilibrium, you can transfer money from some of the market actors to other market actors in such a way that everyone will be better off than in the situation with non-equilibrium production levels.

In the example you gave buyer 1 (reservation price 10) and seller 1 (reservation price 9) have a collective surplus of \$1, and buyer 2 (reservation price 3) and seller 2 (reservation price 2) have a collective surplus of \$1, meaning both pairs 'feel' they gained \$1 by trading. But in the competitive equilibrium, buyer 1 and seller 2 have a collective surplus of \$ 8. If they give buyer 2 and seller 1 one dollars each, everyone would still be more happy than in the other situation. So the second sale is in some way inefficient.

A single price is not necessary to achieve Pareto-efficiency, for example first degree price discrimination yields the same results.


Multivariable Utility functions For a highschool economics/mathematics interdisciplinary essay I will use the Lagrange multipliers and deriving formulas that find the maximum. Could some one maybe suggest any (utility) functions that have 3 (also 4) variables (doesn't matter if it has constants).
Thanks in advance!

Let's say you have $k$ goods $x_1, x_2, \ldots, x_k$. Let $\mathbf{x}$ denote the vector $\mathbf{x} = \begin{bmatrix}x_1 \\ \ldots \\  x_k \end{bmatrix}$.

Some common workhorses to get you started:

Multivariate Cobb-Douglas: $u(\mathbf{x}) = \prod_{i=1}^k x_i^{\lambda_i} $.

Note that $\max_\mathbf{x} u(\mathbf{x})$ has the same solution as $\max_\mathbf{x} \log u(\mathbf{x})$ because the logarithm is a monotonically increasing function. Hence maximizing the utility function $u(\mathbf{x}) = \sum_{i=1}^k \lambda_i \log x_i$ will give the same solution and also is referred to as Cobb-Douglas.

Constant elasticity of substitution $u(\mathbf{x}) = \left( \sum_i \alpha_i ^\frac{1}{s} x_i ^\frac{s - 1}{s}\right)^\frac{s}{s-1}$


Having difficultly to understand two indices with regard to inflation What are these terms "provisional headline inflation" and "imputed index" used to predict in terms of inflation?

Headline Inflation:

Headline inflation is the raw inflation figure reported through the Consumer Price Index (CPI)

Raw means it is not adjusted in any way (like core inflation that excludes energy and food prices). Provisional headline inflation just means the numbers are not final and subject to change.
Imputed Index
If some prices are missing statisticians will impute them (figure out what they likely should have been) using statistics, like in this report.


Does debt include interest owed? If I calculate debt to gdp ratios, do I include the interest payment on the debt as part of the debt?
Is debt defined as a recursive sequence?
Does current debt= interest on debt + previous debt?

Depending on your data source, the debt level will either be the face value of debt, or its market value. The usual choice is face value. The debt level is a stock.
Interest payments are an expense that will show up in the deficit, which is a flow variable.
If nothing else happens, then new debt = old debt + interest. More generally, (new debt) = (old debt) + (fiscal deficit) is the simplified relationship. (Note that this will be an approximation to real world data, as it is possible for some transactions to affect the debt level, but are not part of the definition of the fiscal deficit, and vice-versa.)


Is "$f(k,l)$ is decreasing return to scale $\Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$" always true? For the productions $f(k,l) $ that are continuously differentiable, is the proposition  that

"$f(k,l)$ is decreasing return to scale $\Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$"

always true, I have checked for Cobb-Douglas functions and believe it will also hold for all Constant-Elasticity fuction, can someone give me some hints or show some counter-examples?

Here we define $f(k,l)$ to be decreasing return to scale if $ f(tk,tl)<tf(k,l)$ for $t>1$ for all $(k,l)$ in the domain.

In general the statement is wrong. Here is a counterexample:

Suppose you have $f(k,l) = -k l^\beta$ with $\beta >0$ and $(k,l)\in\mathbb{R}^2_{++}$ (you can interpret $f$ as a production function for a "bad" commodity). Then you have:
$$f(tk,tl) = - t^{1+\beta} k l^\beta = t^{1+\beta} f(k,l) < t f(k,l)$$
so that $f(k,l)$ is decreasing returns to scale.

Now let's evaluate $ f_{ll}f_{kk} - f^2_{kl} $. Since $f$ is linear in $k$ we have that $f_{kk}$ is zero, so it is $ f_{ll}f_{kk}$.  On the other hand, we have $f_{kl} = -\beta l^{\beta-1}$ so that overall we have:
\begin{equation}
f_{ll}f_{kk} - f^2_{kl} = 0 - \left[ -\beta l^{\beta-1} \right]^2 = - \beta^2 l^{2(\beta -1)} <0
\end{equation}

So then, where is the trick?

The fact is that $ f_{ll}f_{kk} - f^2_{kl} > 0$ is not a sufficient condition to conclude that the hessian of $f(k,l)$ is negative semi-definite and so $f$ is concave because you also have to impose restrictions on the sign of the principal minor of order 1 of the hessian matrix.

However, provided the hessian matrix is indeed negative semi-defintie than you conclude $f$ is concave and decreasing returns to scale will follow, the statement then holds.


What happened to the dollar in Nov 1978? Arthur Burns (1979):

"Benign neglect" of the external value of the dollar came to an end dramatically, and I would hope irrevocably, in November 1978.

What event(s) of Nov 1978 is Arthur Burns referring to?

Well, the Fed began raising interest rates to record highs in late 1978. I thought it was mainly to quell inflation. Maybe Burns - who was Fed chairman up to Jan. 1978 - thought it was mainly to strengthen the value of the dollar.


Should I cheer for the bear or bull? In Australia, ~10% of our salary goes into a compulsory retirement savings scheme. I have chosen the default option for young people, which involves a relatively balanced split between stocks, investment in property and a bit of cash.

I have been working for 2-3 years, so have a small balance in my super account.

I am not sure whether I should cheer on the stock market going up (increases the value of my existing 2 years worth of investments), or when it goes down (allows my fortnightly contribution to buy more units of stock, which will/may then go back up later.

I suppose ultimately, this boils down to "If a stock index deviates from its long term average, would a rational economist forecast that:

a) The rate of change of the index will eventually return to the long term average, meaning I should cheer the bull.

b) The value of the index will eventually return to where it would have been if the deviation did not take place and the rate of change stayed at the long term average the entire time (cheer on the bull)"

P.S. I am aware of the common theory in economics that crossing one's fingers does not impact the future direction of the stock market either up or down. I simply refuse to accept this as truth ;) But feel free to pretend this is a question for interest's sake only without any actual implications.

Also, apologies if this belongs in personal finance. I don't believe it does, because it is more intended as a theoretical question around general trends in stock markets and economies than as actual advice for someone's stock choices.

First off, I think it would be deeply against the rules here to give investment advice. Don't take this answer as investment advice.

For the answer to a) and b)

There is no reason why an index must return to the long term average, income or price wise. Whether it does or does not depends on the economic situation as a whole and as such relying only on historical statistics may not be productive. The western economy is going through difficult times right now, where growth and interest rates are low, and there are many structural problems to be concerned about. I would not be so sure that the market is undervalued to begin with (it might have been overvalued before - but possibly less so than some other western exchanges).

In general, you should not decide upon retirement savings based on bets on short term market fluctuation. Especially not, if you are not a professional investor.

As for the general retirement savings advice. Younger people should invest in stocks, since the investment has a long tail. As such the higher standard deviation of the investment is not as relevant as the higher expected return. When getting older, less deviation is preferred, as more certainty regarding the retirement savings is preferred. As such some nations with funded schemes have decided to invest overwhelmingly into stocks for young individuals, and progressively more to bonds for older individuals. This is a sound strategy.


Offer curves for giffen good I learnt that giffen good doesn't satisfy the law of demand, but can we draw an offer curve to represent giffen good?

Below is a graph of the price offer curve of good $y$ when income is $48$ units, $p_x = 8$ and the utility function is
$$
U(x,y) = \min\left(2x+2y,x+10\right).
$$
(Based on "Simple Utility Functions with Giffen Demand" by Sørensen).
Good $y$ exhibits Giffen behavior when $0 < p_y < 8$.

A gif of the optimal choice changing as $p_y$ changes is presented below (budget set is grey, indifference curve and optimal bundle are green, income-offer curve is orange dashed line):


Would some help me fill in missing steps from a textbook exercise left for the reader Question: Suppose $C_t=(1-s)Y_t-\lambda G_t$ where $s>\sigma$ as in the basic Solow model.
Out of the government expenditure , proportion $\phi$ is invested in public capital formation. Hence we assume $K_{t+1}=I_t+\phi G_t+(1-\delta)K_t$
$Y_t=K^{\alpha}_tL^{1-\alpha}_t$
$Y_t=C_t+I_t+G_t$
$K_{t+1}=I_t+(1-\delta)K_t$
$L_{t+1}=(1+n)L_t$
$G_t=\sigma Y_t$
In what case will the steady state level of capital per capita increase in $\sigma$
Attempt:
step (1) $\frac{Y_t}{L_t}=\frac{K^{\alpha}_t}{L_t}\frac{L^{1-\alpha}_t}{L_t}$ which equals $y_t=k^{\alpha}_t$
Using the same process for the national identity we get
The evolution of capital per capita is given by the following equation:
$(1+n)k_{t+1}=i_t+\phi g_t+(1-\delta)k_t$ which then goes to:
$k_{t+1}\approx i_t+\phi g_t+(1-\delta-n)k_t$
$k_{t+1}=[k^{\alpha}_t-c_t-g_t]+\phi g_t+(1-\delta-n)k_t$
Now, we can subtract $k_t$ from $(1-\delta-n)k_t$ and we get:
$k_{t+1}-k_t=-(n+\delta)k_t+\phi g_t+k^{\alpha}_t-c_t-g_t$
=$(n+\delta)k_t+\phi g_t+k^{\alpha}_t - [(1-s)k^{\alpha}_t-\lambda g_t]-[\sigma k^{\alpha}_t]$
= $-(\delta +n)k_t+\phi [k^{\alpha}_t\sigma]+k^{\alpha}_t-[(1-s)k^{\alpha}_t-\lambda [k^{\alpha}_t \sigma]]$
We can simplify this algebraically to:
$k_{t+1}-k_t= \phi [k^{\alpha}_t \sigma] + sk^{\alpha}_t+ \lambda[k^{\alpha}_t\sigma]+(\delta+n)k_t$
Finally divide both sides by $k_t$ and set the LHS equal to 0 and get the steady state equilibrium as:
$0 = \frac{\phi[k^{\alpha}_t\sigma]}{k_t}+\frac{sk^{\alpha}_t}{k_t}+\frac{\lambda[k^{\alpha}_t\sigma]}{k_t}-(\delta+n)k_t$
Comments: I am pretty sure my calculus is correct (perhaps save for the last equation. Can anyone confirm this for me?

Overall it is almost correct but there are some small mistakes and it is incomplete.
1st Mistake:
in step (1) you write:

$\frac{Y_t}{L_t}=\frac{K^{\alpha}_t}{L_t}\frac{L^{1-\alpha}_t}{L_t}$

But it should actually be
$$\frac{Y_t}{L_t}=\frac{K^{\alpha}_t L^{1-\alpha}_t}{L_t}$$
You cannot divide LHS of the equation by $L$ and RHS by $L L \implies L^2$ as that will generally violate the equality between $ Y= K^{\alpha}L^{1-\alpha}$.
However, this error had no impact on the rest of the problem because in spite of making this mistake you still used the correct definition for output per capita:  $y_t=k^{\alpha}_t$
2nd mistake
you say you divide both sides by $k_t$, but you forgot to do that for the last term. You write:

$0 = \frac{\phi[k^{\alpha}_t\sigma]}{k_t}+\frac{sk^{\alpha}_t}{k_t}+\frac{\lambda[k^{\alpha}_t\sigma]}{k_t}-(\delta+n)k_t$

correct steady state equation should be:
$$0 = \frac{\phi[k^{\alpha}_t\sigma]}{k_t}+\frac{sk^{\alpha}_t}{k_t}+\frac{\lambda[k^{\alpha}_t\sigma]}{k_t}-(\delta+n) \tag{*}$$
3rd 'mistake': It is unfinished
I am using here ‘mistake’ in quotes because this is not a mistake in the same sense as other ones but it is still not good practice to leave problem unfinished. If you would do it on an exam it would cost you some points (some professors might even refuse to give any points for unfinished work).
I get the impulse to just call it a day since you are in home stretch now but proper answer should have solution for $k^*$ (unless the problem specifically states it does not want full solution which I don’t see in this case in your Q).
Solving the equation $*$ for optimal $k^*$ yields:
$$ k^* =  \left( \frac{(\phi+\lambda)\sigma +s}{\delta +n} \right)^{\frac{1}{1-\delta}}$$
The above being said don’t get discouraged most of the attempt was correct. Just be more careful about the arithmetic and don’t stop just before finishing.


How to test if the effect of one regressor entirely comes from other regressors? I have a regression model that includes IQ test scores as the dependent variable; my own education, my father's education and my mother's education as independent variables. Suppose I want to know whether the only way parents'education increases my IQ test score is through my own education. How would I test that hypothesis?

For Bivariate Regression

Your model would be :

IQ = B0 + B1(Your Education)

For Multiple Regression:

You would use a correlation matrix/plot to do this. Basically it would give you a matrix with correlation values of all variables to each other 0 being none and 1 being perfect. This will also allow you to see the multicollinearity problem which is when independent variables are related to each other.

You can do this in R or Stata. I can post the R script of a similar regression I have done if you would like.


Relevance of central bank Why do we need central bank ?
surely the government can print currency and regulate banks by conducting audits through finance ministry and so on.
Why do we need central bank ?

So why did we need a central bank? Well, lets look at what the co-author of what has gone down in history as the Aldrich Plan, named after Senator Nelson Aldrich. His co-author on the bill was Edward Vreeland who wrote in August 25th, 1910, in the Independent, a newspaper owned by Nelson Aldrich that, "Under the proposed monetary plan of Senator Aldrich, monopolies will disappear, because monopolies cannot continue at such a low rate. Also, this will mark the disappearance of the Government from the banking business."
An interesting piece of trivia is that when our modern day "Federal Reserve System" was being planned, Paul Warburg who was a European from Germany that worked for the banking house Kuhn, Loeb and Company informed his other colleagues that were also planning for this new system that we have today, to avoid using "central bank" in the name. That's how we got this name of "Federal Reserve System", but it's basically a central bank with a new label, new to the early Twentieth Century.
Another piece of trivia is that the argument for a central bank in 1812 was presented as being that financial distress brought about by the war (War of 1812) required financial relief in the form of a new national bank.
This was at least the argument made for the second central bank that was charted in the history of the United States, the House and Senate passed a bill creating the Second Bank of the United States. I am speeding through history here.
One last piece of trivia that speaks to your statement of, "surely the government can print currency and regulate banks by conducting audits through finance ministry and so on".
At the outset the opinion of Thomas Jefferson made the powerful argument regarding the proposal for the first central bank of the United States:
I consider the foundation of the Constitution as laid on this ground; That "all powers not delegated to the United States by the Constitution nor prohibited by it to the states, are reserved to the states, or to the people."
To take a single step beyond the boundaries thus specifically drawn around the powers of Congress is to take possession of a boundless field of power no longer susceptible of any definition.
The Bill delivers us up bound to the National Bank, who are free to refuse all arrangements, but on their own terms, and the public not free, on such refusal, to employ any other bank.
The bill that Thomas Jefferson referred to was one put before him by proponents of central banks, namely Alexander Hamilton.
Citation:

Charles A. Lindbergh, Sr., Banking Currency and the Money Trust
The Writings of Jefferson, vol. 7 (Autobiography, Correspondence Reports, Messages, Addresses and other Writings)(Committee of Congress: Washington, D.C., 1861) page 685.


Demand-pull inflation intuition According to the theory, monetary growth increases inflation.

But how do companies know that there is more money in the economy now than before?

The basic intuition is that the companies either directly know by looking at what the central bank is saying, OR (and more importantly) the money growth means that money is now put into the hands of various agents in the economy. The second case is the important one.

When that money is put into the hands of various people they go out and spend that money. Thus there is increased competition to buy the same amount of goods. (More $$ chasing less goods). That competition to buy means that firms will profit by raising the price, and so they do that when they see the increase in demand.


Does price cap in emergency situation (COVID-19) reduce the availability of a good? Does unregulated market increase it instead? I was discussing with one of my friend about Italy price cap on surgical mask to control speculation. He says price cap does not allow industries to invest more to increase the production that would then naturally lower the price in accordance with the "demand and offer rule". I say that, because most of the speculation happens at the retail level (pharmacies and shops) surgical masks factories are not affected by price caps and so the quantity of production is not affected.
Am I right? Can some data or real life example backup this?

Capping prices at a low level permanently would presumably lower supply in the long term, but that is not germane to this question.

I will attack a slightly narrower version of this question: does capping prices in an emergency lower investment?

I would argue that the definition of “emergency” means that it is short term, and activity is disrupted. It is extremely difficult to launch a fixed investment project during an emergency. Fixed investments take time to finish, and the emergency is likely past before completion.

What we are seeing in 2020 is existing capacity being re-purposed to new uses. E.g., distillers are switching from producing whiskey to producing hand sanitiser. I doubt a survey has been completed, but anecdotally, many manufacturers are selling at a slim or no profit. (However, they benefit from switching from non-essential to essential production, allowing them to keep workforces employed. This is a benefit, even if profit margins are lower than their usual output.)

Most emergencies are geographically limited; e.g., hurricane. It typically makes no sense to switch production like is happening in 2020, capacity in other regions can be accessed more quickly.

The question then shifts: does a lack of controls create an incentive to have extra capacity/inventory during normal times to take advantage of an emergency?

This is perhaps plausible, but a good portion of manufacturers attempt to reach a global market. The existence or non-existence of price caps in a few countries would not radically shift their investment decisions.

Keep in mind that there is an aversion to price gouging during emergencies. Very few companies want to be publicly associated with the practice. As such, most news stories about price gouging involve largely invisible intermediaries that do no have a public “brand”. (There is an academic literature on price gouging, but I am not familiar with it. However, the reality that there is a public aversion to price gouging is non-controversial.)


How is an spontaneous currency changing phenomenon called? On November 2019 I went back to Venezuela, and the biggest shock for me was that people started trading goods using US Dollars. This isn't "legal", but it has become so common that I hardly ever had to have the official currency "Bolivar" with me during the three week period that I was there. I was told that trading using US Dollars became mainstream during the blackout period on which you had no access to any electronic means to pay and given that Bolivares in cash were scarce, people began using US Dollars as currency. Al tough both are accepted.

Anyway the problem goes much much deeper. But I wanted to know how is this called and if any other country has ever gone through a process similar to this one before?

When the switch from national currency is to US dollar it’s called dollarization (this mostly happens for US dollar but there are exemptions like Montenegro using euros) and in general it’s called currency substitution.  It often happens when people lost the trust in the local currency or if it’s impractical to have local currency (for small states like Montenegro).

Past examples are Equador and El Salvador or Zimbabwe. This list is not exclusive but those are the major ones you want to look at.

Also note that in case that people still use both currencies the currency substitution can be only partial but from my understanding Venezuela is close to full substitution.


How can a good be considered both a luxury and a normal one? Let's say I spend $20$ on pizza with an income of $100$. If my income jumps to $110$, I then spend $25$ on pizza. While my income grew by 10%, my expenditures towards pizza grew by 25%. Hence, I would consider this good a luxury, where $\Delta Q_{D\%} / \Delta I_{\%} > 1$.

How can pizza be considered a normal good in this context.

In case of normal goods, income elasticity of demand is greater than 0 and in case of luxury goods, it is greater than 1.

Supposing the price of pizza here remain constant at $1, thus when your income increased by 10%, the demand of pizza increased by 25%

Income elasticity of demand = 25/10 = 2.5

2.5 > 0, hence normal good

2.5 > 1, hence luxury good

This way, pizza is both normal and luxury good here.


Impact of Import Quota onto Revenues I'm learning about quotas from my textbook but I've found one thing that doesn't make sense to me at all and I think it may be a mistake in the book.
The context: $P_w$ is the price of wheat on the world market. So far the domestic government has allowed free trade but now they set an import quota of $Q_3 - Q_1$.

The text accompanying the graph says:

  Domestic producers now supply $0Q_1$ and $Q_3Q_4$ tons of wheat at a
  price of $P_{quota}$. Their revenue rises from $a$ to $a+c+d+f+i+j$.

What I can't understand is why they included $f$ in the last sentence. In my opinion their revenue rises from $a$ to $a+c+d+i+j$. Domestic producers first sell $0Q_1$ quantity for price $P_w$ so they make profit of $a$ and then they sell quantity $Q_3Q4$ for price $P_{quota}$ which gives area of the rectangle: $c+i+j+d$.  I have no idea what that $f$ is doing there. Can anyone explain?

There is no mistake. The solution: it is assumed that there is only one price at the domestic wheat market. Hence domestic producers will not sell at price $P_w$ and price $P_{Quota}$ as well. This makes sense: Suppose you are a domestic producer and you are aware that the price that results from the quota system is $P_{Quota}$. Knowing this you would not sell your goods for the lower $P_w$.


Where did Adam Smith write the following and in what context? Contra the a certain fetishisation of Adam Smiths thought he wrote:

  The vile maxim of the masters of mankind: all for ourselves and nothing for other people.

I'm assuming that this is from his Magnus Opus, The Wealth of Nations. Is this correct? What is the context in which he felt he had to make such an observation?

This (paraphrase) appears in Book III, Chapter IV of The Wealth of Nations. Smith is discussing how, in his opinion, towns engaged in commerce and manufacturing have contributed to the improvement and cultivation of their country.
Specifically, the quote appears in the context of a discussion about feudalism, and kings being unable to control the violence of feudal lords on page 448 (line breaks and emphasis mine for clarity):

But what all the violence of the feudal institutions could never have
effected, the silent and insensible operation of foreign commerce and
manufactures gradually brought about.
These gradually furnished the
great proprietors with something for which they could exchange the
whole surplus produce of their lands, and which they could consume
themselves, without sharing it either with tenants or retainers. All
for ourselves, and nothing for other people, seems, in every age of
the world, to have been the vile maxim of the masters of mankind.

Smith continues:

As
soon, therefore, as they could find a method of consuming the whole
value of their rents themselves, they had no disposition to share them
with any other persons. For a pair of diamond buckles, perhaps, or for
something as frivolous and useless, they exchanged the maintenance,
or, what is the same thing, the price of the maintenance of 1000 men
for a year, and with it the whole weight and authority which it could
give them. The buckles, however, were to be all their own, and no
other human creature was to have any share of them; whereas, in the
more ancient method of expense, they must have shared with at least
1000 people.
With the judges that were to determine the preference,
this difference was perfectly decisive; and thus, for the
gratification of the most childish, the meanest, and the most sordid
of all vanities they gradually bartered their whole power and
authority.

So, Smith seems to be making a greater historical observation about civilization while specifically discussing the concentration of power, greed, and wealth as it was in feudal society.  Hopefully this helps explain the context of the observation a bit.


What guarantees that endowed agents have non-zero prices in an Arrow-Debreu Economy In my research I am trying to find minimal conditions to guarantee a quasi-equilibrium must always be a typical Arrow-Debreu equilibria in a rather specific production setting.

This may be rather trivial/maybe I'm misunderstanding something, but I am struggling to show that agents endowed with goods will never have zero-prices on their goods. This seems to intuitively be true to me because it makes no sense for an agent to give away a good for free if they might make profit on it/can just keep it for themselves otherwise, but I can't see why market clearing and optimal production would imply that consumers never have zero prices at a quasi-equilibria.

Long story short, could somebody explain to me what stops agents from having zero prices on goods in an Arrow-Debreu production economy? What types of assumptions are necessary? Again, sorry if this is a silly question. I'm a mathematician by trade and have only recently started working with economic models.

A pretty trivial assumption would do it:

If the consumers preferences are strongly increasing, i.e.
$$
x \succ_i y, \mbox{  if $x \geq y$ but $x \neq y$ },
$$
and unbounded for all $i$, then no $x$ can be an optimal bundle if $p \notin \mathbb{R}^C_{++}$ (assuming there are $C$ commodities).
So zero price cannot arise in an Arrow-Debreu equilibrium.


Differentiate a positive externality and the absence of a negative externality. Tax or subsidize? I hope this isn't overly semantic, but I'd like to gain some clarification on the use positive (or negative) externality.

I usually shoot down suggestions for examples of positive externalities like organic agriculture. We can grant that organic agriculture is better than conventional, but that doesn't mean it is producing additional external benefits. Instead, organic agriculture might feature fewer negative externalities compared to the status quo.

I've even seen examples like smoking being a positive externality because smokers die sooner and save governments money on Social Security (perhaps that accounting might be questionable, but let's grant it for the sake of argument). Again, my semantic preference would be to label this as the absence of status quo negative externality.

If the semantics aren't interesting, might there still be something interesting on the tax vs. subsidize side? Returning to the agriculture example, taxing the negative externalities associated with conventional agriculture seems smarter than subsidizing organic. This seems like a case where it's more efficient to regulate the end and not the means. But what market characteristics might make subsidizing specific not-negative-externality-producing things more efficient?

A negative externality arises when the private net marginal benefit (i.e. the marginal benefit minus the marginal cost) of an activity exceeds the net social benefit. In such cases, the self-interested private decision maker will increase their participation in the activity even though it is socially inefficient for them to do so.

A positive externality arises when the private net marginal benefit (i.e. the marginal benefit minus the marginal cost) of an activity are smaller than the net social benefit. In such cases, the self-interested private decision maker will not increase their participation in the activity even though it is socially efficient for them to do so.

This is a semantic distinction to the extend that if one thinks activity $A$ has a negative externality then one can define a new activity $B$, which is simply the "act of not doing $A$" so that $B$ has a positive externality. On this basis, one can argue that every externality is positive or that every externality is negative. For example, many people think that education has a positive externality because educated people make better citizens (e.g they make more informed voting decisions that benefit others). As a matter of semantics, one could argue that this is, in fact, not a positive externality and that what is really going on is that people who do not educate themselves are exerting a negative externality on those who do by virtue of their ignorance.

Whilst there is some merit to this reasoning, I do not find it helpful. Often, when we study the effects of behaviour, we are interested in comparing those effects to some baseline or benchmark in which the behaviour is absent. When communicating economics to others, it is usually the case that some benchmarks are more intuitive that others. We could, for example, rewrite all of consumer theory in terms of "the dis-utility people experience from not having goods" and look at the "problem of non-consumption dis-utility minimisation". Doing so would be formally equivalent to the more conventional approach of consumption utility maximisation (only the language changed), but would probably be less intuitive for people trying to understand the economics.(*) At least to me, it is more intuitive to think that people actively choose to undetake some level of education and exert a positive externality on others than to think that everyone receives infinite education by default and the choice of abstaining results in a negative externality.

Besides education, another example that I think fits most intuitively into the positive externalities box is network effects. If I buy a telephone then all of my phone-owning friends are made better off because now they can use their telephone to call one more person that they couldn't reach before. It seems weird to think of the negative externality of not owning a phone.

In terms of taxes versus subsidies: to get to the socially optimal intensity we need to ensure that the private net marginal benefit is zero precisely when the social net marginal benefit is zero. In the case of a negative externality this can be done either by increasing the private marginal cost (via a tax) for the activity or by increasing the private marginal benefit of not participating in the activity via a subsidy. For example, we could either subsidize low carbon firms or tax heavy polluters. As far as aligning incentives are concerned, the two are equivalent. In most practical cases, the more important consideration is likely to be that of budget constraints and politics:

In the case of a tax: can the person you are taxing afford to pay the tax and can the tax be levied without seeming vindictive (for example, I think that taxing people without a university degree would be a no-no on these grounds).
In the case of a subsidy: can the government raise enough popular support and funding for a subsidy without leaving people with the impression the some parties are receiving unfair government hand-outs?

In most cases, thinking about these political and financial constraints makes it clear whether a subsidy should be used. Sometimes a combination of both is used. For example, in the UK the government both taxes petroleum consumption and subsidises electric car ownership.

(*) Nevertheless, economists do often find it useful to convert the utility maximisation problems into their dual expenditure minimisation problems, which is somehow similar. This technique, though, is usually reserved for more advanced students who already have a well-developed intuition for the economics.


Which areas of mathematical knowledge are required for understanding different genres of theoretical economics literature (and at which level)? I would like to know which mathematical skills are most important to understanding different types of theoretical economics literature. An ideal answer would list disciplines used for different 'genres' of literature; for example: "Mathematical finance requires elementary linear algebra and stochastic calculus" (is this accurate?).

For microeconomic theory, a starting point would be

Basic multivariate calculus,
topology/set theory
real analysis,
probability theory,
a basic knowledge of linear algebra.

For 'applied' micro theory (theoretical industrial organisation, applications in information economics, etc.), or for reading of a graduate-level microeconomics text (such as Mas-Colell, Whinston, and Green's "Microeconomic Thoery"), a good understanding of the basics of these areas will suffice. Most material will be set in something like a Euclidean space and will draw on a fairly restricted set of methods and results from the above domains. You can already get a long way with a good understanding of the basic continuity properties of the reals ($\epsilon$-$\delta$ proofs, open and closed intervals, intermediate value theorem, basic fixed-point theorems, etc.), the ability to do partial differentiation, integration, and to calculate conditional probabilities and expectations.

As one turns to the journal literature and looks more towards pure (rather than applied) economic theory, the level of mathematical sophistication increases somewhat and it becomes more likely that you will encounter more exotic (from the point of view of economics) mathematical methods and results.


What R-squared is a low R-squared? I keep hearing that R-squared does not really matter in economics research and that due to the unpredictable human nature, economics research regressions tend to have low R-squared.

But how much is too low for even economics research?

I am asking this because one of the regressions I ran has an R-squared of around 1%. Is it still okay?

And, in general, what is a low R-squared in economics?

Disclaimer: this answer comes from a microeconomic research perspective.  Time series / macroeconomic specialists will likely have other perspectives.

There is no general rule for what's too low across the entire field of economics.  Yes, microeconomic models (i.e., individual-level observations) will tend to give low R-squared values (often in single percentage point digits) because there are so many factors that can affect human outcomes, a lot of which just cannot be observed.  But more generally, R-squared will depend on your data and model, specifically the nature of your dependent variable, any transformations you may have applied to the variable, what explanatory variables you include and what variables you exclude.

In Economics research, R-squared is rarely of concern because predictive power is often not the main goal.  Instead, economists focus on finding reliable estimates of coefficients for variables of interest and deriving useful inferences from the structure of the model and the estimated values of its parameters.  And standard error of the regression is considered a better metric than R-squared because it comes in the units of the dependent variable, provides the absolute measure of the typical distance that the data points fall from the regression line, and it scales the width of all confidence intervals calculated from the model.

Source for some of the points included in this answer: https://people.duke.edu/~rnau/rsquared.htm


2SLS with endogenous interaction terms Suppose I have a regression model:
$$y_{i}=x_{1i}\beta_{1}+x_{1i}D_{i}\beta_{2}+\epsilon
$$
 where $\mathbb{E}\left[\epsilon_{i}|x_{i}\right]\neq0$ , and there
is a problem of endogeneity. In the above, think of the dummy variable
being equal to $1$ when $i$ is male. As such, this model allows
for a differential effect of $x_{1i}$ on $y_{i}$, if the individual
is a male or female. In order to obtain consistent estimates, suppose
I have an instrument $z_{1i}$, which is both a relevant instrument
for $x_{1i}$, and satisfies the exclusion restriction (such that
$cov(z_{i},\epsilon_{i})=0).$ If there were no interaction term,
it would be trivial to estimate the above using Two stage least squares,
or simply just computing:
$$
\hat{\beta}=\left(\boldsymbol{z'}x\right)^{-1}\left(\boldsymbol{z'y}\right)
$$

However, the complication arises due to the interaction term. How
would I go about obtaining estimates for both $\beta_{1}$ and $\beta_{2}$?
One option is to construct another instrument $D_{i}Z_{1i}$. Would
such a procedure be valid?

Let $X$ be the original regressor matrix and $Z = [z \;\; zd]$ be the intstruments matrix, and consider the IV estimator

$$\hat \beta_{IV} = (Z'X)^{-1}Z'y = (Z'X)^{-1}Z'(X\beta + u) = \beta + (Z'X)^{-1}Z'u$$

As long as the things that are included in $Z$ are orthogonal to the error term, we get consistency... provided that $Z'X$ remains invertible, something that you can easily check in your case.


Why wouldn't other firms follow suit if an individual firm decides to cut its price? Why doesn't the demand curve an individual firm faces in a perfectly competitive market have the same elasticity as it does in a oligopolistic market?
Under perfect competition, if a firm increases its price fractionally, consumers will turn away from it and look for alternatives. On the flip side, if a firm reduces its price fractionally, it can capture the entire market. So why wouldn't other firms follow in footstep like they do in a oligopolistic market?

There could be many answers, but the one that comes to my mind immediately is product differentiation. If you're selling exactly the same thing as everyone else, buyers are going to flock to the lowest price buyer, so you everyone will have to follow a price cut. But say you are selling ice cream cones on the boardwalk at the beach. Any little thing, such as a slightly better location, a better selection of flavors, or a cheerier clerk scooping the cones could be enough to let you keep a good chunk of your customers without cutting the price.
BTW, even a slight perceived difference among sellers would (technically speaking) make the market an oligopoly, not perfect competition. In perfect competition, by definition, there can't be any differences. That is why we call perfect competition an "ideal type," not a description of real-world markets.


Australian Dollar Devaluation I am a layman in economics. I am curious about the current devaluation of Australian Dollar in comparison with the US Dollar. Could someone please explain, in simplest words possible:

What causes currency devaluation? Is it a variety of factors or are there some common factors in all currency devaluations?
What does this devaluation mean for people living in Australia, people living in US, and people living in other countries, say China? I understand that one of the consequences for Australians is that their exports become cheaper, so foreign countries have more incentive to buy Australia products. For Australians, this could potentially mean more incentive to produce/work/innovate, and to decrease their imports. In other (naive) words, tighten their belts, rely more on themselves and less on the external world. This, logically, seems like a positive sign and should have good consequences. Does this interpretation have any element of truth in it? And is there another, completely opposite, possible outcome of this devaluation?
What are good (smart) ways for the Australian government and policy makers to respond to this?
How does devaluation translate in "standard of living". I was looking at the historical exchange rate of AUD and USD here since 2000. Interestingly, in March 2001, the AUD was almost half of USD, and in July 2011, it was more than 1 USD! Surely, it does not mean that the standard of living in Australia in March 2001 was twice as bad as it was in July 2011 (in comparison with US), does it?

I understand that forex rates involve an interconnection of many factors. But, I want to be educated about how much we know about it, and how much of what we know is actually useful for us.

This question is heavily reliant on the context of when it was asked. A lot has happened since February with respect to the Australian Dollar.

A currency devaluation can be caused by quite a few factors. In the case of Australia, the devaluation is occurring with respect to the USD. The AUD remains strong but the US is currently experiencing a surge in consumer confidence. There is also a few larger factors at play. The USD is seen as basically the safest investment one can make. In recent history, govt bonds have been less attractive. As a result, Australian Sovereign bonds have been more attractive as they are very safe. In short, the AUD devaluation has more to do with the strength of the US than any domestic weakness (although Australian economic performance has been underwhelming).
Another key factor relates to the resources boom in Australia. This has primarily been driven by an increase in demand from China instead of an increase in mineral output. The resources book has been a key driver of economic growth. In March/April, the iron ore price took a big hit, partly due to weakening demand from China. As a result of the change in price, the value of Australia's exports dropped very quickly. This directly reduces our Terms of Trade. Manufacturers are pretty happy about this and it is expected they will pick up some of the slack from the stagnating mining sector.

This devaluation has a few flow through consequences. Exporting to the US is cheaper. Importing from the US in particular is more expensive. A good way to think about it is if you are Australian and are thinking about travelling to the US for a holiday, you would be pretty upset. Your trip just got a lot more expensive very quickly. If you own a hotel and you cater to a lot of American tourists, you will be very happy. It will be cheaper for them to come. This change is good for our exporters, including natural resources, manufacturers and services.

The RBA typically responds to these issues very well. Their main instrument of monetary policy is the interest rate.
There isn't much need for a monetary policy response to the devaluation of the dollar. The RBA targets inflation rate which is preferred to Exchange Rate Targeting by many governments.
With respect to a fiscal policy response, The IMF has a working paper on Fiscal Policy and the Real Exchange rate. It doesn't answer it perfectly, but it is definitely worth a read. The key point is that the effect depends critically on (i) the composition of public spending, (ii) the underlying financing policy, (iii) the intensity of private
capital in production, and (iv) the relative productivity of public infrastructure

There should be very low immediate pressure on the standard of living. It gets more expensive to import into Australia, but Australian produced products are more competitive in the international marketplace.


Extracting group effects from individual fixed effects I have a conceptual econometrics question I was hoping to get some help with.

I have a panel of 100 individual firms over time (10 years) at the quarterly frequency across 10 countries. One of the questions I'm interested in is about whether there are fixed differences across countries with respect to the dependent variable.

The initially obvious way to me of looking at this is to drop the firm fixed effects in my regression and include country dummies instead.

But I was wondering if it's feasible/makes sense to get at the same question by averaging the firm fixed effect parameters in some way within country groups.

And if so, would this be unambiguously better (considering that the Hausman test points to the value of including firm fixed effects)?

Thanks for your help and let me know if anything is unclear. This is my first post

Good question.

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

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

More detailed discussions follow.

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

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

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

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


Is there an economic analysis of how piracy allows a product to take a hegemonic position? There's an interesting situation with the likes of Photoshop, where the software being pirated actually increases its market usage, and the software becomes the de facto standard, in part due to software piracy.

In the instance of Photoshop for example, it's likely that people creating funny doctored ('photoshopped') images and spreading them via the internet, were using pirated Photoshop software.

Here's a Life Hacker article on it.

What it means, is that especially for a creative software like Photoshop, or Ableton (music production software), the developers shouldn't make their copyright protection too strict. It should be easy enough to crack so that people can actually use it, but pain enough to get people to fork out if they're serious enough.

My question is - is this a well researched phenomena in economics?

Is there an optimal either pricing strategy, or copyright protection strategy, that takes this into account?

The model is a variant on penetration pricing (effectively $0 for pirates) which is used to gain market share.

The problem is while monopoly may be desirable, the path to monopoly is generally not, as the cost to acquire market share rises relative to the value of each additional unit of market share.

While there is no specific study of Adobe that I know of, penetration pricing and market share are generally well understood concepts in economics.

That being said while the linked MIT paper implies an "uncanny valley" of sub-optimal over-penetration before a monopolistic (~100%) market share/maximal profit scenario, to my knowledge the empirical data on ologopolistic firms and cartels is scant, outside of the energy industry. Historically, however, OPEC and the Seven Sisters, have never actually combined to a monopoly, nor engaged in penetration pricing by giving away oil (again, to my knowledge).

One thing that is agreed on is that a monopoly is only as valuable as the barrier to enter the market (broadly speaking).

Combining those facts one could surmise that for Adobe to maximize profits they would need to choose a strategy that allowed for either:

a) optimal penetration

$$or$$

b) monopolistic dominance of an industry that would need to produce profit per year less than roughly the barrier to entry divided by the discount rate they erected through a combination of R&D costs and $0 penetration pricing strategies.

$$P_{Total} <  \frac{B}{r}$$

Monopoly of a more valuable market would entice a rational actor to break it and leave both in the sub-optimal valley of oligopoly (unless they colluded), hence the prevalence in niche technical markets you mentioned.

Not to say graphic design is a small niche, but of the population at large they represent rouhgly 0.08% (at least in America).


When is an OLS parameter unchanged on a subsample? There is a sample of $n$ observations, each element has a numeric $Y$ and $X$ characteristic. There is an OLS regression over the sample
$$
Y = b_0 + b_1 X + \textbf{u},
$$
$\textbf{u}$ being the vector of residuals. Suppose we remove observation $i$ from the sample, restricting it to $n-1$ observations, and run an OLS regression again, yielding
$$
Y_{-i} = b_0' + b_1' X_{-i} + \textbf{u}'.
$$
Subscript $_{-i}$ denotes that $Y$ and $X$ are not the same vectors as before, as observation $i$ is missing.

Seems to me that if the observation $i$ we removed is on the original sample's 'regression line', that is if
$$
Y_i = b_0 + b_1 X_i,
$$
then $b_0 = b_0'$ and $b_1 = b_1'$.

Example: (in R code)

x = c(5,3,4,5,4,4)
y = c(20,15,14,21,10,25)

plot(x,y)
abline(coef(reg))

plot(x[-1],y[-1])

reg1 = lm(y[-1] ~ x[-1])
abline(coef(reg1))

My questions are:

1) Is this true, and if yes, what is the proof?
[I figured this one out in the meantime, but feel free to give a nicer solution.]

2) Is it possible that after removing an observation (not on the 'regression line') we have

($b_0 = b_0'$ and $b_1 \neq b_1'$)  or ($b_0 \neq b_0'$ and $b_1 = b_1'$)?

I think I figured out 1). I am still interested in 2).

OLS sets $b_0$ and $b_1$ in such a way that

$$
(b_0 \ \  b_1) = \arg\min_{a_0, a_1} \sum_j \left(Y_j - a_0 - a_1 X_j\right)^2.
$$
The first order conditions are
$$
(-2)\sum_j \left(Y_j - b_0 - b_1 X_j\right) = 0
$$
and
$$
(-2)\sum_j X_j \left(Y_j - b_0 - b_1 X_j\right) = 0.
$$
If observation $i$ is on the regression line then
$$
\begin{align*}
\left(Y_i - b_0 - b_1 X_i\right) & = 0 \\
\\
X_i\left(Y_i - b_0 - b_1 X_i\right) & = 0.
\end{align*}
$$
It follows from this and the original first order conditions that
$$
\begin{align*}
(-2)\sum_{j\neq i} \left(Y_j - b_0 - b_1 X_j\right) & = 0 \\
\\
(-2)\sum_{j\neq i} X_j\left(Y_j - b_0 - b_1 X_j\right) & = 0,
\end{align*}
$$
which are the first order conditions of the subsample's OLS problem.


Is there any investment model with time-varying depreciation rate? Is there investment model with different depreciation rate.

For example, d1(depreciation rate in 1 period), d2(depreciation rate in 2 period)

A type of model you might be interested on is one where the depreciation rate is endogenous. This means, it depends on the value of other variables in the model, instead of being exogenous and constant (naturally, you can have a variable depreciation rate but exogenous, but that is as ad-hoc as a constant depreciation rate).

One example is this model. Equation 19.4 shows the formula of the depreciaton rate (which the authors also coll net utilization rate). Then, they state:

  Thus the adjustment path for the capital utilization rate is a flexible accelerator.
  This result rigorously establishes the empirical finding obtained by Nadiri and Rosen (1969) that the adjustment' path of the
  capital utilization rate is similar to the paths of capital and labor growth rates which are governed by flexible accelerators. Along the
  dynamic path, as the capital intensity decreases the net utilization rate declines for two reasons. First, there is the direct effect of the
  capital intensity on the net utilization rate. A decrease in the capital intensity leads the firm to reallocate resources towards capital output
  which decreases the rate. Second, there is the indirect effect, which arises because the decrease in capital intensity causes the price of
  unutilized capital to increase. Since the marginal value of unutilized capital increases, the firm then utilizes less of its capital and so the
  utilization rate falls. Thus $k^° > k^*$ implies that $\delta^° > \delta^*$. These results mean that along the dynamic path the net capital utilization rate
  and the rate of capital investment are inversely related while the net capital utilization rate and the labor investment rate are directly
  correlated.

This paper presents another model. They show that "embodied" technical change (i.e. technical change which comes with new machines rather than occur amid current machines) decreases the lifetime of capital, thereby increasing the depreciation rate.

This paper finds empirical support for a variable depreciation rate.


Are Investments positively or negatively correlated with interest rate Having just begun self-studying economics, I apologise if this question is too simple.

Do investments increase or decrease with increased interest rate?

According to the small, closed economy model (as far as I understand it) increased interest rates make borrowing harder and hence crowed out investment.
However, in the large, open economy model it is mentioned that higher interest rates encourage both domestic and foreign investors to lend in the country, so investment can increase?

I appreciate that this boils down to a difference in foreign vs. domestic, and ultimately into the question wether investment is lending or borrowing. Anybody who could put me on the right track please?

History is plenty of different situations, but usually it works like this:

Low interest rates will increase demand of borrowing money and will decrease the interest of investors in lending (they will probably try to find another place with higher interest rates to invest in).

As a consequence, there will be less people offering money, so the interest rate will increase and the demand of borrowing money will decrease (because it will be more expensive). Maybe it will reach a kind of balance or maybe it will attract imvestors again (it depends on both local and international situation).


Is soil exhaustion rational? I was talking with friends about soil exhaustion in agriculture. They tell me that it is very frequent because of the methods employed in modern agriculture. They suggest that this amount of exhaustion is 'unsustainable'.

What strikes me in contrast with other environmental issues is that there seems to be no externality here : each farmer degrades his own land. So what should we think :

a) These are long-term effects, so that it is a problem of intergenerational equity.

b) Farmers do not know about the effects of these methods, or are not rational.

c) There is no problem : soil exhaustion is the rational outcome of intertemporal planning and is due to time preference of farmers and consumers.

Any references on the subject are welcome.

Thanks,
U.

The true answer is of course it depends. What it depends on is how you define sustainability.

In a natural resources context, with weak sustainability, soil quality is a capital asset, just as a fish stock, a forest or an oil field. Given that we have manure and fertilizer I would argue that it is a renewable resource (until we run out of phosphate perhaps or poison the soil with too many pesticides), but let's start from the simpler case of a non-renewable resource.

In that case the golden rule tells us to gradually exhaust the soil until no more degradation is possible. In the simplest case we should degrade at the rate of interest. You correctly observed that in principle there are no externalities. The individual optimal solution is equal to the social optimal solution, provided the individual discount rate (interest rate) is equal to the social discount rate (see e.g. Clark 2010 for this often missed point).

One can modify such a model to allow for renewable resources with the use of fertilizer or natural regeneration, which would change the solution somewhat. Kenneth McConnel (1983) has a model showing the basics.

The reason that soil exhaustion is optimal is that the proceeds can be invested in alternative assets, which generate a larger rent. The problem is of course that i) this model assumes we discount the future (which we do) so future generations are discounted; ii) such models at an economy wide level typically assume the existence of a backstop technology, something we can use when we run out of good quality soil. Whether or not something like that will exist is debatable.

Moving towards a strong sustainability viewpoint the main thought is that we should not deplete our natural resources beyond their regenerative capacity, unless we already have a substitute. We don't currently have a real good substitute for soil quality, although we can use fertilizers and such to make up for some of that. From a strong sustainable perspective we are therefore not (yet) sustainable.

From a bit broader perspective the production of artificial fertilizer is very energy intensive, and one can question whether the current amounts used (as well as the earlier mentioned pesticides) do not have unintended effects, but then you're back at externalities.


Economic interpretation: IS curve contra GDP in equilibrium I have in a problem shown that for the IS curve (Y) contra the GDP in equilibrium ($Y^*$) it applies that: $\frac{\partial Y}{\partial G}>\frac{\partial Y^*}{\partial G}$. Where G is public consumption. I think my calculations make sense. But what will the economic interpretation of this result be? Can anyone help me?

So graphically this is pretty straight forward, as you may have already understood: Since the LM curve has a positive slope the entire shift of IS curve ($\frac{\partial Y}{\partial G})$ is not fully translated into final output. It would happen when LM curve is flat (which is usually the case at very low interest rates in liquidity trap situation).
Interpretation: As govt's consumption/expenditure increases at a given interest rate, it increases output. But higher output requires more money circulating in the economy to sustain the higher output. Since no additional money is injected into the economy this additional money demand is met from the speculative demand for money. This means that speculative demand should come down.
The decrease in speculative demand comes from increase in interest rates. (Mechanically, this happens because as govt floats more bonds into the market (for expanding its borrowing), it triggers a speculation of increase in interest rates which, in turn, triggers the money held by speculators to invest back in the economy - increasing the money available for transactions). Further there are more bonds in the market too causing the bond prices to fall and interest rates to increase (wealth effect channel).
But as the interest rates goes up, the private investment demand comes down (called - crowding out of private investment) ultimately making final increase in demand ($\frac{\partial Y^*}{\partial G}$) to be lower at equilibrium as compared to $\frac{\partial Y}{\partial G}$.


What is the maximum number of characters in a currency symbol? In the program I am writing, I need to show a currency selector. I would like it to display currency symbols. For this, I need to know what is the longest, in characters, currency symbol (or rather what the maximum length can be, if there is any limitation).

E.g. USD, EUR, RUB all use single-character symbols: $, €, ₽. I initially assumed that it will always be one character. But I am obviously wrong, as e.g. Polish zloty symbol is zł.

Instead of currency symbols, some of which are used by more than one currency as @HotLicks suggests, you may want to consider the three-letter currency codes used in most currency exchanges. Here is a list: https://en.wikipedia.org/wiki/ISO_4217#Active_codes.


Indirect utility from expenditure function I have the expenditure function: $$e(p,u)=\left(p_1^{\rho/{\rho-1}}+p_2^{\rho/{\rho-1}}\right)^{{\rho-1}/\rho}u$$
where $u$ is the utility, $p_1,p_2$ prices and $\rho$ a parameter. How do I derive the indirect utility function?

Mas-Colell, Whinston, Green chapter 3, especially p. 75 explains this. One possible way is $v(p,w)=e(p,v(p,w))$ where $v$ is the indirect utility function, $p$ the price vector and $w$ the wealth.


Macroeconomic Measures of Human Capital How exactly do you measure human capital for a given country and what numbers are included in that measure.

The reason why I ask is because im interested in simulating the Mankiw–Romer–Weil version of the solow Model.

Links to where I can get the data will be appreciated.

The approach developed by Barro and Lee has been used in many empirical analysis. They provide a detailed discussion of how to construct an aggregate human capital measure.


Have automation and technological advance been shown to have a positive impact on society and the economy or a negative one? My friends and I, 2 of which are computer science majors think it is worse because is humans can't work and thus afford necessities, how will they survive?  The definition of automation: the use of largely automatic equipment in a system of manufacturing or other production process.
"unemployment due to the spread of automation"

It is to reduce human intervention mainly in order for tasks to more economically efficient and save on paying unions, benefits to employees, as well as human workers.  A business starts with one person let's say, an assembler.  He hires a few other people to assembly more work he's getting, and eventually has a whole factory. He is able to buy 2 robotic arms and use them to cut his human workforce in half, not needing let's say 20 guys out of 40 he had.  A few years later he buys two more robotic arms and the rest are laid off.  He now only needs a few men (3-4) for monitoring and repairs.  BUT once the CEO can buy technology to fix the robots, pretty much all left is observers, but then the CEO eventually just wakes up, hits a switch, and begins building.  He's rich, made his own job, made his living, he'll probably be fine.

HOWEVER, not everyone has the mindset or means to be an entrepreneur or innovator.  ALSO because the CEOs and owners invested and made their own business, how can they be hated in a fair way? They should have this right since the whole thing is their ownership and job, it just needed other people for a while.

ALSO, during this time, new jobs were made like the observers and robot repair people.  They were eventually automated out too.  This is being done for drivers, surgeons, pilots, military, security, construction, even cashiers are replaced by self check outs now.  They have tested a truck that drives itself, size of a delivery one for products. Drones are already delivering things.

Therefore, I can't see (and neither can others) how advancing technology to be more self-sufficient in itself is good when people will eventually no longer be able to find work and thus afford medical care, food, housing, clothing...from that, it would for the majority (not those who are stocked on riches and resources and were innovated enough to prepare themselves) cause economic collapse. Due to lack of taxpayers now and there be less flow of the economy anyways, a communist type system would unlikely happen so nobody starves or freezes.

Thoughts...does it have a better impact as many I've heard say, or all in all realistically, have a worse one (in the long run at the very least)?

Would you rather work with a tractor or shovel?

Would you rather use one hand to work or two?...

Mathemathically the formula is:

$$EL  = \mathrm{GDP}_r$$

That is, efficiency ($/h) times hours worked per year equals the real GDP. Same is true for your personal life and personal income. Now, if efficiency decreases, you must either work more or live with less, which is not what anyone wants. Note that even as you increase your efficiency, there is little evidence that such thing decrease someone else's efficiency. So thus the result is income inequality and not "lack of necessities". That means, those with lower IQs generally earn less (since IQ is the primary driver of differences in efficiency between people)...

For the example in question, it seems that efficiency has increased, and at least temporarily the L term has decreased (even though the robot arm builders obviously still need to be employed). However, the cheaper robot arms make it easier for other sectors to accommodate people. So more likely result is a sectoral shift in the labor force, which is what historically has always happened. That is, the factory workers take pay cut, but demand for labor increases in a other sector providing a pay increase and more jobs to that sector. Historically L remains the same but E increases for the whole economy.


Deaton's AIDS/QAIDS model Im new to economics and want to understand the AIDS/QAIDs model of Angus Deaton. Can anyone suggest possible readings for the same as a background knowledge??

For starters, the original article. Banks et. al (1997) discuss its assumptions. This survey might also be helpful.


Purchase of the public debts by the ECB In France, one of the presidential candidate said that the European Central Bank should purchase the public debts of the country and transform it into a perpetual debt (this is a literal translation, I don't know if there is a specific word for that in English).

Since I have very little knowledge about economics and how the ECB works, I find it very unlikely that a bank can just purchase the entire debts of a country.

I would like to know if this is really possible and if so, what exactly is a "perpetual debt"?

(The question about perpetual debt was covered by the link to the description of a perpetuity.)

There are two sides to the "is it really possible"?

Could a country that controls its central bank (e.g., Canada, Japan, United States) replace its debt with money issued by the central bank?
Could the ECB do the same thing?

The answer to (1) is that it appears theoretically possible. (In fact, the economic school of thought known as Modern Monetary Theory advocates this.) There is the question of whether this would be a good policy, and the answer to that would be controversial. It should be noted that Quantitative Easing policies of the Federal Reserve and the Bank of Japan involved large purchases of government bonds by the central bank, and there have been no obvious side effects (for example, inflation) yet. These policies represent a step towards the central bank buying up all government debt.

The answer to (2) - could the ECB follow such a policy - is a technical question. The actiona of the ECB are limited by treaties; the usual interpretation of those treaties says that the ECB cannot do this. Certainly, the ECB limited its buying of Greek debt based on its interpretation of the treaties. There would have to be a move to change the treaties that restrict the ECB's actions to allow such a move, which seems like a difficult task.

From the perspective of French policy, the answer to question (2) is more important than (1).


What's the best reference for rigorous study of mixed-strategy nash equilibrium? I am studying game theory, but I feel like I do not understand mixed-strategy equilibrium all that much. Yes, I know how to find them in 2x2 cases, and in some 3xn (n <= 2) cases as well where the normal form has been artificially constructed to make finding the mixed strategies very easily (e.g., one of the actions can conveniently be ignored because it's dominated).

But if I were to write down an nxn matrix right now, n >= 3, I wouldn't be able to solve for it's mixed strategies.

So I am looking for a really good really rigorous really thorough reference to understand mixed strategy equilibria. Any recommendations?

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

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

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


Correlation between salary level and housing prices in a town Is there a measurable correlation in a town between salary level and housing prices?

Or, to put it differently: is it politically meaningful to drive up salaries by new investments if the result is unaffordable housing?

UPDATE: I do not want to edit the original question as others wrote their reply with that in mind, but it is right to suggest that it would have been better to ask about causality, not correlation.

The graph below plots average house prices against average incomes for various US cities. The relationship is strong in the cross-section, especially if you ignore Honolulu.

Richard Florida, Housing and the Crisis, Part IV

Is it also true dynamically, that is, are changes in income associated with changes in house prices (not just levels)? Van Nieuwerburgh and Weill (2010) say yes:

  We set up and solve a spatial, dynamic equilibrium model of the
  housing market based on two main assumptions: households with
  heterogenous abilities flow in and out metropolitan areas in response
  to local wage shocks, and the housing supply cannot adjust instantly
  because of regulatory constraints. In our equilibrium, house prices
  compensate for cross-sectional productivity differences. We increase
  productivity dispersion in the calibrated model in order to match the
  30-year increase in cross-sectional wage dispersion that we document
  based on metropolitan-level data. We show that the model
  quantitatively matches the observed 30-year increase in dispersion of
  house prices across US metropolitan areas. It is consistent with
  several other features of the cross-sectional distribution of house
  prices and wages.

Why Has House Price Dispersion Gone Up?