Will the third Heathrow runway fill up within 25 years? From a Wired article published 9 June 2018 about the proposed third Heathrow Airport runway:

  But Warnock-Smith1 warns that Heathrow will eventually fill up again unless air travel is redistributed to make use of spare capacity at other UK airports. “Otherwise in 25 years, we will be having the same debates about a fourth runway at Heathrow,” he adds.

Did Warnock-Smith base his estimate on something (e.g. a mathematical model) or was it "an off-the-cuff remark"? Have there been published studies on this topic?

1Associate head of the School for Aviation and Security at Buckinghamshire New University

Note 1: This question does not belong on Aviation.SE. (see here)

Note 2: This question does not belong on Skeptics.SE. (see here)

It is difficult for anyone here to know exactly what Warnock-Smith had in mind with his comment or whether he has conducted some analysis prior to his comment.

Nevertheless, he may be referring to the research on congestion in general, which has largely focused on road travel.

It is well-known that, contrary to popular belief, increased capacity can make congestion worse. The reason for this is so-called "induced demand". Once there is a larger capacity, a demand increase will typically follow, thereby keeping congestion at the same rate or making it even worse. One mechanism behind this increased demand is that there could be a latent demand already underlying. This means that there are consumers who want to take trips, but don't due to congestion issues. However, after the capacity increase, the realized demand increases.

This phenomenon has been observed for example with increased highway capacity, as noted in this news piece. For a literaure review on highways, see Susan Handy's 2015 article "Increasing Highway Capacity Unlikely to Relieve Traffic Congestion".


Understanding Rabin's Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion I am trying to understand Rabin's Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion.

I am struggling to completely understand the following:

  Suppose you have initial wealth of $W$, and that you reject a 50-50 lose
  10/gain 11 gamble because of diminishing marginal utility of wealth. Then it must be that
  $U(W+11) - U(W) ≤ U(W) - U(W-10)$. Hence, on average you value each of the dollars between $W$
  and $W+11$ by at most $\frac{10}{11}$ as much as you on average value each of the dollars between $W$ and
  $W-10$.

  By concavity, this implies that you value the dollar $W+11$ at most $\frac{10}{11}$ as much as you value the dollar $W-10$.

  Iterating this observation, if you have the same aversion to the lose
  10/gain 11 bet at wealth level $W+21$, then you value dollar $W+21+11 = W+32$ by at most
  $\frac{10}{11}$ as you value dollar $W+21-10 = W+11$, which means you value dollar $W+32$ by at most
  $\frac{10}{11}\times \frac{10}{11} \approx \frac{5}{6}$ as much as dollar $W-10$.

May someone please provide the mathematics to the bolded italic part in the quote above?

Thank you very much

Gus

From $U(W+11)−U(W)\le U(W)−U(W−10)$ we get that $\frac{U(W+11)-U(W)}{11}\le\frac{10}{11}\frac{U(W)-U(W-10)}{10}$, which is what the sentence before the bolded italic part says.

Now by concavity of $U(.)$ we know that $MU(W-10)\ge\frac{U(W)-U(W-10)}{10}$, and also that $MU(W+11)\le\frac{U(W+11)-U(W)}{11}$.

Therefore $MU(W+11)\le\frac{U(W+11)-U(W)}{11}\le\frac{10}{11}\frac{U(W)-U(W-10)}{10}\le\frac{10}{11}MU(W-10)$.

So $MU(W+11)\le\frac{10}{11}MU(W-10)$, wich is just the bolded italic statement.


What if China did pay US tariffs? The US president Donald Trump has repeated said that China will pay for the tariffs he has or plans to impose on Chinese goods entering the US. Many commentators has said that tariffs are paid at time of import by the importer, and that those costs are simply passed onto the consumer.

What would be the consequences if, instead of adding a tariff cost to the item being imported, the US Government instead deducted the same amount from the US debt that the Chinese Government owns? This would make it literally true that the Chinese are now paying for the trade deficit, and it would automatically stop once the Chinese no longer own US debt.

Besides making lenders extremely wary of buying US debt, what could be the economic repercussions from such a decision?

the US Government instead deducted the same amount from the US debt that the Chinese Government owns

That would be equivalent to a partial sovereign default of the US: we don't like you, therefore our bonds you own are now worth less/crap.

More technically, it would be a repudiation of (some) sovereign debt:

  Repudiation happens when the sovereign rejects its obligation to pay, which could
  happen before or after any payment is due. Governments typically avoid questioning
  the validity of their debts, or announcing their intention not to pay before missing a
  payment, since in practice, repudiation carries all the traumatic consequences of
  payment default [...]. Repudiation may go hand in hand with
  governments questioning the legitimacy of one or more obligations. The literature on
  “Odious Debt” includes a handful of examples (King 2016, Lienau 2014). In 2008,
  Ecuador claimed that two bonds issued by a previous government were illegitimate and
  pledged not to pay them. It launched a buyback offer the following year in the shadow
  of the illegitimacy claim, and ultimately secured nearly 2/3 debt relief with more than
  90 percent of the creditors participating.

  [...]

  Repudiation [...] is rare in modern times. Repudiations most often
  occur after a regime change, and examples of repudiations include those in the wake of
  communist revolutions—such as Russia in 1917, China in 1949, and Cuba in 1960; Rhodesia
  in 1965, after its unilateral declaration of independence from the United Kingdom; Zaire in
  1979; Ghana in 1979 and 1982; and North Korea in 1976.

  Repudiation can go hand-in-hand with the concept of “odious debt,” which posits that a
  government is not obligated to pay for those debts incurred by a previous government contrary
  to the interests of the public. Though, the concept has strong moral appeal, it is difficult to
  define odious debt in a sufficiently limited way to allow its practical application (Reinhart and
  Rogoff 2009). The doctrine has not gained traction with arbitrators, courts, or credit rating agencies (Gelpern 2007; Blair 2014) and, the earlier example of Ecuador aside, states tend not to assert it explicitly.

As for effects, that's harder to predict. China would probably accelerate its sales of US treasuries, since the US move you propose is not going to impact all their holdings at once. The sooner they would sell, the fewer losses they would incur over time from the proposed US tax-like measure. On the other hand, selling too much too soon would hurt them too by dropping the price too much.

Russia substantially reduced its holding of US treasuries in 2018, presumably just based on fears:

  Between March and May, Russia's holdings of US Treasury bonds plummeted by $81 billion, representing 84% of its total US debt holdings. [...]

  "One theory is that this was Russia's revenge for US sanctions," said [Jason ] Bush [an analyst at consulting firm Eurasia Group].

  Another theory is that Moscow feared further US sanctions that could cause its holdings of US debt to be frozen or even seized.

The Russian side didn't acknowledge this explicitly, but their central baker said something like

  Russia assesses "all the risks: financial economic and geopolitical."

Russia however held a lot fewer US treasuries, only around 1/12 of China's even at their peak holdings. So Russia could sell the bulk of theirs relatively quickly.


Could eliminating all taxes and only creating new money theoretically work? Imagine you had the opportunity to found a new country from scratch (in 2020).
Value exchange would be digital, where only the state can create new currency units.
Instead of relying on income tax and/or indirect taxes, there would be no form of tax but instead the government would rely on increasing the overall supply of the currency to perform welfare redistribution, such as providing Universal Basic Income.
(note: UBI was my choice in this example since it simplifies welfare redistribution, making the question clearer)
An example:
Year 1: Initial currency units: 100. Government creates 10 more units (10%) and pays it out as UBI
Year 2: Init. units: 110. Government creates 11 more units (10%) and pays it out as UBI
Year 2: Init. units: 121. Government creates 12.1 more units (10%) and pays it out as UBI
...
Each year the value of the currency is lessened due to inflation, so more money has to be generated.
Would this work if the country was completely isolated?
If so, would it still work if international trade were a factor?
FOLLOW-UP QUESTION:
As far as I know, money was initially created as a means of value exchange, not necessarily a means of storing value.
Since most existing answers highlight (rightfully so) that high inflation rates lead to people not using a currency to store value, but resorting to USD or similar, wouldn't it be plausible that they would still use the currency for everyday transactions, simply because it is universally recognised, thus leading to higher ease of use?

It would not work.
Historically speaking, governments that try to fund their operations primarily via the printing press experience not just inflation but hyper-inflation. Why? Well, one explanation is that without taxes nobody has any reason to want the government's currency. You can try to force people to use it, but that just encourages black marketeering.
Another way to look at it is that a policy of funding the government by printing money is equivalent to funding the government entirely with taxes on holding currency. But since the tax only applies to currency, and not gold, or land, or massive stockpiles of cigarettes, people have an incentive to avoid holding onto money at all costs. No matter the current price of cigarettes, using your spare cash to buy cigarettes for barter later on will always seem like a good deal because the cigarettes are more likely to maintain their value than the cash. But if no one wants cash, by law of supply and demand the value of cash should plummet.
Edit for the benefit of pedants: I am not saying that any "inflation tax" will automatically destroy the value of a currency. I am saying that people need reasons to hold your currency which are strong enough that they'll tolerate the inflation tax—and the larger the de facto tax on holding currency, the better people's reasons for doing so need to be. In the normal world, taxes are a key source of demand for fiat currency, take that away and the system stops working.


Show that an equilibrium in strictly dominant strategies is a unique Nash equilibrium I am new to game theory and I came across this line, " A strategy profile (s1, . . . , sn) in which every si is dominant for agent i (strictly, weakly, or very weakly) is a Nash equilibrium."

But why is that? And how would an equilibrium form in strictly dominant strategies? Do they both just yield the same best payoff?

Any help would be appreciated!

It will be useful to spell out the relevant definitions.

Let $A_i$ be the set of possible actions for player $i$, $A_{-i}$ be the set of possible joint actions of all players except for player $i$, $A$ be the set of possible joint actions of all the players. For $a=(a_i,a_{-i})\in A$, let $u_i(a)$ denote the payoff to player $i$ from action $a_i$, given that the other players play $a_{-i}$.

Definition 1: An action $a_i\in A_i$ is weakly dominant for player $i$ if for every $a_{-i}\in A_{-i}$, $u_i(a_i,a_{-i})\ge u_i(\overline{a_i},a_{-i})$ for every $\overline{a_i}\in A_i$, i.e. no matter what the other players do, action $a_i$ yields a payoff at least as high as any other action available to player $i$. [Strict dominance given by $>$ instead of $\ge$.]

Definition 2: An action $a_i\in A_i$ is a best response to action $a_{-i}\in A_{-i}$ if $u_i(a_i,a_{-i})\ge u_i(\overline{a_i},a_{-i})$ for every $\overline{a_i}\in A_i$, i.e. If I fix other players' actions to some particular joint action, then $a_i$ yields a payoff to player $i$ at least as high as any other action available to player $i$.

Claim 1: If an action $a_i\in A_i$ is strictly or weakly dominant, then it is a best response for any joint action $a_{-i}\in A_{-i}$. [This follows from Definitions 1 and 2 immediately.]

Definition 3: A joint action $a\in A$ is a Nash equilibrium if for each player $i$, action $a_i$ is a best response to $a_{-i}$.

Claim 2 (your question): A strategy profile (i.e. joint action) $s=(s_1,...,s_n)\in A$ in which each $s_i$ is a (strictly or weakly) dominant strategy is a Nash equilibrium.

Note that Claim 2 is a consequence of Claim 1.


How to model the change in fossil fuel price? What is the best way to model fossil fuel prices? I am trying to build an energy-economic model and changes in fuel prices are an important part of the model. I need to know how to model them. Any ideas?

I would like to forecast the changes in fossil fuel price (oil and gas basically). As this is part of an energy model which takes into account those economical trends

You are not going to be able to forecast oil and gas prices with any useful accuracy at all. Lots of people try, and as far as we know, every one of them has failed. If anyone has ever succeeded, then they've become extremely rich through it, and they're not telling anyone the secret. If you did succeed, then your energy economics model would be completely irrelevant to you, as you'd be too busy trading the oil market, and eyeing up which tropical island you should buy next.

The best you can hope for is consistency in your model. And then sensitivity-test your model based on a broad range of assumptions.
For example, my usual 95% credible range for the price of a barrel of oil in 2030 is USD(2016) 5-500.

So, what do you look for, for consistency? Demand and supply. Have short-run and long-run curves for both. If you're forecasting more than five years ahead, you must have some kind of uptake model for substitutes too, as well as short-run and long-run supply curves for them. Depending on how complex your model is, you might want to model storage too, particularly if modelling in less than 5-year time steps.


Example of a utility maximization problem with a non-binding budget constraint Given a utility function $U(x,y): \mathbb{R}^{2} \to \mathbb{R}$, the general utility maximization can be stated as follows:
$$
\max_{x, y} U(x,y) \text{ s.t. } p_{x}x + p_{y}y \leq m
$$
where the $p_{i}$ are prices, and $m$ is total income. In the Cobb-Douglas case, for example,
$$
U(x,y) = x^{\alpha} y^{1 - \alpha}
$$
for some $\alpha \in (0,1)$. We notice that in Cobb-Douglas, the more you buy, the more utility you get. Thus your budget constraint must hold with equality, because the more you spend, the more utility you get.

What are examples of utility functions that don't have positive marginal utility of income after some point? I can think of functions that have bliss points. For instance, if $U(x,y) = -(x-25)^{2} - (y-20)^{2}$, then $(25,20)$ is the best you can get, even if your income allows you to spend more. What are other examples of this?

Assuming positive prices, any utility function that doesn't satisfy strong monotonicity of at least one good would have a non-binding budget constraint. Since you asked for some examples:

$U(x, y) = 0$,
$U(x, y) = -x$.

Re: Giskard's comment.

I'm not sure I used the correct term here when I said "strong monotonicity of at least one good." To be precise, what I meant to say was:

Let $U(x_1, x_2)$ be the utility function. The function would have non-binding budget constraint if there are some $(x_1, x_2)$ such that $dU/dx_1 \leq 0$ AND $dU/dx_2 \leq 0$.


What are the effects of a 12 month sudden stop/shutdown of a capitalistic economy like the US? Consider a scenario where consumer confidence remains low until a virus such as COVID-19 is contained. In this scenario, containment is defined as being achieved once a vaccine is manufactured and distributed in 12-18 months after shutdown. Assume the following criteria:

A synchronous eradication effort amongst all states/countries in a system is highly unlikely.
Countries remain in a long-term suppression phase - a metaphorical game of "whack-a-mole" as researcher Ed Yong describes, where the threat of spread continues to pop up in various regions due to the virus's novel ability to remain undetected in many carriers, new strains arriving seasonally, duration of immunity remains unknown, etc. rendering "easing" of lockdown restrictions a non-option.

What are the effects on a sudden economic shutdown in a capitalistic system for a prolonged period of time like 12 months? 18 months?

In the most optimistic case, there will be a difficult 12-18 months, followed by a return to normal. The factories are still there, but most things are just put on hold in the mean time. That return to normal will involve some changes (e.g. commercial real estate will hurt as many workers continue working remotely), but it could be that the economy loses no real productive capacity. There would be a big increase in public and private debt, but basically it would be like stepping back a few years to a time that was fairly peaceful and productive, just less wealthy.

In the most pessimistic case, all the physical stuff remains, but all the social stuff (contracts, org charts, institutional knowledge etc.) crumbles and has to be rebuilt. Your local bar goes under, and your local economy loses the knowledge currently embedded in that bar's operations/management. Although the building and bar stools remain, the business can't be spun up smoothly because running a business just isn't that easy. It would be sort of like landing on an abandoned alien planet, finding a lot of empty factories, and trying to get them operating again.

Then there are all the political-economy issues. Government debt, political instability, and all the rest. As a general rule, the unscrupulous are best positioned to take advantage of a crisis, so we have reason to expect some degradation of political institutions costing us future productivity.

These are some pretty wide bands on the range of possible outcomes: from "Dang, it's going to take me an extra couple years to pay off my mortgage!" to "Holy Hell, how did this turn into post Soviet-collapse Uzbekistan?!" Of course the truth is going to be somewhere in the middle.

What I can say pretty confidently are these very general points:

There will be shifts in what sectors get resources/attention. People will buy more rubber gloves and chest freezers and will spend less money on something else.
There will be shifts in political coalitions. People will spend more attention to public health issues (and maybe less on national parks). Consequently, lobbying groups will become more/less important.
There will be a recovery period. Once we're back to work, people will be trying to pay down their debts for a while and will delay that vacation they might otherwise have taken.

The first two points are barely predictions at all. Change is constant in markets and politics. The real question is "how dramatic will these shifts be?" My prediction: they'll be big enough to be measurable, but not so big that the world we end up with is unrecognizable compared to what we started with.


"Demand for money" - definition What is the definition of "demand for money". The definition given by Wikipedia appears gibberish to me. And just to double check - what are the units of demand for money? Is it measured in "dollars"? or perhaps "dollars per unit time"? Or a ratio between two things?

If I understand it correctly, the level of demand for any produce (other than money) is the rate of flow of money that is currently being used to purchase that produce. So for example, if there is 1 million dollars per day being spent on VW cars, then you can say, "the demand for VW cars is $1m per day". Clearly the meaning of the word "demand" in the expression "demand for money" can't be the same thing - can it?

EDIT: Some definitions sound an awful lot as though a person's demand for money is exactly equal to the amount of money they currently have (and its units would therefore simply be "dollars"). Please include in your answer, an indication of whether or not your definition is identical to a person's current holding of money.

EDIT: Looking at the suggested answers and doing some more reading, I get the feeling that the word "demand" in economics is actually not a single number, but a set of numbers, or a curve. In the case of normal goods (call them Widgets), then the x axis will be price and on the y axis will be "Widgets sold per unit time" (the unit of time could be days, years etc). Please advise if you think I have this bit wrong.

In Economics, to define/describe "demand for $X$", whatever $X$ represents, we need

a definition for $X$
a measurement unit for the quantity of $X$
a measurement unit for the price of $X$

Given these, the "demand schedule" for $X$ (terminology dating back to A. Marshall), is the geometric locus of pairs (quantity, price) that reflect the quantity demanded for the corresponding price in the pair.

And that's that: why is the quantity demanded what it is for a given price, is (at least) one level deeper in the economic structure and analysis.

As regards "money", I just record here the usual approach taken:

We have in mind something that is perfectly liquid (and in practice we may include in the definition "essentially liquid" assets), where "liquid" means "immediately acceptable by anyone in any exchange"
The quantity of money is measured in some currency unit (like USD, Euros etc),
We use the interest rate as "the price of money"

To go this one step deeper, the reason why "demand for money" is not fixed at infinity, has to do with the question that we pose so as to avoid a useless answer. And the question is essentially a question of allocating a given level of assets between different forms/different degrees of liquidity, money included: Given that my wealth is $W$ (measured in a currency unit), and given that the interest rate I will enjoy if I save it all in an interest-bearing form is $i$ (unitless), how much of this wealth do I want to keep in "money form"?

Enter arguments as to why we want to keep money, functional forms that formalize these arguments, etc.

In dynamic models, it is understood that this question is posed and answered by the demand schedule for money for each time-period of the model. In static models, there is a single time period.

Another usual aspect is that we examine "real  money balances", i.e. the deflated value of the nominal money balances.

"Current holdings of money" is not the demand schedule but equilibrium quantity demanded, given whatever constraints we postulate that they exist.

This gives rise to the concept of a possibly "liquidity constrained" economic agent: given his wealth, the interest rate and his preferences, the agent would want to allocate $W_m^*$ of his wealth to money holdings. But we may observe that it allocates something less, for example because the existing markets where the agent can transform non-liquid assets to liquid ones are "incomplete" (as they say), and so the agent finds himself with non-liquid wealth that he would want to transform into money but he cannot (perhaps due to asymmetric information, risks that cannot be priced, etc). While this is a constrained equilibrium also, it is important for economic analysis and economic outcomes to realize that here we may have an additional "binding constraint" on the agent's behavior, and as this constraint changes, the behavior of the agent will also change.

Detecting the existence of such exogenous liquidity constraints is difficult, because it is difficult to separate their effects on money holdings from the effects of other constraints (like the level of existing wealth of the agent).

So "current money holdings" is tautologically equal to "current equilibrium money demanded", but the challenge of economic analysis is to determine which constraints are binding and so characterize the observed equilibrium.


Where does the money required for reserves and loans come from? I understand that banks must keep a certain percentage of money in its reserves and it can loan the rest out. What I don't understand is how the money supply increases

For example, let's take a scenario where somebody deposits 100 dollars into a bank. So the bank has 10% of required reserves, so 10 dollars is subtracted from this 100 dollars. So 90 dollars can be used for loans.

But wouldn't this mean that if the person who payed the 100 dollars wanted the 100 dollars back in cash, the bank has spent all the money?

Edit: I watched a video stating that the 90 dollars is created by the bank. Is this true?

Well I think that the key to understanding this is to realize that money supply as other macroeconomic aggregates must be defined over period of time.

If you deposit 100\$ bill at a time $t$ with  10% reserve system money supply can increase up to 1000\$ because first bank keeps 10\$ and lend outs 90\$ next keeps 9\$ and lends out 81\$ etc. and sum of this infinite sequence with 10% reserves is 1000.

You are completely correct to say that if people would start withdrawing money let’s say at time $t+1$ money supply would contract. So in this example at $t-1$ money supply would be 100\$, at time $t$ assuming no borrowing constraints and perfect markets money supply would be 1000\$ (because of the multiplier) and at time $t+1$ when you withdraw the money (so there is run on a banks with this one depositor) then money supply would contract back to its original 100\$.

People keep having this misconception about money supply, that in only increases if there is some permanent irreversible increase in quantity of money but that not correct. For example, consider another macroeconomic aggregate - unemployment, you would probably say unemployment increased if a person lost job even if in a year or so that same person gets their job back. The same applies to all aggregates.


Depreciation of local currency and its effect on prices I have problem with an article Lee H., C. Park, 2013, International Transmission of Food Prices and Volatilities: A Panel Analysis.

Authors wrote:
Difference in log of exchange rates (LOC/ $)- As depreciation of local currency (LOC) against the US dollar will result in higher domestic prices of imported food products in local currency, this variable is expected to carry a positive sign.

Variable (LOC/$) has positive sign in there econometric model. How it is possible?

When exchange rate (LOC/$) rises we have aprreciation of local currency so food prices are lower. I think that the sign should be negative

Can someone help me?

I think you're getting tripped up by notation. Instead of LOC/\$, write \$/LOC, since international trade is most likely to take place using $USD as an intermediary currency.

Here's an example:

Suppose world prices for soybeans are \$150/ton USD.  Today, the Wakandan widget (W) trades at 75W/\$ - so, I suggest rewriting this as $1/75W. Then, absent tariffs, taxes, and other frictions, Wakandans can import US soybeans at 11,250W/ton.

Now suppose the widget depreciates - it now trades at 150W/\$.  Notice that the sign of this change is positive, because you need more LOC to buy a unit of USD.  But if you rewrite as $1/150W, the sign of this change is negative, fitting the intuition that the LOC has become less valuable.  And indeed, now Wakandans must pay 22,500W/ton to import US soybeans - a change that would be reflected by a positive sign.

The value change of the LOC is negative, leading to a positive change in the price for imports. Make sense?


Are there two deadweight welfare losses associated with a Pigovian tax? I am constructing a diagram for an indirect tax (specific) imposed to correct a negative externality of consumption.

There is a deadweight welfare loss from the externality (represented in blue) because, although it is reduced,the tax does not achieve to shift the supply curve to a point where MSB=MSC (Qm).

However, the tax itself also should produce a deadweight welfare loss (represented in green). Is it correct that there are two deadweight welfare losses in this situation or is there no deadweight welfare loss associated with a Pivogian tax?

The Pigovian tax is responsible for neither of the deadweight losses in your diagram.

The Pigovian tax has partially, but not wholly, corrected a deadweight loss that was caused by the negative externality.

There is a deadweight loss associated with Pigovian taxes: that is the administrative cost of collecting the tax. This is not pictured in your diagram.


What does it mean to "print money"? In my intro macroeconomics course, my professor tried to emphasize that the money supply changes ONLY by increasing or decreasing lending activity. However, I feel like he was trying to focus on lending because most people have the misconception that the Federal Reserve just "prints money" to increase the money supply. However, is it true that although the MAJORITY of the money supply increases with more lending, that in some cases the Federal Reserve does "add zeros" to their spreadsheets to influence the money supply? For example, if they wanted to increase the money supply they could "print money" and use those funds to buy bonds from banks which in turn would then lend out that money and increase the money supply.

Depends on what you mean by money supply: M0, M1 etc (see here for example). If M0, then printing money is literally issuing new coins and bills.

The Fed can certainly "add zeroes" and use the extra money to buy other assets. The frequency of this is an empirical question.

Ask your professor what she/he meant.


Cost of production plant I'm struggling to find a macroeconomic index which embodies the cost to run an average production plan.

My problem is that I wanted to divide the annual average cost per employee (which I already found to be gross income per capita) with the cost of running an average asset (e.g rent, energy and other expenses).

Did such an index exists?

If you are looking for data on costs for production plants you might consider the BLS productivity data https://www.bls.gov/mfp/mprdload.htm.

Under the combined sector and industry multifactor productivity excel file you can find cost measures organized by NAICS (North American Industry Classification System) at the three digit level [https://www.census.gov/cgi-bin/sssd/naics/naicsrch?chart=2012] .

Depending on what type of production plant you are looking for there is data by energy usage, rent, and other types of costs.


Why it is important to observe if the 10Y treasury yield moves nowadays? in the context of low yields, where fed continues with fiscal stimulus, I've heard from many economists that this week the 10Y treasury rate has been finally increasing. In which situation is this theoretically problematic for the financial market?
Can someone help me understand a little bit the intuition behind? Just want to clarify that this comment was in the context of financial markets.

Theoretically there could be many reasons why interest rates increase. I will present you one possible interpretation (this is the one that is currently discussed in the news, see for example NBC):
Democrats have won the congress and accordingly they have the majority to enact their political agenda. Investors believe now this will increase deficit spending for pandemic relieve plans (like the stimulus payments to low income households) or for infrastructure investments. This directly increases the supply of treasuries and prices will fall accordingly. Prices going down means nothing else than an increase in the interest rate.
Why is this potentially problematic? Well in general it isn't, prices simply adjust to the shift in demand and supply. But in this concrete situation it means states have to pay higher interest rates for their debt and this may restrict possibilities to enact investments plans. During the current global pandemic Central banks try to keep interest rates low in order to give governments greater financial leeway.


Nash Equilibrium of modified Keynes' beauty contest Recently I conducted a small game among students of our institute. The game was based on Keynes' beauty contest game. The participants had to guess a number between 0 to 100 and the participant whose guess was closest to 2/3rd of the average of all guesses would win the game.

The twist was this: We also awarded money to the winner in each round. The money was a multiple say, 5x of the final number (2/3rd of the average).

What will be the Nash Equilibrium of this modified game. The solution to the original problem is of course everybody choosing 0. Will the equilibrium shift in the above described game. Consider n to be greater than 30.
Any help would be appreciated.

Assume the players have to choose integers, otherwise a best response may not exist. Let the payoff of winning be $\alpha\cdot[\frac23\text{ of the average}]$, $\alpha>0$. Consider the two player (A and B) case, and let's verify whether choosing above $0$ is optimal.

Suppose A chooses $x>0$. Then B can guarantee a win by choosing $x-1$, since $\frac23(x-\frac12)$ is closer to $x-1$ than to $x$. However, if B chooses $0$, A choosing $x=1$ is a best response (A gets zero anyway). So we will have a NE where not both players choose $0$, and the one who chooses $0$ gets positive payoff.

This equilibrium can be generalized to the $n$-player case. Let $n-1$ players choose $0$ and the remaining one choose $1$. In this equilibrium, those who choose $0$ would share the positive payoff (each gets $\frac{\alpha}{n-1}\cdot\frac23\cdot\frac1{n}$). They are best responding because choosing any $x>0$ would imply zero payoff. The one who chooses $1$ is also best responding since he gets zero anyway. (Of course this is not the only equilibrium. There is also one where everyone chooses $0$, which is obvious.)

Admittedly, the above equilibrium relies crucially on the assumption that players are only allowed to choose integers. But this is due to the fact that payoff is a function of the choices (compared to a fixed amount in the original version of the problem). Suppose players are allowed to choose any real number in $[0,100]$. Then if A chooses $x>0$, B would best respond by choosing $x-\epsilon$, where $\epsilon=\min\{y:y>0\}$ (B would win of course, but she also wants to maximize her earning by making her choice as close to A's as possible).
However, such an $\epsilon$ does not exist. Therefore, the only equilibrium is for everyone to choose $0$.

The intuition is this: however large the winning is, you don't get it if you don't win. But winning requires that you choose small. So the incentive to win overwhelms the incentive to win big.


How does one do a hypothesis test for elasticity? Given the regression output
  $$\widehat{\ln cons} = \underset{(0.6018)}{0.4054} + \underset{(0.0744)}{1.2739}\, \ln m - \underset{(0.1902)}{0.6666}\, \ln p_1 -\underset{(0.2645)}{1.6146}\, \ln p_2$$
  where

  $\ln cons$ is the log of chocolate consumption,
  $\ln m$ is the log of income,
  $\ln p_1$ is the log of the price of chocolate, and
  $\ln p_2$ is the log of the price of sweets,

  test whether chocolate is a luxury good.

Since $1.27 > 1$, it is logical to test whether $\beta_{\ln m}$ could be less than $1$. When I test elasticity, I base the null hypothesis on what is logical, as in this case if $\beta_{\ln m}$ is significantly greater than $1$, one shouldn't reject a (illogical) null hypothesis $\mathrm H_0: \beta_{\ln m} \geq 1$. So,

$\mathrm H_0: \beta_{\ln m} \leq 1$

$\mathrm H_1: \beta_{\ln m} > 1$

$\displaystyle t = \frac{1.2739-1}{0.0744}\approx 3.681$

Therefore, I reject the null hypothesis in favour of the alternative that chocolates are a luxury good.

Do you agree with the way I have set up this hypothesis test? If the estimate were less than 1, I would have stated $\mathrm H_0: \beta_{\ln m} \geq 1$ against the alternative $\mathrm H_1: \beta_{\ln m} < 1$.

Do you agree with the way I have set up this hypothesis test? If the estimate were less than 1, I would have stated $\mathrm H_0: \beta_{\ln m} \geq 1$ against the alternative $\mathrm H_1: \beta_{\ln m} < 1$.

Setting up null and alternative hypotheses is the first step in a t-test.  You should not set them up after computing your estimates.  In your specific example with income elasticity of demand, you set up the null and alternative correctly, meaning that you want the alternative hypothesis to be the statement about what you are trying to prove.  You should use that null and alternative regardless of what the data then tells you.

P.S. You should report the one-sided p-value from your one-sided hypothesis test, not just the test statistic.


In which market structure does the consumer has almost zero knowledge about the good? Consider goods that are almost identical (e.g. cement) and require technical knowledge to understand their merit, which an ordinary consumer might not possess. What then is the feature characteristic of its market structure?

The market for lemons. Paper is here.

The example most commonly given is used cars. The result is market failure.


What types of 'market mechanisms' are said to exist besides auctions? The book Understanding Auctions states:

  The term auction covers a wide range of market mechanisms that are used to exchange products and services by determining who receives an item and how much is paid for it. Although there are different auction designs, all of them share two properties. First, they are universal, that is, they can be used to sell (or buy) anything. Second, auctions are anonymous, which means that the identities of the participants do not affect the outcome of the auction.

It then goes on to describe a wide range of mechanisms that facilitate the exchange at some agreed price, all classified as types of auctions, including:

dynamic vs sealed bid auctions
single item vs multi item auctions
sequential vs simulataneous auctions
clearing vs continuous double auctions
combinatorial auctions

Combinations of two or more of the above are also possible and still auctions. I'm struggling to think of a market mechanism that is not an auction! So my question is what other types of market mechanisms can be said to exist?! Can someone point me to a good taxonomy of "market mechanisms"?

Aside; this paper discusses "negotiation protocols" and distinguishes between:

Voting
Auctions
Bargaining
General Equilibrium Market Mechanisms
Contract Nets

But this paper is from 1999, and the author classifies 'auctions' only the conventional type - what would be single item, monopolistic forward auctions in the first authors taxonomy. "General Equilibrium Market Mechanisms" kind of seems different but, it could also be interpreted as a multi-item, simultaneous, dynamic, clearing double auction. In fact a well known mechanism used to solve for a general competitive equilibrium is the Walrasian Auction.

Other methods or mechanisms by which goods are traded in a market economy:

1. Seller posts price.

Probably the most familiar method to most people. Examples: McDonald's posts a price of \$1 for a hamburger, an airline posts a price of \$400 for a ticket, etc. Anyone who's willing and able to pay the posted price gets the good.

2. Buyer posts price.

Previously somewhat uncommon, but thanks to the internet most people are now familiar with this method. Example: Buyer of a ticket to tonight's game posts the price he's willing to pay on craigslist. Anyone who's willing and able to sell at the posted price gets to sell.

3. Seller and buyer both post prices.

Mr X announces he's willing to sell one Berkshire Hathaway share for \$300,000. Mr Y announces he's willing to buy one for \$300,000. The New York Stock Exchange (the intermediary) then matches them together and executes the trade.

4. Bargaining.

No prices posted. Typically, the buyer approaches the seller, the seller sizes up the buyer, offers a price, and the two then higgle and haggle till a mutually agreeable price is reached. Such bargaining could be over a US\$0.20 bottle of water on the streets of Hanoi or a billion-dollar takeover deal on Wall Street.

I'm not sure if your book's characterization of auctions is quite right. For example, a trade on the NYSE is quite anonymous but I don't think we could consider it an auction. (Of course, one can define an auction so as to subsume all of the above mechanisms, but in that case we have wasted the word auction.)


How can CVS which has about 3 billion in cash on hand buy Aetna for 69 billion? How will CVS be able to buy Aetna for 69 billion if CVS only has 3 billion in cash without borrowing a large amount of money?  I understand that a company can trade for a multiple larger than 1 of their assets but how can they buy other companies which cost much more than their assets?  The market cap of CVS is 76 billion.  This is what CVS shareholders currently are worth.  How can they spend 69 billion of this and still own CVS?  Wouldn't they have to give Aetna almost all of their CVS equity in exchange for Aetna's equity?

One way this would make sense would be if it is more of a merger and that Aetna shares will become CVS shares.  So the value of the new CVS shares will be worth about the same as the value of the current CVS shares and the current Aetna shares.  There would simply be more shareholders in the new company - all of the existing CVS shareholders plus all the existing Aetna shareholders.

In this case, I suppose I could buy a large company like Google even if I only had a company with a market cap of 1 million.  Google's shareholders would simply own virtually all of the new combined company.

The deal is a mixture of cash and shares. Existing CVS shareholders get some cash, plus some shares in Aetna. It is likely that they would borrow in the bond market to raise the cash.

Yes, existing Aetna shareholders end up diluted. Ownership percentages in the combined firm will reflect the terms of the share conversion. The cash payment is there to reduce the dilution of Aetna shareholders, as it means that CVS shareholders get less Aetna shares.

You would only be able to take over a large firm as a small firm if the large firm’s shareholders want shares in a company that is managed by yourself. Unless you have a stellar reputation as a manager, why would they want that?


Elasticity of demand equals -1 but income decreases! In my textbook, it's stated that:

  When $\epsilon < -1$, demand is elastic and raising price will result in smaller income, while lowering price will result in bigger income.

  When $\epsilon = -1$, demand is neither elastic nor inelastic and change in price won't      result in change in income.

  When $\epsilon > -1$, demand is inelastic and raising price will result in bigger income,                 while lowering price will result in smaller income.

  $\epsilon = \%\Delta Q / \%\Delta P$.

This is the exercise I found confusing:

  Old price: 5

  New price: 6

  Old quantity: 25

  New quantity: 20

  Calculate elasticity

This is my solution:

$\% \Delta P = \frac{\text{new price } - \text{ old price}} {\text{old price}} = \frac{6 - 5} 5 = 0.2$

$\%\Delta Q = \frac{\text{new quantity } - \text{ old quantity}} { \text{old quantity}} = \frac{20 - 25} {25} = -0.2$

$\epsilon = \%\Delta Q / \%\Delta P = -0.2 / 0.2 = -1$

$$$$
This is why I am confused:

$\text{Old income} = \text{old price} \times \text{old quantity} = 5 \times 25 = 125$

$\text{New income} = \text{new price} \times \text{new quantity} = 6 \times 20 = 120$

Old income does not equal new income even though elasticity is -1!

What am I doing wrong? Am I misunderstanding the textbook?

$$$$
Edit: the answer provided is $\epsilon = 1.22$ but I have no idea where it comes from.

We discourage numeric questions as they are unlikely to be useful for future visitors but this is a very good example of why using non-marginal quantities can be misleading.

The exact definition of the price elasticity of demand is
$$
\epsilon(p) = \frac{d D(p)}{d p} \cdot \frac{p}{D(p)}.
$$
(In your notation $D(p) = Q$.)
By straightforward calculation you can show
\begin{eqnarray*}
\max_p & & p \cdot D(p) \\
\\
p \cdot \frac{d D(p)}{d p} + D(p) & = & 0 \\
\\
p \cdot \frac{d D(p)}{d p} & = & - D(p) \\
\\
\frac{p}{D(p)} \cdot \frac{d D(p)}{d p} & = & - 1 \\
\\
\epsilon(p)  & = & - 1.
\end{eqnarray*}
Whether a marginal price change increases or decreases revenue when $\epsilon(p)  \neq - 1$ can be seen from a similar calculation.

Note that the reasoning used above only stated that $D(p)$ reached its local maximum. It is possible that several local maxima exist and the global maxima is elsewhere.

So $\epsilon(p)  = - 1$ implies that the revenue cannot be increased by small (marginal) changes in $p$. So far I have used the concept of point elasticity. But your textbook uses arc elasticity, which measures non-marginal changes:
$$
\frac{\Delta Q}{Q} / \frac{\Delta p}{p}
$$
Some reasons to do this:

Arc elasticity can be measured empirically, point elasticity can only be approximated.
In case of small changes the two should be reasonably close.
Point elasticity requires some knowledge of calculus.

There are however also some problems with this:

No guarantuees are made by the $\epsilon(p)  = - 1$ condition for non-marginal price changes.
What base you should use for arc elasticity is not clear at all. You used
$$
\frac{Q_{new} - Q_{old}}{Q_{old}} \cdot \frac{p_{old}}{p_{new} - p_{old}}.
$$
Why is the old quantity and price the reference for the rate of change? Why is it not the new quantity and price
$$
\frac{Q_{new} - Q_{old}}{Q_{new}} \cdot \frac{p_{new}}{p_{new} - p_{old}}
$$
or the average of the two
$$
\frac{Q_{new} - Q_{old}}{\frac{Q_{new} + Q_{old}}{2}} \cdot \frac{\frac{p_{new} + p_{old}}{2}}{p_{new} - p_{old}}?
$$

These bases give you different values for arc elasticity. The second base gives you $1.2\dot{2}$ so it seems to be the one your textbook expects. I guess it is best if you see the difference between point elasticity that is used by the rule and arc elasticity. Other than this you have to ask your professor what definiton of elasticity she/he expects you to use.


Where can I retrieve a complete history of macro economic data annoucements? I'd like to get the complete ( well at least the last 20 years) history of economic data announcement calendar firstly for US and secondly for G5 countries.
I have found many websites that propose the real time calendar so they yield the upcoming economic announcement dates but do not keep the previous announcement date (or at max the previous year)
For instance:
https://tradingeconomics.com/calendar
or https://www.newyorkfed.org/research/calendars/nationalecon_cal.html
or https://finance.yahoo.com/calendar/economic/
Having the figures of the economic indicators would be a plus.
Any clues guys?
Thanks

Federal Reserve Economic Data (FRED) system may have some of the data you are seeking. For example the links below may be helpful directly or indirectly to inform your further search efforts.
FRED  recent release calendar:
https://fred.stlouisfed.org/releases/calendar
FRED web services release dates:
https://fred.stlouisfed.org/docs/api/fred/releases_dates.html


How the presence of increasing returns to scale lead to market failure How the presence of a sector with increasing returns to scale in a "perfect" economy may lead to market failure ? Can sb explain for me with the support of charts ?

Perfect competition in the economy leads to the theoretical presumption that with firms entering the market when prices are above their average total costs and leaving when they are below average total costs, the equilibrium point comes when prices are equal to average total costs, which in turn is equal to each continuing firm's marginal cost at a point where these marginal costs are increasing.  For each firm, their marginal revenue will be equal to the price set by the market. Consumers will see no firm whose marginal cost is below the market price, and so should regard the result as efficient.

With increasing returns to scale, marginal costs are never increasing for an individual firm.  The effect is to encourage the emergence of a single firm taking the entire market and having pricing power.  This natural monopoly will lead to that firm seeing that its marginal revenue is below its price (if it lowers prices then it may gain new customers at that new price but it will lose money on existing customers) and when it maximises profits by setting prices at the point where its marginal revenue is equal to its marginal cost, that price will be higher than its marginal cost, and so be seen as economically inefficient from the perspective of consumers.


What is meant by "Exchange rate expectations are static" (In the Mundell-Fleming model) When I was studying the Mundell-Fleming Model, I came across the assumptions :

1- Exchange rate expectations are static
2- Capital mobility is less than perfect

I ended up with the following questions :
Q1) Does capital mobility less than perfect implies $r \ne r^{*}$ where $r$ is the domestic interest rate and $r^{*}$ is the foreign interest rate. Or does it mean $r \neq r^{*} + \delta S^{e}$ Which is the UIRP
Q2) What is meant by "exchange rate expectations are static"?

The expression "Static Expectations" unfortunately can be found to be used with two different meanings in the economics literature

1) The one apparently less used but used nevertheless is, for some variable $x$ that needs to be predicted while standing at period $t$ (the superscript $e$ denotes "expectation" in the general meaning of the term, without specifying how it is formed)

$$x^e_{t+1 |t} = b,  \;\;\; \forall\, t$$

where $b$ is some constant. This reflects the following attitude: agents are oblivious to any information accrual as time passes, they even ignore possible movements in the realized values of $x$, and if asked, they always think that "tomorrow" the value will be $b$ (perhaps a better way to describe such expectations would be "fixed expectations" rather than "static").

2) The other and most widely used meaning of "Static expectations" is

$$ x^e_{t+k |t} = x_t, k=1,2,...$$

i.e. "what is will continue to be".

In the Mundell-Fleming model, the expression is used with this meaning.

(I note that with this meaning, "Static Expectations" coincide with Rational Expectations when the $x$-variable follows a pure random walk -but again, in Static Expectations we do not specify how we arrive at the value we expect).

Given this, imperfect capital mobility would lead to the domestic interest rate being different in equilibrium from the international interest rate in the sense $i \neq i^*$, since the exchange rate is not expected to change. So the Uncovered Interest Rate Parity (in logarithmic terms) $i = i^*+\Delta s^e$ becomes under Static Expectations $i = i^*$, and stops to hold under imperfect capital mobility.


Theoretical/Empirical Arguments for Migrant Workers in the US Consider the events that are developing in the US with regards to labor-intensive manual work and migrant workers. If more and more migrant workers are banished from the work pool, it remains a highly contested topic as to whether US nationals will able to pick up the slack. Let's say we're presented with both sides of the argument:

(These are of course generalizations to a certain extent, and I don't pretend to speak for everybody; I'm just simply trying to highlight some of the major concerns of both sides of the aisle)

Liberal: "Rethink your judgment on migrant workers. Americans are too soft for dirty jobs. Why else would so many unemployed people turn down the opportunity to work during a recession?"

Conservative: "It's not that we're too soft to work, it's just that the current labor market has a systemic bias against us. Why should we work for wages that are not fair?"

Liberal Americans put forth a compelling case that migrant workers are not stealing jobs from anybody, they are simply filling the jobs that Americans don't want to do. While in the past, Americans worked in labor-intensive industries like steel and manufacturing, but today's technologically-integrated America is different. Essentially, saying Americans are too soft for dirty jobs. Recent agriculture labor shortages in California illustrate a point along these lines.

Meanwhile, the conservatives also have a strong case that migrant workers are competitors for low-skilled US nationals. The low-skilled demographic are often considered the losers of globalization, as they are out-competed by migrant workers who will work harder on the job for less pay. Conservatives also cite net income flows from local communities. Many migrant workers send the bulk of their earnings back to their home countries, and at the macro level, it all adds up, their local communities lose economic vigor and deteriorate.

My question is: Is there anything in theoretical/empirical economics that can be brought to bear for this debate?

That is my question, although I realize some readers may find it rather broad, so I've included a few optional specific questions that you may answer if you feel so inclined.

Are there moral hazards in place? i.e. People would rather rely on welfare than work in an orchard?
Is it a case of too much/too little regulation? i.e. Due to burdensome regulations, it's too expensive to hire legit workers, and the cheap but illegal migrant worker is preferred?
If there is a "fair" equilibrium price that attracts local Americans, will that even be affordable to agriculture / other relevant industry companies? Might they not just mechanize?

Note: If possible, please do your best to criticize both views in the answer, so that political affiliation bias will be weeded out a bit and it also will not make it appear as though one is "better" than the other.

There is a broad literature that attempts to address the very question you pose- what is the impact of immigration (legal and illegal) on native wages? However, if you're interested in the 'real world' evidence, I'd suggest focusing on empirical labor economics as opposed to more theoretical labor models.

The reason for my suggestion is that theoretical economics makes no clear prediction without a lot more information. There are a variety of factors, such as the production function being considered, the labor market conditions observed, the relative substitutability of immigrant and native workers, etc. which tends to make answering the question more of an empirical exercise.

As far as the findings of the empirical papers, they actually tend to find relatively little impact of immigrant labor on native wages, with a few notable exceptions.

For some examples:

This survey paper, though a bit out of date as it's from 2005 outlines the results of 18 papers and finds wide discrepancies depending on modeling techniques and underlying assumptions used.

Borjas, 2003 is one of the better known works, and finds what one might expect based on Econ101 models- that an increase in immigrant labor supply leads to a decrease in wages for native workers.

A couple very well known articles have tried to tease out the impact of immigration on wages by focusing on particular events (called supply shocks) where the number of immigrants increased "suddenly" for reasons having nothing to do with the economic climate at the time. A pair of papers examined the impact of the Mariel Boatlift, which led to a spike in Cuban immigrants in Miami: The first, a paper by Card 1990 found no evidence of a negative impact of immigration on wages, while Borjas 2015 finds a substantial decrease in the wages for the least educated Miami residents.

Several other papers have found either no negative effect, or even positive effects, of immigrants on various worker wages. For example, this paper by Peri in 2011 finds no negative impact of immigrants on wages, but a strongly positive impact of immigrants on productivity. This paper from 2013 finds significant positive impacts of undocumented immigrants on the wages of native workers in Georgia.

Ultimately, the exercise of determining the impact of immigrants on wages really depends on the method of analysis and a number of underlying parameters, and applying "standard" (i.e. Principles of Micro) models can lead to erroneous results and a false sense of certainty.

If there's anything else in particular you're interested in, let me know and I'll try to improve the answer!

EDIT: Sorry, I forgot to include a link to this additional survey paper in the original answer!


Why does the Laffer curve for consumption have no peak? According to Trabant and Uhlig (2009), the Laffer curve for consumption has no peak.

As far as I can make out, the argument is based on the fact that money extracted by taxing consumption ends up back with consumers and then gets taxed again. However I don't understand why the standard idea that taxes deter activity doesn't create a peak.

This is not a general result. As the auhtors describe in page 10 of their paper, the result obtains only when government lump-sum transfers $s$ do not vary with tax revenues, and instead government spending $g$ does. Then consumption taxes do not affect labor supply, for any level of the tax rate. The relation becomes monotonic, and the Laffer curve with respect to the consumption tax rate becomes also monotonic. This is something that the authors are not very clear in the main text, but it can be detected in the various proofs at the end: they do not argue that the Laffer curve with respect to all three tax rates examined (consumption, labor, capital), becomes monotonic. Only its dimension with respect to the consumption tax.

And more over, on page 9, when government spending is fixed and it is lump-sum transfers that vary with tax revenues (their Proposition 2) they are not clear on what happens, with respect to consumption tax rate. They do say that here the usual Laffer curve emerges, but they comment on a scenario with $\tau^c$ fixed.

Mathematically, the result hinges on the different feasibility constraint that applies in the two cases (eq. $13$ for the fixed government spending case, eq. $14$ for the fixed-transfers case).

In the model, the difference between government spending and transfers, is that the first provides directly utility, while the second increases disposable income in a lump-sum fashion.

Consumption taxes affect utility: a higher consumption tax rate $\tau^c$ will decrease consumption and hence utility of the same income level. When this is offset by higher utility-generating government spending, while transfers remain unaffected, the incentives related to work/income generation ("activity") remain unaffected, pre-tax income remains the same, tax revenues increase: no extremum point in the Laffer curve. Essentially, this affect how much utility the individuals obtain from private consumption, and how much from government spending.

If alongside the increase in the consumption tax rate, we increase transfers keeping government spending fixed, this creates a substitution effect, a disincentive for labor income: it is better to sit back and collect, rather than work and collect. The individual can increase his utility indirectly, by decreasing the disutility from work. This creates conflicting forces: eventually, for a sufficiently high consumption tax rate (and a correspondingly higher level of transfers) he will decrease his labor supply and hence his labor income more than the increased transfers, thus lowering the consumption tax-base.

The above are of course static effects, "inside" each time period, since the Laffer curve is a static concept.


Tax multiplier in IS-LM model I should consider a following modification of IS-LM model:
IS curve is standard: Y = C(Y-T) + I(r) + G
In LM curve the demand for money depends now on after tax income: M/P = L(r, Y-T)
Price level is fixed in the short run
I need to solve for tax multiplier.
What I have done is that I took the full differential of two equations and got the following:

dY = C'(Y-T)dY - C'(Y - T) + I'dr + dG

1/pdM - M/p^2 * dP = Lr * dr + Ly * dy - Lt dT

Lr, Ly, Lt are partial derivatives
Next the book gives a hint to use Cramer's rule to solve for tax multiplier, but I am not sure how I can do it. Because to me it seems that I have 2 equations and 3 unknown variables

Hint:
The $T$ is variable itself so the total differential should read as:
$$dY = C'dY - C'dT + I'dr + dG \implies dY = \frac{1}{1-C'}I 'dr + \frac{1}{1-C'}dG - \frac{C'}{1-C'}dT$$
Furthermore, by Fisher equation $r=i-\pi$. Hence we have:
$$dY = \frac{1}{1-C'}I 'di - \frac{1}{1-C'}I 'd\pi + \frac{1}{1-C'}dG - \frac{C'}{1-C'}dT$$
$$(1/P)dM - (M/P^2) dP = L_r'dr + L_Y' dY - L_T'dT$$
again use the Fisher so:
$$(1/P)dM - (M/P^2) dP = L_i'di - L_{\pi}'d \pi + L' dY - L'dT$$
This is IS-LM model so you are looking for equilibrium output and nominal interest rate $dY$ and $di$. You have two equations and two unknowns. You can solve it even with substitution but you should probably follow the textbook's advice to use Cramer's rule.


Economics of clubs(sport gym, language course, etc) I am looking for economic research, theory or empirics, on production/profit maximization/competition for firms producing goods with network effects, such as clubs in which every one's utility depends on the number of other participants. As a producer, my goal is not only to produce the good, but to ensure that enough people consume it at the same time.

What are key papers in this area? What are keywords for me to search for Relevant papers?

No doubt there are other topics that have network effects, but one place to look is spatial common pool or pollution literature, where actions in location A have an effect in location B, and some coordination is required.

Papers include renewable resources e.g.:

  Kaffine, Daniel T., and Christopher Costello. "Unitization of
  spatially connected renewable resources." The BE Journal of Economic
  Analysis & Policy 11.1 (2011).
  https://www.degruyter.com/view/j/bejeap.2011.11.issue-1/bejeap.2011.11.1.2714/bejeap.2011.11.1.2714.xml

The acid rain problem (admittedly quite old):

  Mäler, Karl-Göran, and Aart De Zeeuw. "The acid rain differential
  game." Environmental and Resource Economics 12.2 (1998): 167-184.
  https://link.springer.com/article/10.1023/A:1008273509255

And things like pollen dispersal (self-promotion, but it is definitely clubs):

  Punt, Maarten J., and Justus Wesseler. "The Formation of GM‐free and
  GM Coasean Clubs: Will They Form and If So How Much Can They
  Achieve?." Journal of Agricultural Economics 69.2 (2018): 413-438.
  https://onlinelibrary.wiley.com/doi/full/10.1111/1477-9552.12235


Bellman equation corresponding to stochastic EZW recursive utility A bit of a basic question maybe, but I am confused how to write down the Bellman of this recursive utility function based on Epstein-Zin-Weil preferences and some stochastic constraints.
$$
U_t = \left \{(1-\beta) C_t^{1-\frac{1}{\eta}} + \beta[E_t(U_{t+1}^{1-\gamma})]^{\frac{1-\frac{1}{\eta}}{1-\gamma}}\right \}^{\frac{1}{1-\frac{1}{\eta}}}
$$
It already looks like a Bellman equation, Any pointers?

What you have there are the preferences under an arbitrary policy -- what some call the prevalue function. The only thing missing is the max operator. Written with maximization (and making the state and choice explicit), the Bellman equation is
\begin{align}
U(K_t, \epsilon_t) =& \max_{C_t} \{ (1-\beta) C_t^{1 - \frac{1}{\eta}} + \beta [E_t(U(K_{t+1}, \epsilon_{t+1})^{1-\gamma})]^{\frac{1 - \frac{1}{\eta}}{1 - \gamma}} \}^{\frac{1}{1 - \frac{1}{\eta}}} \\
\text{s.t. } & C_t \in F(K_t, \epsilon_t) \\
& K_{t+1} = G(K_t, C_t, \epsilon_t), \\
& \epsilon \sim \Phi
\end{align}
where $K_t$ is the state, $F(K_t)$ is the choice set, $\epsilon_t$ is some shock with CDF $\Phi$ (assumed to be revealed before choosing $C_t$; it doesn't need to be IID), and $G(K_t, C_t)$ is the law of motion.
Maximization with recursive preferences is pretty much the same as with standard time-separable preferences, and even plays well with dynamic programming methods (e.g. if you have some VFI code set up you can make the preferences recursive by just changing the prevalue function). The only real change is that we now have different aggregators over states and over time on the RHS of the prevalue function. These notes on recursive preferences may help, in particular section 5 ("Optimization and the Bellman Equation").
Making the constraints stochastic won't change the details of your problem -- it'll be similar to how you would formulate and solve the time-separable equivalent problem with a stochastic constraint -- unless you have some specific structure in mind which would change things for recursive preferences differently than for time-separable preferences. I can't think of such a structure off the top of my head, but I'm sure one could find them with some digging.
One thing that's different with recursive preferences is the utility scaling -- the period utility is scaled by $(1-\beta)$. This is discussed a bit on page 3 of the attached notes. The scaling allows utility to be measured in units of consumption, so that the utility of a sequence of sure-thing constant consumption levels is that same consumption level, i.e. $U(c,c,...) = c$. It's a good exercise to try showing this symmetry without the scaling to see how it comes out (if you do it with the risk aggregator, remember that the certainty equivalent of a sure thing is the sure thing itself).


Is it reasonable, in panel data, to use past values of explanatory variables as instruments to deal with simultaneous causality? I am trying to examine the determinants of economic growth, essentially regressing a number of variables upon economic growth. I face a problem that there is likely simultaneous causality between many of my explanatory variables and the dependent variable. To deal with it I am using instrumental variables. I was wondering would it be reasonable to use the past values of my explanatory variables as instruments for their current values?

Thank you so much for the answers.

I suggest looking into System GMM. It is a panel regression method that uses past values as instruments and is exactly what you're looking for, I think. It has a few restrictions that much be met, the most important requires you to have more cross-sections than time periods. Without seeing your model and other details that is all I can provide for help. I hope this works for you.


How to calculate the optimal wage and the optimal rent on capital in an economic model? In Dhondt & Heylen (2009)*, they specify a certain production function.

Under some standard model assumptions such as perfect competition and so on, they calculate the optimal wage as

$$  w_t = \frac{\partial y_t}{\partial l_t}  $$

and the optimal rent on capital as

$$  r_t = \frac{\partial y_t}{\partial k_t}  $$

with $k_t $ the capital per capita and $l_t $ the amount of labour per capita and $y_t $ the output per capita.

Now what's the reason of this equality? If it because if you maximize for profit, that the maximum is reached in:

$$  0 = \frac{\partial W}{\partial L}  $$
$$  0 = \frac{\partial W}{\partial K}  $$

and that this must mean, as W = TO-TK, with TO total revenues and TK total costs, that

$$  \frac{\partial TO}{\partial L} = \frac{\partial TK}{\partial L}   $$

and

$$  \frac{\partial TO}{\partial K} = \frac{\partial TK}{\partial K}   $$

?

So in this case, it would be explained if you see ... as ... :

$$  \frac{\partial TK}{\partial K} = r_t   $$

and

$$ \frac{\partial TO}{\partial K} =  \frac{\partial y_t}{\partial k_t}  $$

and

$$  \frac{\partial TK}{\partial K} = w_t   $$

and

$$ \frac{\partial TO}{\partial L} =  \frac{\partial y_t}{\partial l_t}  $$

Is this correct?

*Employment and growth in Europe and the US—the role of fiscal policy composition

I hope this answers your question (if not please let me know!), but the reason they get their wage and rental rates:

$$  w_t = \frac{\partial y_t}{\partial l_t} \text{ and } r_t = \frac{\partial y_t}{\partial k_t} $$

(I assume) is for the same reason most papers use that equation. Consider the firm's problem, that they want to maximize profit, which is (total) revenue ($p_t \times y_t$) minus costs (which we can consider as the total cost of labor, which is $w_t \times l_t$, and capital, which is the rental cost of capital times capital used, $r_t \times k_t$). Therefore, we're trying to maximize:

$$\max_{l_t,k_t, w_t, r_t} \{ p_t y_t - ( w_t l_t + r_t k_t ) \}$$

If we normalize price of the output to $1$, we can solve for the optimal prices of labor and capital by solving the above problem. Taking the inputs one at a time, we get the first order conditions for labor:

$$0 = \frac{\partial y_t}{\partial l_t} - w_t$$

Which, of course, rearranges to

$$w_t = \frac{\partial y_t}{\partial l_t} $$

and for capital:

$$0 = \frac{\partial y_t}{\partial k_t} - r_t$$

which rearranges to:

$$ r_t = \frac{\partial y_t}{\partial k_t} $$

Of course, these are pretty standard derrivations across different fields of economics, so their exact reasoning might be slightly different, but this methodology should provide some of the clearest insight into why that's the case.


Regression over the whole population What's the meaning of the standard error of a coefficient in a regression when the whole population is included?

I've been so puzzled by this question. Because it seems to me, standard errors make no sense when the whole population is included -- there is no need for statistical inference since you already have the whole population.

But it is so widely used even by many articles published in top journals. For example, if I am examining the relationship between a country's GDP growth rate and its population density, I run the regression:

$$ GDP_i = \alpha + \beta Pop_i + \gamma \mathbf{X}_i + \epsilon_i$$

with all 195 countries on the earth. In the case, all countries (the population) are included. But all literature still talk about the statistical significance of the coefficients.

Could somebody explain is it a misuse of statistical inference when regressing over the whole population?

It's important to consider what exactly the population is about which an inference is being drawn.  It's easy to overlook the time aspect in this context.

Suppose for example that the aim is to forecast the next two years' GDP for each country in the world. Then the population of interest is a set of pairs of the form "country, year".  It isn't simply "all countries", and even if a forecast model has been estimated by regression on current and past years' data for each country, that doesn't mean that the whole population of interest has been included.

If one really does start from a complete dataset for the whole population of interest, then all one can do is calculate summary statistics. That could include standard deviations, but it would be inappropriate to call these standard errors, since that term relates to a sampling distribution whereas the only "sample" in this case is the whole population.


What's the actual relationship between deflation, spending and saving? I am pretty confused with this concept. Since deflation is a result of decreasing prices, it means that the demand for goods and services rise therefore stimulating more spending. But on the other hand it is also a matter of fact that it encourages people to save (see potential in the increasing value of money over time).

Think about the permanent income hypothesis. People's spending is dependent not just on present income, but also the future stream of income. A deflation usually indicates a recession. The central bank is trying to optimize monetary policy subject to a short run Phillip's curve.

$$\min_{u, \pi} V(u, \pi) = -(u^2 + \pi^2)$$
such that
$$u = u^* + k(\pi^e - \pi)$$

where $u$ is unemployment, $u^*$ is the natural rate of unemployment, $k$ is the sensitivity of the tradeoff, and $\pi^e$ is the market expectation of inflation.

If you find a Nash equilibrium for this game with credibility in the model, then the Federal Reserve will want to target a constant steady rate of inflation. If the economy falls into recession, they will in return try to raise inflation, because in the short run it serves as a tradeoff with unemployment, so though the Fed is causing more inflation, hopefully they will stop too many people from losing jobs (note the loss function for the Fed in this case is convex). If the Fed tries out monetary policy and still sees deflation, then you can tell the recession is pretty rough, if that makes sense.

So even though the price of goods falls, wages on average will fall, and production will fall. So demand in the economy will fall. Those who do still have a good job are doing better on average than those who become unemployed, and they might dissave in periods where expected income in this recessionary period might be lower than future periods where the economy is doing well, but in reality, most people will be liquidity constrained and will be saving what little they can while drastically cutting back on spending. Usually. There are exceptions (think of payday loans).


How to calculate Real GDP from quarterly change How do I calcualte a countries Real GDP from QoQ changes?

Example - Australia
2018 - Real GDP was 1432195178668.32 $Billion
2019  Q1 was 0.5%
2019  Q2 was 0.6%
2019  Q3 was 0.4%

How do I calculate real GDP on Q3?

Assuming 1432195178668.32 was the last value in Q4 2018 you got, just calculate 1432195178668.32 * (1.005) to get the 2019 Q1 Value, save the value. Then take 2019 Q1 * (1.006) to get the next value etc. Easy to do via R or Excel.

Basically if you had an increase x just multiply by (1+x) where x is in decimals, so a change of -0.75 % becomes * (1 - 0.0075)

Then, simply take the average of the four quarters if you want the annual value:
$$ \frac{(Q1.2019 + Q2.2019 + Q3.2019 + Q4.2019)} {4} $$


Real Analysis and Economics Is there any application of the Heine-Borel theorem or the Bolzano-Weirstrass theorem to Economics?
Also where are the notions of compact sets and elementary Real Analysis used in Economics?

There are too many applications of the concepts and results you mention for a list to be of any use. As a first introduction, look at:

Real Analysis with Economic Applications, Efe A. Ok (here, here, and here)

There used to be pdfs of (reasonably high quality) working version of the book available online, but they are harder to find now that the book is out (I believe the author put these working versions online as a way to get feedback and typo-reports but removed them since then). If you look hard enough, some of these working version might still live in corners of the internet though.

Also have a look at this related question: What are some applications of Real Analysis in Graduate Economics?


Did Elinor Ostrom (or others) resolve the tragedy of the commons for common-pool resources? Ostrom (2015: 19) writes:

Individuals or households who have rights to withdraw resource units
from the CPR must be clearly defined, as must the boundaries of the
CPR itself.

Following her definition of goods (see matrix below) I understand that they effectively describe institutional arrangements for organising access to delimitable commons (= high substractability) within delimitable communities (= high exclusion). Consequently they would describe collective action for private goods.
Did they also discuss institutional arrangements for organising access to commons (= high substractability) between communities in a global society (= low exclusion), i.e. for common-pool resources, such as the climate?

Source: Hess & Ostrom (2007)

Depends on your definition of 'resolve'.  In economic there were already proposed solutions for both public good and common-pool resources. However, most of those require some sort of government action, for example Pigouvian taxes/subsidies or in some cases government ownership/provision.
To be more specific before Ostrom and others, literature split goods mainly as either public or private goods (see Samuelson 1954), where it was argued that private goods can be provided by the market and public goods require 'top down' government involvement in one way or the other.
Ostrom's (and her coauthors) contribution was mainly twofold:
First, she showed that actually there is more nuance to this and that there are more dimensions to goods than simply being public or private as the matrix in your question shows (Ostrom 2005). To be fair the category of 'club goods' was already introduced by Buchanan (1965), but she added the idea of subtractability and the fourth category (Ostrom & Ostrom 1977).  Furthermore, she also showed that incentives people face between the public good and common pool resources are different and not similar as previously thought.
Second, she showed that actually once you split public goods into multiple categories, there is a category of common pool resources where 'top-down' government involvement is not necessary and the resources can be managed privately (where by privately in this case is mean to mean without government involvement) or with 'bottom-up' local government (Ostrom 1962; Weschler 1968; Warren 1966; Ostrom 1965, Ostrom 1990, Ostrom 1999, Ostrom 2005). However, her work was not really focused on developing solutions to these problems as much as describing and empirically examining how different communities manage to find solutions to these problems, and those solutions are often case and place specific (for example, the Netherlands where I live has a specific parallel local government for management of dams that is virtually separated from central government with its own local elections and separate structure called Water Boards that would likely qualify as the 'bottom-up' local solution Ostrom was advocating).
However, her work does not really contain specific proposal of resolution, rather as she herself put it in her Nobel Prize lecture:

The most important lesson for public policy analysis derived from the
intellectual journey I have outlined here is that humans have a more
complex motivational structure and more capability to solve social dilemmas
than posited in earlier rational-choice theory. Designing institutions to force
(or nudge) entirely self-interested individuals to achieve better outcomes has
been the major goal posited by policy analysts for governments to accomplish
for much of the past half century. Extensive empirical research leads me to
argue that instead, a core goal of public policy should be to facilitate the development of institutions that bring out the best in humans.

Hence, her solution was to put it simply to just create framework that allows people on local/private level  to find their own unique and specific ways of resolving the problems, which will likely be different depending on local context (e.g. culture etc).
However, I would be hesitant to say that this was a resolution of the tragedy of commons for three reasons:

If you actually take a deep look at the models that study/describe 'resolutions' that arise privately/locally from 'bottom-up' they often show that although this is substantially better than situation without any mechanism or more efficient than government 'top-down' solution they are still not always provided as efficiently as could be done if there would be no such problem (e.g. as in case of private goods). To see that you can have look at the Mueller Public Choice III - the most comprehensive textbook on the public choice (i.e. area of economics that deals with these issues). This is not to say that this would not be the best solution given alternatives, but it does not fully eliminates the problem. To give an analogy if you loose leg, having some modern prosthetic is more efficient than living without leg, but to the extent that the prosthetic is not as good/better as original leg I would be hesitant to call it a resolution of the problem.  In fact Ostrom (1999) herself often describes these solutions as 'coping with the tragedy of commons' rather than 'solving the tragedy of commons'.
Since you wanted to discuss Ostrom, most of the above focuses on her work, but while her work is immensely appreciated, and her Nobel Prize was definitely deserved, it is fair to say that most mainstream economist would argue for much greater top-down government involvement with Pigouvian taxes or cap-and-trade even in cases of common pool resources which she criticized (although here the point 1 would still apply but for different reasons - e.g. it is very hard to know what the optimal Pigouvian tax is).
Rather than developing solution to the tragedy of commons it  was an observation of how people manage to overcome it privately or on local decentralized level of government. This is by no means critique of her work, she was obviously excellent scholar, but saying she resolved the problem would be like saying that Adam Smith resolved the problem of low productivity problem by division of labor, whereas he rather provided an explanation and advocated for something he observed by visiting manufactures and the division of labor was 'invented' as a 'solution' to increase productivity by people not him.


Bidder Count Impact on Uniform Price Economics Say we have an uniform price auction where 1 really rare stamp is for sale.  Only 5 randomly selected stamp collectors are invited to bid and the stamp ends up selling for 1 million dollars.  Now pretend that auction never happened.

If 6 randomly selected stamp collectors were invited instead of 5 in the previous example (again, original auction never happened), what expected percent increase in revenue should the stamp sell for - 10% more, 15% more?  Similarly, what if only 4 bidders were allowed to the auction?

In short, I'm trying to determine how increasing or decreasing bidder participation by 1 impacts the ultimate selling price on a percentage basis.  I'm sure lots of variables are at play, so am not sure if any economic theory can be used to address this.

It is a known result in Mechanism Design that both first-price as well as second-price auctions yield the same expected revenue, under certain conditions (like independence of valuations, private information, etc). Consult   Jehle, G. A., & Reny, P. J. (2011). Advanced Microeconomic Theory (3d ed.), ch.9 on Auctions and Mechanism Design, for a very accessible exposition of the basics, as well as for the full set of conditions that must hold.

The answer to your question is bound to be distribution-specific. Assume as an example, that, from the point of view of the seller, all (unknown to him) valuations of the bidders for the object for sale, come from a Uniform $U(0,1)$ distribution: this implies that we have normalized the value of the object for sale and that we express the possible valuations of it as a percentage of its possible maximum value, which is assumed common for all bidders. I.e. What we say here is :"we don't know how much each bidder actually values the object, but we do know that the maximum possible valuation by a bidder will be some $V>0$, and this $V$ is common to all bidders". We do not assert that there exists some bidder that actually values the object at $V$.

In such a setup, the Expected Revenue of the Seller is

$$ER(N) = \frac {N-1}{N+1} \tag {1}$$

where $N$ is the number of bidders. Again, this essentially expresses expected revenue as a fraction of the object (unidentified) maximum value.

Now you can play around with $N$ to see how the expected revenue changes, in absolute, relative and percentage terms. It sure isn't changing linearly, but it is everywhere increasing in $N$, approaching unity (i.e. the object maximum valuation).

This should be intuitive in the framework adopted: the more the bidders are, the more probable becomes to obtain higher and higher valuations of the object, and so also to sell it at a higher value.


Should the seed be set in forecasting returns in a MCMC Suppose we are estimating a linear model utilizing a Markov Chain Monte Carlo technique such as a Gibbs sampler, drawing from the posteriors in a Bayes framework.  Suppose the full sample of data we have is from time $t = 1, \dots,\tau\dots, T$, and we want to forecast returns one period ahead using a recursive window starting at time $t = \tau$ until time $t = T$. We have trained the model from time $t=1$ to time $t=\tau$, then we want to forecast returns out of sample at time $t=\tau+1$:

\begin{equation} y_{\tau +1} = \beta' \mathbf{x}_\tau + \sigma \varepsilon_{\tau + 1}, \; \; \varepsilon_{\tau + 1} \sim \mathcal{N}(0,1) \end{equation}

When I tried this without setting the seed at each period the error term $\varepsilon_{\tau+1}$ was so stochastic across the $I$ iterations of the MCMC algorithm that $y_{\tau+1}$ was essentially a random walk.  When I set the seed at each period such that the $I$ iterations in the Gibbs sampler used the same $\varepsilon_{\tau+1}$ I found much better results in terms of RMSFE.

Should we set the seed in the random number generator in each period $\tau$, such that all $I$ iterations of evaluating $y_{\tau+1}$ use the same error term $\varepsilon_{\tau+1}$ when computing this forecast?

My understanding is that the standard advice is to randomly select a seed value, and then keep that seed for your entire analysis. This allows the same computer code to give identical results each time.

See, for example, the Stata manual:

  Stata’s random-number generation functions, such as runiform() and
  rnormal(), do not really produce  random  numbers.  These  functions
  are  deterministic  algorithms  that  produce  numbers  that can  pass
  for  random. runiform() produces  numbers  that  can  pass  for
  independent  draws  from  a rectangular distribution over[0,1);
  rnormal()produces numbers that can pass for independent draws from
  N(0,1).  Stata’s random-number functions are formally called
  pseudorandom-number functions.The  sequences  these  functions
  produce  are  determined  by  the  seed,  which  is  just  a  number
  andwhich  is  set  to  123456789  every  time  Stata  is  launched.
  ... If you record the seed you set, pseudorandom results such as
  results from a simulation or imputed values  from mi impute can  be
  reproduced  later.  Whatever  you  do  after  setting  the  seed,
  if  you  set the seed to the same value and repeat what you did, you
  will obtain the same results ... It does not really matter how you
  set the seed, as long as there is no obvious pattern in the seeds that
  you set and as long as you do not set the seed too often during a
  session

However, if you are using parallelization to do many separate simulations then you need to make sure that you do not use the same seed, or a time based seed, on every node:

  Properly seed your generator. Even the state-of-the-art Mersenne
  Twister ran into problems early on because the authors had neglected
  the issue of proper seeding....This rule is VITAL if you are going to
  run parallel simulations on a Beowulf cluster for example.The simplest
  way to seed a RNG is to take something like the current time e.g.
  using the time() function found in Unix and most C libraries, which
  returns a 32-bit integer giving the number of seconds since 1st Jan
  1970. ...Hundreds of jobs on different nodes will be starting at almost exactly the same time –therefore many of your jobs will be
  starting with exactly the same seed and therefore those that have the
  same seed will generate exactly the same results(assuming your code
  has no bugs in it).

Good Practice in (Pseudo) Random Number Generation for Bioinformatics Applications


Maximum-support Nash equilibria in zero-sum games Context: I would like to know how likely a player is to pick a specific action, provided that he plays optimally and the action is optimal. Phrased like this, the question is ill-defined. But is there some way around the problem?

Details: I have a zero-sum symmetric matrix game. Is there some good notion of a Nash equilibrium with a maximum support [edit: maximum among the NE strategies]? Like something along the lines of "take the center of the simplex of NE strategies"?

The question: Is there some canonical solution to the vague question above? Possibly something already written down in a textbook or a paper. (It would feel silly to reinvent the wheel.)

I am not sure about what exactly you mean by the maximum support NE but you may want to check the concept of Correlated Equilibrium. Any convex combination of NE payoff profiles is a Correlated Equilibrium (but not vice versa in general). So, what you wrote made me think about that. However, I don't think it makes much sense to use correlated equilibrium since, you know, there is no obvious advantage of correlation. Also, the NE payoff profile must be constant in your environment.

Another thing that comes to mind is restricting the attention to super-modular games. Then, you get a nice lattice of NE. So, I don't know if this makes sense either.

I would suggest playing around with some examples to understand what exactly it is that you want to characterize and asking a new one based on your examples.


How huge is the multiplicator of social welfare in current societies? If you give somebody with a high consummate some extra money, most likely it will be spent. Having this spent for e.g. groceries this will make sales man, farmer, ... employed so they pay taxes are buy groceries for their own. How huge is the multiplicator on this for modern services oriented societies?

Keynesianism (what you're apparently basing this on) is incoherent and relies on arbitrary eigenvalues such as "autonomous consumption". In real life the multiplier is small and inconsequential.

However, the multiplier may appear close to one or slightly above simply because GDP increases the instant the government approves spending in public-subsidised enterprises, due to the way GDP is defined. For example, let's say the government spends $1 to subsidize Fannie Mae and this is counted as a consumption item (for whatever reason). GDP immediately increases by a dollar. Now Fannie Mae spends this on some irrelevant bureaucratic expense (buying mortgage derivatives, legal fees, financial services etc). GDP increases by a dollar again. So we just achieved a multiplier of two while having absolutely no effect on the real world.

As you can see, measured GDP is subject to all sorts of random problems that make any attempt to calculate the multiplier pointless.

Furthermore, strictly speaking, the "multiplier" is only technically supposed to apply to government consumption, and not transfers as you are asking about.


What is the difference between quarterly GDP and annual GDP? I didn't understand how quarterly GDP is calculated. If GDP means Gross Domestic Product in a year, then what does quarterly GDP mean Gross Domestic Product in a quarter? OR it is multiplied by $4$ to estimate for a annual number? I appreciate the help. I tried google but cannot seem to find a page that explains it.

You might not find a page explaining (in an easy manner) how quarterly GDP is calculated because it is done by several different means in different countries and the calculation/estimation methods can get confusing. If you want to know how a certain country generates a quarterly GDP figure, you should check the country's official economic statistics page - the descriptions of the statistic usually list at least something about the collection process.

Usually quarterly GDP is done with a smaller sample and has some estimations done (often based on last year's data). Annual GDP is usually the more accurate measure with a larger sample and more revision time between collection of data and publishing it.


How does buying assets change net capital outflow? I am really confused and I hope you can help me.
I know NCO is equal to acquisition of foreign assets by residents – acquisition of domestic assets by nonresidents.
But I can't understand the transactions without purchases of goods.
For example, when an American buys a share of a foreign company, acquisiton of foreign assets by residents increases, and I think acquisition of domestic assets by nonresidents(American dollars) should also increase. So these changes should offset each other and the transaction shouldn't affect the net capital. But I know this transaction increases US NCO.
So, what am I missing ?

Net capital outflows from the US would increase. Net capital inflows for the foreign country (investment) would increase. This keeps the accounting equation equal. For the US S-I would increase, thus creating a balance of trade surpluse (even though these are financial assets). For the country receiving the inflow S-I (savings-investment) would decrease, increasing their deficit (assuming the balance of trade began equal). This balances both sides of the trade. Our net capital outflows grow by an equal amount to their net capital inflows in this situation.


What are the widescale economic ramifications of people holding onto their money instead of spending it? Pretty simple question: people get rich by saving more money than they spend. What are the implications of people holding onto their money instead of spending it?

Do rich people save more money (ratio-wise) than less rich people?

The amount that people save depend on the marginal propensity to consume (MPC), i.e., part of the additional income that a person consume, hence, $1-MPC = savingrate$. Keynes assumed that with increase in income MPC would increase, while neo-Keynesian assumed it to be constant in their analysis. But real data shows that MPC increases with elevation of income but decreases with large income gains. Hence, in a way, rich people save more relatively to others. But that is not the reason why they are rich, more saving is the effect, not the cause. Mostly, the reasons behind getting rich are the apt investment decisions.

When an economy hold more money, consumption reduces leading to reduced outputs. This in return decreases real income. Since, in equilibrium savings equals investment ($I = S$), so actually there is no increase in savings and we are left poorer with lower income levels. This is called the paradox of thrift, suggested by Keynes.


Why doesn't Barnes and Noble just lower its prices? For my birthday, I wanted a cookbook. So I went to Barnes and Noble and selected it: $40.

Before I got the register I checked it on Amazon: $20.

I started price matching every single cookbook I was interested in and collectively, i could save 60% on Amazon.

So why doesn't B&N just lower their prices already?

Doesn't it make sense to sell 10 products at 0.50 cents each than to not sell 10 products at 1.00 dollar?

Isn't that how that guy who owns all those Family Dollar stores is able to bank? He makes a nickel to a dime for every product he sells but sells many products that he is now banking it?

USNews stated in an article that B&N themselves stated that their prices are so high because they wanna provide for income for their authors and prevent Amazon from becoming a monopoly. Pardon my French, But that sounds like bologna!

Furthermore, they don't price match. Not even with their own online website.

Is B&N slowly slitting its own wrists? Are these stubborn CEOs who just don't want to face reality?

Or is there some economic strategy here? Like they're waiting out something?

Kling's maxim: Price Discrimination Explains Everything
Who are the sorts of people that purchase at Barnes & Noble? Less price elastic buyers, like those that are purchasing a gift, those less comfortable with buying online, those that value in store recommendations and assistance, and those that just like the in store experience. Barnes & Noble wants to maximize profits, not maximize revenue. Selling to more price sensitive buyers like you means also lowering prices for less price sensitive buyers.
Say the cookbook costs Barnes & Noble \$15 to buy. If they set the price at \$20 they make \$10 of profit selling one copy to you and one copy to the price inelastic buyer. If they set the price at \$40 they make \$25 in profit selling just one copy to the price inelastic buyer.
In summary: Barnes & Noble targets buyers willing to pay high prices and lowering prices means making so much less per unit sold that they cannot make up the lost profits on higher quantities


Simple cost analysis question I am stuck at a very simple problem:

Suppose, I am running out of insurance, and as a result, I am incurring a the cost of A with event 1 + the cost of B with event 2. Now, I go ahead and buy an insurance that will protect me from event 1, but will incur me a total cost of C. I will remain vulnerable to Event 2.

What is the total profit I am receiving from making the investment.

Logical calculation is,
Prior total cost: A+B
New total cost: B+C
Total profit: (A+B)-(B+C) = A-C

But my mind is constantly pesking me with the total profit to be: A-B-C.

I am essentially doing cost-benefit analysis.
Can someone please tell me where I am wrong?

I know my benefit function to be A, and not A-B. Please indicate what is wrong.

This feels like trying to read your mind, so I’m probably wrong. I will venture an answer regardless :D . I think that what is happening is that the benefit from buying the insurance is certainly the reduction in exposure: A-C. However maybe you are thinking about the remaining exposure after buying the insurance, in that case it is (A-C) + B. So I think you are thinking about the total costs after buying insurance while the question was asking about the change in costs. I prefer the term exposure, but I thought that using your terms will make the exposition  clear.

P.S. I hope it is understood that we are not literally adding costs, since they occur in different states of the world, but rather using it as a short hand notation to focus on the relevant issues.


How to average CDFs of one variable across years I have wealth-to-income data for 10 years. I computed the cdf of this variable in each year.
Now I'm trying to average the cdfs across years. In each each, the number of observations is different.
Does anyone know how to do it?
Thank you in advance.
Susan

Why don't you just take a weighted average?
Suppose you have ten years $t \in \{1,...,10\}$ and year $t$ has $N_t$ observations such that in total you have $\sum_t N_t=N$ observations. Let the year-$t$ CDF be $F_t$ with support $[\underline w_t,\overline w_t]$.
You can then define a weighted average CDF as
$$\overline F (w) = \sum_t \frac{N_t}{N} F_t(w).$$
This gives you a cdf, an increasing right-continuous function ranging over [0,1] with support $\cup_t [\underline w_t,\overline w_t]$. However, you have to pay attention to the individual supports, i.e., $F_t(w) =1 \forall w>\overline w_t$ and $F_t(w) =0 \forall w<\underline w_t$.