Stable marriage problem with transferable utilities I'm looking for a package or a code (preferably in R) that finds the solution to the stable marriage problem with transferable utilities (Shapley and Shubik 1971). Specifically, I'm looking for one or more of the following:

The stable allocation, given a matrix of the joint surplus
The set of transfers that support this allocation
Option to specify another matrix of acceptable matches

As far as I know, the package matchingMarkets in R find the solution to that problem only in the case of non-transferable utilities. Any ideas?

There's two implementations that should somewhat cover your needs, matchingR which does reduced-form algorithmic matching and matchingMarkets, which estimates estructural matching models with some baysean tools to correct for endogeneity.

The problem is you're looking for some very specific models which may require some tweaks on these implementations.


Who performs the checks for regulatory compliance at trade borders? Customs officers check for tax compliance at trade borders.

But who performs the checks for regulatory compliance at trade borders?

Is it simply the various Government ministries (eg the one responsible for food and agriculture), or is it Customs Officers?

The most simple and universal answer is that it is up to each government to decide if checks should be made and if so by whom.  Some have none, either because of international agreements, because they see no need, or because they lack the capacity to do so.

The most common case is, as you say, that officials from different ministries inspect goods, and food/agriculture are the most common because it's too late if you find out that pests or diseases have been imported once they're past the border.

But otherwise, countries often make efforts to reduce and simplify border checks by doing risk assessments of traders or containers (and inspecting only the risky ones), by improving cooperation between ministries, or by improving enforcement of regulations and standards behind the border.


Solow model reparations I have the following task:

At some moment of time (1953), the government of a country (Israel) signs an agreement with
another country (West Germany) stipulating that West Germany would pay reparations to Israel
during the following N years. For simplicity assume that N is large enough, that the amount or
reparations is proportional to Israeli output, and that the economy of Israel reaches the new steady
state while the reparations are stil paid.

Need to use Solow model. But I really do not understand what the change will happen. Probably it is the same as an increase in s. Help is needed.

What changes is the macroeconomic identity of the model: from
$$F(K,L) = S + C$$
it becomes

$$F(K,L) + V = S+ C = (1+v)F(K,L) = S+C$$

where $V$ denotes the value of reparations per period, and the last expression reflects an assumption made in the question, that reparations are a constant proportion of domestic output.

"Using the Solow model" means I guess, using the standard Solow model, and so it implies that you don't change its basic assumptions. So there is no distributional issues related to this transfer payment from abroad, while also the savings rate remains fixed, and it is applied to the whole available income (irrespective of how it becomes available). I guess you can take it from here.

PS: It appears interesting to also consider a fixed level of $V$, which would reflect a situation where as time passes and the domestic economy grows, reparations become less important in relative size (which is a "reasonable" scenario, something like "we will help more when you are weak, and as you get economically stronger, helped also by the reparations, our contribution will diminish in relative importance")


how to calculate the average annualized return? I can do average return, I don't know what is annualized thou. can somebody say where (in a textbook hopefully) can I read about this? thanks!

Annualized return simply means average amount of money that a investment earns each year over a given amount of time.

If the compounding rates are the gains you've earned on your investment, The annualized return is:

$$AR = (1+totalreturn)^{\left({1\over{n}} \right)}-1$$

This equation shows the return each year over a full span of time.  Total return is the total change in the variable over all periods.


Algebraic demand curve in a perfectly competitive market for a firm I've had a few years of economics courses already but still there are some basic things in the field that I just can not wrap my head around... (let's say economics is not my favorite field of study)

The problem that I'm having is about an algebraic representation of a demand curve in a perfectly competitive market.

Say that there is a set of N suppliers (with |N| possible tending towards infinity, hence a perfectly competitive market; let's just assume free entrance to the market too), consider a supplier i. The market demand function in terms of the output of supplier i can now be written as:

Here what is in the curly brackets is just the total market output. Now here's my problem, if you take the derivative of this function wrt. q_i, then you find that this derivative equals beta. However, I've also heard that the derivative of market demand with respect to a firm's output, in a perfectly competitive environment, is 0; as in perfect competition, a firm cannot control the price through its output this effect is very very small because of the many other suppliers.

Where in my reasoning did I go wrong?

If we're considering the canonical case of one firm facing perfect competition, then we're faced with a demand curve (for each firm's goods) that's perfectly flat- regardless of how many units any given firm produces, consumers are willing to pay a certain market price $p$ and no more (all of this is just a restatement of what you've mentioned in the question, of course).

What we can do is then consider how to have a model that incorporates this definition of perfect competition with your given definition of the demand facing firm $i$. As you point out, the derivative of the demand as you've defined it is $\beta$. (Again, all a restatement of what you've pointed out).

The next question to ask, then, is "what is $\beta$?" Effectively, it's the slope of the demand curve each firm faces. If we assume perfect competition, then we assume a flat demand curve, which leads us to conclude that $\beta=0$. I'd suggest that your reasoning didn't go wrong anywhere, just that the two threads need to be directly connected!


What do you call a game that is both simultaneous and sequential? Is there a standard term for a game that has both simultaneous and sequential parts? Is it a mixed game? A combined game?

A sequential game with imperfect information?


Is Currency Devaluation a cause or effect of interest rates? I understand that Federal bank/Goverment can manipulate the currency market and devalue its currency by printing more money or buying foreign currencies/assets (essentially increasing the supply of home country's currency). Devaluation eventually leads to cost-push/demand-pull inflation (not necessarily though, for eg: in times of recession, this might not happen). To combat inflation, interest rate would need to increase.
However, on the other hand, another theory states that - lower interest rates gives rise to inflation and eventually leads to currency devaluation.
What I cannot get my head around is what is the cause and what is its effect? Or do they function in sync and are basically two different tools of goverment to maintain the balance and control the economy?

The bond market is a market, albeit following the lead of the central bank at the short end.
The currency market is a market.
The simplest and crudest version of the Efficient Markets hypothesis is that it is difficult to “beat a market” using a simple rule. The argument is that if such a simple rule exists, everyone would do it, causing prices to shift. (There can be regularaties like the term premium - bonds tend to outperform cash in the long run - but one needs to take risk exposures to achieve such gains.)

Taken together, the previous statements suggest that there should be no simple relationship between interest rates and currencies. If the previous logic is incorrect and such a relationship exists, feel free to use it to make a fortune as a currency strategist. (Disclaimer: this is not a recommendation to trade currencies without understanding the risks involved.)
Textbooks love discussing interest rate parity relationships. This is an arbitrage relationship used to pin down the pricing of currency forwards. However, the predictive power of forwards is at best weak, leaving us back near the possibility of efficient markets.
Finally, the exception to the bond and currency markets is the possibility of a pegged currency, or pegged bond yields (relatively rare). At which case, one needs to look at the behaviour of currency pegs, and runs on such pegs.


Can an In the Money Put Option's price $>$ its Strike Price? The screenshot below suggests thatan ITM put option's price can't overstep its strike price? Why or why not?

If you own a put, you have the right but not the obligation to sell at the strike price. For most financial assets generally including stocks and bonds(although some commodities have been known to take negative prices), the minimum price they could possibly sell for is zero, because of limited liability. The worst they can be worth is zero, meaning that they generate no cash flows. If an asset has a price ($P$) of zero and you can sell it for the strike price ($K$), then you take a profit of $K-P = K-0 = K$. This is the maximum in the money value of the put because the asset price can't be below zero).
As you can see in the figure below (a call option, but it is the same idea), the time value of an option falls as the underlying price gets farther from the strike price. Therefore, when the ITM value is maximized you are as far as possible as you can get in one direction from the strike price, and we should expect the time value to be small. In fact, if you have a American option where you can exercise early, you will want to exercise this put option early if the price of the underlying ever reaches 0, because you can't make any extra money by waiting, which implies the time value is not just small but actually zero. NB: I believe this is only true when interest rates are positive. With negative rates it pays to wait just to avoid getting negative interest.

I believe it is not generally possible for the total value (ITM + time value) of an option to be above the strike price, which includes when it is out of the money, again as long as interest rates are positive. At exercise, the most the option can be worth is $K$. The expectation of a random variable that takes only weekly positive values less than $K$ must be less than or equal to $K$ ($0 <  E[X / (1+r)^t| 0 \leq x \leq K]  <  K/(1+r)^t < K $ where $t$ is the remaining option life.
Let me say this another way. The most you can ever get at this option at maturity is $K$. What's this worth to you? The absolute maximum this should be worth to you is if you knew for certain that it would be $K$. Then you would have a certain payoff of $K$ and the price would be $K/(1+r)^t$, just like any risk free cash flow. If anything else happens and the price of the underlying is anything higher than zero, this option is worth less than this. An option is out of the money if the price of the underlying is above the strike $P>K$. But the higher $P$ is, the lower the probability of the stock hitting zero is. This means that the total value of the option (ITM + time value) should be falling as the underlying price increases. This convinces me that that it cannot be that the total value of the put option is ever higher than strike price.


How does the U.S agriculture subsidy not constitute export subsidies under the WTO? The WTO explicitly prohibits subsidies on export goods to prevent dumping and market distortion but the United States spends $2.4 Billion annually on corn subsidies and has a trade surplus of $19.5 billion in agricultural goods.

How does this subsidy not constitute dumping under the WTO guidelines?

Certain types of agricultural subsidies are permitted under the WTO's Green Box. These include direct income support for farmers, and environmental and regional development programmes. However the rules state that, to qualify, such subsidies must be no more than minimally trade-distorting.  Whether such subsidies (in the US and other countries) actually meet that requirement is a matter of controversy, as discussed in this ICTSD Information Note which also shows (in Figure 1) the very high Green Box proportion of US subsidies.


Why do different countries have different currency ? Why not there are different currencies for each 10-20 kilometers? I have researched a bit in different forums.

Main answers include:
1. So Different countries can control different monetary policies
2. So different countries can handle shocks(up and down).
3.Based on region,human resource, natural resources, geographical position, cultural diversity, ethnicity etc

1.My question is why not control money as if there is a single country (with more than one states(suppose each state is a country))?

2.Why currency will be divided based on region,human resource, natural resources, geographical position, cultural diversity, ethnicity etc? (states/places in a single country can also have diversity then how they can be managed and several countries cannot be managed?)

3.Because if that is the case who decides we need different currencies based on which conditions (eg. eurozone)?
If the division is true why not there are different currencies for each 10-20 kilometers(or where there is more rice growth,or where there is no agriculture but more tourism difference based on these differences)?

Edit : please don't make it duplicate because I am asking after seeing the other questions. After checking now I want to know more derived from that answers.. please refer q 2,3

If the division is true why not there are different currencies for
  each 10-20 kilometers(or where there is more rice growth,or where
  there is no agriculture but more tourism difference based on these
  differences)?

If I'm grasping your question correctly, that type of hyper-fragmentation of currency areas would largely wipe out the standardization advantage that money has over barter (By standardization I am not referring to the ISO classification of currencies, but to their feature of being a mutually-acknowledged unit for trading).

Historically, fragmentation of currency areas has occurred during wars and/or early postwar. Two examples come to my mind. One is the Mexican Revolution (1910-1921), where various groups of rebels and armies got in the habit of inventing their own currency and deploying them in territories they occupied. It was jokingly said that Francisco "Pancho" Villa used to print his bills while on horseback.

Another, more recent example dates from the mid 1990s, during the precarious period once the Balkan war was brought to an end (see Dayton Agreement). I recall a Polish reporter of name Kasia Wyderko mentioning during a TV roundtable from late 1990s that there were three currencies in Bosnia-Herzegovina, their areas being delimited by the ethnic profile of each territory (croats, serbs, and muslims, accordingly). Unfortunately, the roundtable doesn't appear to be uploaded, but some reference to the multiple currencies in Bosnia-Herzegovina in the mid 1990s is this Wikipedia site.

Other than the answers to the "duplicate" question, the aforementioned instances reflect that fragmentation of currency areas is somehow a "last resort" where marked distrust, instability, or resentment precludes economic cohesion and the adoption of a common currency. The isolation and barter-like limitations that ensue from that fragmentation in a small economy most often hinders its dynamism or adaptability.


What would be the consequences of Downsizing on the economy? In the 2017 movie Downsizing, a chunk of the population decides to reduce their body size to just a few inches. What would be the consequences of this on the economy? I'd like to know chronologically what the important steps would be until the economy goes back to some stability.

In my scenario, the proportion of small vs big people in the country stays stable, let's say 50% of the population decide to Downsize, 50% stay normal-sized. I am considering an essentially free economy (let's say the current day US like in the movie) where trade between small and big people is initially not restricted, but could be in the form of laws or taxes later on.

(I do not have any background in economics, please make it as lay audience as possible!)

It would decrease consumption, lowering demand on many markets, meaning that prices would go down. If downsizing would rampant enough it's possible that economy would experience deflation, maybe even recession. As the result, maybe central banks would be decreasing key interest rates (i.e. make new debts cheaper), start buying bonds and lowering reserve requirements for banks in order to stimulate economy. While governments could increase government spendings, decrease tax burden and relax business regulations for the same reasons. Accumulation speed of government debts would be increasing (i.e. government would be borrowing more in order to finance their deficits caused by increased government spendings and decreased taxes). It would also make workforce more rigid, unemployed downsized people wouldn't be able to take some jobs. Like you can't take job of a burger-flipper at MacDonalds if you're downsized. Nations with downsized workforce would be able to offer lower prices while exporting their services abroad. Downsizing would be most widespread among countries with big service sector, like many deindustrialized and post-industrial countries. Imports of countries with downsized workforce would decrease, possibly leading to positive trade balance.


Methods or models to predict activity of clients of a bank? I'm a Physicist but I'd like to know if there are some methods or models to predict the activity of the clients of a bank. I heard that banks are interested in this sort of analysis so I got curious about it. The thing is I don't know where to find information about this. Is there a name for such type of analysis? Can you recommend any good book to learn such methods?

EDIT (19/11/15)

In particular I'm interested in methods to predict the activity of the clients, say we know their banking movements and we want to know who of them will no longer be active the next month/year, for example.

Some keywords you might search for will be profiling, RFM, CRM and customer analysis.  clv (or customer lifetime value) might be your best keyword though.

An example CLV calculator: http://www.clv-calculator.com/customer-lifetime-value-formulas/clv-formula/

Here is an interesting clustering model: http://www.iieom.org/ieom2011/pdfs/IEOM068.pdf

An article on how surveys are used to classify customers: http://www.finreghq.com/articles/bank-customer-profiles-and-why-they-are-important-sample-profile-questions/

Again, a lot of good stuff if you search for banking and clv:

https://www.google.com/search?client=ubuntu&channel=fs&q=banking+clv&ie=utf-8&oe=utf-8


If you charge a single (indirect) tax rate, x% on all goods and services in a country, will you get x% back as tax revenues? Assuming 100% compliance and no leakages, will charging a single tax rate of, say, 10% give us back 10% of the GDP back as tax revenues?

What could these leakages be in real life that reduce this?

Depends on the type of tax, and on whether you assume the government gives the money to people back or just keeps them, but generally no. The exception would be any non-distortionary tax (lump-sum tax, Pigouvian tax etc). But if it is tax that is applied to all consumption then it will create distortions.

This is because while you can tax consumption of goods and services you generally can’t tax leisure (which can be viewed as another good - just sitting and enjoying yourself) so this tax will distort the marginal rate of substitution between consumption of regular goods and services  and leisure. The amount of distortion will depend also on whether you assume that for leisure you need to still consume some goods but generally there will be still distortions. So the tax will induce shift from consumption of goods and services (and consequently from their production and production determines the output/income or GDP) to leisure and the government should collect less than 10% of GDP.

Leakages like the fact that some sources of consumptions are hard to tax (like consumption of home production) just make this worse.

What I described above is the substitution (Hicksian) effect. If we assume that government redistributes the money back to people this is the only relevant effect.

If the government decides to keep the money on its account there will be second effect. This is so called income (Marshallian) effect. If the taxes are not returned to people they become poorer and as a result their decision between consumption of standard goods and services (and hence production) and leisure will get affected again by this income effect. In principle, depending on the parameters we would put on utility function, the income effect could cause people to consume more standard goods and services than previously. In that case GDP could actually increase (although overall utility would be lower - but GDP only looks at consumption of standard goods and services, consumption of leisure is not measured by it). Hence in case you assume that government keeps the money it would depend on how income effect would affect consumption of goods and services and leisure and whether this effect would be stronger or weaker than substitution effect.


symmetry of equilibria with heterogeneous players I have a question about game theory terminology. I am working on a model in which players are heterogeneous in two dimensions, and there are four types of players. For example one type of players receive some reward and have some cost of playing, while the other type differs in this reward and cost.
I am interested in the equilibria of the game in which the strategies of users who face the same reward and costs (i.e. same type) are the same.
I think symmetric equilibrium in this case is misleading since not all players are expected to have the same strategies, but it is something more like a separating equilibrium across types. However, there is perfect information so I'm unsure whether separating/pooling equilibria concepts can also be applied here.
Any thoughts/references would be helpful!

the equilibria of the game in which the strategies of users who face the same reward and costs (i.e. same type) are the same.

This sounds like an ex ante (or ex interim or ex post) symmetric equilibrium, depending on the timing of the realization of the types. If both dimensions of the types are realized at the beginning of the game, then I'd go with the term "symmetric equilibrium", which is typically understood to mean the ex ante sort.
I think you may be confusing between "strategy" and "action", which may be why you rejected the term "symmetric equilibrium". In the context of Bayesian games, a strategy is a function of types while an action is a particular value of that function. For example, in a first-price sealed bid auction with uniformly distributed private values (types), the symmetric Bayesian Nash equilibrium involves each player bidding according to the same strategy function $s(v_i)=\frac{n-1}{n}v_i$, where $n$ is the number of players and $v_i$ is player $i$'s value of the auctioned object, even though the actual bids will differ based on each player's realized type $v_i$. Nevertheless, players with the same value will place the same bid.


Duality Proof - Consumer Theory For solving this question, which assumptions/axioms should be used and should Lagrange multipliers be equal or different?

Think of an agent with utility function u() and wealth w. Assume that u() is continuus and represents a locally non-satiated preference relation. The utility maximization problem of this agent can be stated as:

max  u(x)
 s.t. p.x ≤ w

On the other hand, when the agent’s constraint is to attain a utility level h, her expenditure minimization problem can be stated as:

min  p.x
s.t. u(x) ≥ h

Show that if x* is optimal in the utility maximization problem when w > 0, then x* is optimal in the expenditure minimization problem when the constraint is to attain a utility level u(x∗).

Let us prove it by contradiction. Suppose that $x^{*}$ is optimal for the first problem but not for the second. Since $x^{*}$ is not optimal for the expenditure minimization problem, there exists a bundle $x$ such that
\begin{equation*}
u(x) \geq u(x^{*}) \text{ and } p \cdot x < p \cdot x^{*}
\end{equation*}

Since the function $y \rightarrow p.y$ is continuous, and $p \cdot x < p \cdot x^{*}$, there exists $\epsilon>0$ such that $\|y-x\|<\epsilon \Rightarrow p \cdot y < p \cdot x^{*}$. In addition, since preferences are locally nonsatiated, there exists $y$ such that $\|y-x\|<\epsilon$ and $u(y)>u(x)$. Take such a $y$. We have \begin{equation*}
u(y) > u(x) \geq u(x^{*}) \text{ and } p \cdot y < p \cdot x^{*} \leq w
\end{equation*}

Or, in other words,
\begin{equation*}
u(y)>u(x^{*}) \text{ and } p.y < w
\end{equation*}
which contradicts the assumption that $x^{*}$ is a solution of the utility maximization problem.


Does Efficient Market Hypothesis make anticipated monetary policies useless? Since the market perfectly captures all the information, is it true that any anticipated monetary policy has no impact on equity prices? Or the “information” has an immediate impact but the “event” itself has no impact.

We begin our story at time $t-1$, where we have a Goldilocks economy (not too hot nor too cold). At time $t$, the economy gets worse. At time $t+1$, it becomes obvious that the central bank will cut the policy rate by 25 basis points at the next meeting and that this is sufficient to move the economy back to where it was at $t-1$. At time $t+2$, the central bank cuts the policy rate by 25 basis points. If markets are semi-strong efficient and the worsening of the economy is public information (along with the monetary policy action), then we would expect stocks to fall on $t$, rise on $t+1$ to the same level as $t-1$, and be unchanged on $t+2$ (assuming nothing else is happening in the economy).

However, this does not make monetary policy useless in this situation. If the monetary policy authority, meeting on $t+2$, left rates unchanged (instead of cutting them), then we would expect equities to fall on $t+2$. While there are many monetary policy channels, in most of them, the changing of the policy rate actually improves the economy. This can raise equity prices by boosting firm cash flows.

When the central bank cuts rates, this isn't useless, even if expected, because it caused the economy to be better, which also boosted the value of financial assets. Yes, if the rate change is fully anticipated, there is no effect seen on the day of the rate change, but that is not because it is useless. Rather, it is because it is already priced into the value of financial assets before the rate change actually occurs.


Most significant factors in the price of a goverments bonds As a follow up on Long-,short-term interest rates and inflation.

Inflation is clearly a factor(tho not possible to model mathematically) when it comes to the market price of a bond. I can think of two ways in which it enters(in the short run), let me know weather these two are true or not i.e this is my main question,

Via the loss in value of nominal amount;this I extraced this from this quote

"Inflation is a bond's worst enemy. Inflation erodes the purchasing power of a bond's future cash flows. Put simply, the higher the current rate of inflation and the higher the (expected) future rates of inflation, the higher the yields will rise across the yield curve, as investors will demand this higher yield to compensate for inflation risk"[1]

Long term rates are the expected average of short term rates and the shortest i.e the funds rate is set to control inflation, the inflation expectations should be pretty much the same as short term rate expectations due to this, if this is how one should think about it. In conclusion, short term rate expectations and inflation expectations are pretty much the same thing and these in turn determine the longer term government bond rate.

Any comments on other factors and the logic behind their impact would be great to have

[1]https://www.investopedia.com/articles/bonds/09/bond-market-interest-rates.asp

1) The following quote is a poor description of how to look at bond markets.

  Inflation is a bond's worst enemy. Inflation erodes the purchasing
  power of a bond's future cash flows. Put simply, the higher the
  current rate of inflation and the higher the (expected) future rates
  of inflation, the higher the yields will rise across the yield curve,
  as investors will demand this higher yield to compensate for inflation
  risk"

The statement that higher expected inflation will raise nominal bond yields is outright incorrect. It assumes that real yields are constant. We can look at the inflation-linked market to see that real yields are highly variable, and in fact have moved more than inflation expectations in countries like Canada and the United States in the past couple of decades.

Trying to change that to assuming that inflation expectations rise and we assume that real yields are constant is just a way of saying that higher nominal yields generate capital losses for bonds. Everybody knows that already.

A proper analysis needs to look very carefully at what we mean by "inflation."

Is it observed inflation? Which measure - e.g., headline or core (ex-food and energy)?
Is it breakeven inflation, which can be extracted from inflation-linked bond prices?
Is it a survey of inflation expectations? However, we need a survey of bond investors, not economists or consumers - and such surveys are not available.

However, we can look at any of these definitions of inflation, and find cases where nominal bond yields fell, yet the inflation measure rose. For example, an oil price spike can be associated with a recession, which causes the central bank to cut interest rates.

As was pointed out in a comment, one could argue that poor inflation performance could raise term premia. (Essentially, adding an inflation risk premium on top of existing term premia.) This is a plausible argument. However, it is not exactly in line with the quoted text. It is not just “inflation” itself that is the problem - we already have inflation - rather, it has to be a significant burst of unanticipated inflation. However, most central banks would probably react violently to a big burst of inflation, and the curve would likely be fairly flat. Hard to distinguish between a term premium and rate expectations in that environment. In any event, that story is quite different than the quoted text from the external article.

2) The statement:

  the funds rate is set to control inflation, the inflation expectations
  should be pretty much the same as short term rate expectations due to
  this.

is incorrect. Once again, it assumes that the real rate is constant. This is certainly not the case.

We can look at the Fed Funds rate (link to FRED database) and see that it has varied in a range from 0-5% since the early 2000s. Meanwhile, core PCE inflation (the Fed's preferred measure of inflation) has been stuck between 1-2.5% over that period. (link to FRED). Surveys of inflation have been similarly far more stable than nominal rates.

The only way to phrase this is to say that the central bank sets nominal interest rates at a level to keep inflation near target. Bond market pricing is heavily influenced by the expected path of those nominal rates -- although a term premium exists. However, if the inflation targeting is effective, there will be no link between observed inflation and nominal yields -- since real yields are being adjusted to keep inflation stable.

Take a look at the post-1995 history in Canada and the United States (and working from memory, the U.K., Australia, New Zealand...). Just plugging in "2%" (or sometimes 2.5%, depending on the inflation series) was a very effective "forecasting algorithm," and probably outperformed a lot of human forecasters. This did not mean that nominal yields were constant.


When does an economic theory become true? When does an economic theory become true?

When does it satisfy requirements for true knowledge, e.g. similar to those in empirical sciences?

It's just the same as in the physical sciences:

an economic theory, like any theory or model in physics or chemistry or biology, is wrong (H/T George Box), but it can be useful.

"True knowledge" is not a really a useful concept; not in physical sciences, not in social sciences. The important question is whether a model gives us useful insights, and whether it can constructively inform decisions.

An economic theory gains acceptance when it turns out to be useful.


What are the economic implications of regressing the same set of independent variables with different outcome variables I was wondering if it is possible to make any economic implications by regressing the same set of independent variables with different outcome variables.

For instance, regressing [Industry, Years, Production Level] on [Revenue, Profits].

Given the above variables, if both models are significant, what would be the implications? Does it imply that [Industry, Years, Production Level] can be used to explained both the change of [Revenue, Profits].

If it is, what are the appropriate regression models? Are there any concerned issues regarding the results?

Using matrix notation, denote profits by $\Pi$, revenues by $R$, and the explanatory variables by $\mathbf X$.

Assuming a linear setup, we look at

$$\mathbf \Pi = \mathbf X\mathbf a + \mathbf u \tag{1}$$

and
$$\mathbf R = \mathbf X \mathbf b + \mathbf v \tag{2}$$

Are profits correlated with Revenues? Experience say they are. So there is also a relationship

$$\mathbf \Pi = \gamma \mathbf R  + \mathbf \varepsilon \tag{3}$$

Inserting $(2)$ into $(3)$ we get

$$\mathbf \Pi = \mathbf X(\gamma\mathbf b) + \gamma \mathbf v + \mathbf \varepsilon \tag{4}$$

Looking at $(1)$ and $(4)$, we have the equivalence

$$\mathbf a = \gamma \mathbf b \tag{5}$$

Will we obtain it through estimation? Not that easily.

Least -squares estimation will give us, for $(1)$

$$ \mathbf  {\hat a} = \left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\mathbf \Pi \tag{6}$$

and for $(2)$

$$\mathbf  {\hat b} = \left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\mathbf R \tag{7}$$

Insert $(3)$ into $(6)$ to get

$$\mathbf  {\hat a} = \left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\left(\gamma \mathbf R  + \mathbf \varepsilon\right) $$

$$\implies \mathbf  {\hat a} = \gamma \mathbf  {\hat b} + \left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\mathbf \varepsilon \tag{8}$$

The interesting realization comes at this point: given the postulated relation $(1)$ it is unlikely that the variables in $\mathbf X$ will be uncorrelated with $\mathbf \varepsilon$, the error term in $(3)$.

This means that even with a large sample, calculating the ratios of the individual coefficients in the vectors $\mathbf  {\hat a},\;\mathbf  {\hat b}$, we will not recover $\gamma$, since $\left(\mathbf X'\mathbf X\right)^{-1}\mathbf X'\mathbf \varepsilon$ won't converge to zero.


Where can I find charts with the amount of treasuries in existence? Is there a place where I can see a chart with the amount of treasuries in existence organized by treasury type?

Ideally it would be a resource that has multiple charts (for bills, notes, bonds etc...)

I cannot find anything on the fred.stlouisfed.org site

SIFMA: US Marketable Treasury Issuance, Outstanding, and Interest Rates

The hint here is that repurchases are relatively rare and prepayments are not an option so gross issuance that hasn’t yet matured is a decent proxy for outstanding amounts.


Why war can remit the economic crisis？ In the history, like Japan, in the World War II, they had a hand in the war, the root cause is the economic depression.

And in this century, some country use this method many times to remit the economic problem.

So, why war can remit the economic crisis, I just don't understand?

It is not war itself that helps to counteract economic crises, but rather the increased spending needed to support the war. In terms of the evidence to support this claim, Lee Hudson Teslik from the Council on Foreign Relations writes:

  There is an ongoing debate about the extent to which war spending affects a country’s economy. Experts disagree on the most fundamental point—whether war helps or hurts national economic prospects. Massive U.S. national defense spending during World War II is sometimes credited with rejuvenating U.S. economic prospects following the Great Depression. The journalist Robert J. Samuelson, in a primer on the topic, says there can be little doubt that military spending and mobilization during World War II reduced U.S. unemployment rates and revitalized the economy. A recent paper from the National Bureau of Economic Research concludes that countries with high military expenditures during World War II showed strong economic growth following the war, but says this growth can be credited more to population growth than war spending. The paper finds that war spending had only minimal effects on per-capita economic activity. The effects of more recent wars are equally disputed. A historical survey of the U.S. economy from the U.S. State Department reports the Vietnam War had a mixed economic impact. The first Gulf War typically meets criticism for having pushed the United States toward a 1991 recession. In a 2003 op-ed in the Guardian, economist [Joseph] Stiglitz wrote that the aftermath of the Gulf War exposes the “myth of the war economy.” Indeed, he argues that increased military spending is “unambiguously bad” for the living standards of normal citizens. Other economists argue the opposite.

I would argue the consensus generally leans towards wartime spending as beneficial to a nation's economy.


elasticity of income if price changes by 10 percent Arista always spends  10
 % of her income on whatzits. Assume that her income increases by some percentage while the price of whatzits remains constant (and that all whatzits cost the same). What is her income elasticity of demand for whatzits?

I know elasticity of demand is either less than 1 or more than 1.
Since the equation for elasticity of income is quantity divided by income I dont understand what number to put for the numerator.

? / 10 %.  = 1

Will the answer be positive 1 or negative 1.

Try work it out step by step and don't just concentrate on the math.

Suppose Arista has income of $w$, and the price of whatzits is $p$. She spends 10% of that on whatzits, so how many whatzits does she buy? Let's call this $q$.

Now suppose income is now $x \cdot w$ (so if her income increases by 3% then $x$ is 1.03.) The price of whatzits is still the same, $p$. How many whatzits does she buy now? Let's call this $q'$.

The income elasticity of [quantity] demand[ed] is simply the percentage change in quantity demanded divided by the percentage change in income:

$$e = \frac{\frac{q' - q}{q}}{\frac{xw - w}{w}}.$$


How to make unequally spaced grid? I want to make a grid [0,1] with 100 points but I want points to be concentrated at the edges close to 0 and 1. So I want 60-70% of the points to be in the intervals [0, 0.2] and [0.8, 1]. Any ideas on how I can do this?

One quick way to do this is through inverting a distribution c.d.f.. For example, the distribution Beta(alpha,beta) has density concentrated at small and large values when alpha and beta are less than one. Thus, you can first generate equally spaced grid, and then use the inverse function of Beta c.d.f to map the grid to unequally spaced grid. You can change the percentiles you want (60-70%, e.g.) by setting the appropriate alpha and beta.


How do interest rates affect the distribution of wealth? How do interest rates, on local and global scales of an economy, affect the distribution of wealth?

Good question! But difficult to answer.

A) Typically, economists think of most interest rates as being set by markets. Under that assumption, you can't change rates by themselves because the market would bring them back to a value that equilibrates demand and supply of savings. Economists try to model how everything is in equilibrium with "general equilibrium" models. Of course, in reality, the fed does set an interest rate...

B) In the "life cycle model" of an individual's life, people borrow when they are young and need to study and create businesses, save when they are middle aged and draw down their savings when they are old. In that context, young people suffer from a high rate and old people gain from a high rate. However, its often the case that people invest in long-term bonds and so it's not really clear that they benefit from an increase in interest rates, because it pushes down the price of their bonds (and their houses too).

C) If instead the idea is to figure out what happens when the equilibrium interest rate is low, then it's good to try to imagine the scenarios when it is indeed low. Economists think that the real interest rate is low when economic growth is low and when there is little demand for capital from firms or a lot of supply of capital by savers. These two things have happened together many times, but they don't have to. For example, a disaster that wipes out a very productive asset, like port infrastructure, will lead to a lot of investment but not a lot of net growth. Similarly, an extra supply of savings should lead firms to invest more and should lead the economy to grow. But now in 2016, we are in a low growth, relatively low investment scenario.

D) It doesn't seem like the interest rate is the biggest determinant to the wealth distribution out there. Some evidence to think this way is that capital  markets have become very open, making interest rates very similar everywhere, but inequality remains very different across countries: Commonwealth + Europe+ Japan (low) vs. Russia,+ US +China + Latin America +Africa(high). The distribution of income seems to depend more on the link between political power and economic power that is the norm in many countries, some because of corruption, others by design. It also seems to be more dependent on the quality public education and other public services.

Some similar ideas are discussed in a sort of reasonable Forbes article here: http://www.forbes.com/sites/jeffreydorfman/2015/05/12/the-feds-low-interest-rates-are-increasing-inequality/2/#65fdfe4679cc


Why are Canadian provinces' debt-to-GDP so much higher than the US? By the current account, the highest debt-to-GDP state in the US is NY, which is around 23%, with most states around 18%. By comparison, Canadian provinces tend to have much higher ratio, with Ontario at around 37% and Quebec over 40%. What accounts for this? Are the Canadian provinces responsible for distributing social benefits that would be under the federal jurisdiction in the US which skews up their %? Or are they just spending more irresponsibly than the US?

The Canadian provinces implement most of the welfare state programmes. The role of the Canadian Federal Government is to set out guidelines, and undertake fiscal transfers to allow provinces to stay near national standards. Since they have much larger budgets, they necessarily end up absorbing more of the economic cycle as being an automatic stabliser (i.e. they issue more debt).

There are no balanced budget laws for Canadian Provinces. American states generally have balanced budget rules, so debt levels are necessarily low. The states that do not have balanced budget laws are pretty much forced to follow the borrowing norms set by states with balanced budget rules.

Finally, the funding mechanism is different. Canadian city governments do not issue much debt, and there is very little project-based bond issuance. In other words, debt that shows up at the Provincial level ends up being financed otherwise in the United States (and does not show up in State level debt).


What does price embody ? Do we constantly undervalue some type of products? I'm not sure to fully get the meaning of prices. If I understand well, there
are two drivers of it :

The theory of demand and supply and thus prices are driven partly by the utility that agents get from it.

Production costs : On the long-run, prices look to converge towards something like the minimal cost of their production due to the fact that the supply side innovates enough to reach this (that's my interpretation). So on the long run prices of things tend to decrease.
But then, is there something such as the price reflecting the actual utility that consumers get from it ?
Indeed, some goods are really cheap because there is a strong competition on it but nevertheless, they
give their consumer a big utility (coffee for instance). Given the competition, even if the disposal to pay of consumers is more than 2€, they pay it 2€ (because no supplier could raise its price
withou losing all the market).
Therefore, we could have something like : all the goods that are produced at their marginal cost are underrated, have an underrated value and the true disposal to pay of people for it is higher. There's probably a flaw in my argumentation but I don't see it.
Does anyone have an idea ?

People have different tastes, needs, and budgets. So it doesn't make much sense to speak of the willingness to pay (WTP) of "the consumers". Each consumer has his or her own WTP for, let's say, a cup of coffee. If Alice' WTP is 1€ and the price is 2€ she will not buy. If Bob's WTP is 5€  then he will buy and enjoy the surplus. From Bob's perspective the cup of coffee might then seem "undervalued", and from Alice' perspective it is "overvalued", but that's not how you would generally use this term.
And forget about the price reflecting a consumer's "actual utility". Utility is an ordinal concept. Under some technical assumptions you can turn it into a cardinal concept by "measuring" utility by WTP. But then, as above, the price "reflects" this utility (price = WTP) only for the marginal consumer, i.e. the one who is indifferent between buying and not buying.
So to answer your title question: Price just "embodies" an amount of money per unit with the property that in some given time period consumers want to buy as many units as producers want to sell. And "we" don't "undervalue" some products, since there is no "we" that values products, there are only single consumers who do so.


Argentine default: "Rights upon future offers" Argentina defaulted on its sovereign debt in 2002. It has reached an agreement with most but not all of its creditors. Wikipedia has a pretty good summary. The agreements included a 70% hair cut but also a RUFO or "Rights upon future offers" clause stating that if in the future agreement is reached with the holdouts with better terms (lower loss percentage) those better terms automatically apply to the creditors signing the current agreements. (This is similar to a most preferred customer clause.) Perhaps the Argentine government used this as a negotiation tactic as it makes it impossible to offer better terms to the holdout creditors.

Unfortunately the holdouts bought a lot of CDS insurance and now stand to win more from a default then they do from a 100% repayment. Lawsuits lasted for years. Argentina made payments to the creditors it agreed with but made no payments to the holdouts. In 2014 (maybe 2015) a court blocked payments to the non-holdout creditors because you cannot differentiate between identical bonds in case of default. This is plunging Argentina into default again which is bad for the country and the creditors with whom it already came to an agreement. (There is another court hearing scheduled for April 2016 and the US government is advocating in favor of Argentina.)

Why haven't the non-holdout creditors and Argentina signed a new agreement in 2014 without the RUFO clause but identical in all other ways? Seems like both of them would have benefited from it, just as they have by coming to an agreement in the first place. (I am not necessarily looking for the 'exact' or 'real' reasons. Any plausible reasons that make economic sense are fine.)

This is a good question! It turns out that exactly as you predict, if you get the transcripts or recordings from the meetings with judge Griesa in NY, some of the representatives of the non-holdouts said they were willing to sign off on the RUFO clause, voiding it. The logic, as you describe is that this would free Argentina to pay the holdouts, letting Argentina continue its payments to the non-holdouts too, without a risk of the debt ballooning suddenly. This would have saved everybody lots of headaches!

Argentina's government at the time did not pursue this option, perhaps because they saw more political gain in being the victims of 'the US empire's courts' than in solving the problem. The lack of professionalism and interest in solving the problem that their executives displayed during this episode suggests this is the main reason.

Alternatively, it's plausible that they did not pursue this option because they thought that default was so terrible to non-holdout investors, that these would be of help in pressuring the holdouts to accept a lower payment from Argentina in negotiations to avoid default.

In any case, neither strategy worked. The government lost popularity and was kicked out of office, and the new government eventually reached an agreement beneficial to the holdouts.

One, more thing: the Rufo clause actually wasn't such a big deal because it was set to expire soon! So, the non-payment appears to have been a big circus for the Argentinian president then to try to score some points with the more manipulable fraction of that country's population.


a question on the endogenous growth model I have such a question on the endogenous growth mode”:

  In the macroeconomics literature there are various ways in which the growth process in the Ransey-Cass- Koopmans model has been endogenized. For this question you are required to incorporate one of these endogenous growth mechanisms into the model. You can select the mechanism, but make sure that you explain and/or show how it will generate growth endogenously. Setup the optimization problems faced by the various types of agents in your model. Derive and interpret the first order conditions (or efficiency conditions) in these optimization problems. Finally, to the best of your ability use the model to explain the stylized facts of economic growth and development.

What I want is exactly not to give an answer. I just want to be explained this question. Summarize it. Give hint! especially on dark statement. For example can I explain something like AK MODEL Or ROMER MODEL, LEARNING BY DOING ...? What means endogenous growth mechanism?

I just try to understand the question. Thus I’m asking here.

"Endogenous Growth" is actually the short version of saying "Endogenous Technology Growth"

Exogenous (Technology) Growth Models

The rate technological progress $g$ is Exogenously given.

In both Solow and RCK, we can find $A_t = (1 + g)^t A_0 \ \ $(or $A(t) = A(0) e^{gt}$ if in continuous time). $Y$ increases over time because $A$ increases over time. This assumption of growth rate is very strong.

Endogenous (Technology) Growth Models

The rate of technological progress is Endogenously determined.

For example in Two-Sector Growth Model (Rebelo), we have

production $Y = C + I_K =  A \ (vK)^\alpha \ (uH)^{1-\alpha}$ and education $I_H = B \ ((1-v)K)^\alpha \ ((1-u)H)^{1-\alpha}$

Now $v$ and $u$ are endogenously determined, and thus $H$ is endogenously determined. $A$ doesn't change, but $Y$ will increase over time due to increase in $H$.

Another example will be the Learning-by-Doing Model.

Recall in Exogenous Models $A_t$ is exogenously given by $A_t = (1+g)^t A_0$

But now we want $A_t$ to be determined endogenously. Thus we assume technological progress is due to knowledge creation, and knowledge is a side-production of investment. And thus we let $A_t \equiv \sum_{i=0}^N K_{it}$ (there are N identical firms)


Coefficient of Determination with Weighted Coefficients I want to compare coefficients of determination (i.e., $R^2$) of the following two models. $fe_{t+h}$ is a forecast error in $t+h$ and $\mathbf{\varepsilon}_t$ is a shock of interest occurring between $t$ and $t+h$. The idea is to interpret the coefficient of determination as the share of forecast error variance (FEVD) which can be explained by my shock of interest.
Model 1
\begin{align*}
fe_{t+h} = \beta_0 \mathbf{\varepsilon}_{t} + ... + \beta_h\mathbf{\varepsilon}_{t+h} + u_t
\end{align*}
Model 2
\begin{align*}
fe_{t+h} = F(z_t) \left(\beta_0^I \mathbf{\varepsilon}_{t} + ... + \beta_h^I \mathbf{\varepsilon}_{t+h}\right) + \left( 1-F(z_t)\right) \left(\beta_0^{II}\mathbf{\varepsilon}_{t} + ... + \beta_h^{II} \mathbf{\varepsilon}_{t+h}\right) + u_t
\end{align*}
where $F(z_t)$ is a smooth logistic function with $F(z_t)\in [0,1]$ which weights the coefficients $\beta_0, ..., \beta_h$ between regimes 1 and 2.
In my model at hand, $h$ is equal to 15.
Is it ok to use the non-adjusted $R^2$? I am aware that typically, $R^2$ will rise with the number of additional explanatory variables. However, in my case I have no additional variables but only weighted coefficients.

If you want to explain the fraction of variance explained, use $R^2$. If you want to compare $R^2$'s but adjust (very weakly) for model size, use adjusted $R^2$'s. If you want to compare these models, use an $F$-test since Model 1 is nested in Model 2.


The Intuition of CES Utility Suppose a (symmetric) CES utility function $$U(\mathbf{x})=\left[\int_{\Omega}\left(x_{\omega}\right)^{\frac{\sigma-1}{\sigma}} d \omega\right]^{\frac{\sigma}{\sigma-1}}, \sigma>1$$
1 The indirect utility function is $U\left(\frac{\mathbf{p}}{h}\right)=\left[\int_{\Omega}\left(\frac{p_{\omega}}{h}\right)^{1-\sigma} d \omega\right]^{\frac{1}{\sigma-1}}=\frac{h}{P(\mathbf{p})}$ where $h$ denotes the expenditure and $P$ is the price index. How to understand this indirect utility intuitively, especially the meaning of $\frac{p_{\omega}}{h}$?
2 The CES utility has the property of direct explicit additivity, i.e. $U(\mathbf{x})=M\left[\int_{\Omega} u\left(x_{\omega}\right) d \omega\right]$, where $M[\cdot]$ denotes a monotone transformation. This property imposes the strong restriction that income elasticity of a good must be proportional to the price elasticity of that good (i.e. the Pigou's Law), which has been argued to be too strong and rejected empirically. What is the intuition behind the linkage of direct explicit additivity and this restriction?
3 Standard homothetic CES is the only preference that satisfies both direct explicit additivity and indirect explicit additivity. The indirect explicit additivity, i.e. $U\left(\frac{\mathbf{p}}{h}\right)=M\left[\int_{\Omega} v\left(\frac{p_{\omega}}{h}\right) d \omega\right]$, again impose the similar restriction between the income elasticity and the price elasticity of the goods as direct explicit additivity. How to understand this intuitively?
4 Under either direct explicit additivity or indirect explicit additivity,  only homothetic preferences can be CES. What's the intuition?

This is going to be a long answer, and I'm not completely sure if it is going to answer your questions as I'm mostly going to focus on the derivations of the own and cross price elasticities. Most of the derivations can also be found in Houthakker (1960), "Additive Preferences"
TLDR:

If the utiltiy function is additively separable and if the share of the goods are small, then indeed own price elasticities are proportional to income elasticities. The ratio of cross price elasticities (for different goods) are proportional to income elasticities.
If the indirect utility function is additively separable, I could not show that the own price elasticity is proportional to the income elasticity. The ratio of cross price elasticities (accross different goods) is constant.
If both the direct and indirect utility function is additively separable, then Engel curves are linear.

Additive separability
Let start from a utility function that is additively separable. For the utility function $u$ let's write $u_i = \dfrac{\partial u}{\partial x_i}$ and $u_{i,j} = \frac{\partial^2 u}{\partial x_i \partial x_k}$. From additivity, we have that if $i \ne k$ then $u_{i,k} = 0$.
The following conditions gives the first order condition and the budget constraint:
$$
u_i = p_i\lambda,\\
\sum_i p_i x_i = \mu
$$
Differentiating with respect to $p_k$ ($k \ne i$), $p_i$ and $\mu$ gives the following 5 conditions:
$$
\begin{align*}
&u_{ii} \frac{\partial x_i}{\partial p_k} = p_i \frac{\partial \lambda}{\partial p_k}, \tag {1}\\
&u_{ii} \frac{\partial x_i}{\partial p_i} = \lambda + p_i \frac{\partial \lambda}{\partial p_i}, \tag{2}\\
&u_{ii} \frac{\partial x_i}{\partial \mu} = p_i \frac{\partial \lambda}{\partial \mu}, \tag{3}\\
&\sum_i p_i \frac{\partial x_i}{\partial p_k} = - x_k, \tag{4}\\
& \sum_i p_i \frac{\partial x_i}{\partial \mu} = 1. \tag{5}
\end{align*}
$$
Condition $(4)$ and $(5)$ are the cournot and Engel aggregation. Then substituting $(1)$ and $(2)$ in $(4)$ and $(3)$ in $(5)$ gives:
$$
\begin{align*}
&\sum_i p_i p_i \frac{\partial \lambda}{\partial p_k}\frac{1}{u_{ii}} + p_k p_k \frac{\lambda}{u_{kk}} = - x_k,\\
\to &\frac{\partial \lambda}{\partial p_k} \sum_i \frac{(p_i)^2}{u_{ii}} = - x_k - (p_k)^2 \frac{\lambda}{u_{kk}}. \tag{6}\\
&\sum_i p_i p_i \frac{\partial \lambda}{\partial \mu} \frac{1}{u_{ii}} = 1,\\
\to & \frac{\partial \lambda}{\partial \mu} \sum_i (p_i)^2 \frac{1}{u_{ii}} = 1. \tag{7}
\end{align*}
$$
Combining $(6)$ and $(7)$ together with $(3)$ gives:
$$
\begin{align*}
\frac{\partial \lambda}{\partial p_k} &= \frac{\partial \lambda}{\partial \mu}\left(-x_k - (p_k)^2 \frac{\lambda}{u_{kk}}\right),\\
&= \frac{\partial \lambda}{\partial \mu}\left(-x_k - \frac{\lambda}{\frac{\partial \lambda}{\partial \mu}} p_k \frac{\partial x_k}{\partial \mu}\right),\\
&= \frac{\partial \lambda}{\partial \mu}\left(-x_k - \chi \frac{\partial x_k}{\partial \mu}\right)
\end{align*}
$$
where:
$$
\chi = \frac{\lambda}{\dfrac{\partial \lambda}{\partial \mu}}
$$
which is called the money flexibility (according to Houthakker).
Substituting this into $(1)$ and using $(3)$, we get that for $i \ne k$:
$$
\begin{align*}
\frac{\partial x_i}{\partial p_k} &= \frac{1}{u_{ii}} p_i \frac{\partial \lambda}{\partial p_k},\\
&=\frac{1}{u_{ii}} p_i \frac{\partial \lambda}{\partial \mu}\left( - x_k - \chi \frac{\partial x_k}{\partial \mu}\right),\\
&= \frac{\partial x_i}{\partial \mu}\left(-x_k - \chi \frac{\partial x_k}{\partial \mu}\right) \tag{a}
\end{align*}
$$
Then from $(4)$ (and using $(5)$) we can compute the own price elasticity:
$$
\begin{align*}
p_k \frac{\partial x_k}{\partial p_k} &= -x_k - \sum_{j \ne k} p_j\frac{\partial x_j}{\partial p_k},\\
&= - x_k - \sum_{j \ne k} p_j \frac{\partial x_j}{\partial \mu}\left(-x_k - \chi \frac{\partial x_k}{\partial \mu}\right),\\
&= - x_k + \left(x_k + \chi \frac{\partial x_k}{\partial \mu}\right) \left(\sum_{j \ne k} p_j \frac{\partial x_k}{\partial \mu}\right),\\
&= - x_k + \left(x_k + \chi \frac{\partial x_k}{\partial \mu}\right)\left(1 - p_k \frac{\partial x_k}{\partial \mu}\right),\\
&= -x_k + x_k - p_k x_k \frac{\partial x_k}{\partial \mu} + \chi \frac{\partial x_k}{\partial \mu} -\chi p_k \frac{\partial x_k}{\partial \mu} \frac{\partial x_k}{\partial \mu},\\
&= \frac{\partial x_k}{\partial \mu} \left(-p_k x_k + \chi\left(1 - p_k \frac{\partial x_k}{\partial \mu}\right)\right)
\end{align*}
$$
Dividing both sides by $x_k$, we can express this In elasticity terms:
$$
\begin{align*}
\varepsilon^k_k &= \varepsilon^k_\mu\left(-s_k + \kappa \left(1 - s_k \varepsilon^k_\mu\right)   \right),\\
\end{align*}
$$
Here we use the notation $\varepsilon^k_i$ for the $p_i$ elasticity of $x_i$ and we use $s_k = \frac{p_k x_k}{\mu}$ to denote the share of good $k$ in the budget. Also:
$$
\kappa = \left(\frac{\partial \lambda}{\partial \mu}\frac{\mu}{\lambda}\right)^{-1} = \left(\frac{\ln \lambda}{\ln \mu}\right)^{-1}
$$
which is the inverse of the income elasticity of the marginal utility of income.
If there are many goods, then $s_k$ is very small, so:
$$
\varepsilon^k_k \approx \kappa \varepsilon^k_\mu
$$
So indeed, own price elasticities are close to approximate proportional to income elasticities.
Let's now look at the cross price elasticities. Writing $(a)$ in elasticity terms gives:
$$
\varepsilon^i_k = \varepsilon^i_\mu(-s_k - \kappa \varepsilon^k_\mu)
$$
So cross price elasticities are proportional to the income elasticity. Also for $i, j \ne k$, we have:
$$
\frac{\varepsilon^i_k}{\varepsilon^j_k} = \frac{\varepsilon^i_\mu}{\varepsilon^i_\mu} \tag{A}
$$
As such, the ratio of the cross price elasticities are equal across goods.
Additive indirect utility
Let $v$ be the indirect utility function, which depends on prices $p_i$ and income $\mu$. Similar to before, write $v_i = \frac{\partial v}{\partial p_i}$, $v_\mu = \frac{\partial v}{\partial \mu}$ and we use 2 indices for the second order derivatives. If $v$ is additive, then for $i \ne k$: $v_{i,k} = \frac{\partial^2 v}{\partial p_k \partial p_i} = 0$.
We start from the following equations (the first one is Roy's identity):
$$
x_i = -\frac{v_{i}}{v_\mu},\\
\sum_i p_i x_i = \mu.
$$
Taking derivatives with respect to $p_k$ ($k \ne i$), $p_i$ and $\mu$ gives:
$$
\begin{align*}
&\frac{\partial x_i}{\partial p_k} = \frac{-v_{i,k} v_\mu + v_i v_{\mu,k}}{(v_\mu)^2} = -x_i \frac{v_{\mu,k}}{v_\mu}, \tag{9} \\
&\frac{\partial x_i}{\partial p_i} = \frac{- v_{ii}v_\mu + v_i v_{\mu, i} }{(v_\mu)^2} = -\frac{v_{ii}}{v_\mu} - x_i\frac{v_{\mu,i}}{v_\mu}, \tag{10}\\
&\frac{\partial x_i}{\partial \mu} = \frac{-v_{i,\mu}v_\mu + v_i v_{\mu,\mu} }{(v_\mu)^2} = -\frac{v_{i,\mu}}{v_\mu} - x_i \frac{v_{\mu,\mu}}{v_\mu}, \tag{11}\\
&\sum_j p_j \frac{\partial x_j}{\partial p_k} = - x_k, \tag{12}\\
&\sum_j p_j \frac{\partial x_j}{\partial \mu} = 1. \tag{13}
\end{align*}
$$
Use $(9)$ into $(12)$:
$$
\begin{align*}
\sum_j p_j (-x_j) \frac{v_{\mu, k}}{v_\mu} - p_k \frac{v_{kk}}{v_\mu} = -x_k,\\
\to -\mu \frac{v_{\mu,k}}{v_\mu} = - x_k + p_k \frac{v_{kk}}{v_\mu}
\end{align*}
$$
Substituting this back into $(9)$:
$$
\begin{align*}
\frac{\partial x_i}{\partial p_k} &= -x_i \frac{v_{\mu, k}}{v_\mu},\\
&=-x_i \left(\frac{x_k}{\mu} - \frac{p_k}{\mu} \frac{v_{kk}}{v_\mu} \right) \tag{b}
\end{align*}
$$
Then use $(12)$ again to compute the own price effect:
$$
\begin{align*}
p_k \frac{\partial x_k}{\partial p_k} &= -x_k - \sum_{j \ne k} p_j \frac{\partial x_j}{\partial p_k},\\
&= -x_k + \sum_{j \ne k} p_j x_j \left(\frac{x_k}{\mu} - \frac{p_k}{\mu} \frac{v_{kk}}{v_\mu}\right),\\
&= -x_k + \left(\frac{x_k}{\mu} - \frac{p_k}{\mu} \frac{v_{kk}}{v_\mu}\right)(\mu - p_k x_k) \tag{14}
\end{align*}
$$
Where the last line follows from the budget constraint: $\mu = \sum_j p_j x_j$.
Also from $(10)$ and $(11)$:
$$
\begin{align*}
\frac{v_{kk}}{v_\mu} &= -\frac{\partial x_k}{\partial p_k} - x_k \frac{v_{\mu,k}}{v_\mu},\\
&= -\frac{\partial x_k}{\partial p_k} + x_k \frac{\partial x_k}{\partial \mu} + (x_k)^2 \frac{v_{\mu,\mu}}{v_\mu} \tag{c}
\end{align*}
$$
Substituting this back into $(14)$:
$$
\begin{align*}
p_k \frac{\partial x_k}{\partial p_k} &= -x_k + \left(x_k - p_k \frac{v_{k,k}}{v_\mu}\right)(1 - s_k),\\
&= -x_k + \left(x_k + p_k \frac{\partial x_k}{\partial p_k} - p_k x_k \frac{\partial x_k}{\partial \mu} - p_k (x_k)^2 \frac{v_{\mu,\mu}}{v_\mu}\right)(1- s_k),\\
\to p_k \frac{\partial x_k}{\partial p_k} s_k &= - x_k + \left(x_k - p_k x_k \frac{\partial x_k}{\partial \mu} - s_k x_k  \mu \frac{v_{\mu, \mu}}{v_\mu} \right) (1 - s_k),\\
\to p_k \frac{\partial x_k}{\partial p_k} & = - \frac{x_k}{s_k} + \frac{1 - s_k}{s_k} \left(x_k - s_k \mu \frac{\partial x_k}{\partial \mu} - x_k s_k \mu \frac{v_{\mu,\mu}}{v_\mu} \right).
\end{align*}
$$
If we divide both sides by $x_k$, we can express this in elasticity terms:
$$
\begin{align*}
\varepsilon^k_k &= -\frac{1}{s_k} + \frac{(1-s_k)}{s_k}(1 - s_k \varepsilon^k_\mu - s_k \delta),\\
&= -1 - (1 - s_k)\varepsilon^k_\mu - (1 - s_k)\frac{1}{\kappa}. \tag{14}\\
\end{align*}
$$
where
$$
\mu \frac{v_{\mu,\mu}}{v_\mu} = \frac{\partial \ln v_\mu}{\partial \ln \mu} = \frac{\partial \ln \lambda}{\partial \ln \mu} =  \frac{1}{\kappa}
$$
Expression $(14)$ gives the own price elasticity

There's a small difference here with Houthakker's derivation as I have a minus sign for the last term while he has a '+' sign so I might have made a mistake.

If $s_k$ becomes small we have:
$$
\varepsilon^k_k = -1 - \varepsilon^k_\mu - \frac{1}{\kappa}.
$$
So, here we do not really obtain that $\varepsilon^k_k$ is proportional to $\varepsilon^k_\mu$. On the other hand, if $1/\kappa$ is very small then in this case:
$$
1 - \varepsilon^k_k \approx \varepsilon^k_\mu
$$
So one minus the own price elasticity equals the income elasticity.
For the cross price elasticities, we can write $(b)$ in elasticity terms (and using $(c)$):
$$
\begin{align*}
\varepsilon^i_k &= -\left(s_k - \frac{(p_k)^2}{\mu} \frac{v_{kk}}{v\mu}\right),\\
&= s_k\left(-1 + \varepsilon^{k}_k + s_k \varepsilon^k_\mu + s_k \frac{1}{\kappa}\right)
\end{align*}
$$
Taking ratio for $i, j \ne k$ gives:
$$
\frac{\varepsilon^i_k}{\varepsilon^j_k} = 1. \tag{B}
$$
Both direct and indirect additivity
Let's see what happens if both the direct and indirect utility functions are additively separable,
Take $i,j \ne k$  Then $(A)$ and $(B)$ give:
$$
\frac{\varepsilon^i_k}{\varepsilon^j_k} = \frac{\varepsilon^i_\mu}{\varepsilon^j_\mu} = 1.
$$
This shows that all income elasticities are the same. Using $(5)$ in elasticity form, i.e.:
$$
\sum_i s_i \varepsilon^j_\mu = 1,
$$
shows that all income elasticities are equal to 1, so we have linear Engel curves.


Difficulty in an economics' optimization problem using Kuhn-Tucker conditions (interpretation difficulty) I am having troubles in solving correctly the following problem:

A company wants to minimize its total costs, on the condition that the income obtained from the sale of the quantities $x_1, x_2$ of the two products it produces exceed a certain minimum threshold. Knowing that the unit costs of manufacturing each good are linear functions of the produced outputs in the form $C_1 = x_1, C_2 = 2x_2$, that everything that is produced is sold and that the sale prices of the products are: $p_1 = 1$ and $p_2 = 3$, respectively. Determine the quantities $x_1, x_2$ that minimize the cost of the process.

Solution:

$x_1 = 6/11$

$x_2 = 9/11$

$\lambda = -12/11$

$TotalCost(x_1,x_2) = 18/11$

I tried to solve it through the common way: using Lagrange function with Kuhn-Tucker conditions. However, I cannot reach the correct solution, despite I tried several times. I think I am not building Lagrange function correctly as a consequence of not understanding properly the economical meaning of what the problem want me to solve.

So I would be really greateful if you can help me to understand how to reach the correct solution to this specific problem, knowing that clarifying how to build Lagrange function and its restrictions is probably what it is needed here to fully understand the problem and its solution.

The OP clarified in a comment that a) "income" here means "revenues" and not "profit" (it is not always the case), and b) that Karush-Kuhn-Tucker multipliers work just fine if we define them to be non-positive instead of non-negative (they do, but it is not a widely known fact).

The other bad terminology in the statement of the problem is the "unit cost" one -it is really meant "marginal cost". So we have to obtain the Total Cost function from its partial derivatives. This is easy to do since we see that the cross-partial is zero.

So if

$$\frac {\partial TC}{\partial x_1} = x_1,\;\;  \frac {\partial TC}{\partial x_2} = 2x_2$$

it follows that

$$TC = \frac 12 x_1^2 + x_2^2 + FC,\;\;\;FC\geq 0$$

and we want to minimize it subject to the constraint $p_1x_1 + p_2x_2 \geq \bar R$.

PS: It appears that the revenue floor is $3$?


Tadelis ‘trading places’ Bayesian game My question concerns the following problem: two players, $1$ and $2$, each owns a house. Each player $i$ values his own house at $v_{i}$. The value of player $i$'s house to the other player, i.e. to player $j\neq i$, is $\frac{3}{2}v_{i}$. Each player $i$ knows the value $v_{i}$ of his own house to himself, but not the value of the other player's house. The values $v_{i}$ are drawn independently from the interval $[0,1]$ with uniform distribution.

Payoffs and actions are defined as follows: each player announces simultaneously whether they want to exchange their houses. If both players agree to an exchange, the exchange takes place. Otherwise no exchange takes place.

As far as finding a Bayesian equilibrium is concerned, I have reached the following stage:

Given $j$ exchanges, $i$ exchanges so long as $v_{i}\leq\frac{3}{2}v_{j}$ and given $i$ exchanges, $j$ exchanges so long as $v_{j}\leq\frac{3}{2}v_{i}$. This means that $j$'s expected utility from exchanging (given $i$ exchanges) is $\frac{9}{8}v_{j}$ and $i$'s is $\frac{9}{8}v_{i}$. From this I do not know how to proceed.

This is a static Bayesian game. The two players share a common prior over the type space which is characterized by the uniform distribution. For Bayesian games, you have to specify the belief of each player given his/her type, and the belief of each player determines their action. Basically, the strategy is a mapping from one's type to an action through belief specification.

What is player $i$'s belief about $v_j$? It is independently drawn from the uniform distribution over $[0,1]$, so $E(v_j) = 0.5$ for now. And he will exchange only when $v_i \leqslant \frac{3}{2}v_j$, but he does not know exactly the value of $v_j$, so he takes an expectation over $v_j$, then as long as $v_i \leqslant \frac{3}{2} \times 0.5 = \frac{3}{4}$, he will choose to exchange.

The same goes for player $j$ because they are symmetric, so player $j$ will only exchange when $v_j \leqslant \frac{3}{4}$.

Given this, $E(v_j)$ now decreases to $\frac{3}{8}$, player $i$'s expected payoff from exchange decreases to $\frac{3}{2}\times \frac{3}{8} = (\frac{3}{4})^2$. Therefore, player $i$ will only choose exchange when $v_i \leqslant (\frac{3}{4})^2$.

Since $\frac{3}{4} < 1$, this process will go on and on such that no one will choose exchange in the end which is the only equilibrium.


Why's a penny stock basically a call option with a strike price of 0 that doesn't expire? This Reddit comment proclaims:

A penny stock basically IS a call option with a strike price of zero that doesn't expire.
I suspect there's a high correlation between penny stock investors and people who buy deep OTM options hoping for a home run.

I understand the concept of a call option that doesn't expire, but I don't understand "strike price of zero". Though penny stocks can $\rightarrow 0^+$, they must $\in (0, 1)$. So why would the strike price be 0?

Your misunderstanding comes from the fact you are treating a penny stock as an option. They are not the same this is just a metaphor. The difference that makes the difference here is ownership.

The reason the strike price would theoretically be zero is, for a penny stock you own the underlying asset, so you would not pay to own something you already own. A strike price is how much you need to pay to purchase the asset, but you own the asset in this case.

The OP Reddit poster is dead wrong and is referencing a huge amount of underlying assumptions about penny stock trading and options trading. You can't treat them as the same.


How much money was distributed during quantative easing? I am trying to discover how much money was created as a result of quantative easing. I do not want to start a political debate. But, I am genuinely interested in learning how much money was signed into law by President Bush and then how much money was signed into law by President Obama. I would also like to learn how much money has been distributed while President Obama has been in office.

I expected to be able to find this information on the web somewhere. However, I have not been able to find a real breakdown. Once again, I have no interest in a political debate. I'm simply seeking the real dollar numbers.

The easiest way to estimate the total amount of quantitative easing is to look at the change in the balance-sheet of the Federal Reserve because every bit of money put in through quantitative easing involved the purchase of assets which grew the central bank's balance sheet.

You can see in the graph above that the total growth is about \$3.6T. There are non-quantitative easing reasons for these reserves to grow over time so this should be treated as an approximate figure.

Additionally, if the proceeds of the QE are used to purchase still more assets those asset purchases might not be universally agreed on as QE. However, the quantity of QE was decided on as the amount of purchases to do taking into account these other issues. If the other considerations had lead to lower asset growth it is possible that the FRB would have done more QE, leaving the balance sheet unchanged. If so, the total change in assets during active QE could be regarded as the intended level of QE.


How is real wage growth achieved? Someone asked a simple question: when wages increase, why don't companies just raise prices such that it cancels out the wage increase?

Of course, this isn't what happens in real life since real wage growth exists. But what's the best way to intuitively explain why that's the case?

A simple explanation could be that the demand curve shifting outward due to higher wages leads to an increase in quantity and price, but that's just from looking at lines on a graph.

Why would companies want to "cancel out" the wage increase? Their goal is to make money, not to keep real wages constant.

Many things factor into the pricing decisions of companies. There are competitive pressures: if rival vendors are decreasing prices the company has to follow suit or lose market share. There are also cost factors: if the price of an input (e.g. labor) rose, than the company may have to increase prices to stay profitable, or just to achieve maximum profit.

If technological improvements, economies of scale, or similar factors enable the company to produce the same quantity of goods at a lower cost, they can afford to decrease prices while keeping wages the same. This enables real wage growth. There are several similar scenarios where prices rose, but nominal wages rose even more.


What are good books about monopolies and market failures? Is there a good undergraduate level book specifically about economic monopolies and market failures?

Your question is quite broad in the sense that various forms of market failure cover a significant portion of all of microeconomics. I presume you have already looked in a general undergraduate micro book such as Varian's Intermediate Microeconmics, which provide coverage of many of these topics.

More detailed coverage of market power and monopoly can be found in Church and Ware's Industrial Organization: A Strategic Approach. Discussion of market failures caused by public goods and externalities can be found in  Hindriks and Myles' Intermediate Public Economics. For market failoures originating in information asymmetries, a good source might be Bolton and Dewatripont's Contract Theory.


Game theory and differential equations Does anybody know, any (advanced/classic) textbook that combines game theory with differential equations in mathematical economics. Specifically, I an interested in asymmetric information problems.

At the intersection of differential equations and game theory one can find differential games. Arguably, the most famous applications of differential games are in warfare, e.g., the homicidal chauffeur problem. However, not all differential games are of the pursuit-evasion kind.
Whoever wants to learn differential games may wish to learn optimal control theory first. To the neophyte, I would recommend Evans's book (chapter 6 is on games):

Lawrence C. Evans, An Introduction to Mathematical Optimal Control Theory [PDF], Department of Mathematics, University of California, Berkeley.

The next step could be the following books on applications to economics:

Engelbert J. Dockner, Steffen Jorgensen, Ngo Van Long, Gerhard Sorger, Differential Games in Economics and Management Science, Cambridge University Press, November 2000.

Luca Lambertini, Differential Games in Industrial Economics, Cambridge University Press, April 2018.

and, more on the stochastic side:

David W. K. Yeung, Leon A. Petrosjan, Cooperative Stochastic Differential Games, Springer, May 2006.

Unlike Evans's book, I have never read these ones. My listing of these books is not an endorsement.


Why do banks offer less interest on larger deposits? This may be a UK only thing but...

I have noticed that it is very common to see current accounts that offer some interest on the first couple of thousand pounds deposited with them and then less interest on sums over that amount. Why is this so? Surely they should offer more interest due to economies of scale.

Examples:

Starling bank 0.5% up to 2,000 - 0.25% above

Nationwide FlexDirect 1% up to 2,500 - 0% over 2,500

Tesco current account 3% up to 3,000 - 0% above

When you lend your money to a bank (by depositing it), they don't just make money off of lending out your money. They also make money out of charging you for banking services. If the bank makes more money off of offering you services then they can afford to pay you a higher rate of interest (all other things equal). Check out: How do banks make money? The fallacies of fee income (Rice and DeYoung (2004))

  But banks also earn substantial amounts of noninterest income by
  charging their customers fees in exchange for a variety of financial
  services. Many of these financial services are traditional banking
  services: transaction services like checking and cash management;
  safe-keeping services like insured deposit accounts and safety deposit
  boxes; investment services like trust accounts and long-run
  certificates of deposit (CDs); and insurance services like annuity
  contracts. In other traditional areas of banking-such as consumer
  lending and retail payments—the wide-spread application of new
  financial processes and pricing methods is generating increased
  amounts of fee income for many banks.... Remarkably, noninterest income now
  accounts for nearly half of all operating income generated by U.S. commercial  banks.

If spending on banking services increases more slowly than account balances and the sums involved don't make it worth the trouble of having multiple accounts then banks will be willing to offer higher rates on smaller balances. But, empirically, my impression is that this is atypical. It is more common to see higher rates on higher balances, because the transaction costs on serving one \$100k account are smaller than those of 10 \$10k accounts, and so they can pass some of those economies along as higher rates.


Intertemporal consumption question This question is driving me nuts.

Suppose, an individual lives for two periods. In each period she consumes only one good,which is rice. In period 2, she can costlessly produce 1 unit of rice, but inperiod 1 she produces nothing. However, in period 1 she can borrow rice at
an interest rate $r$ > 0. That is, if she borrows $z$ units of rice in period 1,
then in Period 2, she must return $z(1 + r)$ units of rice. Let $x_1$ and $x_2$ denote her consumption of rice in period 1 and period 2, respectively; $x_1$, $x_2$ ≥ 0. Her utility function is given by $$U(x_1, x_2) = x_1 + βx_2$$, where β is the discount factor, 0 < β < 1. Note that there are only two sources through which rice can be available; own production and borrowing.

Now suppose that there are N agents in the above two period
economy. The agents are identical (in terms of production and utility
function) except that they have different discount factors. Suppose that
β follows uniform distribution in the interval [ 1/2, 1]. Assuming r ≤ 1, what would be the demand function for rice in period 1?

My approach is integrating $\beta$ from 1/2 to $\frac{1}{1+r}$, and my answer comes out to be $\frac {N(1-r)} {1+r}$, but I dont think that's right.

Due to the linearity of the utility function the utility maximization problem for individual $i$ has either one of the two corner solutions, or it is indeterminate.

The individual $i$ has to solve the following problem

$$\max_{x_{1i},x_{2i}}[ x_{1i} + \beta_i x_{2i}]$$

$$s.t. x_{2i} = 1-(1+r)x_{1i}, \;\;x_{1i} \geq 0,\;\;x_{2i} \geq 0 $$
Solvency is also imposed -i.e. the individual cannot borrow in the first period more than what he can repay in the second period (including interest).

One can deduce that

$$\text {"flatter" budget constraint:}\;\; -(1+r) > -\beta_i^{-1}   \implies \{x_{1i}^* = (1+r)^{-1},\;\;x_{2i}^* = 0\} $$

$$\text {"steeper" budget constraint:}\;\; -(1+r) < -\beta_i^{-1}  \implies  \{x_{1i}^* = 0,\;\;x_{2i}^* = 1\}$$

.."steeper" and "flatter" with respect to the utility (linear) indiference map, and with $x_{2i}$ in the vertical axis.

Working the implied inequalities we re-write the solution as

$$\beta_i < \frac 1{1+r} \implies \{x_{1i}^* = (1+r)^{-1},\;\;x_{2i}^* = 0\}$$

$$\beta_i > \frac 1{1+r} \implies \{x_{1i}^* = 0,\;\;x_{2i}^* = 1\}$$

In the $N$-identical individuals case, and with $\beta_i, i=1,...,N$ being a random variable we can only talk about expected demand in the first period, denote it $E(d_{1i})$ for the individual and $E(D_1) = N\cdot E(d_{1i})$ on aggregate.

We have

$$E(d_{1i}) = \frac 1{1+r} \cdot \Pr\left[\beta_i < \frac 1{1+r}\right] + 0 \cdot \Pr\left[\beta_i > \frac 1{1+r}\right] $$

The second term vanishes.

Given the assumptions on the distribution of the $\beta$'s its density function over the domain is $f(\beta_i) =2$ and so the remaining probability is (as long as $r \leq 1$)

$$\Pr\left[\beta_i \leq \frac 1{1+r}\right] = \int_{1/2}^{(1+r)^{-1}}2{\rm d}\beta_i = 2\left(\frac 1{1+r}-\frac 12\right) = \frac {1-r}{1+r}$$

and so we have

$$E(D_1) = \frac N{1+r}\cdot \frac {1-r}{1+r} = \frac {1-r}{(1+r)^2}N$$

which is decreasing in $r$.

If $r$ hits unity, expected demand will be zero -because
a) It would place a solvency ceiling to loan demand to be not higher than $1/2$ so that with interest rate $100\%$ all production of the second period would then be needed to repay the loans. This means that with $r=1$, maximum consumption (and utility) in the first period will not exceed $1/2$.
b) the discount factor being greater or equal than $1/2$, implies that by taking zero loan in the first period, one would enjoy the full unitary production of the second period, with utility higher than $1/2$. So for non-zero demand for loans in the first period, it must be the case that this demand can exceed $1/2$. When $r\geq 1$ it cannot, hence the zero expected demand.

Note: if instead of a "stochastic distribution" of the $\beta$'s we think of a "uniform allocation" of them in the $[1/2,1]$ interval, then we can think of expected demand as deterministic demand.


Is there a dutch book argument for the "independence of irrelevant alternatives" axiom? There is a dutch book argument to show that nontransitive preferences are in a sense "unreasonable", which justifies why we pose the axiom of transitivity in the definition of "rational preferences", when it comes to no-uncertainty utility.

When it comes to utility functions over lotteries, Von Neumann and Morgenstern additionally pose the Independence axiom w.r.t. lotteries.

Are there Dutch-book arguments to justify the independence axiom?

Yes, and it's actually quite simple. Start with alternatives {A, B}, where you prefer A to B. If there exists some C such that introducing it causes you to prefer B to A instead, then the following holds:
I start by offering {A, B}, and you take A. Then I offer C as well, and also let you trade B for A so long as you give up some arbitrarily small amount of utility denoted dx. This means that your options are {A, (B-dx), C}, where dx is some arbitrarily small amount of utility that you will lose which is chosen so as to not change your opinion that B-dx is better than A. As a result you choose B-dx instead of A. The result is that you have given up utility for no benefit -- you could originally have chosen B originally, but instead took B-dx -- i.e. that you have been Dutch booked.


Financial manipulation and Inflation as tools for sovereign debt default In the book This Time Is Different, by Reinhart and Rogoff, in chapter 8, the authors state that

Higher minimum level of reserves (?)
And/or upper bound/ceiling to interest rates ( will help increase real inflation rate... however, isn't the nominal rate that which matters most for defaults?)

coupled with surges in inflation were, at certain historical moments, used to default on sovereign debt.
I understand how inflation can be used to 'default' on debt, but I'm not getting how the financial measures stated above would help...

After reading a few more chapters, the authors in their, by now very known, terse and often imprecise style, state that a financial repression is a method used by some governments to obtain indirectly more revenue.
This channel works when the government makes bank accounts as the main possible saving tool available to the common folk. Afterwards, the banks are obliged to acquire government debt, which often comes in form of higher minimum level of reserves (They don't explain how... but, maybe gvt debt may count as reserves, since the Central Bank may act as a 'printing money factory' of the government).
Nominal interest rates are those which usually direct the interest rate that the market asks for holding government debt. By keeping it artificially at a lower level, national investors/savers will have to abide by that low interest rate. Futhermore, by making inflation surge, the real burden of government debt will decrease as time goes by (assuming there's no way to circumvent national regulators/markets, legally or illegally).


If Gross Savings is less than Gross Investment, could we say that investment is being made with borrowed money? For example, gross savings of India in the financial year 2014 - 2015 was $30.2%$ of GDP, while the Gross Investments during this same period was $31.6%$ of GDP.  Can we then conclude investments are being made with borrowed money?

Also, if "Gross Savings" is $30.2%$, can it be said that an average person in India saves about $30.2%$ of his income?

Yes, in particular, the Home country is borrowing from abroad.

In a closed economy,

$\text{GDP} = C + G + I$. And savings is defined as $S = \text{GDP} - C - G$. And thus, it is necessarily the case that $S = I$.

Example. In 2015, India produces 10 bananas, each valued at ₹10, for a total value of ₹100. Private consumers consume 4 bananas ($C = ₹40$), government consumes 5 bananas ($G = ₹50$), and 1 banana is stored for consumption in future years ($I = ₹10$). (Bear in mind that additions to inventories, as with this last banana, count as investment.)

$GDP = C + G + I = ₹40 + ₹50 + ₹10 = ₹100$. Total final consumption ($C + G$) was ₹40 + ₹50 = ₹90. Hence, $S = ₹10$. This is a closed economy, so savings must necessarily equal investment. And sure enough, $I = ₹10$.

In an open economy, it need no longer be the case that $S = I$.

Example. In 2016, India produces 10 bananas, each valued at ₹10, for a total value of ₹100. India also imports 5 bananas ($M = ₹50$).

Private consumers consume 4 bananas ($C = ₹40$), government consumes 5 bananas ($G = ₹50$), and 6 bananas are stored for consumption in future years ($I = ₹60$). There are no exports ($X = ₹0$).

$GDP = C + G + I + (X - M) = ₹40 + ₹50 + ₹60 + (0 - ₹60)= ₹100$. Total final consumption ($C + G$) was ₹40 + ₹50 = ₹90. Hence, $S = ₹10$. But $I = ₹60$.

So $S < I$. How is this possible? The reason is that the gap between investment and savings of $I - S = ₹60 - ₹10 = ₹50$ is made up for precisely by imports. So our shortfall in savings (relative to investment) is made up for by borrowing from abroad, in this case through imports.

As for your second question,

Yes, we can say that on average, each Indian saves 30.2% of income. But this average is not necessarily very meaningful. For example it may be that the vast majority of Indians spend all of their income on consumption and it is only a tiny minority of the wealthiest Indians who do the saving.


Ireland wholesale electricity prices are higher during the weekends Some data from Ireland SEMO (weekday electricity prices) and quarterly prices from the European Commission imply that Irish weekend prices are greater than weekday prices.

The same datasets used showed the correct relationship (weekend prices lower) for France, Denmark, Netherlands, Belgium, and Norway.

Is this actually the case?
If so, why is it the case? Typically wholesale electricity prices are lower during weekends in most countries.

To clarify, I have wholesale hourly prices for weekdays only for Ireland in 2013 and 2014, from the power exchange: http://sem-o.com/marketdata/Pages/default.aspx For intellectual property reasons I cannot upload them, but taking the mean across these weekday-only prices gives quarterly means in 2014 which are lower than that reported by the European Commission Quarterly Report on European Electricity Markets. An example of a quarterly report: https://ec.europa.eu/energy/sites/ener/files/documents/quarterly-electricity_q3_2014_final_0.pdf (page 14, in the little map of Europe with average prices on the map)

Since the mean of weekdays only is below the mean of all days in a given quarter, this implies that the weekends have higher mean prices than the weekdays. This isn't usually the case for most countries, since generally factories and offices use up more energy than people relaxing at home.

From looking at the data I have access to, I'd say that things stop early on Friday afternoon in Ireland. So the Friday evening peak is lower than evening peaks on other weekdays: it's the only day of the week where the evening peak is about the same price as the morning peak.

As you haven't provided the metadata of the data you're using, nor links to find that out, I've looked at the SEMO data I know about.

The Single Electricity Market Organisation (SEMO) for Ireland gives prices by trading period (half-hours, starting at midnight), for every day of the year. So I took a 3-month period at random, 1 Feb - 1 May 2015, and looked at the average price for each half-hourly period, for each day of the week. Note that this is a simple arithmetic mean: there's no weighting by volume, no special handling of public holidays, no weather adjustments.

Friday, Saturday, Sunday have heavier lines, because they're the ones I'm emphasising. The four weekdays Monday-Thursday are very similar to each other. Saturday and Sunday each have later and lower morning peaks than Mon-Fri.

But Friday's evening peak is the lowest evening peak of the week. Much lower than any other day. Whereas in-day prices normally peak around 18.00-18.30, due to most industry still being powered, most commerce still being powered, and most homes being active, that's not the case on Friday: peak prices are a lot lower.

Note that there is no single price of any one MWh of electricity. Electricity gets traded many times over, starting maybe a year in advance, a month, a week, a day, an hour in advance, and then within the half-hour trading period itself there will be varying sell and buy prices. So there are huge dangers in trying to draw inferences from two different sets of price data, particularly when you don't have the metatadata that tells you what the data actually represents. The SMP price data I've used here is the System Marginal Price. There's a good description of pricing and scheduling from SEMO here (pdf), including on page 9 the calculation of the SMP.

Electricity prices are complicated. Unit commitment is complicated.


When were the First and Second Welfare Theorems proven? What years and by who were the first and second welfare theorems first proven?

Perhaps you have heard the competitive equilibrium referred to as the Arrow-Debreu equilibrium.

The idea of the theorems existed earlier but Arrow introduced the theorems formally in a way that is equivalent to what we today call the first and second welfare theorem in 1951 in his paper

AN EXTENSION OF THE BASIC
THEOREMS OF CLASSICAL
WELFARE ECONOMICS.

Debreu is more associated with proving that the equilibrium exists under certain conditions. If you think about it this makes the first welfare theorem much stronger. His seminal paper on the subject is

The Coefficient of Resource Utilization.


Can monetary union work without fiscal union? If I understand correctly, when a state joins a monetary union it relinquishes its ability to competitively devalue/increase the money supply during downturns.

Another mechanism Governments use to work their way out of downturns is to participate in the economy themselves, for example by undertaking infrastructure projects. Does monetary union somehow limit the ability to use this lever too?

Can monetary union work without fiscal union?

Yes, and that facilitates a comparison of economies & policies.

Note that the governmental participation you outline (tending to government's prominence in an economy) is only one approach of policy making. Another, opposite approach is neoliberalism, whereby a government's role in an economy is mostly supervisory and promotes market freedom.

It is the absence of fiscal union what allows a government to make the domestic economy more competitive by lowering taxes. And in a context of monetary union, the spectrum of fiscal differences becomes more evident, which streamlines an assessment of which economies or policies are more effective. In short, the combination of monetary union and lack of fiscal union is the "best of both worlds".

  for example by undertaking infrastructure projects. Does monetary union somehow limit the ability to use this lever too?

It certainly does because monetary union removes a degree of freedom: The members of a monetary union are subject to an additional constraint necessary to preserve stability of the currency they have in common.

But more important is that the constraint that ensues from a monetary union makes it more difficult for a government to go too far on policies that ultimately are detrimental or unsustainable.


How bad is piracy hurting the entertainment industrie's economy? Are they going bankrupt or have a good outlook? By entertainment I mean book publishing, music uploads like on iTunes or even movies whether DVD, Blue Ray, Netflix, Hulu whatever.  So much is moving online, that's the future.  Piracy cannot be stopped, Sean Parker of Napster a site that was hit hard and sued for piracy lawsuits of releasing music for free, he even said, "The war on piracy is a failure."  If a war is something to be won, piracy will win, but how much is what I and others are worried about.

Along with the big suits and artists/writer/actors/singers whatever, there are movie theater employees, Apple store employees, programmers for online entertainment companies, etc...the economy for this industry is huge and can be hurt a lot since as online media is growing so is online theft, hacking, and piracy.  While it is good to go into a field of medicine, engineering, business (which this is), entertainment is a cultural classic and the people in it mostly work hard and moved up to get where they were in turn making jobs for everyone.

Star Wars made like a billion last month, but that's now and that a big movie.  Kick@ss 2 stars said another sequel can't be made because the last two were pirated too much.  Scary.  Is the industry's outlook more collapse than still being profitable in the future?

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

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

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

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

Some messages that emerge from the literature:

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

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