What are some different methods for pricing electricity? I know that in New Zealand, the wholesale price of electricity is set using a spot market, whereby every half hour, each of the electricity producers provide offers for how much electricity they can supply at each price level, and then when the actual amount of electricity is used, they producers are paid at the highest value need for all units of electricity supplied, with the lowest offers being utilised first.

The market is regulated by the Electricity Authority, which is an independent crown entity, while the transmission of electricity is managed by Transpower, which is a state owned enterprise.

In practise what this means, is that the producers will offer their renewable energy for free, and price their coal/oil at a higher rate. Some coal/oil is always needed and so this higher rate is determines how much the producers are paid for their cheaper energy supplied.

My question is, how else can and are electricity prices determined around the world?

In most of Europa the physical price for electricity is determined in day-ahead spot auctions. Essentially it is a free market, where anyone can buy and sell power, given you that you can fulfill the regulation set forth by the different national power exchanges and system operators.

This means that every day before 10.00 - 12.00 AM all producers and consumers must have told how much power they wish to sell and buy. From 12.00 and to around 12.42 a number of welfare optimization algorithms are run. After this, the different power area prices are published, along with the supply and demand curves for almost all countries.

In essence it is a where supply meets demand. This is complicated a lot by different bid-types, power connections across borders, physical constraints on cables and so on, but you can download the newest curves from Germany and France each day from epex.com if you want.

Because there is a lot of competition, you will mostly see power producers selling their power at their marginal costs. Because of subsidies this means that renewable energy sells as low as -300 euro pr. MWh - yes, they actually in some cases pay people to take their product. Nuclear and lignite power is around 10-18 EUR, the comes cheap coal and hydro (depending on season), the more expensive coal, gas and finally oil. From the price you can more or less tell which kind of production is running in any given hour.


How can countries be in so much debt? You regularly hear in the media how countries are billions or even trillions of US dollars in debt. How does a country get so far in debt, and who is it in debt to? How can countries of the world operate owing such vast amounts of money?

How does a country get so far in debt, and who is it in debt to?

Mostly because of government-issued bonds. These can be held by other governments, private entities or even the various government agencies: In the US, starting with the last category:

  Intragovernmental Holdings. This is the portion of the federal debt owed to 230 other federal agencies. Intragovernmental holdings total $5.6 trillion, almost 30 percent of the debt. Why would the government owe money to itself? Some agencies, like the Social Security Trust Fund, take in more revenue from taxes than they need. Rather than stick this cash under a giant mattress, these agencies buy U.S. Treasurys with it.

  Debt Held by the Public. The public holds the rest of the national debt of $14.7 trillion. Foreign governments and investors hold almost half of it.

Since I see you're from the UK... over there bonds are called gilts. And here's a breakdown of their ownership from 2009 (since that's what I could easily find):

  The biggest owners of gilts are insurance companies and pension funds. For them, gilts are predictable investments, which are particularly useful when a low-risk product is needed. Pension funds, for example, will usually switch an individual's holdings from higher risk investments, such as shares in companies, and put them in gilts as the person gets closer to retirement.

  Next on the list comes investors overseas. Unfortunately, nobody keeps records showing in which countries these gilts are held. This is in contrast to, for example, the US, which regularly publishes lists of the countries that own its Treasury Bills. So we know that at the end of 2009, $302.5bn (£196bn) of US government debt was held in the UK, making the UK the third-biggest investor behind Japan and China.

  The next biggest category holding UK government debt is banks, which includes the Bank of England. Since March 2009, as part of its quantitative easing programme, the Bank of England has bought just short of £200bn of gilts, making it the third-biggest holder of UK government debt.

And a more recent (2017) article (although lacking a pretty graph) roughly paints the same picture for UK's debt:

  Traditionally, around 40% of UK public debt was held by pension funds and insurance companies, which form a captive market because of their need for predictable and safe long-term investment returns. Around a quarter was held by other UK financial institutions and households, and the rest by overseas investors.

  QE [quantitative easing] has disrupted this pattern. Now, around a quarter of issued gilts are held by the Bank of England under its Asset Purchase Facility. Official data still show overseas holdings at around 27%, with insurance and pension funds’ share down to 28%, and other UK financial institutions holding around 40%. But once the store of gilts sequestered on the Bank of England’s balance sheet is excluded, overseas buyers account for 35% of gilt holdings and other central banks another 11%.

  Uniquely, more than 10% of the UK’s debt cannot be traced to either domestic or overseas buyers due to the paucity of data from the regular auctions. Lack of clarity on who’s holding the debt makes it harder to judge the risks of buyers selling-off or staying away. That fuzziness that may have helped to keep the markets calm.

How can countries of the world operate owing such vast amounts of money?

It depends on the country. Countries whose currency is attractive enough, e.g. the US dollar can "get away with it" by "printing" more money (see quantitative easing), although they can't do that too fast because that can cause inflation. The bonds of the big countries have had somewhat of "miraculous" negative real interest rate in the short run recently (although lacking a pretty graph):

  UK national debt is currently issued at a yield of less than 1% – far below the rate of inflation (2.6% in July). And this means Britain can effectively raise money free of charge in real terms. [...]

  So why are UK bonds still flying off the shelves, allowing the government to plug the gap in its spending plans with virtually “free” money? It is possible that investors are snapping-up new gilts simply through a lack of alternatives. If (as some fear) overpriced stock markets and property are about to crash and once-buoyant emerging markets are in trouble then the public debt of stable rich countries becomes the least worst option. US and German debt issues are proving similarly popular at rock-bottom yields.

Although this year the bond rates are expected to tighten, they are still mostly negative in real terms (for the big boys, but not so much for the smaller fish with weaker economies; the exception being the US which slighly above zero):

  Negative real borrowing costs add fuel to markets that are already on fire, limiting the downward pressure on bonds, keeping corporate spreads on the tight side and pushing stocks to new high after new high. [...]

  For investors, it’s a chicken and egg scenario. They’re crying out for policy “normalization” - higher rates and less central bank “interference” in markets - but are enjoying the asset price boom that’s in large part a direct consequence of central bank largesse.

Countries whose debt is denominated in a foreign currency, or a currency they can't print for some other reason, e.g. being in monetary union (ahem, Greece) can be in a world of hurt if they suddenly are threatened by default (inability to pay back on schedule). Typically the IMF steps in but it also imposes conditions in terms of structural reforms etc. for their bailouts.

E.g. news from July this year:

  Greece is scheduled to end nearly a decade of external help this August, after implementing more than 400 policy measures demanded by creditors. The yield on the 10-year government bond has fallen about 30 basis points in the wake of the recent debt deal. It moved from standing at about 4.2 percent to 3.9 percent. In contrast, Italy’s 10-year yield currently stands at 2.668 percent and the U.S.’ at 2.85 percent.


A market correction for an industry which has had long-run negative externalities Take a market where there have been long-run negative externalities. That is to say, the negative externalities have been in place long enough to have played a part in the investment decisions for all extant fixed capital.

Capital costs are a significant part of total costs.

The proposal now is to correct this market inefficiency, efficiently and quickly. Pricing in the negative externality should eventually, in the long term, correct this efficiently. However, as all the extant capital is a sunk cost, and can continue to operate at low operating cost, it can hinder and crowd out new entrants.

So the ongoing costs by the incumbents are low: their fixed capital was built and initially operated in a world of negative externalities, and those capital costs are both (a) sunk costs and (b) fully written off by now. Merely pricing in the negative externalities from their ongoing activities won't change the effective subsidy they've received that allowed them to build up their incumbency in the first place; so they'll have no incentive to leave the market.

What else can be done, in addition to simply pricing in the negative externality, to ensure prompt replacement of fixed capital which only exists because it was built in a time when it did not need to bear its full cost? Differential taxation for incumbents versus new entrants, or something else? How can this be done with economic efficiency?

The market in this case is fossil fuels for transport, heat and electricity generation; so the long-term is of the order of decades, whereas the need is for faster capital replacement. Additionally, several large suppliers exert oligopolistic influence, and there is a global cartel operating (OPEC), and has been for over 50 years.

An aspect of the matter could be described as follows:
We want

  prompt replacement of (existing) fixed capital

because, I guess, it creates currently "unacceptable" levels of negative externalities, and we know better than to think that through the pricing of the externalities we will be able to reverse the damages, and all swell.

From this point of view, we don't care about distribution between suppliers: it should be equivalent to us whether the existing companies change their capital base, or whether there appear new entrants with new cleaner technologies which will somehow drive out of business (or marginalize) the incumbents.

Let's describe the situation with very simple relations:

Prior to any pricing of externalities, the typical incumbent (symbolized by $h$ where needed) has a after-income-tax profit function at current time $t$

$$(1-\tau)\pi_{t} = (1-\tau)\big[p_{t}q_{t} -c(q_t)\big] \tag{1}$$

The OP writes that installed capital is "fully written off by now". This means that there is no income tax offset from accounting depreciation, Of course there is a capital base here that operates, needs maintenance, some marginal replacements etc. These costs are captured in the operational cost function (i.e. we assume 100% depreciation rate for them).

Assume now that we declare that anyone who continues to use the existing technology will pay an enviromental tax that is linear in quantity, $T_t = \xi\cdot q_t$ (naturally, this tax does not decrease taxable profits). Alternatively, he will be exempt from the tax if he completely renews his capital base, with new technology.

The incumbent now has to compare two discounted cash-flow scenaria:

$$\text {OLD} : NPV_{Oh} = \sum_{t=0}^{T} \left(\frac 1{1+r}\right)^t\big[(1-\tau)\pi_{ht}-\xi q_t\big]$$

and

$$\text {NEW} : NPV_{Nh} = -C_R-I_N+\sum_{t=0}^{T} \left(\frac 1{1+r}\right)^t\big[(1-\tau)\pi_{ht}+\tau\cdot\frac 1T(C_R+I_N)\big] \tag{2}$$

where $C_R$ measure the (capitalized) side-costs of renewal (disposal, disruption of operations etc), while $I_N$ is the needed new investment (including perhaps adjustment costs). $r$ is some average measure of opportunity cost (and not interest rate). We have assumed that the operational costs of the new technology are the same. $\tau\cdot\delta(C_R+I_N)$ is the tax benefit from accounting depreciation of the new investments. $\delta$ is the depreciation rate. We use the Fixed percentage method of Accounting depreciation here.

What the situation is for a prospective new entrant? It is easily seen that if he attempts to install Old Technology, he will make less profits than the incumbent (due to the necessary investments). So $NPV_{Oe} < NPV_{Oh}$. If he opts for the new technology for production capacity equal to that of the incumbent described above, we have

$$\text {NEW} : NPV_{Ne} = -I_N+\sum_{t=0}^{T} \left(\frac 1{1+r}\right)^t\big[(1-\tau)\pi_{ht}+\tau\cdot\frac 1TI_N\big] \tag{3}$$

It is easy again to determine that, here, $NPV_{Ne} > NPV_{Nh}$ i.e. the entrant is in a better position from the point of view of investment evaluation, because he does not have to bear the side-costs of renewal The tax benefits of the incumbent for depreciation of $C_R$ do not offset in NPV terms $C_R$.

Why do we care whether $NPV_{Ne} > NPV_{Nh}$? Because we want, conditional on both using the new technology, the new entrant to have an advantage over the incumbent in terms of financial strength, in order to have the resources to sustain a possible war from the part of the latter.

If we want that everybody has an incentive to use the new technology, then we must have

$$NPV_{Oe} < NPV_{Oh}< NPV_{Nh} < NPV_{Ne}$$
The first and third inequalities already we already have. For the middle one, which will connect the chain, we need to set the tax rate accordingly:

$$NPV_{Oh}- NPV_{Nh} <0 \Rightarrow -\sum_{t=0}^{T} \left(\frac 1{1+r}\right)^t\xi q_t +C_R+I_N-\sum_{t=0}^{T} \left(\frac 1{1+r}\right)^t\tau\cdot\frac 1T(C_R+I_N)\big]$$

Using an average period quantity produced $\bar q$, and denoting

$$R\equiv  \frac {(1+r)^{T+1}-1}{r(1+r)}$$

this becomes

$$NPV_{Oh}- NPV_{Nh} <0 \Rightarrow - R \cdot\xi\cdot \bar q +C_R+I_N-R\cdot\tau\cdot\frac 1T(C_R+I_N) < 0 $$

$$\Rightarrow \left(1-R\cdot\tau\cdot\frac 1T\right)(C_R+I_N) < R \cdot\xi\cdot \bar q $$

$$\Rightarrow \xi > \left(R^{-1}-\frac {\tau}T\right)\frac {C_R+I_N}{\bar q} \tag{4}$$

Inequality $(4)$ determines the minimum level of the environmental tax rate from the point of view of financial incentives in order for the incumbents to switch technologies.

So, does it matter whether this minimum level is consistent with the tax rate that would reflect the proper pricing of negative externalities, since by setting it above it, we expect that the old technology will be wiped out? It doesn't seem so. This is important: it says that we can see the environmental tax rate as a threat that it won't be necessary to realize.
From a "political point of view", is this minimum tax rate feasible in view of possible reaction, lobbying etc? This is a different chapter.

Note that it does not affect our goal what will happen in an oligopolistic framework, where possibly, the market demand cannot sustain both the incumbent and the new entrant (i.e. double output): whatever happens, the one, the other, or both, the appropriately set tax rate ensures that we will see only new technology in operation.


What's a "relative pair trade" for currencies? Is the U.S. Dollar About to Crash? – Pairagraph

The way I see currencies is that they are a relative pair trade. Against gold, with its stability characteristics, I don't like the US dollar. But despite all the warts, pimples, and scars on the greenback, I think most other countries have far deeper problems.

I'm not Rosenberg, but he appears upright.

From 2002 to 2009, he was Chief North American Economist at Merrill Lynch in New York, during which he was consistently ranked in the Institutional Investor All-Star analyst rankings. Prior thereto, he was Chief Economist and Strategist for Merrill Lynch Canada, based out of Toronto, where he and his team placed first in the Brendan Woods survey of Canadian economists for ten years in a row.
Mr. Rosenberg received both a Bachelor of Arts and Masters of Arts degree in Economics from the University of Toronto.

It means you can make money trading a pair of currencies if both lose value compared to a standard. Likewise you can make money trading a pair of currencies when both increase in value compared to a standard. You mostly care about the change of a currency's value relative to another.
If you think USD will decrease in value 10% versus gold and you think EUR will decrease 15% versus gold, you sell EUR to buy USD and wait to see if you were right. You don't have to compare currencies to gold. There are other standards for what a currency is worth. It doesn't matter what the standard is because your profit depends upon the value of a currency compared to another.


Fixed Effects Estimation and Inconsistency Consider estimation of the following population regression function:
$G{Y_{it}} = {\beta _0} + {\beta _1}IN{F_{it}} + {\beta _2}DE{M_i} + {\beta _3}POI{L_t} + {\varepsilon _{it}}$

Where:
$GY_{it}$ = percentage growth in real GDP per capita in country $i$ in year $t$

$INF_{it}$ = percentage rate of inflation in country $i$ in year $t$

$DEM_i$ = 1 if country $i$ is a democracy, 0 otherwise

$POIL_t$ = a price index of crude oil on the world market.

If you were to explore estimation with fixed effects both for countries and for years of observation. Which coefficients in the above model could be estimated?
 Suppose that INF and POIL are correlated over time, and INF is correlated with DEM
across countries. Do the omitted variables in the fixed effects estimate result in
inconsistent estimates? Why?

My guess is that the estimates are biased and consistent but I haven't been able to figure out why.

You can't identify the effect of oil price when Year FE are applied, since the world oil price is perfectly correlated with year Fixed Effects.
You can't identify the democracy indicator if you country does not change its value in your observed period.

For the other variables, it should be possible to obtain estimates. You should apply a fairly large sample to avoid collinearity issues (sth like 100 countries, 50 years). Further problems with your model are reverse causality, i.e. does growth cause inflation?


If rent control "doesn't work" and supply induces demand, how can cities improve affordability? Suppose we aim that moderately poor people (let's say 1.5× minimum wage) can afford the rent for an apartment meeting minimum quality standards and located within city limits.  This may be a political aim.

What economic policies are effective to achieve this?

Rent control.  Popular, but economics appears to tell us it creates more problems than it solves.  See also the questions Why did Berlin freeze the rent prices as opposed to letting the market set the price? and What is the likely result of rent control in Berlin?.
Increase supply?  In cities, it appears supply may create demand (the more people in a city, the more services, the more people want to live there) so this may not always work either, or only under limited circumstances (perhaps unless building huge amounts, but developers hate vacancies, so I doubt that limit would be surpassed in a free market).
Social housing, owned by the government?  I don't know what economic theory says about this.
Reduce demand?  Not sure how that would work without harming the city.
Impossible?  Should we give up on the idea that poor people can live in alpha world cities such as London, New York, Tokyo, Paris, Singapore, Amsterdam, Seoul, Berlin, Hong Kong, or Sydney?
Something else?

I'm aware that most economists say that rent control "doesn't work" — what are the alternatives that economists may prefer?

Disclaimer: this answer was significantly rewritten to spell out explicitly how it answers OPs question and to add some sources (thanks to @Fizz). The gist remains the same.

The only case I know where housing policy seems to work the way you envision is Vienna (the Austrien capital). They use a combination of several of the policies on OPs list, they have been doing this for a long time and they seem to be very good at implementing them in productive ways.

First, the city owns a significant proportian of all apartments, enough to have pricing power in the market (about 60% according to source). Additionally there are rent control laws on the privately owned housing (see for example here for some housing policies). Nevertheless private housing is more expensive than public housing (source).

Second, the city is engaged in long term planning for housing and they do that wholesale. So they are not just building houses on existing ground attached to existing infrastructure but they are creating entire new suburbs including attachment to public transportation, schools and all the other infrastructure needed for a successful city. The sources above also talk about that in more detail.

This is hard to pull of because it takes much longer to bear fruit that a typical election cycle. Doing things that cost money now and are very useful in 20 years is difficult for elected politicians. So even if politicians or people in general in other cities like to copy the Vienna model, it is not just a few simple policy changes.


Indifference Curves and Preferences Why are averages preferred to extremes on the same indifference curve? Doesn't everything along an indifference curve have the same preference?

Why are averages preferred to extremes on the same indifference curve?

That is false. Whoever told you this is mistaken.

Or it could also be that you misheard/misread and are confusing this with the idea that the bundle of 100 apples + 100 oranges is (usually) preferred to the bundle of 200 apples or the bundle of 200 oranges.

  Doesn't everything along an indifference curve have the same preference?

Yes.


question about derivatives and net exposure What is the point, for a bank, of engaging in derivatives trading to cover risk if the intent is to reduce "net exposure" to zero, or as close thereto as possible? If the best case scenario is that you come out with zero gained, zero lost, why do this if there is no desire to make a profit? Doesn't all effort to profit involve some risk? If you write risk out of a transaction, thus have no expectation of profit, then why go to all the trouble? And, in any case, there is always some risk that a counter party might be unable to pay, despite putting up collateral. Sorry if this question is stupid, but I'd really like to understand this.

The main roles of banks are taking deposits, transmitting and changing money, making loans, and perhaps more generally providing liquidity for their customers.

So if a customer wants to change yen for dollars, the bank does not consider whether its buying yen would be a good medium-term investment for the bank.  Instead it considers whether it can sell the yen back to dollars in the short-term at a better price either to other customers or in the wholesale market.  It sets the price (and any fees) to the original customer so that it can expect to make a margin on the overall transaction, at little or no risk to the bank.

Similarly with taking deposits and making loans, the profit for the bank is in the margin between the two interest rates (allowing for credit defaults), and the bank earns this because it is cheaper and more convenient for the customers than trying to act without the bank as an intermediary.  And if a customer wants to buy or sell bonds immediately, the bank acts as a dealer with the aim of re-selling those bonds to or buying them from somebody else at another time with a profit from the margin rather than from possible future changes in value.

With derivatives, if say a customer wants to buy a call option, then the bank may write one, not with the aim of taking the full premium and hoping things turn out right but with the aim buying another or of other balancing transactions (e.g. a put and the underlying security) and taking a margin based on providing the customer with an immediate contract in what otherwise may be an illiquid market.

The best case for the bank is that it profits from being an intermediary in these transactions, not as a speculator taking a view on how markets will move.  If it gets into an unbalanced position overall, the bank will want to hedge its position to reduce risk, as this makes it more likely that the bank will survive to make profits in the future.


What is the estimated propensity to consume out of wealth, and how does it depend on income levels? What is the estimated propensity to consume out of wealth, and how does it depend on income levels?

To make sure we are talking about the same thing: I am asking what estimates we have on what percentage of their wealth people turn into spending (on pure consumption - not investment) annually. And I want to know how it depends on income levels. Do poor people have a higher percentage than others, since otherwise they'd starve? Do middle income people have a higher or lower percentage than high income people? And how big is that difference, if it exists?

This is the "wealth effect". It has been shown empirically that as one's assessment of their wealth increase, the more they spend. An important point to be made is that this may be disconnected from actual wealth. If you are counting on a big inheritance that may lead you to spend a higher % of your wealth now in expectation of the future payoff.

There's a good paper that empirically looks at the correlation between wealth and spending but it's important to understand that the factors that influence an individual to spend money are numerous and it's virtually impossible to completely remove the signal from the noise.


What's the econ word for "Savings and efficiencies gained via consolidation"? For example, say you had 5 kitchens making cookies in 5 parts of the city.
But, then you bought 1 big kitchen, and moved all of your 5 kitchens to this 1 big location.

Due to mass production, we would expect the 1 big kitchen to operate more efficiently, and use fewer employees.

Is there a name for this in econ?

consolidation efficiencies?
mass production?

If you are looking for term for the reason why the efficiencies occur it would be the increasing returns to scale.


Empirical ranking of firms based on productivity I want to rank firms based on a metric, let's call it productivity.
Theoretically, this firm productivity measure may be well defined. Empirically, however, data that account for all dimensions of productivity are generally unavailable.
On the other hand, typically available data (e.g. output/worker) does not suffice to rank firms across industries/sectors because sector-specific differences, for instance in production technology, need to be taken into account.

What empirical approach would be both feasible in the light of data availability and non-trivial with respect to the theoretical understanding of firm productivity?

There is a scientific tradition of decades that occupies itself with the measurement/estimation of the productivity/efficiency of firms. The three strands of the literature are Data Envelopment Analysis (DEA), Discriminant Analysis (DA), and Stochastic Frontier Analysis (SFA).

I am familiar with the third one. Stochastic Frontier Analysis starts with the observation that firms do not operate all the time on their efficiency frontier, i.e at maximum efficiency, either due to unanticipated shocks, or because, while competitive market forces may push firms to be efficient, they nevertheless are not that strong or that perfect in their effects in order to make firms to be fully efficient, as it is usually assumed in theoretical models. Therefore, inefficiencies due to organizational problems and the like, may persist.

"Efficiency" in the context of SFA, has many facets: output-oriented technical efficiency, input-oriented technical efficiency, cost-efficiency, revenue efficiency, profit efficiency. All have been developed in the literature. One can choose the approach  or approaches most suited to the purpose at hand, and to data availability.

To consider the case of output-oriented technical efficiency, SFA modifies/augments the production function of a firm as

$$Q = F(\mathbf x) + u -v$$

Where $u$ is a zero-mean normal random variable and $u$ is a non-negative random variable (usually specified as a half-normal or as an exponential r.v.). The $v$ component captures the inefficiency (measured in terms of output), while the $u$ component captures stochastic disturbances that may affect production (either positively or negatively).  $F(\mathbf x)$ represents the full-efficiency level of output.

Econometrically, this is estimated by using Maximum Likelihood (the least-squares method cannot decompose the error term in its two components), on a data set that contains data on output, and on quantities of input factors (in other words, no more than the usual data set required to estimate a production function).
The estimation procedure itself will provide of course estimates that are averages over the data set. If one wants to rank the firms present in the sample, one can implement the approach developed in Jondrow, J., Knox Lovell, C. A., Materov, I. S., & Schmidt, P. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of econometrics, 19(2), 233-238.

A comprehensive book on Stochastic Frontier Analysis is Kumbhakar, S. C., & Lovell, C. K. (2003). Stochastic frontier analysis. Cambridge University Press.


Whats the math behind calculating the price of cryptocurrency through supply and demand? "The value of currencies (including most popular cryptocurrencies) is set by a market. Price rises or falls until the supply and demand of the currency are equalized"

Why exchange rates of national currency are usually stable, where as cryptocurrency like bitcoin and ethereum is highly volatile?

But how does the market calculate the price based on supply and demand that is visible in the cryptocurrency exchange? Can someone give some kind of simple math to understand? For example, I mint some utility coins or cryptocurrency on ethereum from thin air, decide an incentive system. How will the cryptocurrency gain value through trading?

Prices are set the same way as in any other market, which is to say that there is a (continuous, ongoing) process of tâtonnement where (say) buyers find that they cannot purchase at the maximum price they are willing to pay, or sellers find that they cannot sell at the minimum price they are willing to accept, creating pressure to adjust those prices. In some markets, this will eventually lead to relatively stable prices (say, street food), while in others, prices are more volatile, depending on how elastic supply and demand are.

Conceptually speaking, the classic notion of price-setting is that of the Walrasian auctioneer who receives, from each participant in the market, the amount said participant is willing to buy / sell at any given price, and who then proceeds to calculate the equilibrium price, only after which trade will actually take place. Needless to say, like the "invisible hand", this is merely an aid to understanding.


Unexplained economic puzzles? Science is full of apparent puzzles and paradoxes, some of which still remain unexplained. Economics is not an exception.

It would be interesting to get a list of  unresolved puzzles in Economics. By unresolved I mean there is a considerable divergence of opinions and evidence on what explains the puzzle, or perhaps not sufficient evidence to provide a clear explanation to the puzzle.

As always with these type of question, one puzzle/paradox per answer would be ideal. When doing so, please back up your answer with references that certify that the issue is currently a puzzle/paradox among academics and researchers. Resolved puzzles are off-topic (another thread for that might be appropriate).

An important field in current research is the yet unexplained

Equity premium puzzle

originally published by Mehra, Prescott (1985). Considere a multiperiod investment consumption equilibrium model (CCAPM) with its important result:
$$E_t\left[m_{t,j}\right]=\frac1{\left(1+R_{F,t+j}\right)}$$
where $E_t\left[m_{t,j}\right]$ donates the expected value of a stochastic discount factor (sometimes also referred to as a pricing kernel) and $R_{F,t+j}$ a riskless rate of return.

The model states, that the maximized Sharpe-Ratio $SR_{max}$ can be represented as the ratio of the standard deviation of the optimal stochastic discount factor $\sigma_{m^*}$ to its mean:

$$SR_{max}=\frac{\sigma_{m^*}}{\overline m}$$

Linking this result with common time separable power utility function shows, that the above equation is approximately the risk-aversion coefficient times the standard deviation of the logarithm of consumption.

The problem

The average risk premium of the market measured in units of risk is far too high to be explained by any consumption-based representation of the stochastic discount factor. As Cochrane(2001) notes, the Sharpe ratio measured in real terms has been about 0.5 on the basis of the past fifty years (in the US). This implies, that investors are very risk averse, with a coefficient of risk aversion at least 50.

What does that number mean? Suppose an individual faced with a 50-50 gamble of doubling or halving his savings. With a level of risk aversion of 50, he would pay 49% of his savings to avoid the loss of 50%. This individual would forgo a 50% chance of doubling his money and accept a certain loss of 49$ to avoid losing an additional 1% more.


Game Theory Question |

|     |Adv| ---------|N\A|

Adv| 300,300     | 900,0          |

N\A| 0,900     | 700,700           |

Player 1= Pepsi

Player 2= Coke

A) Solve for the pure strategy Nash equilibrium

B) Is this game a prisoner's Dilema?

C) Is there a cooperative equilibrium? If so, what is it?

D) Does coke have a dominant strategy? Does Pepsi?

My Attempt

|     |Adv| ---------|N\A|

Adv| (300),(300)     | (900),0          |

N\A| 0,(900)     | 700,700           |

A) Nash Equilibrium: (Adv, Adv)

B) Not sure how to answer this

C) Yes. If they both got in contact and made the option to not advertise

D)

I would appreciate some help!

Here are a couple hints for the two that you haven't answered:

The prisoner's dilemma is characterized by the inability to sustain the Pareto optimal payoff as a Nash Equilibrium due to the existence of a profitable deviation for both players. Each player has a dominant strategy to "Defect" and so the unique Nash Equilibrium is one where both players "Defect". Does that hold here?

A (possibly mixed) strategy $a$ (weakly) dominates another strategy $b$ for a given player $i$ if player $i$ (weakly) prefers playing $a$ to $b$ for any strategy vector of the other players. In your case, there is just one other player, $j$, and so $i$ simply has to prefer $a$ to $b$ for any strategy played by player $j$.

You just need to see if that holds for your two players.


Is it possible to have a modern economy without a central bank? Many mainstream economists say that such thing is impossible. Is there some specific reason why the financial system needs a central bank?

In this video http://m.youtube.com/watch?v=BcuAOdXD0Go, Krugman says at 03:00 it's impossible to leave the central bank out of the equation today. Why is this?

It surely is possible: For a long while, Gold was the basis for the value of money in many "modern" countries, leaving central banks with little room for policies.


Can the Gross Value Added be negative? Can the Gross Value Added be negative when calculated using the production approach?

That won't really happen in reality. A sales promotion which runs losses, as in your example, will not mean that the gross value added is negative. The final selling price of the item is the gross value added and that will not typically be negative. So, if an item is sold for 5 dollars then the gross value added is 5 dollars only. No matter if someone in the value chain made losses.
So, gross value added will never be negative unless and until the final selling price of something is negative.


How much heath expenditure is due to conditions that people are born with? The CDC says that 90% of US healthcare costs are attributable to chronic conditions. I am interested in an overlapping set of conditions: those that people are born with, including genetic diseases, birth defects, etc.

In various geographic areas, does anyone have a good estimate of what percentage of health expenditure is due to conditions like this?

I am aware that there could be some definition questions, since many medical conditions are partially but not fully due to factors present at birth, often in ways that may be changeable due to circumstances. I'm open to a range of ways of thinking about this.

Thanks!

After reviewing the two sources linked to by the CDC (a Rand report on the impacts of comorbid chronic conditions and a brief breakdown of US health expenditures) the exact methodology behind the 90% figure is not at all clear to me.

What you are asking for would be a considerably more complex calculation. The most directly relevant study I'm seeing so far is an old one, "An Epidemiological Model for Health Policy Analysis" G. E. Alan Dever (1976). In the following table (p. 462), the author attempts to break down how four different causes (one of which is "Human biology") contribute to mortality from various kinds of diseases:

Notice that even for "congenital abnormalities", the contribution of human biology is only weighted at 79%. The rest is accounted for by the health care system, lifestyle and environment. The average contribution of human biology for all causes of deaths is estimated at 27%. This is not directly relevant to the question, but I think it illustrates how the author is thinking about the contribution of different factors to disease.

Taking in to account the relative prevalence of different diseases, the author uses these estimates to further project that about 7% of federal healthcare expendatures are the direct result of human biology, independent of other factors.

There may be more up-to-date studies out there with better methodologies, but I hope this is helpful as an example of how an expert might approach the question.


Do import tariffs tend to increase a country's exchange rate (if so, why)? From Prof. Stiglitz' Vanity Fair article:

  How, one might ask, is this possible, given Trump’s rhetoric, his
  determination to move against China with a 45 percent tariff? There’s
  a global macroeconomic variable that Trump left out of his calculus,
  and that’s America’s exchange rate—not just with China, but with the
  entire world. If America’s exchange rate increases, our exports become
  more expensive, and imports become cheaper.

He doesn't explicitly say that tariffs tend to increase a country's exchange rate. He leaves it as a standalone conditional. If it's simply a conditional, he could mean that there's a nonzero chance that the Dollar's value will increase independently. However, I felt like maybe he infers some causality.

I feel like a tariff would change the trade balance such that the US will import less, while exports are fixed.

Do import tariffs tend to increase a country's exchange rate? If so, why?

Suppose that there is no 45 percent tariff and the market is in some kind of equilibrium. That is the demand for yuans equals the supply of yuans at the current exchange rate.

Now assume Trump does impose a 45 percent tariff. This makes imported Chinese goods in the US more expensive for the American consumer. As a result the consumers will buy fewer Chinese import goods. So far they paid for these goods with dollars and the corporation importing the goods used those dollars to buy yuans and pay for the goods. As a result of the decreased import demand the corporation will want less goods and hence it will buy fewer yuans. Thus decreasing the demand for yuans. The currency exchange market is similar to other markets: If at a price (in this instance this is the USD/CNY exchange rate) the supply outstrips demand the price will decrease. This means that the dollar becomes 'stronger', you will have to pay more yuans to get a dollar.

As a result exports do become somewhat more expensive (in yuans) and imports do become somewhat cheaper (in dollars) until an equilibrium is reached on both the currency and the good markets.


Estimating elasticity of substitution in nested CES functions I have aggregate data on $L_t, K_t$ and $X_t$, and want to estimate elasticity of substitution parameters, $\gamma$ and $\sigma$ for these factors. Assuming the production function takes the following form: $$Y_t=(A_lL^{\gamma}+[A_kK_t^{\sigma} +A_xX_t^{\sigma}]^\frac{\gamma}{\sigma})^{\frac{1}{\gamma}}  $$

Technology parameters, $A$s are not observable and hence need to be controlled for in an econometric specification. I am thinking of first estimating the parameter, $\sigma$, on the inner CES function combining $K$ and $X$. Then I should be able to estimate the outer CES parameter, $\gamma$. In a way, the two parameters are not jointly estimated. Would this method be valid, I mean, in statistical sense? Will I get consistent and unbiased estimates?
I've read papers on non-linear regression methods, but was wondering if this simple approach is feasible.
Thanks.

Neglecting technology parameters and assuming constant returns to scale, the parameters $\sigma$ and $\gamma$ are jointly estimable via dynamic (least squares) programming.
See this paper.


Why is the ten year interest rate lower for Spain/UK bonds than for US? Take a look at the government bonds interest rates, https://www.marketwatch.com/.

For the US is 2.9, and for Spain and UK are 1.5 and 1.1 respectively. Spain is an economy with high unemployment, a high deficit and debt and low growth. The UK is suffering through Brexit, massive uncertainty on its future. Meanwhile, the US solidly grows.

Why would investors charge more to the US, perhaps the most powerful country in the world, than to other countries?

Inflation forecast is higher in the US than the rest of countries. US here: https://www.statista.com/statistics/244983/projected-inflation-rate-in-the-united-states/

Spain here: https://www.statista.com/statistics/271077/inflation-rate-in-spain/

Japan here: https://www.statista.com/statistics/270095/inflation-rate-in-japan/

UK here: https://www.statista.com/statistics/270384/inflation-rate-in-the-united-kingdom/

Because inflation is higher, central banks will raise interest rate higher. Long term rates are higher in consequence.


JNK and SPY price movements question I am looking at the graph of JNK and SPY prices close prices since 2008.  From 2008 to 2011, the two prices seem to move together.  However, somewhere in the beginning of 2012, the prices all of a sudden began to move in opposite directions.  Does anyone know the reason for this?  A picture is provided below.

When JNK appeared on the market on Dec 04 2007 it started at approximately the same price level at SPY (143 vs 146). It is however not true that after this they moved together. I downloaded the price data and calculated the correlation of the price differences* for the first 180 days. The correlation coefficient was -0.0526.

They seem to move together because

both fell during the financial crisis
in Dec 2007 the prices were roughly the same
later the two prices drifted apart, this increases the scale and makes it hard to discern visually what happened in the early days.

So in essence this is an optical illusion.

*I did not run statistical tests for integration, but this seems very likely. Calculation was done in R using cor(diff(SPY$Close[1:180]),diff(JNK$Close[1:180])).


Effect of a US Federal Reserve rate hike on the Dow Jones Industrial Average There is speculation that the Federal Reserve of the United States will raise interest rates by 0.25% in the near future. What is the expected effect on the stock market if interest rates do rise by that amount? More specifically, what is the predicted effect on the Dow Jones Industrial Average?

Each component of the Dow Jones Industrial Average (DJIA) has a yield, computed as the earnings divided by the price, expressed as a percentage. For example, if a stock is priced at $100.00 and yearly earnings of $10.00 per share, then the yield for that stock is

yield = earnings / price = $10.00 / $100.00 = 10%

That yield could be paid out as a dividend, or retained and reinvested to grow the company, doesn't matter to this analysis.

The first step in the analysis is to determine the yield for each of the 30 components of the DJIA. On August 18, 2015 the DJIA closed at 17511.34, and the yields for the component companies were

    Company     Price Earnings  P/E  Yield
Visa            74.47   2.16   34.5  2.90%
Microsoft       47.27   1.46   32.4  3.09%
Nike           114.82   3.70   31.0  3.22%
Procter         75.13   2.44   30.8  3.25%
HomeDepot      122.80   4.71   26.1  3.84%
Coca-Cola       41.30   1.60   25.8  3.87%
WaltDisney     106.94   4.26   25.1  3.98%
Pfizer          35.52   1.42   25.0  4.00%
UnitedHealth   125.50   5.70   22.0  4.54%
McDonald's     100.76   4.82   20.9  4.78%
3M             148.31   7.49   19.8  5.05%
Verizon         47.46   2.42   19.6  5.10%
Boeing         144.60   7.38   19.6  5.10%
Johnson         99.37   5.70   17.4  5.74%
GE              26.07   1.50   17.4  5.75%
Cisco           28.25   1.73   16.3  6.12%
Merck           59.66   4.07   14.7  6.82%
AmExpress       81.24   5.56   14.6  6.84%
UnitedTech      99.41   6.82   14.6  6.86%
WalMart         69.48   5.05   13.8  7.27%
DuPont          53.90   3.92   13.8  7.27%
Apple          116.50   8.66   13.5  7.43%
Caterpillar     78.82   5.88   13.4  7.46%
IBM            156.01  11.90   13.1  7.63%
JPMorgan        68.21   5.29   12.9  7.76%
Intel           28.91   2.36   12.2  8.16%
Goldman        201.18  17.07   11.8  8.48%
Exxon           77.90   7.60   10.3  9.76%
Travelers      107.82  10.70   10.1  9.92%
Chevron         83.44  10.14    8.2 12.15%

The next step in the analysis is to determine the adjusted yield after the Federal Reserve increases the interest rates by 0.25%.

The expectation is that the market will adjust prices to increase yields by 0.25%. In other words, market yields represent a premium above the Federal Reserve rate.

So for example, the yield on Visa must increase from 2.90% to 3.15% to compensate for a 0.25% increase in the Federal Reserve rate. Given earnings of $2.16, the price must drop from $74.47 to $68.56 (a 7.9% drop) to compensate for the rate increase.  At the other end of the scale, the yield on Chevron must increase from 12.15% to 12.40%. Given earnings of $10.14, the price must drop from $83.44 to $81.76 (a 2% drop).

We can now augment the previous table to include the adjusted yields, adjusted prices, and the drop in price as a percentage of the original price.

                                                  Adjusted    Price
    Company     Price Earnings  P/E  Yield     Yield   Price  Change
Visa            74.47   2.16   34.5  2.90%     3.15%   68.56  -7.94%
Microsoft       47.27   1.46   32.4  3.09%     3.34%   43.73  -7.49%
Nike           114.82   3.70   31.0  3.22%     3.47%  106.55  -7.20%
Procter         75.13   2.44   30.8  3.25%     3.50%   69.76  -7.15%
HomeDepot      122.80   4.71   26.1  3.84%     4.09%  115.29  -6.12%
Coca-Cola       41.30   1.60   25.8  3.87%     4.12%   38.80  -6.06%
WaltDisney     106.94   4.26   25.1  3.98%     4.23%  100.62  -5.91%
Pfizer          35.52   1.42   25.0  4.00%     4.25%   33.43  -5.89%
UnitedHealth   125.50   5.70   22.0  4.54%     4.79%  118.95  -5.22%
McDonald's     100.76   4.82   20.9  4.78%     5.03%   95.76  -4.97%
3M             148.31   7.49   19.8  5.05%     5.30%  141.31  -4.72%
Verizon         47.46   2.42   19.6  5.10%     5.35%   45.24  -4.67%
Boeing         144.60   7.38   19.6  5.10%     5.35%  137.85  -4.67%
Johnson         99.37   5.70   17.4  5.74%     5.99%   95.22  -4.18%
GE              26.07   1.50   17.4  5.75%     6.00%   24.98  -4.16%
Cisco           28.25   1.73   16.3  6.12%     6.37%   27.14  -3.92%
Merck           59.66   4.07   14.7  6.82%     7.07%   57.55  -3.54%
AmExpress       81.24   5.56   14.6  6.84%     7.09%   78.38  -3.52%
UnitedTech      99.41   6.82   14.6  6.86%     7.11%   95.91  -3.52%
WalMart         69.48   5.05   13.8  7.27%     7.52%   67.17  -3.33%
DuPont          53.90   3.92   13.8  7.27%     7.52%   52.11  -3.32%
Apple          116.50   8.66   13.5  7.43%     7.68%  112.71  -3.25%
Caterpillar     78.82   5.88   13.4  7.46%     7.71%   76.26  -3.24%
IBM            156.01  11.90   13.1  7.63%     7.88%  151.06  -3.17%
JPMorgan        68.21   5.29   12.9  7.76%     8.01%   66.08  -3.12%
Intel           28.91   2.36   12.2  8.16%     8.41%   28.05  -2.97%
Goldman        201.18  17.07   11.8  8.48%     8.73%  195.42  -2.86%
Exxon           77.90   7.60   10.3  9.76%    10.01%   75.95  -2.50%
Travelers      107.82  10.70   10.1  9.92%    10.17%  105.17  -2.46%
Chevron         83.44  10.14    8.2 12.15%    12.40%   81.76  -2.02%

The adjusted DJIA computed from the adjusted prices is 16747.96. Thus, the DJIA was expected to drop from 17511.34 to 16747.96 (a 760 point 4.4% drop) to compensate for a 0.25% increase in the Federal Reserve rate.

What actually happened was the DJIA dropped to a low of 15666.44 low on August 25, 2015 (an 1840 point 10.5% drop) before recovering to a range between 16300 and 16500, slightly below the expectation.


Missing values in economic time series I am trying to run a time series analysis on some variables - GDP being my dependent variable, and my independent variables are oil revenues, government expenditure, exports and FDI inflows. My data contains missing values for some years for at least 3 variables. I have been able to ascertain that they are non-stationary. However, I am unable to perform the Johansen test of cointegration due to the missing variables in between the data set. How do I resolve this?

The paper Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error (J. Isaac Miller (2009)) seems to have what you are looking for.

  We consider a cointegrating regression in which the integrated
  regressors are messy in the sense that they contain data that may be
  mismeasured, missing, observed at mixed frequencies, or have other
  irregularities that cause the econo- metrician to observe them with
  mildly nonstationary noise. Least squares esti- mation of the
  cointegrating vector is consistent. Existing prototypical variance-
  based estimation techniques, such as canonical cointegrating
  regression (CCR), are both consistent and asymptotically mixed normal.
  This result is robust to weakly dependent but possibly nonstationary
  disturbances.

Here  is the bit on testing for cointegration:

  In cases where cointegration between ($y_ t$) and ($x_t$) is not
  obvious or expected, 5 testing is desirable. The variance ratio test
  and multivariate trace statistic proposed by Phillips and Ouliaris
  (1990) rely on the estimation of the long-run variance of a different
  residual series. Specifically, ($y_ t, x'_t$ ) is regressed on one lag
  of itself, and the long-run variance of the residual series from that
  regression is estimated. This series is I(0) under the null, so we can
  expect that adding ($z^*_t$) – i.e., using ($y_ t, x^{'*}_t$)  – would
  have a similar effect to adding ($z^*_t$) to the residual series
  below. Specifically, it would inflate the variance of both the
  numerator and denominator of these statistics, so that the limits
  would be preserved. Approaches using more robust variance ratio tests
  (Wright, 2000; Müller and Watson, 2008) hold more promise still.


extremum Estimator (possibly tobit?) This question is related to extremum estimators. I am looking to propose an estimator that I think may be a Tobit estimator, but I am unsure. The question is as follows:

Let $z$ be a random variable with a strictly increasing CDF $F( \dot ) $ everywhere on its support. The median of $Z$, $\gamma$ is defined as:

$ \int _{-\infty, \gamma} dF(z) > \frac{1}{2}$ ; $ \int _{\gamma, \infty} dF(z) > \frac{1}{2}$

It is known that $\gamma$ minimizes an expected absolute deviatin criterion:
 $\gamma = argmin_e E(|Z-e| - |Z|)$.

We consider a model $Y=max\{c, f(X; \theta)+\epsilon\}$ where c is a known constant and the conditional median of $\epsilon$ given  $X$ is 0. Suppose we have an i.i.d sample $\{X_i, Y_i\}$, that is generated by this model.

1) Propose an extremum estimator for $\theta$.

Here, I was thinking that a Tobit model would be appropriate since the model is truncated by the constant $c$.

2) Show the estimator you proposed is consistent.

First of all, this is not a Tobit-type estimator. A Tobit estimator is a maximum-likelihood estimator, which is based on a full specification of the error distribution. You have only the median specified, so it can't be an MLE.

What can we do? To begin with, note that, for a random variable $Z$, the median of $\max(c,Z)$ is $\max(c, \mathrm{med}(Z))$, which can be proved by using the definition of the median.

Thus, for your problem, you have
$$\mathrm{med}(y|X) = \max(c, f(X,\theta))$$
under the assumption that $\mathrm{med}(\epsilon|X)=0$. A natural extremum estimator would be the minimizer of
$$\frac{1}{n} \sum_{i=1}^n |y_i - \max(c, f(X_i,\theta)) |.$$
You defined the median as the minimizer of $E(|Z-e|-|Z|)$, but this is the same as the minimizer of $E|Z-e|$ without $-|Z|$, so I dropped the "$-|y_i|$" from the objective function.

This is a generalization of Powell (1984), Least absolute deviations estimator for the censored regression model, Journal of Econometrics, 25, 303-325. See the paper for more details including consistency. https://web.stanford.edu/~doubleh/eco273/powell1984.pdf


Changes to lookup code/symbols on the NASDAQ? I'm not entirely sure if I've asked the right question, but does anyone know why certain symbols (I assume they are the symbols) change on NASDAQ?

In particular I'm wanting to keep a track of the Natural Gas price. It's current code is NGH16.NYM and I've been following it here http://finance.yahoo.com/q?s=NGH16.NYM&ql=0

However last month the code was NGG16.NYM and had this URL http://finance.yahoo.com/q?s=NGG16.NYM&ql=0

I've been struggling with this for a while now, and at first thought it was an incremental code. That pattern didn't seem to stick.

Any ideas? And any idea if I can predict the next ones?

Thanks :)

You are tracking futures on natural gas. Therefore, the name changes because you look at contracts with different maturities: the first has a maturity in March 2016, whereas the second that you mention is due to expire next month (February 2016).

Future contracts are derivative which reflect accurately the expectations of market participants at a defined maturity. You should try to track indexes instead of futures if you want to track commodity prices without changing the tickers and without looking too much at expectations.


Is it accurate to state that an economist cannot assign a true numerical value for utility? Investopedia article - What is the utility function and how is it calculated?
https://www.investopedia.com/ask/answers/072915/what-utility-function-and-how-it-calculated.asp
Article describes ordinal versus cardinal utility:

When economists measure the preferences of consumers, it's referred to ordinal utility. In other words, the order in which consumers choose one product over another can establish that consumers assign a higher value to the first product. Ordinal utility measures how consumers rank one product versus another.

Economists take the utility-function concept one step farther by assigning a numerical value to the products that consumers choose or choose not to consume. Assigning a value of utility is called cardinal utility, and the metric used to it is called utils.

Article includes the following statement under limitations and benefits of utility function:

Of course, in reality, economists can't assign a true numerical value to a consumer's level of satisfaction from a preference or choice. Also, pinpointing the reason for the purchase can be difficult if there are many variables being considered.

Is this an accurate description of economic reasoning? Utility functions are models  constructed by a particular economist who cannot assign a true numerical value?
To further develop my question, if it is not clear, in a scientific measurement there is a procedure which defines a standard unit of measure. Instruments are calibrated in terms of these procedures and then calibrated instruments are applied to assign the numbers with units in the models. Is there a standard procedure for assigning numbers to specify utils or is it constructed when the economist assigns numbers arbitrarily to the ordinal set?
Another article - Constructing a utility function:
http://planning.cs.uiuc.edu/node469.html

Unfortunately, establishing the existence of a utility function does not produce a systematic way to construct it. In most circumstances, one is forced to design $ {\cal U}$ by a trial-and-error process that involves repeatedly checking the preferences. In the vast majority of applications, people create utility and cost functions without regard to the implications discussed in this section. Thus, undesirable conclusions may be reached in practice. Therefore, it is important not to be too confident about the quality of an optimal decision rule.

I think the Investopedia article does not use clear terminology which leads to confusion.
In Economics, utility can be split across two categories as ordinal and cardinal utility.
In the case of ordinal utility assigning numeric values is meaningless. For example, if A is proffered to B, assigning 200 utils to A and 100 utils to B is meaningless because that would imply that A is twice as good as B, but the ordinal utility can only measure preferences, not intensity.
In the case of cardinal utility, which measures both preference ordering and their intensity it is completely valid to assign some value like $u(A)=200$ utils or $u(B)=100$ utils. In this case, the numerical values can be assigned and they are, mathematically,  'true' numerical values.
However, from my reading of the Investopedia article, they seem to be referring to the measurability problem.  That is an old discussion in economic theory that revolves around whether utility can be actually measured in some way (i.e. can we somehow scan a person's brain to measure precisely utility).
Now from a purely practical perspective whether the utility is measurable or not we definitely cannot measure in any direct way presently. Right now we can only observe people's choices and their revealed preference which is only solid basis for ordinal utility, not cardinal utility. However, this does not mean that utility would be immeasurable. In fact, famously  Von Neumann and Morgenstern (1944) in their Theory of Games and Economic Behavior argued that utility even if we cannot measure it yet is measurable. The authors argued that utility can be viewed the same way as temperature in physics. Temperature also originally could not be measured beyond just saying it is getting colder or warmer but developments in thermodynamic theory later allowed us not just to cardinally measure temperature, but even allowed us to recognize that there is actually some absolute zero and absolute units temperature (presently even Celsius scale is actually a derived measure in terms of Kelvins).
Consequently, in the view of  Von Neumann and Morgenstern utility should also be measurable and their view is quite influential although not accepted by all. If utility is measurable then there is a 'true' underlying measurable utility value to any choice. Whether we actually have instruments to do the measurements or not is irrelevant for the problem.
However, from my reading of the Investopedia article I think that what Investopedia refers to is the present practical inability to directly measure utility. I cannot see any indication from the article that it is taking stance on the measurability problem itself. Economists definitely don't go around hooking jumper cables to peoples heads and directly measuring utility from their choices (yet). Consequently, it is an accurate statement from a present-day practical perspective but not necessarily valid statement from the perspective of measurability problem.
Response to second question after edit:
The issue here is that true numerical value does not necessarily depend on measurement. As explained in this article from Science Campus site:

The measurement value (which is sometimes referred to simply as the measurement) is the value given by a measuring instrument and the true value is the actual value of the property being measured.

Of course, there are no instruments to measure utility, however that does not mean that there are no true numerical values for it. In fact, as argued by  Von Neumann and Morgenstern (1944) in cardinal utility there will be some mapping of the underlaying preferences on the set of real numbers. Hence, cardinal utility actually does represent the 'true' values of utility (within the vNM framework at least).
However, Investopedia is correct in pointing out that economists do not measure it when constructing utility because (presently) there is no practically viable way that would in real life make it possible to create such mapping from the unobservable preferences onto real numbers. But just because we are not able to practically make such mapping does mean it cannot exist (again in past people were unable to map the true values of temperature onto real numbers - in fact for the  most part of the human history such mapping was impossible until technology and science advanced enough to make it possible).
Furthermore, of course there are economist who are pure ordinalist but from my reading of the Investopedia article they are not taking pure ordinalist position rather they mean that we are simply unable to measure utility in practical sense.


When is expenditure function non-decreasing? I have to find parameters m and d for which expenditure function is non-decreasing and homogeneous of degree 1.
My expenditure function is:
I think that I should find ∂e/∂p which has to be >= 0 but I have a problem with this because expenditure function is for n-good. Can someone help me?

One possibility is to reparameterize your expenditure as follow: $$e(\mathbf{p},u) = E(f(\mathbf{p}),g(\mathbf{p})u),$$ with $f,g:\mathbb{R}^n\rightarrow \mathbb{R}$. Then use the chain rule to find $\partial{e}/\partial{p_j}$, $\partial{e}/\partial{u}$ and to prove that $e$ is homogeneous of degree one in $\mathbf{p}$ iff ...


How do international organizations collect statistics regarding a country? How do international organizations like IMF, WB, and CIA Fact Book collect statistics regarding a country's economic indicators?

What is their primary source of information?

I don't know how CIA gets its information from other countries on their economic performance, but I can tell you that IMF and WB have residence representative offices in member countries. Central Banks, various ministries and other government agencies supply periodic performance records to these offices.


In Blackwell's condition for T to be a contraction mapping, we require that satisfies discounting. What is the intuition of discounting? The discounting condition is as follow:

There exists some $\beta \in (0, 1)$ such that $[T(f + a)](x) ≤ (T f)(x) + βa$, for all $f ∈ B(X), a ≥ 0, x ∈ X$.

While the monotonicity condition makes sense, I can't give a nice meaning to this property.

Without discounting, you cannot show either

$$
T(g + || f - g||) \leq Tg + \beta || f - g||
$$

or

$$
T(f + || g - f||) \leq Tf + \beta || g - f||
$$

and thus you cannot demonstrate that $T$ is a contraction mapping in the traditional proof.

For intuition, note that Blackwell's sufficiency conditions for a contraction mapping is a fixed-point theorem used to establish the convergence of value function iterations. In the simplest case possible of a collapsed state space with the linear operator $T(W) = \sigma + \beta W$, it is clear that $\beta \in (0,1)$ will always lead to an intersection of $T(W)$ (from above) with the 45-degree line $T(W) = W$ and thus converge at a fixed point independent of the initial guess. The discounting condition that pins down such a $\beta$ assures this.

In systems with fully specified state spaces, however, discounting is no longer sufficient to establish uniqueness. Monotonicity is additionally required in these cases to establish the sufficiency of Blackwell's conditions because of additional concerns over dynamics.


Public randomization device I am reading the paper "The Blockchain Folk Theorem"  by Biais et al (2019) (http://publications.ut-capitole.fr/26234/1/32/5/1662/5427771). It is a stochastic game and the authors include a sunspot random variable to "enable players to coordinate their actions using a public randomization device". I went around and tried to look more into this and I couldn't really find any intuitive explanation for what a public randomization device is (there seems to be some information on the mathematical properties of including such a device, specifically the authors reference a paper on noisy stochastic games by Duggan (2012) (https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA10125)).

I guess my question is, could anyone here provide some explanation of this concept? Or even just some reference to better understanding the concept of public randomization devices?

A sunspot is just a publicly observed random variable upon which players can condition their actions (formally it's part of the history of the game).

It's helpful because it is a nice easy way to convexify the set of equilibrium payoff vectors. In many papers (in my experience) it is a convenient assumption that simplifies things, yet may not be necessary--that is the effect of sunspots can be accomplished without their use, it's just more of a hassle.


Can fiscal consolidation be expansionary? In reading this article of Paul Krugman, we immediately see that in his opinion the literature that defended the possibility of the fiscal multiplier being negative for some high-debt countries, i.e. austerity have expansionary effects on output, is no longer supported.

Is this true?

What papers have since then been produced that support austerity? and what papers have been produced that go against austerity?

Any help would be appreciated.

There has been some papers and articles put forth from the IMF over the last few years suggesting that Austerity has caused many European economies to drag and not recovery from the great recession as well as they otherwise could have.  I pulled the first article I found referencing the IMF research (from Washington post): https://www.washingtonpost.com/news/wonk/wp/2012/10/12/imf-austerity-is-much-worse-for-the-economy-than-we-thought/

I think the largest concern with respect to expansionary fiscal policy in today's economic climate is the crowd-out effect that huge public debt can have on private investment.  Perhaps someone can link a solid paper about that effect.


Intuition of the Kolmogorov Equations So I understand the derivation of the Kolmogorov Forward and Backward Equations, but I don't quite understand the intuition.  Here is from Stokey, 2008:

"The backward equation involves time $t$ and the initial condition $x$, with
the current state $y$ held fixed. A similar PDE, the Kolmogorov forward
equation (KFE), involves $t$ and $y$, with the initial state $x$ fixed. The forward
equation is useful for characterizing the limiting distribution, if one exists."

In what situations do the two arrise?  For instance, if I know the current state and am interested in a probability distribution over possible initial states, I use the backward equation.  If I know the current state and am interested in the probability distribution over the state in the future, I use the forward equation.  Is this correct?

On a more technical note, how does one define boundary conditions for these PDE's?  Are the boundary conditions a result of the derivation?  Perhaps Stokey is not the best reference on this topic...

I will try to answer to your last question. I did not read the paper but in models with higher dimensions, it is always difficult to find an analytical solution.
If there exists an analytical solution (for a very basic model with a one-state variable), it is possible to derive the initial conditions for your control and state variable from your differential equations.

However, in systems where there does not exist an analytical solution, you are supposed to solve it numerically, in which case you must give a numerical value for one of your variables (or more until you find steady state values for all your variables.)

After, you can find the steady-state values of your variables in which case, your initial conditions should not be so far from the steady state level (otherwise, there would be some convergence problems in your model if you don't choose the appropriate initial values, close to steady state. It is another issue.)


Calculations regarding Buffer stocks? Here's a question which I don't quite know how to answer. Originally, my answer was (D), though when I checked it the correct answer was (A). As far as my knowledge goes, buffer stocks are buying/selling of stocks by the government to help manipulate supply. Please help provide some elucidations, many thanks.

The answer is indeed A:

Initial farm income is $\$5 \times 2,000 = \$10,000$.

If the supply is $S_2$, then current income is below that figure.
However,  if the government takes away from the market 1,000 tonnes,  then the supply curve will shift left by that amount, resulting in a new equilibrium with 4,000tonnes @ \$2.
Therefore farm income is now:  $\$2 \times 4,000 = \$8,000$. The government buys the buffer at market price,  thus $\$2 \times 1,000 = \$2,000$. We end up with the same farm income as in the initial situation: $\$8,000 + \$2,000 = \$10,000$.


Who exactly foots the bill if Greece defaults Apologies if the topic is not appropriate (economics newbie here) but I am curious as to who exactly would foot the bill if Greece defaults on the ~300 billion dollars it owes. It looks like most of the money is owed to EU, IMF and ECB but what does that really mean in layman terms? Does it mean that tax-payers in other (mostly EU) countries end up paying one way or the other.

Who would pay depends on the terms of the default. Sometimes holders of similar debts are not treated equally, and this can play out in different ways. Greeks could default on external debts but continue to pay internal creditors. Or because the ESM and other entities are providing ongoing financing, perhaps they will continue to be repaid when others are not to keep those spigots open. Or, less extremely, they could vary the degree of forbearance, term changes, and extent of default.

I found the following two charts from 2013 and 2014 helpful for understanding who are the current holders of Greek public debt and how that compares with other rich countries.

Source: STARLING CITY

Update:
I couldn't find a time series of the holders of Greek debt but here are some additional charts to see the evolution. The first one is more comparable to the pie chart above than the second one which shows only bank holdings. If this is of interest, the BIS's consolidated banking statistics could be used to create a time series of the bank holdings of Greek debt


Is a mixed strategy ever the best response to a pure strategy? Suppose you are playing a game against an opponent whom you know only uses pure strategies.  My question is, is there any such game in which using a mixed strategy in response is better than all the pure strategies you have at your disposal?

Fixing the strategy of the opponent, a mixed strategy never yields a strictly higher utility if you are expected utility-maximizing.
The reason is that the expected utility from a mixed strategy is at most as high as the highest utility from the pure strategies which this mixed strategy plays with positive probability.
That is not to say that a mixed strategy cannot be a best response, though.
Consider for example rock-paper-scissors and a imagine your opponent playing each of the three actions with equal probability.
This leaves you indifferent between all three actions and hence any mixed strategy is a best response.

Things can be different when players are not expected-utility maximizers. If that's what you're interested in, you could take a look at the paper "Equilibrium without independence" by V. Crawford, 1990, as well as some of the references therein.


Why did the proportion of household savings in the USSR decrease during its transition period? This question came out as a multiple-choice in my A-Level Economics exam. The answer choices were:

A) Rising income inequality
B) Increased availability of consumer goods
C) Rising medical expenses

Without actual information, the question is debatable. I am not sure why this we were asked to hypothesise without adequate information.

I couldn't say what was the actual explanation but Increased availability of consumer goods could deliver this result. Say people in the USSR expected that eventually there would be a consumer revolution where their choice of goods would be better. Then utility would look like something like this:
$$ U(c_1, c_2, c_3) = ln(c_1) + \beta \cdot \xi \cdot ln( c_2) + \beta^2 \cdot \xi \cdot ln( c_3)$$

where $c_i$ is the consumption in period $i$, $\beta$ is the discount rate, and $\xi > 1$ indicates how much better consumption is in time 2 than 1. A higher value of $\xi$, meaning a greater improvement in consumption acts like a higher value of $\beta$, meaning lower discounting of future consumption in period $1$. That means that households will (all else equal) save more in period 1. In period 2 there is no expected increase in the quality of consumption, only the standard time discounting differentiates consumption in the present and future, and so the savings rate (relative to period 1) falls, just as it would if $\beta$ fell.


How much revenue could an 100% land value tax be able to generate for the Indian government? So as a Georgist (follower of Henry George), I believe most form of taxation is immoral and economically inefficient except the land value tax (not to be confused with property taxes) and other pigovian taxes. However, I'm also a pragmatic person and therefore, it may not be possible to fund an entire government through these taxes alone as most Georgists believe.
That is why I want to ask how much revenue would an 100% land value tax be able to generate for the Indian government, assuming no changes in the current levels of the government.
I do realise such a tax would be difficult to practically implement due to poor land records in India but nevertheless, I'm interested to know if it is feasible in theory.

In Australia, Prosper compiled a survey of all economic rents and came to the conclusion that the Australian government could effectively be funded with rents alone.
This is without taking into account that abolishing taxes will further increase the value of economic rents, i.e. in the absence of taxation firms and households will have more net income to pay for economic rents (land, carbon, licences, fees) which further increases government revenues.
Mason Gaffney (2009) argues that all taxes come out of rents (ATCOR). According to this a tax reduction would increase rents by at least the same amount. This would imply that a government funded with taxes could just as well be funded with rents. See my question about ATCOR here.


Why (neoclassical) economic models have no profits, unlike the real world? Consider a simple neoclassical model of an economy populated by firms with a constant returns to scale production function, using homogeneous labour and capital. Firms are equal, and are price takers in all markets. Thus, firms pay factors their value marginal product. In the long run, any economic profit is wiped out by changes in the price of the good, due to the menace of entry of new firms.

In this setting, no income remains after paying out competitive wages to workers (L) and competitive return to the capital hired for production (K). This is, for firm $i$,

$$pY_i = L_iw + K_ir $$

Now, in real markets, even in competitive ones, firms do make profits, even if these profits are not abnormal. Part of these profits might be distributed as dividends.

In the trivial economic model however, the ownership of the firm is not explicitly modeled. Firms do not pay dividends.

Why is this? Why is ownership not relevant? Are profits uninteresting? That is what the capitalistic firms cares about! I'm puzzled.

It seems economic models do not explicitly include ownership of the firm (not of the physical capital, an input used to produce).

Many economic model do have profits. We're just more careful about what we call it. See the definition of "economic profit." When you think of profits, you need to ask yourself if the money you are making is simply a fair exchange for the costs you incur---explicit and implicit costs---or whether some portion of that profit represent money gained above and beyond the (true) costs of production (see "economic rent"). Indeed, this is the only sensible way to think about the world.

  It seems economic models do not explicitly include ownership of the firm

Many economic models do in fact include ownership of the firm. However, most economic models are built for demonstrating some particular idea in relative isolation, as opposed to trying to model every single detail. So if someone wants to demonstrate some effect in a world without economic rents, then a lot of the time modeling the ownership of the firm is less important than modeling the ownership of the capital---and thus it might be excluded.

If you want to see models that dig deep into the issues of economic rents and the ownership of a firm, I would recommend taking a look at the subfields called "industrial organization" and "corporate finance." (For example, take a look at Jean Tirole's book on corporate finance.

  Meanwhile, in real life, even in competitive markets, firms do make profits on the long run.

This is a bold claim. If you want to be scientific, you're going to have to be precise about how you (1) define profits and (2) define competitive markets, and (3) show (with data and sound analysis) that firms very commonly do make profits as you've defined them. This is how an economist would operate.

  Firms are just an ethereal "thing" that take inputs and produce output with a technology freely available.

Hidden in this comment is an very interesting object of study. What is a firm, really?
This was an important question (first?) and most famously raised by Ronald Coase. How do we define a firm? Why do they exists? etc. See the "theory of the firm."


Ban an import that is exported Norway intends to shutdown the fur farming industry over the next 5+ years. In the meantime, can Norway ban imports and sales of fur without violating WTO regulation?

Are there alternative strategies? Examples of countries doing something similar (banning imports of goods it exports)?

In general, no, it can't impose stricter rules on imports than it does on domestic production. Or more accurately, it could, but the countries exporting fur to Norway could challenge this. The guiding rule is that domestic industry cannot receive preferential treatment over importers.

Norway can do it the other way around - that is to say, WTO rules would allow it to continue to import furs after closing down its domestic industry.

But there are always way around this. For example, by setting very specific standards (which are not explicitly to do with country of origin) that apply to everyone, but that only domestic industry complies with. If the standards are crafted well enough, they'll pass WTO's scrutiny.


Theoretical economy calculation of closed country Is there any well-known theoretical solution to the problem as described below? I am considering an ideal very simplified case.
There is a closed country/community of N people. All people are working. Let's say they have A% out of N people producing food, B% out of N people working in the industry (producing everything from the phones to cars), C% work in government, D% work in the service like a haircut, cleaning, etc. Initially, the GDP of this community is G or maybe it is better to tell, that initially, they have G amount of money. Let's assume that everything that is produced will be bought by others.
In other words, I can formulate it like this. N people decided to leave this planet and move to Mars/another planet because they fed up with unfair live on The Earth :) They decided to take with them things with total costs G (initial GDP). Let's assume they have everything on the other planet like air, water, Sun, good climate, resources, etc. the same as on The Earth. They divided the people between different occupations as mentioned above.
The questions:

I am not an economist, but I would expect this kind of problem was solved already a long time back and it is well-known and has some specific name. Is not it?
How this economy (GDP) will depend on time G(t)?
Are there any conditions when it will grow or it always will go down at some point?
Does G(t) depend on how big is N?

You are basically asking for a growth model and yes there are plenty of them the two most popular are:

Solow-Swan growth model.
Endogenous growth model.

I will go over simplified version of both in order to answer how 'G' depends on time and also how 'N' plays a role but I will change the name of all variables to follow standard economic terminology and notation as your non-standard terminology is bit confusing and all over the place. Furthermore, I will present only the most simplest versions of such models, skipping some derivations for the sake of brevity, for more advanced versions and full treatment I would direct you toward Romer Advanced Macroeconomics or Barro & Sala-i-Martin Economic Growth.
Solow-Swan Model
The Solow-Swan model is currently the more dominant model in mainstream economics as the latter endogenous growth model, while theoretically appealing, is very hard to empirically test.  A long story short in this model evolution of GDP (real output - denoted by $Y$) would depend on a) exogenously given technology (denoted by $A$) growth ($g$) and also population ($L$) growth ($n$). However, living standards depend not just on total of $Y$ but on $Y$ per head (country with 100 GDP but 10 people is arguably richer than country with 100 GDP but 100 people).
The model goes as follows:
We need to start with specifying some production function as we need to have some way of determining the output $Y$. A classical example would be:
$$Y = F(K,L) = K^{\alpha}AL^{1-\alpha}$$,
where $K$ is the stock of capital and $L$ the labor which is for simplicity assumed to correspond to population. Furthermore, the production function will be expressed per unit of effective worker ($AL$):
$$\frac{Y}{AL}= F(\frac{K}{AL},1) = (\frac{K}{AL})^{\alpha} = f(k) = k^{\alpha}$$
with $0<\alpha<1$ and $f(0)=0, f'(k)>0$ &  $f''(k)<0$. The evolution of population and technology in the model would be given by $\dot{L}(t) = nL(t)$ and $\dot{A}(t) = gA(t)$. Furthermore, the evolution of $K$ is given by $\dot{K}(t)= sY(t) -\delta K(t)$ where $sY(t)$ is the proportion of output saved under savings rate $s$ and $\delta$ is the depreciation rate -i.e. the rate at which capital breaks down.
I will skip most of the derivations but under the above conditions it can be showed that the capital per person has following dynamics: $\dot{k}=sf(k(t))-(n+g+\delta)k(t)$. Given this conditions in a steady state (a state where $\dot{k}=0$) it can be shown that the evolution of capital ($K=ALk$) will be given by:
$$\frac{\dot{K}}{K} = n+g \implies \frac{\dot{Y}}{Y}=n+g  $$
The reason why above implication holds is because in this case production function implies constant returns to scale. When expressed in per capita terms the growth of $Y/L$ will simply be $n$.
Hence, your closed martian economy will grow at the rate of $n+g$ in absolute terms and in per capita terms at the rate of $n$. Hence, In this model the output/GDP of your martian economy would grow as long as combined growth of population and technology is bigger than zero ($n+g>0)$ and would shrink if the inequality would go other way. In per capita terms only the growth of technology would matter.  The stock of $Y(0)$ and population $L(0)$ as well as capital $K(0)$ (which you dont mention) that people will bring to the mars will determine the initial conditions but not the growth rate of the colony.
As mentioned by Giskard in his +1 comments the exact solution depends on assumptions about the production function. For example, if we would not have constant returns to scale there would also the $Y$ would not grow exactly at $n+g$ but generally speaking the  growth rate of total output would still be a function of $n$ and $g$ and per capita output of $g$.
Endogenous Growth Model
I wont cover endogenous growth model in such explicit detail as Solow-Swan model as endogenous growth model is far more complex and even surface level treatment would take several pages. However, I will cover some departures from the above Solow-Swan model.
In endogenous growth model the rate at which technology grows ($g$) is not just exogenously given but determined by the model. For example, according to Romer's textbook mentioned above a simple endogenous model inspired by the works of Romer, Grossman and Helpman and Aghion and Howitt would use the following production function:
$$Y(t) = ((1-a_k)K(t))^{\alpha} (A(t)(1-a_L)L(t))^{1-\alpha}$$
with the change in technology given by:
$$\dot{A}(t) =B(a_k K(t))^{\beta} (a_L L(t))^{\gamma}A(t)^{\theta}$$
Translated to plain English the first equation says that the output will be given by the share of capital and people devoted to production of goods and services   ($(1-a_k)K(t)$ and $(1-a_L)L(t)$ respectively as well as technology $A$ - this is really just modified version of production function in the first part.
The next equation in plain English says that the change of technology in time depends on how much capital and labor is devoted to production of this new technology as well as on the current stock of technology ($a_k K(t)$,  $a_L L(t)$ and $A(t)$) respectively.
I wont provide rigorous solution to this problem but the solution would show that depending on exactly what are the parameters of the model - especially the $\theta$ parameter which tells us what the effect of current knowledge and 'success' of future R&D will be. If past knowledge makes generating future knowledge easier $\theta>1$ if harder $\theta<1$ and if its effect is constant $\theta=1$. I will grossly oversimplify here but generally if $\theta<1$ the model will predict virtually the same result as Solow model. If $\theta>1$ the model will exhibit ever increasing rate of economic growth and in such case having more people will have dramatic impact on speeding up economic growth. If $\theta=1$ the population growth will still matter but the effect wont be as dramatic as in the previous case and even if population growth is zero the saving rate will play a crucial role in determining long run growth.
To sum it up, in this case depending on what are the parameters of the model we can either say that the result will be similar to the one from Solow model or that here population growth and choose savings rate will also matter for the growth of economic output in your Mars colony. As in the previous case growth would cease or output would decline if either technology or factors of production would decline.
Furthermore, again endogenous growth models have many variants but general takeaway from these models is that population growth or peoples decisions to invest in R&D can also affect the rate of per capita growth of output. Hence in this case the rate of growth of your martian colony would also depend on the number of people on mars and how many of them are engaged in 'production' of R&D or more generally how much they decide to invest resources in such endeavor.

PS: You will note that none of the models above really care about how people are distributed between different sectors of economy (your A, B, C and D) - aside from the fraction of factors of production devoted to R&D in endogenous growth model or how much money economy has. Money stock should be not confused with output or GDP and since in the long run money is considered by most economists neutral most economic growth models will not even explicitly include stock of money as it is not considered important.
Moreover, the treatment here is surface level just to showcase some different ways how you could think about the problem. For more full treatment you should refer to sources I cited and sources cited therein.


Is there a good mechanism to incentivize leveraged firms to take less risks? It seems that there are some circumstances, say when the government foresees a financial crisis, where it would like firms to hedge, take less riesk etc. However, leveraged agents benefit from risk, and so they don;t benefit from risk eduction expenses.

Is there some theory or idea, out ther eon how to design a mechanism that incetivizes firms to reduce their riskiness? Maybe subsidize financial hedging? Maybe tax profits very progressively/convexly?

You could augment an externality mechanism, where people are punished for the effect they have on other people, and use a convex function or variance of outcomes. You could also transform their payoffs with a concave function to induce risk aversion. Look into the VCG mechanism and extensions for more info.


How can I best estimate a company's contribution to GDP? Would revenues be a good proxy variable? If not, what are the other proxy variables that I can use?

As a comment noted, value-added is the way to go. And how do we measure value added at the level of an individual firm?

It is

$$\text{Value-added} = \text{Wages and Salaries incl. Insurance}+\text{Depreciation}+\text{Profits before Taxes}$$

"Wages and Salaries including social security fees" is the reward of Labor, while "Depreciation plus Profits before Taxes" is the (gross) reward of Capital.

This makes sense because if one views GDP from the "income" angle, it goes to these two aggregates of productive inputs, "Labor" and "Capital".

All other expenses that appear in a company's Profit & Loss Statement are "third-party costs", or value that other productive entities create.

Depending also on the jurisidiction, in most cases Labor costs, Depreciation and Profits before Taxes can be found as separate items in the financial statements of a company.


Optimization of Households' utility in " Rule-of-Thumb Consumers and the Design of Interest Rate Rules " (Gali et al., 2004) I can't figure out how the calculation of first order conditions was carried out.

I can't figure out where the stochastic discount factor came from.

In this case, the stochastic discount factor appears in equation (7), the intertemporal optimization equation. You can derive (7) by taking the first order conditions of the Lagrangean function with respect to consumption, and then investment (or capital, K_t+1, if you want to substitute out the capital accumulation equation). You then combine these two optimality conditions to yield (7).

The stochastic discount factor, then, is just the ratio of marginal utilities of consumption in period t+1 and t. The ratio of prices appears in the stochastic discount factor because this is a nominal model, and you need to discount future nominal payoffs by inflation between time t and t+1.


Why do we say that trade and specialization according to comparative advantage lead to one-time increase in PPF of given country? PPF shows us different combinations of goods that we would be able to produce if we employed existing resources of our country in the most efficient way.

One thing to notice about PPF: It's completely independent from our agregate utility function. For an example, if we have only two types of goods, wine and cheese, then maximum production of only cheese (like 100;0) will be on our PPF, even if we would want to have some wine too or if we don't need so much cheese.

Now suppose we (Cheesetopia) trade with another country (Winetopia) and specialize in our comparative advantage (cheese). We will be able to consume, for an example, 50 cheese and 50 wine at the same time, a feat impossible for us under autarky. We would be consuming outside our production capabilities, outside of our PPF. But our current production would be on our good old PPF.

Thus I fail to see how free trades causes any shift in PPF or causes a country to produce outside its PPF. At the least for the Ricardian model.

For this you first have to put some numbers on the problem to be able to draw PPF and consumption. Lets assume that Cheestopia can produce 1 cheese at 1 labor, and 1 wine at 2 labor and Winetopia 1 cheese at 2 labor and 1 wine at 1 labor, and both country has 100L avaiable for production, this gives you the following PPFs for both countries in autarky (the chart was created by 1muflon1):

Now, I wont post full solution for a Ricardian model because it is not part of your question but in this case valid solution would be that the trade prices will be 1 cheese for 1 wine (if you want to know why maybe post it as a separate question about solving Ricardian model). Now under this trade scenario both cheestopia and Winetopia can produce only the good in which they have comparative advantage (i.e. only cheese in Cheesetopia and only wine in Winetopia) and at the trade 1ch for 1 w they can now access all the following points in consumption (note the points for two countries overlap but I ploted them next to each other so you see that second country does not disapear):

Now, whether anyone agrees that this increases a PPF it is indisputable that it increases the consumption possibilities of two countries. Thats plain from the picture. So now a question is following. Can we call this expansion of consumption possibilities increase in PPF? I think yes and also many textbooks call it like that for the following reasons:

From economic point of view there is no difference between producing, say, X of wine and between producing Y of cheese and then trading Y of cheese for X of wine. Just imagine that there a wizard/machine that converts Y of cheese in X of wine. From an economic perspective trade is like having access to production technology of the other country. Also macroeconomically consumption must be in long run equal to income and income in the long run must be equal to production.
By standard measures of production (such as GDP) this increases the production at any other point than the vertex (100ch, 0w) which overlaps with autarky PPF and PPF is by definition all possible combination of production. To show that this is the case lets consider one point on the new consumption line and lets use one standard output/production measure - GDP.

Lets select Cheesetopia and lets select point of consumption (0c,100w) which is a point of consumption only accessible by trade. Now if you claim that this point does not represent new PPF, at this point the production then a consumption point (0c,100w) should not show up on aggregates as GDP which measures the production as that would imply that production is outside PPF which by definition must include all production possibilities of a country. To calculate GDP we have to choose some good as numeraire (money) it does not matter which one we choose lets do cheese. So at the consumption point 0 cheese and 100 wine the components of GDP will be C= 100ch (here ch is the currency cheese they actually consume wine), X = 100ch (they export cheese) and M = 100ch (they import 100 wine and again cheese is the currency here). So GDP in this case is GDP = 100 + 100-100 = 100. So here we have a contradiction and there is only two ways how to resolve this contradiction:

You will say that GDP does not measure production. Which I dont think even the biggest critics of GDP would say.
PPF must be at consumption point (0ch,100w) at least 100 because by definition PPF is the combination of all production possibilities of the country, so if GDP measures production it must be within PPF it cannot be outside.

Now you can pick your 'poison' from the above option. Economically, the second makes sense. Intuition is that there is no meaningful difference between producing cheese at home and via trade transform this production of cheese into production wine and between actually being able to produce wine at home at the terms of trade. Or another way how you could express that intuitively is that in the new PPF any combination of goods can be produced by producing just cheese which is the highest point on the pre-trade PPF and which is also the single point where pre and post trade PPF will be exactly same.

Furthermore, to see that this is the same lets consider this scenario. 1 Winetopia gets destroyed by a tsunami so only Cheesetopia is left in the world. Now imagine that Cheesetopia will send some scubadivers to recover the Winetopia's wine production technology hence now Cheesetopia can produce both wine and cheese at 1 labor. Now the PPF is exactly the same as with the trade (meaning there is no meaningful economic distinction between trading.)