If every company in the economy earns zero economic profit, can they contribute to real economic growth? I understand that zero economic profit does not equal to zero accounting profit. It means that every resource that goes into the production is perfectly utilized considering alternative uses in the economy and nothing more. If every company in the economy is earning zero economic profit, can they contribute to real economic growth? (Ceteris paribus)

The standard measure of the size of an economy is total income. Profit is just one type of income (accruing to owners of firms). Wages that accrue to the workers in a firm can increase, which can be taken from the profit of the firm. In that way, income from other sources can continue to increase even though firms earn zero profit.

Other sources of income are rent (from land), and interest (from owning productively-used capital), but I'll stick to wages to keep it simple.

So, you can see that there are different markets at play—the labour market, the market for land, and the market for capital (or input goods). The important thing is that one does not, for example, simply take profit away from firm owners and give it to labourers. It must be a result of equilibrium in these markets. So, for example, if equilibrium in the labour market determines that wages for that sector must be high (e.g. due to scarcity of skills or an abundance of demand for those skills), then that high wage is just a cost of production that firms in that sector must swallow, in order to produce in that sector. Even though competition drives profits down to zero, all the other firms in that sector will also be having to pay the market wage rate.

I'm answering your question in a highly theoretical fashion, but then again, zero economic profit across the economy is a highly theoretical situation itself.

Edit:

To clarify, I'm arguing that aggregate income can increase through other forms of remuneration, even though profits stay at zero.

If you had a ceteris paribus clause that said these additional income sources remained the same, then economic activity would remain constant (i.e. growth would be zero). Take note that even if the wage rate (or interest rate or price of renting land) remained the same, an increase in the number of firms entering the market would increase economic activity. So, this ceteris paribus clause is not so much talking about the rate of remuneration remaining constant, but rather the aggregate level of income from other sources remaining constant.


What is the mechanism for when the fed purchases a gov't or corporate bond from a non bank? My understanding is when the fed buys a bond from a bank they use bank reserves (bank reserves are swapped for a bond). How does the transaction differ when a non bank (ex hedge fund) is involved?

When the Fed buys a bond as part of a Quantitative easing program, they execute with Primary Dealers through a website interface.  Hedge funds do not execute directly with the Fed, although they could execute with a Primary dealer who executes with the Fed.
When the Fed executes with a primary dealer, it credits the account of the primary dealer using newly created funds.  The dealer deposits the fund in a bank account, which increases bank reserves in the system.


Why is everyone suggested to specialize their education? Why is so common to suggest university students to specialize in order to get a better paid job?

This goes completely against the principle of diversification of investments, in order to decrease risk by spreading it over a portfolio.

Instead, students are driven towards specialization, investing their most valuable asset, time, in a single high risk endeavor. Specialization might be good for society as a whole, but can have disastrous consequences for the individual.

Note: I did not vote down on this question, and it is not clear why anyone would do so.

  Why is so common to suggest university students to specialize in order
  to get a better paid job?

Because the industry evolves and encounters increasingly harder, diverse challenges. Specialized knowledge is essential for coping with those challenges. At the same time, it is impossible for everybody to achieve expertise in all the diverse disciplines or branches of knowledge. In the labor market, that implies that the supply of workforce is more constrained as we move along the "specialization axis".

It is noteworthy, though, that specializing in order to get a higher compensation is not always profitable. For specialization to be profitable, there also needs to exist enough demand for a skills set. A specialist in semantics of Etruscan dialects spoken in the Po Valley will have a much harder time to find a job in his field (let alone to earn a satisfactory salary) than a specialist in 4th generation nuclear reactors.

  students are driven towards specialization, investing their most
  valuable asset, time, in a single high risk endeavor.

Not really. A certain extent of diversification is inherent to the individual's university background. In the case of the nuclear reactor specialist, his background includes calculus, probability, numerical analysis, thermodynamics, heat transfer, electricity, etc. That background makes it easier for him to adapt to drastic changes such as switching careers.

By contrast, a company is much more static and, thus, much unlikelier to cope with drastic changes successfully. Here are some factors that impair a company's adaptability:

Managers, first and foremost, aim at retaining their power;
it is harder for various stakeholders to agree on what the new
direction needs to be;
synchronizing an update of skills set of all its members is expensive
and possibly out of reach;
some members of the organization might leave during the transition;
new processes might entail new redundancies, frictions, and
additional overhead.

A shareholder has little-to-no control on how the company will fare, or whether it will adopt a unified, effective approach at all. Things are different with the individual, provided that he is determined, not erratic, and has a rational/realistic vision of what he wants.


Why do we have VAT on (most) services? My knowledge of economics is quite limited, but as far as I understand, the "added value" which is taxed by value-added tax refers to the difference in the cost of production and the cost in the store. Since the product has to be processed, packaged, transported etc. the cost will rise because every person in this chain wants a bit of money for themselves. The government then taxes this added value. Correct?

If this is true, then why is there VAT on services? Most of the services are "supplied" directly to the customer. For example, if a hairdresser cuts your hair, there were no intermediate persons in this process and the cost of the hair cutting service didn't rise because of them. If you're a web designer, you make a website and provide it directly to the customer - it doesn't have to be transported etc.

Basically, why would someone have to pay value-added tax if there is no added value?

(This also goes for all goods that are sold directly to the customer - but unlike services, goods can be passed on (the customer can sell the good that he has bought) whereas services can't, so I think that most services should be exempt from VAT).

Services are just as much VATable supplies as pyhsical products are

It is a mistake to think of the increase in price along the supply chain as just each person wanting their cut. For them to achieve this they need to be increasing the value that can be delivered to end customers, even if - for example - it is simply bringing a pallet of product to a convenient location and being there so that customers can buy single items at a time and place that suits them. That adds value to the pallet of goods in a warehouse.

The value added is the differemce between the VATable outputs I can make and the VATable inputs I use.

If my  business uses a consultant's time I pay input VAT on the money they charge me. I can offset this against the VAT I had to collect from my customers and send to HMRC.

If I hire a employee instead I pay their salary without VAT (so save input VAT) but then can't offset that amount against my output VAT, meaning I have to write a cheque to HMRC that is larger by the same amount as the input VAT I didn't have to pay (and which the consultant would have had to pay to HMRC).

It ends up a lot like a sales-tax but collected across the supply chain.

The problem with exemptions and zero rating

(I don't want to go into it, but making something VAT-exempt and making it zero-rated are very different things.)

One major problem with zero-rating activities from VAT is that it creates arbitrage opportuntiies if you can shift some or all of the supplies you make into the zero-rated category.

As most supplies have in some sense a service and a product component, general zero-rating of services would create huge incentives to artificially split out product and service compoments to save on VAT, leading to huge tax bureaucracy and litigation.

That this is a real issue can be seen in the hard-fought court cases over, for example, whether a jaffa cake is a cake or a biscuit or whether shops can save the VAT on a small transactino processing cost component of every transaction.

Ultimately VAT is very similar to a retail sales tax but with collection distributed across the supply chain.


Can't a country grow its GDP without foreign investment? Whenever various developing countries around the world talk about growing their economies, they talk about facilitating foreign investments and they put so much emphasis on it as if a country's economic growth can survive only if foreigners bring money into the country.

To me this is a cynic and dystopian way of thinking as you are dependent on other country's mercy, and those countries which developed themselves in the 1st phase of industrialization-wave are the only ones who rule the roost.

Is it impossible for a country to grow its economy without foreign investment?

No, you can definitely grow GDP without foreign investment or even trade.

There are 3 basic ways to grow GDP. One is increasing human capital, which includes increasing population as well as allowing women to work. Basically, anything that increases the number of people in the labor force.

Second, we have physical capital, which is where foreign investment comes in. This includes machines and computers, etc.

But both of these eventually have diminishing marginal returns. The final way is innovation, which means more efficient ways to do things, as well as new markets and ways to use goods, etc.

But foreign investment also helps with innovation, especially in developing countries, as the investment usually involves bringing innovation from foreign countries to the developing one.

So while it is not necessary, it is definitely helpful.


Must a EU bank pay 500€ to the ECB, if I deposit 100k€ into that bank? Given that the current ECB reserve rates are negative (-0.5%), I suspect that if I deposit 100k€ into a EU commercial bank, that bank must in turn deposit my money at the ECB and pay 500€/year to ECB (negative interests).
Is that correct? How does the mechanism work?

Banks do not make matching deposits into central banks, other than in a hypothetical 100% reserve system. As such, the answer is “no”.
What happens is that the private bank has a liquidity inflow, and it would need to find a corresponding asset, normally a money market instrument. The yield on that instrument is likely negative, but the “negative interest” is flowing to the seller of the instrument.


Allocative efficiency -- correlation between MB and p in populace with wealth inequality I was reading a paragraph in an economics textbook that was talking about
resource allocation, and felt that it missed an important point, leading to
a conclusion that I disagreed with.
I was hoping that someone could either explain why I'm wrong, or point me to
alternate resources that talk about this facet of the problem.

My textbook asserts that a competitive market would produce an efficient
allocation of resources.
Resources would be moved from less profitable products to more profitable ones,
and this would necessarily increase the monetary value to consumers of the
total products sold.

I understand the reasoning, but I question that total monetary value to
consumers can be related to total satisfaction of consumers when applied to a
large populace.

I accept the implicit assumption that the amount a single actor is willing to
pay for something would be directly proportional to the amount of satisfaction
they expect to get from it, but don't think this property can't be generalised
to a system of people with different total wealth.

As an example, a beggar would not be willing to spent \$30 on a good steak
dinner while a millionaire might.
One would not reasonably use this fact to argue the millionaire gains more
satisfaction from the meal than the beggar, but rather that it would require
more expected satisfaction to get a beggar to part with \$1 than a millionaire.

Applying this observation to how markets determine a price, we can see that a
products price (and by extension its profitability) is not solely determined by
its utility.
Rather it reflects the products utility combined in some way with the wealth of
its consumers.
A simplistic view might say

(price a consumer is willing to pay) = (wealth of consumer)*(expected satisfaction)

and so

(price of a product) = (wealth of consumer base)*(expected satisfaction)

In the above both the price and satisfaction represent their marginal values.

Working from that conclusion we can say that while allocating resources from a
less profitable product to a more profitable product will increase the monetary
value of products sold to the entire populace, we say the same
about the total satisfaction of the populace.
It may simply be that this moves satisfaction from a poorer section of the
populace to a richer section.

i.e. in a situation where different products can be supplied to different
sections of the populace, a products price can no longer be used to directly
infer its utility.
Hence optimising for monetary value to all consumers is not necessarily
optimising for total consumer satisfaction.

Just to note:
The paragraph in the textbook never explicitly drew a conclusion between
monetary worth to all consumers and total satisfaction, but there were phrases
like "\$20 worth of consumer satisfaction".
It's this conflation between satisfaction and monetary value over an entire
populace that I don't follow.

EDIT:
I re-read my question, and thought I didn't make it clear what I was asking:

It's:

1) Is there an obvious flaw in my argument?

2) If not, does anyone know of textbooks/articles that look into this (especially any that include data).

My textbook asserts that a competitive market would produce an efficient allocation of resources. Resources would be moved from less profitable products to more profitable ones, and this would necessarily increase the monetary value to consumers of the total products sold.

The textbook is correct (provided the assumptions behind "competitive market" and other implicit ones hold).

First, assume the distribution of wealth is given. Then, based on their budget constraint, consumers will have a certain demand for goods. Firms will compete for such demand, offering the lowest price that earn them an economic profit. In competitive markets, such profits are zero. Resources are allocated such that consumers are maximising their utility at the given prices. The allocation is Pareto Optimal.

This result is summarised in the First Welfare Theorem.

Second, through some form of lump-sum taxation, we could redistribute wealth in order to change that allocation. A competitive market will make the equilibrium Pareto Optimal too. This is the Second welfare theorem (see link above).

So, your intuition that the wealth/income distribution affects prices and the final allocation is correct. But the key to allocative efficiency is in the mechanism (market), not in what is being allocated.

I hope I am answering your questions.


Is elasticity of substitution between goods empirically constant? In New Keynesian models, we use a lot of CES assumption, usually Dixit-Stiglitz, to develop an economic model. Is CES, constant elasticity of substitution between goods, empirically (approximately) true?

Constant elasticity of substitution (CES) Utility functions imply demand functions that are linear in (i.e. conditional on prices they are constant fractions of) income (see Rutherford's Lecture Notes on Constant Elasticity Functions). However, there is empirical evidence for both superior goods (demand that increases faster than income) and inferior goods (goods that decrease in income), this does not actually hold for real preferences.

The fact that household budget shares on each consumption good (or even category) are not constant is probably additional evidence against CES. In principle it is explainable if different consumers face different costs for goods but shouldn't explain why some people choose to do entirely without certain categories of consumption (no TV rather than an inexpensive one). I say probably because:

If you define the category wide enough (say two, durable and non-durable consumption), everyone does likely does consume something in every category and maybe in close to fixed proportions.
For certain important forms of consumption like cars and house, adjustment costs and indivisibility may make households face very different prices.

But, as @regressforward suggests, it may still be an acceptable approximation.


Homogeneity of degree zero and normalization One of the first assumption is that the demand function is homogeneous of degree zero. The reason and the proof is easy.

It should also be easy why this implies we can normalize the price of one good to 1, but I cannot see exactly what's going on.
A counterexample would be of great help i.e. a function with homogeneity different from zero showing that the normalization is not possible/leads to wrong conclusions.

Demand $x(p, m)$ is the solution to the utility maximization problem:

$\max\limits_{x\in\mathbb{R}^n_+} \ \ u(x) \\ \text{s.t.} \ \  p\cdot x \leq m$

where $p\in\mathbb{R}^n_{++}$ is price vector, and $m$ is the income.

When we multiply both sides of the constraint in problem above by $\lambda > 0$, and look at the revised problem we get

$\max\limits_{x\in\mathbb{R}^n_+} \ \ u(x) \\ \text{s.t.} \ \  \lambda p\cdot x \leq \lambda m$

Since this operation does not affect the constraint, the solution remains unaffected i.e. demand satisfy $x(\lambda p, \lambda m) = x(p,  m) $ which shows that demand is homogeneous of degree 0 in $(p, m)$. So, this is always true for demand function. Given that $p_1 > 0$, we can take $\lambda  = \frac{1}{p_1}$, and find $x\left(\frac{p}{p_1}, \frac{m}{p_1}\right)$ to get $x(p, m)$.

It is helpful to note that for any function $f(p)$ that is homogeneous of degree $k > 0$, it is the case that $f(\lambda p) = \lambda^k f(p) \neq f(p)$ for $\lambda \neq 1$.


Does the Efficient Market Hypothesis Solve the Tragedy of the Commons? My layman understanding of the Efficient Market Hypothesis is that there is so much brain power focused on the maximization of profit in the marketplace, that the market will find the best solution both in the short and in the long term.

The particular instance of "Tragedy of the Commons" I have in mind is global warming, for which there is a fair amount of scientific consensus that it will disturb our civilization to an extent that does not guarantee that markets will continue existing as usual (stable governments being somewhat important for markets).

So here is my question: It seems that market players are not investing in ensuring the effects of global warming are minimized (i.e. market players are not ensuring the continuing existence of a market place). Does this mean that the Efficient Market Hypothesis is a model that does not describe our actual reality? If that is the case, how is one supposed to know when the Efficient Market Hypothesis is a good model?

A side question: Is this whole "exploiting the commons before someone else exploits them, irrespective of the fact that we are all doomed without the commons" more closely described by a Prisoner's Dilemma? But if that is the case, would you not expect the intelligent efficient actors in the marketplace to decide to work together to save themselves?

My education is not in economics so maybe my question is not well defined. My hope is that even if this is the case, an explanation of why the question is not well defined would be useful on its own.

Your description of the Efficient Market Hypothesis (EMH) is not correct.

The EMH simply states that asset prices fully reflect all publicly-available information. It does not make the wild claim that:

  the market will find the best solution both in the short and in the long term.

You write:

  It seems that market players are not investing in ensuring the effects of global warming are minimized (i.e. market players are not ensuring the continuing existence of a market place). Does this mean that the Efficient Market Hypothesis is a model that does not describe our actual reality?

Market players do not invest with the goal of minimizing the effects of global warming. Instead, their goal is to maximize their returns.

To the extent that their interests and those of society's (or the world's) are not aligned, we have a problem of externalities. But this says nothing whatsoever about the EMH.

Example. At a horse-racing track, individuals place bets with the goal of maximizing their winnings. They do not place bets with the goal of raising the horses' welfare or of sustaining the horse-racing business. Their goal may not align with that of the horses or the business owner. But this says nothing whatsoever about the EMH.

(What the EMH would say in this example is that the bets reflect the expected performances of the horses. The bets do not say anything about the welfare of the horses of the viability of the horse-racing business.)


What are the economics of bike sharing companies? Bike sharing seems to have originated in China.

And it has spread to the UK.

And at least a decade on it continues to spread into the provinces.

So it has longevity.

So what are the economics of this industry?

At first glance it would appear to be a horrible model: lots of liability, lots of maintenance, lots of criminality and endless opportunity for annoyance through dumped bikes causing inconvenience.

So what is the economic model of bike sharing?

Interest is their profitability mechanism. Pretty much everything else is a cost.

Let's make an example:

I start a bike share business.
I buy 100 bikes. Costs me \$10K.
I make the fee of using the bikes so cheap, lots and lots of people have no problem using them as its so cheap.

Here is the catch: To cover my liability (lost bikes, stolen, wrecked, etc.) there is a  one time fee (before you can use any of my bikes) that is a 100% REFUNDABLE security deposit of \$50 (you get your \$50 back whenever you want, so it's still cheap for you).

Everyone's \$50 adds up to quite a lot of money just sitting earning no money. But I want to make money. So what do I do? I invest it in super safe short/medium term bonds or whatever I want at a low/decent interest rate and collect my profit.


Are urban land (location) markets considered competitive even though the market price does not equal marginal cost (zero)? Urban land (location) supply is fixed and the marginal cost of bringing an urban plot into production is zero. Even when land owners do not collude to limit the supply, the fixed supply arguably results in the same market power (monopoly rent).
If urban land (locations) could indeed be replicated, wouldn't that imply that demand would move to rent-free land on the edge of civilisation thereby driving the urban land (location) market price to zero? In the absence of the latter doesn’t the presence of rent in the urban land (location) market imply that it is not competitive?

Existence of rent has nothing to do with whether market is competitive or not. First there are different definitions of rent. As explained in the Palgrave dictionary of economics (Alchian 2017):

Rent’ is the payment for use of a resource, whether it be land, labour, equipment, ideas, or even money. The term is often restricted to payment for use of land or equipment. ‘Economic rent’ is payment for use of any resource whose supply is fixed. Rent serves a social purpose because market levels of rent indicate which uses of fixed resources are the highest valued, and direct such resources to those uses. ‘Monopoly rent’ is paid to producers in markets that are artificially restricted; it may be dissipated by ‘rent seekers’ who compete for monopoly status.

Hence rent can have various meanings depending on the context. Only the last definition of rent that is:

‘Monopoly rent’ is paid to producers in markets that are artificially restricted; it may be dissipated by ‘rent seekers’ who compete for monopoly status.

Has anything to do with competition. Even here there must be some artificial restriction on the market so there is some monopoly (i.e. one seller). All other definitions of rent have nothing to do with competition and some of the above definitions are fully compatible with perfect competition (e.g. even if there would be perfectly competitive market for land and there would be some marginal costs of making it productive - which there actually are although usually they are small (you have to maintain land for it to be usable for housing etc) - the perfectly competitive price for land would still be called rent).
For example, it can trivially be proven that in oligopolistic competition firms can make positive profit, and prices will be higher than marginal costs (see examples Belleflamme & Peitz Industrial organization: markets and strategies). However, oligopolistic profit would not be considered monopoly rent - even if firms have market power.
In order to have monopoly rent in this case you need to make argument that the plot of land is sufficiently distinct from other plots of land so it can be considered to be unique and its owner would thus become a monopolist because there would be only one seller of this one unique piece of land. You can probably make this assumption for any special location (some place with unique excellent view) or locations with some historical value making them special (e.g. land under the White House), but such assumption would be inadequate for any random slot of land in some city. In many cases all plots of land in a given block or even in a whole section of city can be treated as completely homogenous without loss of generality.


Why has QE produced hyper-inflation in other countries, but not US and China? QE and similar methods ("printing money", increasing M2 money supply) have caused currencies in countries such as Zimbabwe and Venezuela to collapse.

Why hasn't it caused similar issues in countries such as the US and China which have also increased their M2 by large amounts over the past decade?

That is because inflation is a change in price level and price level can be expressed using the basic monetary model as:

$$P=\frac{MV}{Y}$$

Where M is money supply, V is velocity of money and Y is output.

Hence, while it is true that the price level is increasing in money supply (M) it is also decreasing in (Y). Hence if your money supply grows for example by 5% but also your output grows by 5% and velocity stays the same your country will experience 0 inflation.

Countries that experience high levels of inflation such as Venezuela have a double problem of increasing money supply while their output is plummeting making their inflation very bad, while other nations get less inflation than you would normally see given change in M due to growth in output.

Furthermore, in certain types of recessions when there is a liquidity trap all increase in M can be offset by decrease in V. This is the reason why for example US or Euro-Area experienced low inflation even though they had large recessions and large expansion in money supply in the recent recession.

In more complex models expectations play role as well but I don’t want to go too much into technicalities as the main lessons carry from them to the above mentioned simple model.


Why doesn't national savings, in aggregate, always equal to zero in monetary terms? Referring to this question and this one
Imagine you had a closed economy with two people and they both started off with $100 dollars. How would net savings in aggregate ever not be zero? Anything spent, net, by person 1 would be a positive savings for person 2, and a negative savings for person 1. The same is true vice versa.
I understand that if person 1 and person 2 both produced 10 bushels of wheat and then ate only 5 of them, and then ground up the other five and used them as fertilizer (bad example, I know) that they would have 'saved' and 'invested' 10 bushels of wheat in aggregate. However, in monetary terms, the personal savings rate in aggregate would still be zero because they didn't sell the wheat to anyone and thus had no personal income (again, in dollar/monetary terms).
So, to sum up, my first question is, in monetary terms, in a closed economy will aggregate savings always be zero?
Second, how does the BEA get a positive savings rate, and how do we have positive gross national savings, in addition to running a trade deficit?

I think this boils down to misunderstanding what saving in macroeconomics is. Saving does not cancel each other out. In closed economy, private saving is difference between income (which is by definition equivalent to output so I will be using output and income interchangeably) and consumption $S=Y-C$ and public saving is difference between government spending and taxes $T-G$. In your case there are only private individuals so let us assume there is no government so that $T=G=0$ and consequently national identity will be given just by $Y=C+I$ (also note this shows that investment and saving must be equivalent since $Y=C+I \implies Y-C=I \implies S=I$). See Blanchard et al Macroeconomics a European Perspective for further explanation of those identities.

You you can't just save without having income. The money you saved in previous time periods would be part of your net wealth. For example, if in 2010 nothing is produced and sold both individuals have no income  and thus cannot form any new saving. In this example saving for 2010 would be 0. The money they hold from previous time period would be their net wealth.   However, note in this case there cannot be any consumption either and consumption will be zero. Why? If there is no income and production there cannot be any consumption as well. If something would be produced in 2009 and it was not consumed in 2009 so that it is still avaiable for purchase in 2010 it would be recorded as an inventory investment. So in your example, no matter what those people do $Y, C$ and $I$ are all zero $Y=C=I=0$.

If they actually produce something saving is totally possible. Consider the following trivial  example, suppose the person A produces in 2010 $\\\$75$ worth of widgets and person B produces in 2010 $\\\$50$ worth of food. This means that the national income in 2010 will be $Y=50+75={\\\$}125$. Now let us suppose person A buys all food from person B for $\\\$50$ and person B buys $\\\$50$ of widgets from person A. In this case consumption for B is $C={\\\$}50$ B has zero savings since for $B$ $Y_B-C_B=0$. However, A will have some saving since for A income was $Y_A={\\\$}75$ and consumption was $C_A={\\\$}50$ so there is $S_A=Y_A-C_A={\\\$}75-{\\\$}50={\\\$}25$ which on national accounts will turn up as and inventory investment. So everything balances since $Y=C+I$ holds as we have $Y_A+Y_B ={\\\$}125$

Note it makes no difference whether everything is expressed in purely monetary units or real terms. In above I assumed all those quantities are expressed in nominal, so monetary terms, but I could as well just make them real by deflating those prices by some deflator. The equality would still hold equally well.


Are lexicographic preferences strictly monotonic? I'm a bit confused about lexicographic preferences and whether they abide by the strict monotonicity axiom.

The definition we were given for strict monotonicity is:

  For any two bundles $x$ and $y$, if $x_i \succsim y_i$ for each good $i$, then $x$ is strictly preferred to $y$

The preferences are summarized below:

  (1) The bundle that has more of good 1 is better, regardless of the amount of good 2.

  (2) If the amount of good 1 is the same, the bundle that has more of good 2 is better.

I'm confused about part (1), because a bundle can have much more of good 2 but still be preferred if it has a bit more of good 1, e.g. $(2,5)$ is preferred to $(1,100)$, even though it has so much more in it. Surely that can't follow the provided definition of strict monotonicity (or am I really thick)?

Thanks!

It seems you are not confused about part (1) because that's exactly what it means.

Lexicographic preferences are monotone. Monotonicity means more is better. If I have more of every good in the bundle, then I like that bundle more. This is still true for lexicographic preferences, even though parts of the bundle may not matter. A condition for monotonicity is e.g. that (5,4) is preferred to (3,1). In other words if 5>3 and 4>1 then the first bundle is preferred. This is true for lexicographic preferences.

Your definitions of strict monotonicity and lexicographic preferences seem to deviate a bit from conventional definitions though. Here is a proof using your definitions.

Proof:

Let us compare two bundles with $n$ elements each: $x=(x_1, x_2, ..., x_n)$ and $y=(y_1, y_2, ...,y_n)$

It is best to start with the if statement when going about proving such claims. The condition and therefore starting point is $x_1>y_1$ and $x_2>y_2$, .... , and $x_n>y_n$.

In that case since  $x_1>y_1$ we have according to your preference definition that bundle $x$ is preferred to bundle $y$. Furthermore we have that bundle $y$ is not preferred to bundle $x$. So bundle $x$ is strictly preferred.

Hence, we have shown that if $x_i$>$y_i$ for each $i$, then $x$ is preferred (because in that case $x_1 > y_1$), which is your definition of monotonicity. The preferences are therefore monotonic.


How is the cost of equity for a specific stock calculated using the Fama-French 5 factor model? The Fama-French 5 factor model is as follows:
$$R_a = R_f + \beta_m \left( R_m - R_f\right) + \beta_s\text{SMB} + \beta_v\text{HML} + \beta_p\text{RMW} + + \beta_i\text{CMA}$$
It is quite easy to find $\beta_m$ for a specific stock (most stock websites have it listed), and the market premium is also quite easy to determine since $R_f$ the US Treasury 1-month bond and the annual return of the market in the long term (at least in the U.S.) hovers around 8-10%.
However, I am not able to find a resource to find out the size, value, profitability, and investing premiums nor can I find the specific betas for each risk factor for a specific stock.
My question is if I want to calculate the cost of equity for a specific stock, using the CAPM model is quite easy as most of the numbers are readily available, but how could I go about finding the relevant figures for the rest of the risk factors?

If you visit Ken French's website (specifically, his data library), you can download monthly and daily returns for the 5-factor model (as well as similar returns for the Carhart momentum factor).
You can then find annual averages for those and compute the cost of equity in a similar way as for the CAPM.


Can someone explain graphically why MRS is invariant under monotonic transformation? Let $U(x,y)$ be a utility function. Suppose I have an indifference curve for which $U(x,y) = \bar{U}$. Then $dU = 0$ along the curve and I can rearrange to find the MRS.

Suppose I have a monotonic transformation of my utility function. That is, some function $$W(x,y) = f(U(x,y))$$ $$f'(\cdot) > 0$$

Since it too is an indifference curve, $dW = 0$ and I can rearrange as follows

$$\frac{dy}{dx} = -\frac{W_x}{W_y} = -\frac{f'(U(x,y))U_x}{f'(U(x,y))U_y} =-\frac{U_x}{U_y}$$
Thus, we observe MRS is invariant under monotonic transformation.

My Question:

Can someone explain what this means graphically? I don't get why the slope remains the same. Why does MRS remain the same but MU changes?

You're right that it's a bit counterintuitive that the shape of the indifference curves shouldn't change when you transform the utility function. The reason is that you are transforming along an axis that is perpendicular to the plane where the indifference curve lives.

Let's imagine we have two goods, x and y, and let's say that the original utility function is given by $U(x,y)=x^\frac{1}{3}y^\frac{2}{3}$. We can create a 3D plot of the utility function where $z = U(x,y)$. Any transformation $f(z)$ will work on the z dimension. In the following example, the transformation $f(\cdot)$ is multiplying the utility function by a positive scalar

If you look down on the $x-y$ plane from above, you will notice that you can plot an indifference curve through a point on that plane and it will look identical before and after the transformation. Note that it will not be the same indifference curve because the utility level will change under the transformation. Going back to the multiplication example, let's look at the indifference curve (red line) that goes through the bundle $(x,y) = (10,10)$ (red dot). Regardless of the multiplier, the indifference curve maintains its shape but the associated utility level increases from 10 to 20.

I have also included other level curves, for utility levels 4, 8, 12, ... 40. Note that as the factor with which we multiply the original utility function gets larger, these level curves get squeezed into the lower left corner.

You can see the same thing happening with other monotonic transformations, for example translation (adding a constant) and power transformation.


Relationship between interest rate and rental price of capital In Daron Acemoglu's Introduction to Modern Economic Growth (2009), P.32, it is stated that given assumption of exponential depreciation at the rate $\delta$ and normalization of price of final good to be 1, $r(t) = R(t) - \delta$ where $r(t)$ is interest rate, $R(t)$ is rental price of capital and $\delta$ is depreciation rate. The reason, which I agree, is that:

  A unit of final good can be consumed now or used as capital and rented to firms. In the latter case, a household receives $R(t)$ units of good in the next period as rental price for its savings, but loses $\delta$ units of its capital holdings, since $\delta$ fraction of capital depreciates over time. Thus the household has given up one unit of commodity dated t-1 and receives $1 + r(t) = R(t) + 1-\delta$ units of commodity dated t.

But, on P.330, when talking about overlapping generations model where $\delta = 0$, it is stated in equation (9.3): $1 + r(t) = R(t)$. Shouldn't it be $r(t) = R(t)$? I cannot find this is a typo like from http://www.econ.ku.dk/okocg/VV/VV-2015/Lectures%20and%20lecture%20notes/Errata-to-Acemoglu-book-VV-2015.pdf. Do I miss something?

The equation is exactly the same,

$$r(t) = R(t) - \delta$$

Now, set $\delta =1$ per assumptions, to obtain

$$r(t) = R(t) - 1 \implies 1+r(t) = R(t)$$

which reasonably continues to say that the accepted rental rate of capital $R(t)$, covers the depreciation rate plus $r(t)$ which is also the net return to capital.


How to calculate the average wage increase? What is the average wage increase and how does one calculate it? Gottfries (2013, p. 166) refers to the following formula as the "average wage increase:"

$$\frac{\Delta W_t}{W_{t-1}}$$

If the above formula is meaningful, then my question is more a clarification about terminology and notation.

As to terminology, what is a more popular way to refer to this equation other than the average wage increase?

As to notation, Gottfries refers to $W$ as the "average wage level," but what do the other symbols mean? Is it safe to assume the expressions $W_t$ and $W_{t-1}$ refer, respectively, to the average wage levels at times $t$ and $t-1$? What then does $\Delta W_t$ represent? Is $\Delta W_t$ the difference in average wage levels at times $t$ and $t-1$ (i.e., $\Delta W_t = W_t - W_{t-1}$)?

I think this question is worth asking since 1) there has to be a more popular way to refer to this equation (Gottfries book was all that came up when I Googled "average wage increase") and 2) I don't want to assume, as far as notation goes, more than I have to (Gottfries doesn't define these symbols).

This is a very standard % change over time formula.

It is simply:
Change Between Years / Original Value

$ΔW_t$ means the change in wage from year $t-1$ to year $t$ (where $t$ represents an arbitrary amount of time). You can easily calculate that by: $ΔW_t=W_t−W_{t−1}$.

Thus it is simply saying % change over time is $\frac{New - Old}{Old}$.

Middle school math with more symbols.


Bayesian Nash Equilibria in Battle of Sexes Consider the static Bayesian game as described below. $\ t_1$ and  $\ _2$ are the types of the row and column player respectively, which are both uniformly distributed on the interval $[0,1]$. The first part of the question is asking us to find a Bayesian Nash Equilibrium. Trivially, don't the the top left and bottom right corners correspond to equilibrium outcomes? Unless I've misunderstood the definition of a BNE.

Yes, you are correct. All types $t_{1}$ choose O (B) and all types $t_{2}$
choose O (B) are both Bayesian equilibria.
Note that there are other Bayesian equilibrium in this game, if you are interested this is explained in detail here (p. 10, see reference below) for this particular battle of the sexes with two-sided incomplete information. The basic idea is to note that in this game, each player has a continuum of types, and so the set of types is infinite. You can look for a Bayesian equilibrium in which player 1 goes to the $Opera$ if $t_{1}$ exceeds some critical value $x_{1}$ and chooses $Fight$ otherwise, and player 2 chooses to $Fight$ if $t_{2}$ exceeds some critical value $x_{2}$ and goes to the $Opera$ otherwise. To find the values $x_{1}$, $x_{2}$ that make these strategies a Bayesian equilibrium you can calculate each player's expected payoffs given the other player's strategy and find the optimal values based on this.
Game Theory: Static and Dynamic Games of Incomplete Information
Branislav L. Slantchev Department of Political Science, University of California – San Diego


Errata for Wooldridge graduate econometrics book Does anyone know where I can find an errata to the 2nd edition (2010) of «Econometric Analysis of Cross-Section and Panel Data» by Wooldridge? I've tried the accompanying website, but I could not find it.

Any help would be appreciated

I know I've referenced that text before so I ran a quick search. Here's the instructor's solution manual.

Wooldridge Instructor Edition - Cross Section & Panel


What Math is used in Development Economics? I would like to ask what kind of math is used in Development Economics?

I have one more semester in my Master of Math programme before hopefully entering a PhD in Economics and am considering specializing in this; so I would like to know what I should take or review next semester.  Are the topics listed on the wiki-page for Mathematical Economics applicable?  Being differential equations, linear algebra, optimization, and analysis.  Or would statistics or data science be more applicable?

Thank you

This does depend on whether you're looking to do applied econometric work, in which case statistics is definitely the way to go or something theoretical, in which case a good understanding in the maths you listed will go a long way. Of course it's always better if you understand both - since you're doing a master's in math, you should already be quite fluent with the math required, so I'd go with econometrics.

There's a growing amount of literature available, but if you have time to spare, I'd give the topics in Nafziger's "Economic Development" a glance: http://tabesh.edu.af/Books/economic/Economic%20Development.pdf


What is the difference between personal consumption expenditure price and PCE quantity? What is the difference between these two things? How is PCE price different from PCE quantity? Also, I am confused about the difference between PCE quantity and measure of real output. For example, what is the difference between PCE quantity and Industrial Production?

Personal consumption expenditure (PCE) is the primary measure of consumer spending on goods and services in the U.S. economy.   It accounts for about two-thirds of domestic final spending, and thus it is the primary engine that drives future economic growth.  PCE shows how much of the income earned by households is being spent on current consumption as opposed to how much is being saved for future consumption.
https://www.bea.gov/resources/methodologies/nipa-handbook/pdf/chapter-05.pdf
The PCE price index is a measure of the prices that people living in the United States pay for goods and services. The PCE price index is known for capturing inflation (or deflation) across a wide range of consumer expenses and reflecting changes in consumer behavior.
https://www.bea.gov/data/personal-consumption-expenditures-price-index#:~:text=A%20measure%20of%20the%20prices,reflecting%20changes%20in%20consumer%20behavior.
Most PCE price indexes are derived by extrapolating consumer and producer price indexes from the U.S. Bureau of Labor Statistics.
The PCE quantity index derived by deflating current-dollar estimates at the most detailed category level by appropriate PCE price indexes with the reference year equal to 100.
Prices and quantities are prepared at a detailed level and are aggregated based on a Fisher chain-weighted formula  https://www.bea.gov/sites/default/files/methodologies/nipa-handbook-all-chapters.pdf#page=64
This source can provide some answers: https://www.bea.gov/help/faq/521
The difference between PCE quantity and industrial production is that PCE come from consumer spending.   Industrial production measures the output of the industrial sector, which typically comprises mining, manufacturing, utilities and, in some cases, construction.
The difference between PCE quantity index and real output is that PCE come from consumer spending while Real output comes from spending from consumers, business/industries, and government/government enterprises.


What is the reason why ARIMA(0,1,0) on $y_t$ and ARIMA(0,0,0) on diff($y_t$) are not identical time-series models? I studied at BA level, that ARIMA(0,1,0) on $y_t$ and ARIMA(0,0,0) on diff($y_t$) are the same models. I am doing the Box–Jenkins model estimation on the historic data of US unemployment rate.

My results (in R):

> arima010a

Call:
arima(x = munrate, order = c(0, 1, 0))

sigma^2 estimated as 19.23:  log likelihood = -2126.56,  aic = 4255.11
> arima010b

Call:
arima(x = diff(munrate), order = c(0, 0, 0))

Coefficients:
      intercept
         0.0708
s.e.     0.1618

sigma^2 estimated as 19.23:  log likelihood = -2126.46,  aic = 4256.92

As you can see, the information criterion (AIC) differs and the $log(L)$, too. My question is, why do they differ in the two model?

I'm looking forward to any answer.

I tried the same later in gretl, and there wasn't any difference between the two models.

I don't know R code but are you estimating an intercept in the ARIMA(0,1,0) model? Because if not, this could be why there is a difference, since you are estimating an intercept in the ARIMA(0,0,0) model.


Is First Order Stochastic Dominance (FOSD) relation convex? A convex relation is that $x\succeq y$ implies $\alpha x+(1-\alpha)y\succeq y$.

Let $>_{FOSD}$ be $\succ$, is the FOSD convex? Intuitively it seems convex.

The first order stochastic dominance relation is convex.

An easy way to prove this is to use the property that a cdf $F$ FOSD another cdf $G$ if and only if $F(x)\le G(x)$ for all $x$. That is, $F$ FOSD $G$ if and only if the graph of $F$ is never above the graph of $G$. It is then easy to show that $F$ is never above any convex combination $H(x)=\alpha F(x)+(1-\alpha)G(x)$, which in turn is never above $G$.


Looking for discussion on equilibrium vs dynamic models in econometrics I'm a statistician/machine learning scientist more familiar with molecular bio than economics.  Trying to find out if an issue I perceive in bio modeling also occurs in econometric modeling.

A common task in computational biology is to build a model of some biochemical process from data.  These biochemical processes are always dynamic, i.e. something you might model with an ODE or Kalman filter.  However, there is a bias towards modeling such a process from equilibrium data.  This means, you wait until the process has reached some equilibrium (homeostasis), and you take measurements across subjects/replicates.  This is because for many reasons it is much easier and cheaper to acquire equilibrium data relative to time series data.  Training a model only on equilibrium data is a problem of course if you want the model to be predictive when the system is not at equilibrium.

I wonder if the same bias happens with econometric models?  Clearly, in terms of statistical methodology, cross-sectional data is typically cheaper and easier to acquire than time-series data.  And I know economists are concerned with modeling equilibria.
 I'm hoping there is a place someone can point me to that talks about this issue in the econometric context, perhaps with an example?

Economists (most of them) build their models assuming most of the time stochastic dynamic equilibrium. So Economics does not contrast "dynamic" with "equilibrium" - it synthesizes them.

It is stochastic in the sense that random shocks are acknowledged. It is dynamic in the sense that it may revolve around a deterministic or stochastic trend. And it is an equilibrium because, exactly, it is assumed "chained" -not necessarily to some level but at least to some trend.

The "bias induced" here, the price to pay, is that mainstream economic models are not very good at predicting derailment and crises. On this, perhaps it would be useful to read this column article by well-known economist Robert Lucas.


Budget constraint in Radner Sequential Trade Equilibria Suppose that $q$ is a k-tuple vector of prices for the k assets whose quantities are given by the k-tuple $\theta$. I have just read that in the Radner Sequential Trade Equilibrium (not sure if this goes by another name), where the trading of assets occurs in period t=0 (as opposed to t=1), the period-zero budget can be expressed as $q*\theta$, where $*$ denotes the inner product, and that this budget is non-positive.

I feel like I must be misunderstanding something about this particular setting, because I have no idea how a budget could possibly be non-positive, as opposed to non-negative.

Can someone give me some intuition for what's happening here?

In Radner's model each actor starts with an initial endowment, an asset vector $\omega$. You can trade this to any asset portfolio $x$ that has lower or equal value, so
$$x * q \leq \omega * q.$$
Denoting asset trades by $\theta = x - \omega$, you can also express this as
$$
\theta * q \leq 0.
$$


How does demand-supply equilibrium interact with profit maximisation? My understanding of supply and demand is that at higher prices sellers are more willing to supply and buyers will demand less, and the total transaction volume will be supply or demand, whichever is less. At some finite price the two are equal, given an equilibrium; and whereas at a higher price demand and hence transaction volume would fall, at a lower one supply and hence transaction volume would fall. Thus the equilibrium price should also maximize transaction volume.

But here's where I get confused. Excuse my inventing notation. Suppose at selling price $P$ there is a transaction volume $V(P)$, maximised at equilibrium price $P=P_E$ so $V'(P_E)=0$. If the unit cost to the seller is $c$, their profit is $\Pi=(P-c)V(P)$. Hence $$\dfrac{d\Pi}{dP}=V(P)+(P-c)V'(P),$$ which at $P=P_E$ is $V(P_E)>0$. Thus the profit-maximising price exceeds $P_E$. This logic seems to imply profit maximization won't occur at the equilibrium price.

So what does microeconomics actually predict happens in a market?

I think one source of confusion in your question is that you are piecing together assumptions from different models that are incompatible. In particular, you've implicitly referred to a supply curve, but attempted to write down the optimisation problem of a monopolist. This doesn't work because a monopolist has no supply curve: a supply curve describes how much a seller would be willing to sell for a given price, taking prices as given. However, monpolists do not, by definition, take prices as given. Supply curves only make sense when the seller faces perfect competition.

Hopefully I can make this clearer by giving you an overview of the two different models.

One standard assumption in basic models is that markets are perfectly competitive. For sellers, this means that they take prices as given, and nothing they do can affect the price of the good that they are selling. (Alternatively, they solve their profit maximisation problem while ignoring any effects their choices have on the market price.)

Formally, a seller chooses the output quantity $q$ to maximise

$$ pq-c(q), $$

where $p$ is the price of the good, and $c$ is the (convex) cost of producing $q$ units of the good. Hence, the seller's profit-maximising level of output is given by

$$ p = c^\prime(q). $$

This gives us the seller's supply curve

$$ q^s(p) = (c^\prime)^{-1}(p). $$

Given some demand curve $q^d$, the relevant equilibrium condition is now

$$ q^d\left(p^*\right)=q^s\left(p^*\right) = q^*, $$

where $p^*$ and $q^*$ are, respectively, the equilibrium price and quantity. (This treatment needs to be slightly modified when $c(q)$ is linear, as in your question, but this can be done.)

We can, of course, relax the assumption that the seller is a price-taker. Suppose now the seller realises that their choice of $q$ can affect the equilibrium price. Here, we say that the seller is a monopolist. They now choose $q$ to maximise

$$ p(q)q - c(q), $$

where $p(q)$ is the inverse demand curve. That is,

$$ p (q) = (q^d)^{-1}(q). $$

(Equivalently, as in your question, they would choose $p$ to maximise

$$ p q^d(p)-c\left(q^d(p)\right). )$$

The equilibrium quantity is then given by the solution to

$$ p^\prime (q^m) q^m + p(q^m) = c^\prime (q^m). $$

Note that it now doesn't make sense to ask what the seller's supply curve is. The seller's profit-maximising level of output isn't determined by a given price, because their choice of output affects the price.

One can show, as you've found above in the case with constant marginal costs, that (assuming demand is downward sloping)

$$q^m < q^*$$

and

$$p(q^m) > p^*. $$

In other words, when the seller is a monopolist, the seller's profit-maximising output (which they will sell in the equilibrium where the seller is, in fact, a monopolist) is smaller than the equilibrium output under perfect competition.


What is the ideal way to update an old value to today's currency value? For example, how much is $25 million in 1790 considered today?  How do I update such value?  It doesn't make sense to me to use, say, price indices.  Shouldn't such update be done based on the expansion (or contraction) of monetary supply?
Clarification post-comments.  My thinking --- please educate me if it is nonsensical --- is that inflation is an expansion of the monetary supply, so I would like to do a computation from the phenomenon of inflation itself, not of its effect, one of which is an increase in prices. So I would like to be able to estimate a loss of value merely from the the increase in monetary supply.  I could then compare it against real facts --- which would be the market prices.  I'd be willing to read an entire book just to learn how to do this.  So feel free to advise.  Thank you!

I think this question stems from misunderstanding from what inflation is. My best guess is that this happened because most macro books will say that inflation is a monetary phenomenon as in mainstream economics it is accepted that inflation over long periods of time is affected mainly by money supply. This is illustrated by equation of exchange (see Blanchard et al Macroeconomics an European Perspective) which is given by:
$$P= MV/Y$$
This is the same equation that Brian also mentioned in his comment just solved for prices. Here $P$ are the average prices, $M$ money supply, $V$ velocity, and $Y$ real output. The standard textbook argument for inflation being monetary phenomenon goes like this. Velocity is assumed to change over business cycle but not really over long run and hence it cannot be responsible for all inflation and we can hold it constant. Moreover, real output tends to increase over time which should be deflationary. Hence the argument goes that over long run inflation should be caused by $M$.
However, this does not mean that inflation is defined in terms of $M$. The definition of inflation is simply the change in average prices for example:
$$\pi_t= \frac{P_t-P_{t-1}}{P_{t-1}}$$
This is what inflation is. Moreover, inflation also is measure of how money looses value. The issue is that money especially in short run might not loose value just because there is more of it (i.e. by $M$ increasing) but also because velocity changing or real output dropping. Furthermore, $M$ and $V$ are not always independent. At zero lower bound any increase in $M$ will be offset by changes in $V$ because at zero lower bound peoples preference for holding (but not necessary spending) cash will be infinite (abstracting from issues such as storage costs for large sums of cash). What even more, models that are above simple undergraduate textbooks rely not just on actual values of $M$, $V$ and $Y$ but also on peoples expectations of these (see Krugman 1998).
Hence you simply cannot calculate how money looses its value from $M$. At minimum to calculate change in $P$ using $M$  you would need to know and control for not just what $M$ is but also what real output is and velocity is but here you will run into problem that real output is usually calculated by deflating nominal output by CPI - so you introduce the same problem you wanted to avoid. What even worse velocity itself is usually not directly observed but imputed from data. And this is all before we start factoring in all the expectations we should that are extremely difficult to measure. Compared to such convoluted way using CPI directly is far more sensible even if it may be imperfect measure.


What makes the Balance of Payments (BoP) to imbalance? Theoretically the capital account balance should fully offset the current account balance and the BoP should be zero for any economy. What causes the imbalance or discrepancy in the overall BoP ? What makes countries run BoP surplus or deficits ?

This depends on the exchange rate regime. For a floating exchange rate, the balance of payments is always in equilibrium, that is, the financial account always offsets the current (and capital) account. A hypothetical deficit is avoided by a depreciating exchange rate, a hypothetical surplus is avoided by appreciation.

For a fixed exchange rate regime, the central bank will offset the exchange rate adjustments that guarantee the equilibrium under floating exchange rates. In order to offset these adjustments, the CB has to intervene in the exchange markets. To prevent a currency from depreciating, the CB has to use its foreign reserves to buy its own currency. To avoid an appreciation, the CB has to buy foreign currency and icrease its foreign reserves.

To sum up, as an answer to your question: BoP imbalances only occur in a fixed exchange rate regime and are caused by foreign exchange interventions of the CB. Therefore, the imbalance is equal to the settlements balance, or the change in the CB's reserve assets.


Reference request on "post-scarcity" economics? Some friends and I have been discussing, speculatively, what might happen in the future after technology/increased automation greatly reduces the need for human labor.

The Marxists / leftists among us think that there will be a coming class conflict as more and more of the productivity gains from automation are captured by an elite, and that there will be a widespread political push from the left for something approaching a basic income.

Other, less left-leaning folks among us worry that there will be a collapse in aggregate demand as the purchasing power of a sizable, jobless part of the labor market essentially exits the economy. How government might respond to that is unclear.

I have the equivalent of an undergrad degree in economics and figured that there had to be some good discussion out there.

Can anybody point me to any papers or extended discussions of this topic?

A related question is in asking when (if ever) will we be post scarcity. The paper Are We Approaching an Economic Singularity? Information Technology and the Future of Economic Growth by William D. Nordhaus should be of use.

Abstract:

  What are the prospects for long-run economic growth?, the present
  study looks at a more recently launched hypothesis, which I label
  Singularity. The idea here is that rapid growth in computation and
  artificial intelligence will cross some boundary or Singularity after
  which economic growth will accelerate sharply as an ever-accelerating
  pace of improvements cascade through the economy. The paper develops a
  growth model that features Singularity and presents several tests of
  whether we are rapidly approaching Singularity. The key question for
  Singularity is the substitutability between information and
  conventional inputs. The tests suggest that the Singularity is not
  near.

(emphasis mine)

Another possibility is to consider those sectors, like digital media, where we are already post-scarcity, in that marginal costs are zero or very near to it. I recommend Carl Shapiro and Hal Varian's Information Rules for an accessible and interesting discussion of the economic issues that arise in this setting.


Why does price drop as a result of increase in supply According to the Law of Supply, if price increases, there is an incentive for producers to produce more, and therefore the quantity supplied increases. However, for an inelastic good, if there is a supply shock and supply significantly increases, why is there a drop in price? Can't the suppliers sell their product at the same or a higher price to increase total revenue?

Low price elasticity of demand, together with fluctuations in supply over short periods of time, creates serious problems for primary commodity producers, because they result in large fluctuations in primary commodity prices, and these also affect producers’ incomes. A good crop resulting in a supply increase leads to lower prices and lower farmers’ revenues. We come, therefore, to the ironic conclusion that a poor crop may be good for farmers because it increases their revenues while a good crop may be bad for them. Can't the farmers sell their product at the same or a higher price to increase total revenue?

You are describing a special (although very important) market where the short-run market supply function is vertical : farmers will attempt to sell whatever they have produced, irrespective of what that will do to the unit price. I am not saying this is not reasonable: many agricultural products are not really storable (or require special infrastructure in order to be stored), and there is certainly increased pressure to sell, compared to other products.

And indeed, in such a case, one can see a "good crop" bringing in lower total revenues, due to relatively inelastic demand. This is after all the core reason why government price subsidies in the agricultural sector (i.e. supplementing the farmer's income to compensate for low market price) is the rule rather than the exception, in virtually all market economies around the world, where very few other final products enjoy price subsidies (and only temporarily, while for the agricultural sector, it is essentially a permanent situation, of course not for all agricultural products).

Also, as another real-world remark,  it is not uncommon for farmers to withhold and even destroy part of their crop in order to safeguard prices (and thus end up with higher total revenues compared to what they would have get if they have sold all the crop at a lower price).

I am not sure I understand the last sentence/question in your post. In what sense farmers "can" or "cannot", "sell at the same or higher price"? And "same" compared to what?


Why are there two formats for the Solow capital evolution equations? I have seen the capital transition equation take two forms

$$K_{t+1} = sY_t +(1-\delta) K_t $$
$$\dot{K}_t = sY_t - \delta K_t$$

Obviously I can rewrite the top one to get

$$K_{t+1} - K_t = sY_t - \delta K_t $$

So that suggests somehow

$$\dot{K}_t \equiv K_{t+1}-K_t$$

But as far as I know,

$$\dot{K}_t \equiv \frac{\partial K_t}{\partial t} = \lim_{h\rightarrow 0} \frac{K_{t+h} - K_t}{h}$$

which is, as far as I know, not the same as $K_{t+1}-K_t$.

my question

Is
$$\dot{K}_t \equiv K_{t+1}-K_t$$
right? If so, what does this mean and why isn't it the usual derivative?

The Solow-Swan has the two versions, one is in discrete time (first equation) and other in continuous time. Both give the same results, but you cannot mix them - as you did.

In the first equation (discrete time) you can take the first diference but never a derivative, since the variable is not continuous. The point above the variable means that it has been diferenciated with relation to time.

So the last equation does not make any sense because tried to mix both models.


Maxmin and minmax strategies I was solving for a stable equilibrium in the following 2 player zero sum game. I need to calculate the equilibrium using maxmin and minmax strategies. In this game they should come out to be identical and coincide with the mixed strategy Nash's equilibrium.

                        P2
               L                R
   L       (0.6,0.4)         (0.8,0.2)

P1

  R        (0.9,0.1)         (0.7,0.3)

If I solve it formally, the expected payoff of P1 will be the expression:

$E = 0.6(pq) + 0.8p(1-q) + 0.9(1-p)(q) + 0.7(1-p)(1-q)$

where p is probability of P1 playing L and q is the probability pf P2 playing L. Now, P2 is trying to minimize E keeping in mind that P1 is trying to maximize it

i.e. min max {E}

and P1 is trying to maximize E keeping in mind that P1 will try to minimize E i.e.

max min {E}

and vice versa. Essentially both strategies played simultaneously should give the same equilibrium. How to go about it, I am stuck in the maths part of the problem now.

The question was clarified in the comments as

  How to calculate $\min\limits_q \max\limits_p E(p,q)$ for a given function $E(p,q)$?

What this notation means is that $p$ is chosen first, and $q$ is chosen afterwards.

Assume that $p$ is a given parameter. Then $E(p,\cdot)$ is a function over $q$ only. So you take the minimum of the function $E(p,\cdot)$. In economics this usually means taking the first derivative with respect to $q$. From this you get the optimal value of $q$, given $p$. This is basically a function $q^*(p)$. So you know how $q$ will be chosen given the choice of $p$. This gives you the function $E(q^*(p),p)$. You choose $p$ to maximize this function. Again in economics this usually means taking the first derivative w.r.t. $p$.

With $\max\limits_p \min\limits_q$ the procedure is essentially the same, but there you first derive the maximum for $p$ given $q$. This yields $p^*(q)$. Using this, you minimize $E(p^*(q),q)$ w.r.t. $q$.

A sidenote:
If $E(p,q)$ is linear in both $p$ and $q$ the functions $q^*(p)$ and $p^*(q)$ are usually not continuous. To be more precise they are not functions but mappings. As such, they upper hemicontinuous but that is very technical and you may not need to know what it means.


Possible regression biases with GDP [x] vs Health expenditure [y] (both per capita) I am regressing per capita health expenditure on per capita GDP. I have 3 data columns (health expenditure, gdp, population)

So my regression function is healthexpenditure/population = b0 + b1.(gdp/population)

1) My question will be what are the possible problems of this model? Is dividing dependent and independent variable with population number problematic? This is a theoritical question, I want to explore possible biases in my simple model.

2) Suppose that I have plotted my data and it looks like this. Do you see a problem that are related?

There could be a question of whether your model and graph should be based on a linear relationship or a log-log relationship

The slightly widening residuals apparent in your linear graph seems to understate the real issue illustrated in a linear-axis graph from Gapminder. The green outlier at the top is the USA while the small red outliers on the right are rich but small Gulf and SEAsian countries, and the presence of both of these could exert excessive leverage on your regression coefficients

This left-right disparity in residuals does not look so bad with the same Gapminder data plotted with log-log scales.  It also spreads out the big cluster of developing countries in the bottom-left corner between those which are extremely poor and those which are not so poor and so allows their relative difference to influence your model estimates


Can't we measure the growth in the income levels of poor? Inflation has been a challenging aspect
of policymaking. In such situations growth in
the income levels of the population living below
the poverty level can never be measured
accurately (due to higher infation poverty section will
show higher income) . My question is: Due to higher inflation why cannot we measure growth in the income levels of the population living below poverty line accurately?

That's not specific to poor, any income increases with inflation.

The real problem is that the poor receive goods for free (charity, squatting, rent nonpayment) so their real income can never be measured.


Who owns the federal reserve? Does anyone know who actually owns the federal reserve? It's like a public private institution, who are the private owners, and who are the public owners?

The Federal Reserve is a system, consisting of the reserve banks, which are "owned" (in a limited fashion) by their member banks (members select the leadership of the reserve banks), and the Federal Reserve Board of Governors, which oversees the member banks and is independent within the government (that is, the Governors are nominated by the President and confirmed by the Senate, but neither has direct control over the Board beyond its composition and the legal authorities assigned to it). All of this is covered in the law that gives the Fed its authorities, the Federal Reserve Act.


what can be the proxy variable for measure of product innovation? My objective is to prove that international trade leads human capital formation which leads to economic growth. I am regressing GDP on multiple variables among which Human capital is one. According to a paper, I've read, new lines of product provide more learning by doing opportunities for workers and hence accumulation of human capital. Since panel data on product innovation is not available, it uses 'first time export' of a commodity as an indicator of product innovation. The source for the data is https://comtrade.un.org/db/
But I don't understand how to identify first time exported commodities.
i need suggestion for what other variables can be used as a proxy for product innovation.

UN COMTRADE has export data by country-product at the HS 6-digit level. What you could do to find out when the product was first exported is to get data for a country's export for product, say, with HS code 123456, from as far back as possible, and see when was the first year that the export of this product is not zero.

I've seen number of patents filed used as a proxy for product innovation in some papers. That might work for your paper as well?


Capital/Income Ratio in Pikketty's Capital In Capital by Thomas Pikketty, https://www.robertdkirkby.com/blog/2015/summary-of-piketty-i/, he states that World War I and World War II were the main reasons why the Capital Income to Labour Income ratio was lowered.

However, why is this the case if two world wars lead to capital destruction. Surely the remaining capital is more valuable? And possibly less is more labour to service this relatively than in the past.

First, important thing to note here is that $K/Y$ is not the capital income to labor income ratio, but ratio of capital to total income (or output which is macro-economically equivalent to income). $K$ is not an income derived from capital it is the stock of capital.

Wars destroy the stock of capital so even though returns to capital $r$ indeed increase the fall in the stock of capital makes the capital-income ratio fall.

Furthermore, the share of income going to capital is according to Piketty given by $\alpha = r \frac{K}{Y}$, and hence even if the rate of return increases when capital becomes more scarce the actual share of income going to capital might decrease if the capital-income ratio falls sufficiently to offset an increase in $r$.


Does 0% interest rate mean the minimum value of a currency? I would like to know if there are other factors that can devalue a currency. I think the effect of the negative interest rates will not be much greater than the 0% interest rate because simply a very few people would put their money in the bank.  Maybe increasing the salary of the governmental employees would devalue but I think it's not a practical solution. Does 0% interest really mean the minimum value of the currency?

Can the inflation rate rise even if the interest rates are below 0%?

In short, yes. The inflation rate rises when more money chases goods and services than before. This can happen because there is

more money circulating
less goods and services output
money is circulating at a faster pace (increased money velocity)
money is chasing a narrower set of goods and services

Note the last point decreases the inflation rate for the goods and services that are no longer chased.

In the short term, when interest rates lower, people borrow more money to spend as borrowing is cheaper. Assuming no change in the goods and services output, the inflation rate should rise.

As you mention, you can raise government employee salaries. And you don't have to necessarily limit the salary raise to government employees: an earned income tax credit would have the effect of raising most people's salary. Or more generally, you can expand on fiscal spending: build bridges, fix roads, launch rockets, etc. Assuming this fiscal spending is financed through government debt and there is a budget deficit, there is now more money chasing existing goods and services in the short term, and thus the inflation rate should rise in the short term. Over the long term, productivity gains from fiscal spending should increase the output of goods and services and offset the inflation spike.

You can also just print money and dump it off a helicopter. This will again cause more money to circulate and raise the inflation rate in the short term. What happens over the long term depends on how effectively people spend helicopter money.


Explanation Rational Expectations I am struggling understanding the concept of rational expectations. Can someone explain in simple words the concept of rational expectations? Does someone know a good (online) source explaining rational expectations?

The concept of rational expectations can indeed be confusing.

One of the nicest pieces that I read online on rational expectations is the following:

https://economictheoryblog.com/2012/05/18/rational-expectations

It very nicely describes the concept of rational expectations in very simple words.

The most important thing one needs to understand is that rational expectations do not imply that all people act optimal under all circumstances, it rather implies that people behave optimally given the information they have.


Are There Giffen Inputs? I am studying for my candidacy exams and I came across this question on a previous exam. The question is in the TFD (True, False, Debatable) section of the exam. The claim is:

  There are no Giffen inputs in production.

I think this question is a very fascinating one, and should spark some interesting discussion. My intuition tells me that this is false because if there are Giffen goods on the consumer side then surely there are Giffen goods on the producer side. However, I cannot think of a concrete counterexample to the claim. In consumer theory, they claim that Giffen goods occur when the good is so important to the consumer that when the price increases, they decide to just buy that good and not buy any other goods. For example, economists believe that one of the only real life Giffen good situations is potatoes in the Irish potato famine. They claimed that potatoes were such a staple in the Irish diet that when the prices rose, the Irish people decided not to buy other foods (such as meat) and dedicated all of their food budget to potatoes.

Are there any situations where we might see a firm/industry act in a similar way? What do you guys think? Are there any Giffen inputs in production?

I believe the answer is true.

Giffen goods are goods where the income effect overpowers the substitution effect.

$$\begin{align}
\max_{\vec x} \ \ \ & U(\vec x) \\
& \text{s.t.} \ \ \ \vec p \cdot \vec x \leq I
\end{align}$$

To start, if you think about the consumer's problem (for example utility maximization, here), a change in a good's price affects both relative substitutability of goods through the marginal rate of substitution AND it affects purchasing power through the budget constraint.

Let us consider a profit maximizing firm with a constraint on how much they can spend. For simplicity let us use a single output technology, with differentiable production function $f(\vec z)$. Let $\vec z$ be a vector of inputs (expressed as negative values), $\vec w$ a vector of input prices, and $p$ the output price.

$$\begin{align}
\max_{\vec z} \ \ \ & pf(\vec z) + \vec w \cdot \vec z \\
\text{s.t.} & \ \ \ \vec w \cdot \vec z \leq B \\
& \ \ \  z_i \leq 0 \\
\end{align}$$

Normally we would have a constraint on production, but instead we have a "budget" constraint. What happens if we form the Lagrangian here?

$$\mathcal{L} = pf(\vec z) - \vec w \cdot \vec z - \lambda(\vec w \cdot \vec z - B) + \vec\mu \cdot \vec z$$

Take first order conditions:

$$\frac{\partial \mathcal{L}}{\partial z_i} = pf_{z_i}(\vec z) - w_i - \lambda w_i + \mu_i = 0 \tag{1}$$

$$\frac{\partial \mathcal{L}}{\partial f(\vec z)} = p = 0 \tag{2}$$

$$\frac{\partial \mathcal{L}}{\partial \lambda} = \vec w \cdot \vec z - B = 0 \tag{3}$$

At an interior solution where the budget constraint binds, we should have the optimum $\vec z^*$ to solve the FOCs

$$p \frac{\partial f(\vec z^*)}{\partial z_i} = w_i$$

but instead you solve out (1):

$$p \frac{\partial f(\vec z^*)}{\partial z_i} = - \frac{\mu_i}{1 + \lambda}w_i$$

and (3) does not provide any help to solve the Lagrangian multipliers. (2) is nonsense.

A better constraint would be something like $y - f(\vec z) \leq 0$, where $y$ represents the scalar of output.

Without an "income effect", there isn't much to study Giffen behavior. Producer theory doesn't use a budget constraint to solve these sorts of problems. Increasing input price will always decrease use of that input except with corner solutions, where there might be no change. So there can't be a Giffen input.


Moral hazard vs hidden information. What is the difference between hidden information and moral hazard?

I cannot understand these two terms mainly. Please explain. Thank you.

Hidden information concerns characteristics that are unobservable by one side of the market. For example, a consumer's willingness to pay, a worker's productivity, the quality of a used car all fall under this category. The characteristics in question are typically assumed to be fixed or very costly to modify.

Moral hazard concerns actions that are unobservable by one side of the market. For example, the effort that a CEO puts into managing a company and the care that an insured driver takes to maintain the condition of his car both fall under this category. By their very nature, the (unobservable) actions can be easily changed to suit the incentive structure of the problem.


Could markets compute equilibria? It has been shown, for example in the papers

Deng, Du, The Computation of Approximate Competitive Equilibrium is PPAD-hard
Hirsch, Papadimitriou, Vavasis, Exponential Lower Bounds for Finding Brouwer Fixed Points

that finding competitive equilibria is in a certain sense computationally intractable.
So how does economic theory expect a market to reach a competitive equilibrium if each agent is presumably representable by an efficient computational process?
In fact, parallel computation doesn't really help because a polynomial number of processors can be simulated in polynomial time.

Computing an equilibrium is not needed for implementing it. This was the mistake of Lange and co. and was decisively rebutted by Hayek.
If you want a mathematical formulation, simply take a tatonement process. Given prices, each individual needs to compute her net demand correspondence. Under different tatonement mechanisms, which are an idealization of the dynamic process of price adjustment in the real-world economy, prices should converge to approximate equilibria. In both experimental settings and in financial markets, there is ample evidence for convergence.


What is the equation $\mathbb{E}[mR]=1$? I have just joined this Stack Exchange site and I was reading the following question: What are the foundational equations of Economics?. I have seen a couple of times the following equation in that post:

$$\mathbb{E}[mR]=1$$

I have a certain idea of what it might mean, but could someone explain its meaning (or at least what do $m$ and $R$ stand for? It is difficult to Google it if I don't know what these 2 quantities are).

Also, is the expectation $\mathbb{E}[\cdot]$ taken w.r.t to any particular probability measure, or simply with respect to the real world measure?

PS: I apologize if the tags are not well-suited to the question, I have tried to guess what this equation might be related to.

This is an important result in financial economics (asset pricing) but not trivial to explain intuitively. I do my best to give you the big picture and get you started on your research.

R is the return on an asset or portfolio.  Any asset or portfolio.

m is the stochastic discount factor or pricing kernel.

The expectation here is over possible states of the world given information at time t (m and R are as of t+1).

These are physical, not risk-neutral, probabilities. In fact, a (positive) stochastic discount factor is what is used to translate physical to risk-neutral probabilities.  In a discrete case, the risk-neutral probability is the risk free rate times the physical probability times the value of the stochastic discount factor in that state.

The stochastic discount factor takes on a different value for each possible state of the world (that's the sense in which it is stochastic).  But it doesn't change for each different asset.  If it exists, a stochastic discount factor can be applied to every asset in the economy and price them all correctly.

Facts about the SDF:

The existence of such a factor is equivalent to the law of one price holding.
If it is always positive, there are no arbitrage opportunities in financial markets.
If and only if markets are complete, then the stochastic discount factor is unique.
The expectation of the SDF is the risk-free rate

There are a lot of theoretical uses of this relation and important related results---many fundamental results in finance can be interpreted in an SDF context, though many of those results came before development of SDF theory.  For many common utility functions we can derive the form of the SDF for a representative agent theoretically.

I'm sorry if my answer isn't super accessible.  The equation is simple, but stochastic discount factor theory can be a little opaque.

Resources to consider reading:

Cochrane and Culp's chapter in Modern Risk Management: A History

Asset Pricing and Portfolio Choice Theory, by Kerry Back


Compute Nash Equilibrium in median voter game Consider a spatial model in which two candidates A and B compete for office. The policy space ranges from -1 to 1 and each candidate can take one of three positions, -1, 0, and 1 (so that they have only three pure strategies). Voters vote for the candidate closer to their ideal points, but the location of the median voter is not known to the candidates: the median voter is located at either -1 or 1 with probability s < 1/2 and is located at 0 with probability 1 - 2s. Assume that candidate A is slightly more advantaged than B: A prevails if A and B are equidistant from the median voter but B wins if he is closer to the median voter. Winning yields a payoff of 1 and losing 0. The candidates simultaneously choose a position. Answer the following questions.

Draw a 3-by-3 payoff matrix and show if there are any pure-strategy Nash equilibria.

My attempt:
$\begin{array}{r|ccc}
A\backslash B & -1 & 0 & 1\\
\hline
-1 & 1, 0 & s, 1-2s+s & 1-2s+s, s\\
0 & 1-2s+s, s & 1, 0 & 1-2s+s, s\\
1 & 1-2s+s, s & s, 1-2s+s & 1, 0
\end{array}
$

This simplifies to
$\begin{array}{r|ccc}
A\backslash B & -1 & 0 & 1\\
\hline
-1 & 1, 0 & s, 1-s & 1-s, s\\
0 & 1-s, s & 1, 0 & 1-s, s\\
1 & 1-s, s & s, 1-s & 1, 0
\end{array}
$

Computing PSNE:
If A chooses -1
-- if s>1/2, B chooses 1
-- if s=1/2, B chooses either 1 or 0
-- if s<1/2, B chooses 0
If A chooses 0
-- B chooses either -1 or 1
If A chooses 1
-- if s>1/2, B chooses -1
-- if s=1/2, B chooses either -1 or 0
-- if s<1/2, B chooses 0
If B chooses -1
-- A chooses -1
If B chooses 0
-- A chooses 0
If B chooses 1
-- A chooses 1

There's no PSNE.

Or can I say the following? Since the BR for either player should result in a strategy that helps them win the median voter, it can't happen that both players win the median voter. Therefore, there exists no PSNE.

Characterize a MSNE if it exists. Hint: let A's mixed strategy to choose -1, 0, and 1 be p, q, 1-p-q, respectively, and B's mixed strategy be x, y, and 1-x-y, respectively.

For B to be indifferent, EU(-1)=EU(0)=EU(1). Thus, sq+s(1-p-q)=(1-s)p+(1-s)(1-p-q)=sp+sq

Solution: p=s/(2-s), q=(3s-2)/(s-2)

For A to be indifferent, EU(-1)=EU(0)=EU(1). Thus, x+sy+(1-s)(1-x-y)=(1-s)x+y+(1-s)(1-x-y)=(1-s)x+sy+(1-x-y)

Solutions: s=o, y=0, or
x=(s-1)/(s-2), y =s/(2-s)

I don't know how to translate these into MSNE. Can you also let me know if I have got everything right so far?

Thanks in advance.

The calculations look correct.

For the PSNE, I would just say since there is no mutual BRs in pure strategy, there is no PSNE, and leave it at that.

In the MSNE, A would play $-1$ with probability $\frac{1-s}{2-s}$, $0$ with $\frac{s}{2-s}$ and $1$ with $\frac{1-s}{2-s}$; B would play $-1$ with $\frac{s}{2-s}$, $0$ with $\frac{2-3s}{2-s}$ and $1$ with $\frac{s}{2-s}$.


If strict preferences map onto $\Bbb{N}$ what do weak preferences map onto? Suppose I have $$\text{apples} \succ \text{pears} \succ \text{pineapples}$$

I can map this onto the natural numbers as follows

$$\text{apples}\mapsto 1$$
$$\text{pears}\mapsto 2$$
$$\text{pineapple}\mapsto 3$$

But for weak preferences we might have $$\text{apples} \sim \text{pears}$$
But this wouldn't map bijectively onto the natural numbers because then for example
$$\text{apples} \mapsto 2$$
$$\text{pears} \mapsto 2$$

My Question:

What do we map weak preferences on to? Or do we relax the assumption the map has to be bijective and allow it to be a surjective mapping onto $\Bbb{N}$?

First of all, I don't know if there is a convention as I never use weak preferences myself. But I can give you some suggestion that should work:

Do you have a finite number of goods, lets say $n$? Then $\mathbb{N}$ is clearly enough:
Just map the best good to 1, the second best to $n$, third best to $n^2$,... .
If you are indifferent between 2 goods (lets say they would be ranked third overall) assign them to $n^2$ and $n^2+1$. As @MettaWorldPeace already pointed out: it is kind of "wasteful" to use $\mathbb{N}$, so can we use less? And clearly we can never need more than $(n-1)^n+1$ numbers, so a mapping on $\{1,2, ..., (n-1)^n+1 \}$ would be sufficient (you can use even less numbers, but it is annoying to write down, so I just leave it at that).

What if we have a (countably) infinite number of goods? Here we can use the same trick, using $\mathbb{R}$ (or, if you like to, use $\mathbb{Q}$) just assign the best good $1$, the second best $2$, ... . If there are indifferences (i.e., you have three second best goods, the first one is assigned $2$, the second one $2.1$, the third $2.11$(or whatever you like)). Again, as before it is kind of wasteful, what else can you use? You could use a mapping on $\mathbb{N}\times \mathbb{N}$.

The same idea clearly works for every other number of goods, but I guess you can figure that out yourself.

Remark: This is not more than a different way to write preferences. You can not use this, e.g. as a utility function. However, all of these examples have the property that you can compare the ranking by simple mathematical operations (i.e., comparing $\lfloor \frac{x}{n}\rfloor$ for the first example).


Why do different countries have different currency? Why do different countries have different currency?

 I have this question because I want to know why to divide it? If it's not divided then we can easily use the money anywhere and we won't need to use currency exchange.

Two reasons: history and ability to control the money supply.

History: paper-money started by being issued by trustworthy agents from kings/governments, as a way to be able to transfer the ownership of gold without moving the gold physically. This looked something like "This paper is exchangeable for 10 gold coins at this location". This meant you had to go to that specific kingdom to get the paper (bill) converted into gold. These papers evolved into what we now call banknotes, and kept tied to a specific country.

Money supply control: having your own currency allows governments to fund themselves by producing more money, or stimulate exports by devaluing their currency. Look at the euro-zone difficulties with the government debt of Greece: this could be solved (with consequences, of course) if they had their own currency.


Is wealth inequality actually a problem I have been searching around online, but cannot really find an answer to my question.

I can find a lot of material covering wealth inequality and how it has developed over time, but haven’t found any material to support my theory (or the opposite).

My question is: Is wealth inequality actually a problem? With this I mean the super wealthy vs the rest (if that makes a difference).

I will try to explain my thinking as good as possible. My theory is, that super wealthy people tend to not spend all of their money, they may invest it or set it aside.

Consider a scenario where an individual owns 99% of all the wealth (i.e. money, disregard stocks, bonds etc in this scenario) in an economy, but spends roughly the same as everyone else in the same economy, effectively “disabling” a huge portion of the wealth. Would the “poor” actually be affected by this negatively? Would prices on goods reflect that “effective” wealth, or the total wealth in said economy?

Another scenario could be where one person owns most or all shares in all companies in the economy, and everyone else living of of salary. Would this actually be a problem? I imagine that it is same as above scenario.

Obviously these are silly extreme scenarios, I was just trying to paint a bit clearer picture of where I am coming from.

If the super rich (or perhaps top 1%) have an average spending similar to everyone else in an economy, with the only difference that they own more wealth, would that actually be a problem; or perhaps in reality a smaller problem than how it is depicted in the media?

I am not looking for political standpoints, but a more fact based answer.

I think that you are more or less than correct in thinking that cash that is never spent (nor expected to be) may as well not exist. Thought experiment: suppose that, unbeknownst to you and everyone else, £1 million suddenly appears under your mattress. If you never discover the money, it is hard to see how it could change anything in a meaningful way.

There are some caveats, however. First, a game theoretic point: even if rich people never spend their money, threats to spend their money might influence outcomes. For example, they could pledge to donate lots of money to the political opposition unless the government does what they say. If this threat works, they will never need to pay out.

Second, a ‘non-economic’ point: money gives you options, and people might enjoy having options in itself (even if they don’t spend the money). One might object to the kind of ‘options inequality’ brought about by an unequal wealth distribution even if rich people never spend their cash.

Third, to bring us back to the real world, we should stress that, usually, rich people do consume more than poorer people. So while it might be interesting to discuss wealth inequality without consumption inequality, this is not a phenomenon which we are actually facing today.


Why is there less price transparency in some industries (especially healthcare) than in others? To give a specific pair of contrasting examples:

If I search for homes for sale in say Michigan, I can quickly see the listed price for each home. (See e.g. Zillow.) Sure, there might be taxes, commission, fees, discounts, etc., but the final price I pay will almost certainly be within ±50% of the listed price I see.
But if I search for an assisted living or adult foster care home (for the elderly) also in Michigan, I am unable to find a single home that lists any price on its website, Facebook page, or anywhere else. Instead, every single home asks you to call or email them, or arrange for a tour. I have no idea what I'll have to pay, even very roughly, perhaps not even to an order of magnitude. I truly have no idea if the cost per month will be \$1,000, \$5,000, or \$10,000.

Unfortunately, from my brief search, there doesn't seem to be much research by economists on this topic (but let me know if I'm mistaken).

Here are some possible explanations I've considered:

Price transparency tends to be decreasing in price.

This might be generally true, but fails to explain why there is so much less price transparency in healthcare than in real estate.

In healthcare, there is much more uncertainty and variation as to what each patient will end up costing.

But each healthcare facility does have standard rates for particular items, such as "a standard type X blood test", "a brain MRI in Machine #566", "a 24-hour stay on Bed #125", "a month's long stay in Room #351" (excluding all miscellaneous costs). Just like any restaurant or business has standard rates for particular goods and services.

The difference is that most restaurants and other businesses do publish these prices, while healthcare facilities do not.

Why is it advantageous for healthcare facilities to keep these prices shrouded in secrecy? Why have market forces not forced them to reveal these prices (in contrast to other industries)?

The US healthcare industry is perhaps exceptionally egregious. But I think it is also generally true in most countries that there tends to be much less price transparency in healthcare than most other industries. Why is this?

Please note that any successful explanation must explain why there is less price transparency in some industries (especially healthcare) than in others (real estate, airfare, food, cars, car repair, university tuition, etc.).

Obviously nursing homes are a.smaller market...

Large, liquid markets with frequent buying and selling of standard products have the most information.

Also, Zillow is bad, home assessors exist for a reason.


Rawlsian SWF and Arrow Impossibilty Theorem given Arrow impossibility theorem the only social welfare function that satisfies unrestricted domain, pareto and the independence of irrelevant alternatives is Dictatorship. However I was wondering which one of these criteria the Rawlsian SWF fails. I was suspecting Independence of irrelevant alternatives, however I can't come up with a proof.
Thanks in advance for your help.

Independence of irrelevant alternatives prevents you from using the information needed to implement a Rawlsian SWF; the information who is society's worst-off cannot be used.
Indeed, the relevant information is not even specified in a profile of preferences.


What causes the US media obsession with tariffs; The EU and others have charged tariffs on US stuff forever? The EU has about a 50% tariff on US beef and higher tariffs on US liquor (typical EU bureaucracy has many categories and quotas, so a single number is impossible). So why is a relatively low US tariff on 2 materials, (the EU has tariffs on about 100 materials from the US) make so much news time?

Nations frequently have tariffs between each other. However, the trend since WW2 has been fewer tariffs and other trade barriers. For example, even recently the EU has significantly reduced tariffs.

Likewise, the US has also both practiced and preached free trade, reducing tariff rates.

Economists have strong consensus that tariffs are bad. This isn't dependent on political leanings, it has wide agreement. "The economics profession continues to show a consensus in favor of unfettered international trade, as 83 percent agree and only 10 percent disagree that the United States should eliminate remaining tariffs and other barriers."

The reason the new tariffs are reported by the US media are because they are a new policy change which oppose the existing trends and expert opinion, although they do have public suport