Can savings and poverty coexist? Many governments try to decrease savings in the economy so that recessions do not occur. Does it make sense for savings and poverty to coexist though at significant scales?

Let's say a population was both in widespread poverty and they had savings. If they had unmet needs, they would spend their money on those needs. This would occur until either savings where expended or the needs where met.

If savings where bad and caused poverty, it would eliminate itself it seems. So either it is bad, but doesn't need to be discouraged since it eliminates itself, or is good and doesn't need to be discouraged.

I guess the problem could be if savings where uneven, but then

That doesn't mean savings are universally bad, just savings of the non-poor.
If there is a recession, people will have less money to buy things, and so things will need to be sold for less. This will encourage people with savings to spend.

First we must address the nature of savings. Savings are not bad or good per se. It depends on the context. It is true that in the short run, increased savings will lower consumption, thereby lowering GDP. However savings also increase investment, which in the long run increases economic growth. Therefore, the optimal savings rate is found by solving the trade-off between the short and long-term.

If you are interested only in the short-term (GDP right now and a few periods more) then you would see savings as bad. If you are interested only in the long-term you would see savings as good. If you are interested in both, then it is ambiguous.

The optimal savings rate is certainly not 0 for a standard economy. One way the optimal savings rate is characterized is through the so-called "golden rule" in a simple Solow growth model. You might want to look this up.

Empirically, we typically observe that most countries save too little, i.e. are below the golden rule savings rate. If you are below the optimal rate, whatever that may be, then more savings are good. If you are above it, then more savings are bad. Hence, it is not straightforward to make a case about the desirability of savings.

Your second question was about poverty and savings. Yes, they can and do coexist empirically. In fact, many economists are puzzled why savings rates are so low in poor countries, since more savings increase growth over the long-term.

To see why savings and poverty can coexist, you must think about the reason we have savings. Individuals save more today, so that they can consume more tomorrow. Hence, you cannot really detach the two completely and say that savings are bad. Imagine a poor country that is primarily agricultural, as is often the case. Farmers there make money a few times a year, maybe once or twice, when the crops are sold. However, they must live off this money for the whole year. The only way to make sure you can survive the winter is to save money from crop sales. Furthermore, the poor also need to make big purchases in the future and the only way to do so is to save. E.g. they are poor, but must save up for a wedding, etc. Or they need to buy fertilizer for the next season and the only way to do so is to save enough money. All these things are possible as long as death from starvation is not an imminent threat, which for the majority of poor people today it is not.

Savings do not exclusively occur when all other current consumption needs are totally met, as it seems to be implied in your question. In fact, they can never truly be met, as ressources are scarce. Savings are instead determined by the optimal decision of how much to consume today vs. tomorrow, or how many of my needs to leave unfulfilled today vs. how many unfulfilled tomorrow. Hence the fact that poor people cannot fulfill all their needs today does not imply that they should not save, since they also think about the future and how to fulfill those needs tomorrow. Think of surviving on an island with limited food. You would likely consume a bit everyday and be hungry in order to survive, than eat everything in one day, be full and then die in a few days.


Quasilinear Utility Functions We know if the utility function is quasilinear (QL) w.r.t good 1, then the demand for other goods is independent of income (no income effect for goods $(2,\dots, N)$).

But is the reverse implication also true: i.e can we say if all the goods except one have demand functions independent of income then the utility function must be quasilinear?

I have been looking up all the standard micro grad level text books but haven't got an answer yet. I see books defining (rather characterizing) QL by just one side of implication (i.e QL implies No income effect) but are silent about the other.

Any reference in this regard will be highly useful.

Is that first claim right? I guess it depends what you mean by an income effect.

Say your quasi-linear utility form is:
$$U(x,v) = x + \ln(v)$$
Say $P_v = P_x=1$ and so for wealth $w = P_v\cdot v + P_x \cdot x = x + v$.
If $0<w\leq 1$ the household strictly prefers to buy $v$ to $x$ and buys no $x$ but $w>1$ is then exclusively $x$ is purchased beyond that. So demand for $x$ looks like this:
$$w<1: x^* = 0$$
$$w<1: v^* = w$$
$$w\geq1: x^* = w-1$$
$$w\geq1: v^* = 1$$

So the marginal demand for $x/v$ depends on $w$.


The Printing of Money for Paying Debt I know that printing money causes inflation, but what if we print it to pay back our debts?

For example, we have N dollars of debt to China.  We can just print the N dollars and give it to China.

This way, we would not have more money in our country which would cause inflation, and we would not be giving from our own money, which would cause deflation.  Also, China gets back the money U.S. owed it.

My guess is that it would cause some kind of weakening of the Chinese money against the USD, but could anyone verify that?

Printing money causes inflation because someone (or some institution) will get the money and will spend it somehow. This increases demand for goods, but the number of goods, the supply was not affected by printing money. Hence demand at the old price level is larger than supply at the old price level. Prices will rise until a new equilibrium is reached.

The problem is that you seem to think that the N dollars you give to China would be gone. But it wouldn't be, the people who got it in China can now spend it in the US. They can import things, come as tourists, make investment purchases etc. This increases demand and results in inflation again.


Study guide (and...) for "Intermediate Microeconomics with Calculus" by Varian I have been googling study guides, solution manuals and other helpful material made by professors. But I have not found anything useful.

Q: Do you guys know anything that will make the book easier and faster to digest?

Kind regards,

Nothing will be better than going through the textbook. Lecture's slides can be beneficial, you can google newer versions or access older here: http://www.mtholyoke.edu/~mirobins/econ212.html. I also used notes done by Łukasz Woźny, from SGH: http://web.sgh.waw.pl/lwozny/LectureNotes.pdf - they are not entirely based on Varian's textbook but might be helpful as well. There is also an Instructor’s Manual to each of Varian's books where he points out what is the most important from each chapter - also you should be able to find one online, and can also be quite helpful if you want to consume his textbook faster.


Equilibrium price and quantity - consumer and producer surplus Inverse function of market demand for certain good is equal to $P=100-0.25Q$, inverse supply function is $P=20+0.55Q$. Calculate equilibrium price and quantity. Furthermore calculate consumer and producer surplus.

Equlibrium price and quantity i think i know how to calculate:
$$20+0.55Q=100-0.25Q$$
and this will be the quantity whereas the price will be (substituting Q with value calculated above):
20+0.55Q=P
am i correct with this?
I am lost with consumer/producer surplus need more help.
edit: I have and idea about consumer/producer surplus:
consumer:
$0.5 \times 100 \times 25=1250$ and producer $100 \times 55 \times 0.5=2750$
is this correct?

Equating supply and demand we obtain the equilibrium

$$P^* = 75, Q^*=100$$

The corresponding diagram is

Consumer Surplus is the area of triangle $B-E-C$ so

$$CS = \frac 12 \cdot (100-75)\cdot 100 = 1250$$

Producer Surplus is the area of the triangle $B-E-A$ so

$$PS = \frac 12 \cdot (75-20)\cdot 100 = 2750$$


Entrepreneurs and risk aversion The are various opinion whether entrepreneurs are more or less risk-averse than the general population. The commonly held belief is that they are less so, but the contrary opinion exists as well. There's even one small survey in the UK that seems to back up this view.

Is there more empirical research in this respect?

Interestingly—and much in contrast to recent research—our data supports the conventional wisdom that persons with a higher inclination towards risk have a significantly higher probability of becoming entrepreneurs. However, sensitivity analysis reveals that this result holds only for those individuals who were previously employed. For previously unemployed or inactive persons, we find no significant influence of risk attitudes, indicating that other variables drive their decision towards self-employment.

Caliendo et al. (2009)

The Conclusions section of the paper lists several other research papers with slightly different conclusions, you may also want to read those.


Can a Discount Rate be Inferred within a Solow-Swan Growth Model? I'm trying to understand the implications of a Solow-Swan growth model with, to keep things simple, constant population, and constant Cobb-Douglas technology written in per capita form as $y=k^{\alpha} (0<\alpha<1)$. Given an initial capital stock, depreciation rate $\delta$ and assumptions on the saving ratio s, I understand how to obtain time paths for y, k and per capita consumption c, properties of steady states and of the golden rule steady state.

Question: Is it possible within this model, perhaps with plausible additional assumptions, to infer the path of discount rates $\rho$, and consequently of interest rates r, corresponding to a given feasible time path of y, k and c?

In the Solow-Swan model, the interest rate will be determined by market-equilibrium: under the baseline assumption of competitive markets (and constant-returns-to-scale technology), we get the familiar per-period equilibrium relation

$$f'(k) = r + \delta \tag{1}$$

Regarding the rate of pure time preference, think of the following: in this model, savings is a fixed percentage of output. So consumption is also a fixed percentage of output:

$$c = (1-s)f(k) \implies \dot c = (1-s)f'(k)\dot k \tag{2}$$

while also we have

$$\dot k = sf(k) - (n+\delta)k \tag{3}$$

Combining, we have

$$\dot c = (1-s)f'(k)\cdot [sf(k) - (n+\delta)k]$$

$$= (1-s)f(k)f'(k)s - (1-s)f'(k)(n+\delta)k$$

and using the previous relations,

$$\dot c = s(r+\delta)c - (1-s)(r+\delta)(n+\delta)k \tag{4}$$

In the "Ramsey" model with consumer intertemporal utility maximization, we get the relation (for log-utility for simplicity)

$$\dot c = (r-\rho(t)) c \tag{5}$$

Note that I made the rate of pure time preference time-varying and this is indeed the case when we examine time-varying preference rates in the Ramsey model (see for example Barro, R. J. (1999). Ramsey meets Laibson in the neoclassical growth model. Quarterly Journal of Economics, 1125-1152).

For the consumers in the Solow-Swan model to behave like the consumer's that optimize intertemporaly equation $(4)$ must be equivalent to equation $(5)$ so (using now the time variable to clearly indicate what is time-varying and what is not), we get after eliminating and re-arranging

$$s(r(t)+\delta)c(t) - (1-s)(r(t)+\delta)(n+\delta)k(t) =[r(t)-\rho(t)] c(t)$$

$$\implies \big[s(r(t)+\delta) - r(t)+\rho(t)]c(t) = (1-s)(r(t)+\delta)(n+\delta)k(t)$$

$$\implies \rho(t) = (1-s)(r(t)+\delta)(n+\delta)\frac {k(t)}{c(t)} +r(t) - s[r(t)+\delta]$$

$$\implies \rho(t) = (r(t)+\delta)(n+\delta)\frac {k(t)}{f(k(t))} +r(t) - s[r(t)+\delta]$$

The consistent rate of pure time preference is endogenous, and time-varying under diminishing marginal product of capital, and becomes constant only in the steady state. The relation tells us to what $\rho(t)$ must be equal so that the optimizing consumer finds optimal to maintain a constant savings rate.

If the production function has constant output elasticities (say, Cobb-Douglas $f(k) = Ak^a$), then the above simplifies to

$$\rho(t) = (n+\delta)a - s\delta + (1-s)r(t) $$

or

$$\rho(t) = (n+\delta)a  - \delta + (1-s)f'(k(t)) $$

so it is still time varying (it would be constant in a model with constant marginal product of capital). If capital increases to its steady state, we see that the consistent rate of pure time preference should fall over time (which is also the result we get in the Ramsey model with time varying $\rho$).

At the steady-state we have $f'(k^*) = a(n+\delta)/s$ so

$$\implies \rho^* = (n+\delta)a  - \delta + \frac{(1-s)a(n+\delta)}{s}$$

$$\implies \rho^* = \frac {an+ (a-s)\delta}{s}$$

That's a nice one since $a$ is the golden-rule savings rate. To mimic the Ramsey model we should set therefore $s<a$ so we will be to the left of the golden rule (and even in the Solow context, setting $s >a$ is dynamically inefficient). Then the steady-state consistent $\rho$ will certainly be positive.

Just for a taste, set $a=0.45, s=0.35, n=0.01, \delta =0.05$, to get

$$\rho^* \approx 0.027$$

Not far from the benchmark value $\rho =0.02$.


Help finding the right term - Behavioural Finance / Pricing jargon There is a phenomenon used in Economics(?)/Marketing/Pricing/Psychology when selecting the right price for your product. Within a certain price range, the customer is insensitive to changes in the price, considering the price or changes in it as too low and insignificant.
Also within the same (acceptably low) range, the customer makes an easy purchasing decision since the price is too low to affect one's budget - I'd call it a "spare change" item here.
For example, in NZ for the top 10% of the market, products below NZ$10 are automatically considered to be "spare change" facilitating customer's trying a new product within that price range. As a seller it will be rational to price your product up to 9.99 than to settle on anything lower than that number.
What's the name of this phenomenon/term describing this sweet-spot price range?

A related concept you might be looking for could be "mental accounting", first introduced by Richard Thaler.
According to mental accounting, people treat money as less fungible than it really is. Fungibility means that, all money is the same, regardless of any other factors, including intended use. However, people often budget money into mental accounts for expenses (e.g., saving for a home) or "spare change".
In your example, the average person in NZ may have a 10$ mental account for "spare change".
How optimal pricing works in behavioral theory is another discussion altogether though.


What is the purpose of interest? What is the purpose of interest? Why do most economies permit the charging of interest? Could an economy function without interest at all, or is interest necessary for an economy to function?

Interest is a key mechanism to ensure that resources are properly allocated within an economy. There are lots of uses to which money can be put: consuming goods, building highways, constructing a new factory, investing to develop a new drug, etc. Just like goods, the allocation of money is governed by the price system—where the interest rate is the price (because the interest rate is how much you have to pay to get access to money). If the price is too low (i.e. if there is no interest) then few people will be willing to lend money and valuable investments (in, for example, infrastructure or new business ventures) will not take place because the funds aren't available to pay for them. A positive interest rate ensures that people with money they don't need right now have an incentive to lend it to people with valuable projects to fund.

We know that it is possible for economies to function without interest, though, because the charging/payment of interest is prohibited by Sharia law, giving rise to so-called Islamic banking.


Fiscal budget: spending in real vs nominal terms What does it mean in the context of a budget to “freeze spending in real terms”? And how would this differ from freezing spending in “nominal terms”?

I am looking to understand how this would be implemented and the broader macro relevance

If there is no inflation then the two phrases would mean the same

But if there is positive inflation, then "freezing spending in nominal terms" would involve spending the same amount of money, and since prices are rising, would involve buying less.  Meanwhile "freezing spending in real terms" would involve spending an increased amount of money corresponding to the increase in prices, with the effect after taking price changes into account of buying the same amount.


What explains why Puerto Rico has much lower GNP than GDP? I can understand why some countries like Luxembourg, Singapore, and Ireland have much lower GNP than GDP.
But why is the same true for Puerto Rico? I would've thought that since lots of Puerto Ricans work outside Puerto Rico, its GNP should be higher than its GDP. Yet the reverse is true.
(In 2019, Puerto Rico's real GDP per capita was \$36,045, while real GNP per capita was \$24,300. So GNP was about 67% of GDP.)

This is impossible to answer completely objectively given the data availability.
The GNI is given as:
$$GNI = C + I + G + NX + NFFI$$
where, C is consumption, I investment , G gov. spending, NX net exports,  and  NFFI is net foreign factor income. The first 4, terms are by definition GDP so the relationship between GNI and GDP is:
$$GNI=GDP+NFFI \text{ or } GNI-NFFI= GDP$$
Hence if $GNI<GDP$ we know that NFFI must be negative. NFFI is the net factor (e.g. not just wages but return on capital and other factor income) income that Puerto Rican residents.
However, note that since it is a net factor income separate observations like that more Puerto Ricans work abroad than foreigners there are not helpful. First, what matters is the value of wages so if Puerto Rican firm hires one foreign scientist whose yearly wages are 10x that of low skill Puerto Rican worker abroad than NFFI portion from wages will be still negative even if the ratio of foreign workers in Puerto Rico and Puerto Ricans working abroad will be less than 10.  Second, since it includes income from other factors it might easily be that many foreign own companies locate in Puerto Rico and so their incomes count toward GDP but not GNI.
Hence to answer your question definitively we would have to take apart the NFFI term and analyze its components. However, problem is that such data is likely not publicly avaiable. Most statistical offices do not provide the breakdown for NFFI. I checked the world bank statistics and couple of other main sources for publicly avaiable macro data but I was not able to find any source that would provide decomposition of NFFI for Puerto Rico.
Consequently, we can only conjecture why GDP is larger than GNP. I think likely reason is that Puerto Rico offers lower tax rate than US and does so for a long time (Boles, 1988; Grubert & Slemrod, 1998), which is attractive for US firms (especially since Puerto Rico is US territory with US citizenry). Subsequently, when these firms eventually get income and distribute it to their 'foreign' owners it counts negatively towards NFFI.
However, at the same time as found by Borjas (2007):

Puerto Rico attracts high-skill in-migrants and exports low-skill workers.

So the argument I mentioned above applies as well and likely every Puerto Rican working abroad contributes less to GNI than any high skill workers that come to Puerto Rico, meaning that even if large numbers of Puerto Ricans work abroad it might not be enough to offset the influence of relatively less high skill workers.
In my personal opinion, the former reason likely dominates but absent of any more detailed statistics you should take it with grain of salt.


Drug pricing, amount of sales and R&D costs I've recently learned about Zolgensma drug that is currently priced at \$2.1 million (read more here)
Since the biggest factor in price is probably R&D costs I wonder why won't they decrease the price in order to sell more of it in a given year and hence get more revenue and pay back R&D costs faster.
With current price of $2.1 million the potential customers are incredibly limited:

Millionaires, but the chance that some of them might need this specific drug is so low that this category probably can be dismissed.
Governments. Some countries may pay for expensive drugs, but I suppose there is always a limit of how much they can spend on this kind of things, so it's a bit risky for the pharmaceutical company to hope they will be stable primary customers.
Charity organizations. While it might be possible for charity to raise this amount of money I wouldn't expect that it is certain that every charity campaign aiming to raise \$2 millions will be successful. There is one campaign right now in Russia that aims to buy this drug, but they barely even got 40% of the price despite being quite visible in the media.

So it seems that with this kind of price tag there is absolutely no guarantee that even 1 package of this drug will be purchased in a given year, so the risk of returning \$0 revenue in the end of the year is highly probable. I might be wrong because I don't have enough understanding of economics of this kind of drugs, but at least from layman perspective it sure looks risky.
Then why won't they decrease the price substantially, for example make it only \$200000? This would be much more manageable amount of money for governments, individuals and charities. Of course you'd need to sell 10 packages of the drug to get the same amount of money as with current price, but at least the risk of turning \$0 by the end of the year seems much lower.

The previous +1 answer gives the correct economic mechanism but let me give you some case specific answer here.
First of all there actually already is another drug that targets the same disease called Spinraza (see here) with cost of \$750,000 for the first year and then \$350,000 per year after that, so about \$4 million a decade.  Assuming people with this deasease can live up to 70 years (which would cost patient \$28 million over life time) that means the Zolgensma drug is already $92.5\%$ cheaper than their competitors over patients lifetime (although the figure is less impressive if this person dies earlier - but even at 10 years it is already almost half the price of the other treatment). Sure this does not answer question why it could not be even more cheaper - but it already puts the high price tag in some perspective.
Given that these more expensive therapy exists I assume that the market for it wont be 0. Even if the cost is high it can be manageable with insurance that spreads the high cost over large number of people. I doubt most patients will pay the price out of the pocket.
Second, the article you cited says that this drug was developed for a rare disease that affects only about 1 in 10000 people, so it is not like this drug can be sold by thousands.
Let us just do some back of an envelope calculation. These gene therapy treatment is particular valuable and applicable to those diagnosed in early childhood. According to the Our World In data the population increase in 2019 was about 80 million. Now many of these people will live in countries without sufficient infrastructure/supply chains etc to administer any treatment. Especially in sub-Saharan Africa there are issues even with giving people cheap deworming pills due to conflicts/anarchy, people living in rural areas without clinics, lack of education etc. so no matter what is the price it won't be accessible to about $33\%$ of world population. That gives us about 50 million.  Since the disease will affect about 1 out of 10000 people that means yearly the market for the drug is about 5000 people.
Next, we actually know exactly in this case how much the medicine costs because it was not developed by the company but acquired from another company reportedly for $8.7 billion from US firm AveXis. Furthermore, patents for drugs last 20 years from the day they are patented and since the FDA approval process takes some time and there is always a threat of a new competitor coming up in with a new drug it is not reasonable to say company will have all 20 years to recoup costs. Let's for a sake of argument say that it will have 10 years. Furthermore, these are just development costs. As far as I understand gene therapy is not as easy to manufacture as regular pill (but I am not medical professional), plus there are all other associated with running the business but let us forget about those for a second.
Well that gives us the total market for this drug over 10 years to be about 50000. Now we need to spread all the 8.7 billion over 50000 people. Hence to break even (just on development costs and nothing else) the drug would have to be priced at \$174000. Again this is just development cost so I would guess that at your proposed \$200000 the company would still not break even.
In addition any company needs also some healthy profit because R&D is risky business any wins have to pay for all failures to successfully develop drug. Even in cases like here where R&D was done by different firm there is still an issue that you never know when the new competitor arrives. If we would change the above assumption that the company will enjoy monopoly for 10 years to just 1 year because maybe better treatment will come next year suddenly just to break even on development the treatment would have to cost \$1740000 which is much closer to current price.
In fact according to  Institute for Clinical and Economic Review, that took into account wide range of factors the new gene therapy would be justifiable at cost \$1.1 million to \$1.9 million per treatment. Now this is still lower than the \$2.1 million per treatment but less so.
Now this answer is actually complementary to the answer of Bayesian above since undoubtedly thanks to their monopoly on the drug the company charges more than it would if there would be more competition and this mechanism is correctly described by Bayesian, but the point is that even without this issue assuming that price would have to cover the development cost etc it would still have to be priced around million.


Does the FDIC's insurance of your money in your bank account cause inflation of the bank were to go under? If the fdic insures money in each account for a bank, and that bank goes under. Won't that mean the fdic will have to borrow more money from the fed and thus lead to substantial inflation?

No, for three reasons. First, FDIC bailouts are funded via the guarantee fund, which is a pre-funded insurance fund that has never required an injection of cash. Second, if such an injection were to occur, it would happen through an appropriation from Congress, which would be implemented via a debt issuance from the Treasury— the Fed has zero authority to bail out the FDIC guarantee fund. Third, bank failures actually tend to involve a net contraction of the money supply, as distressed banks are less able to engage in new credit extension.


Econometric test for detecting change from trend stationary to stationary process I am stuck with the following problem from research. Is there an econometric test which detects change from trend stationary to stationary process.

I tried to search for this but the literature is quite vast. Can somebody point to the relevant literature ?

Any help is appreciated.

The OP is examining a deterministic trend, and whether it stops being present after a point in time. So the model could be something like

$$y_t = \alpha t + \beta y_{t-1} + u_t,\;\;\; t=1,...,T_A$$

$$y_t = \beta y_{t-1} + u_t,\;\;\;\; t=T_A+1,...,T$$

So we want to test whether $\alpha =0,\;\; t=T_A+1,...,T$

This is a test for "structural change". Interestingly, in the last 15 years there has been a lot of research around unit root testing if a stuctural break in deterministic components is present, but I could not find anything that tests directly for the disappearance of a deterministic trend.

At least "in spirit", it will be a Chow test (don't lookup the wiki page, it says really nothing), when the point of the structural break is assumed known -for example, we can "see it with our own eyes" because the effect of the trend was strong (steep slope) and "suddenly" the series levels off and starts to fluctuate around what appears to be a constant mean.

If we want to search for the point of structural change to a rather wide interval of observations (typically the middle 70%), then this is a Quandt Likelihood Ratio ("QLR") test.

...And the main question is: Do these tests need modification because a deterministic trend is assumed initially present and then absent?

Hamilton (1994), ch. 16.3 "Asymptotic Inference for an Autoregressive Process Around a Deterministic Time Trend" (pp. 463-472), analyzes in detail the first equation in the above model. By providing the asymptotic distribution of the coefficient estimators (it is not the same as when the autoregressive term is absent - for this last case, see Ch. 16.1) I believe it provides all that is necessary to execute validly a Chow or QLR test.


US Student debt volume and default rate data source I would like to see data for private and public student loans and their default rate over time

With regard to your title, I assume you're looking for data for the US. This report from the U.S. Department of Education presents data and selected findings about the repayment of federal student loans using data from the 2015 Federal Student Aid Supplements to two Beginning Postsecondary Students Longitudinal Studies (BPS).

The report focuses on two cohorts of borrowers: those who began their postsecondary education in the 1995–96 academic year (BPS:96/01) and those who began in the 2003–04 academic year (BPS:04/09).

The report presents estimates of both cohorts' cumulative borrowing, repayment, and default statuses as of June 30, 2015, some 20 years after the 1995–96 cohort and 12 years after the 2003–04 cohort began postsecondary education.

Interesting key findings

Some 55% of students in the 1995–96 cohort and 63% of the 2003–04 cohorttook out federal education loans within 12 years of entering postsecondary education.
Overall, 25% of borrowers in the 1995–96 cohort had defaulted on at least one loan within 20 years of beginning postsecondary education, and 14% defaulted on their most recent loan.
Among borrowers in the 2003–04 cohort, 45% of those who had never attained a credential and were not enrolled in 2009 had defaulted on a loan within 12 years. Among those who attained undergraduate certificates, the rate of defaulting within 12 years was 44%; for associate's degree recipients, it was 22%; and for bachelor's degree recipients, it was 8%.


Why do we consider purchase of house by households as investment? According to what I have read, investment is the expenditure on  creation of capital goods, which means that it is done by producers.

Then why do we treat buying of house by households as investment when they are not doing any production?

In the sense of treating house as investments, we can treat other consumer goods also like investments. For example, if a consumer buys a TV, we could treat that like an investment because he's receiving a benefit for as long as he owns the TV. Why do we treat houses differently?

Definitions:

Investment is the purchase of any (new) capital goods.
A capital good is any good that is used to produce other goods and services.

A house produces a stream of housing services. Hence, a house may be regarded as a capital good. And thus, the purchase of a house may be regarded as investment.

Note though that definitions and lines in economics can often be fuzzy and there can be grey areas. You are quite right to question whether we should count the purchase of a house as investment. One could argue that we shouldn't. However, by convention in national income accounting, we do, with the above as our rationale.
As noted in the UN System of National Accounts (2008, p. 8):

No matter how simple and precise concepts and classifications may appear in principle, there are inevitably difficult borderline cases which cannot easily be fitted into predetermined categories. ...
The general nature and purpose of the distinction between gross fixed capital formation and consumption, whether intermediate or final, is clear. The distinction is fundamental for economic analysis and policymaking. Nevertheless, the borderline between consumption and gross fixed capital formation is not always easy to determine in practice. Certain activities contain some elements that appear to be consumption and at the same time others that appear to be capital formation. In order to try to ensure that the SNA is implemented in a uniform way, decisions have to be taken about the ways in which certain difficult, even controversial, items are to be classified.

In response to an incorrect comment that claims that "The purchase of a new house is not counted as investment":
BEA glossary:

Consists of purchases of private residential structures and residential equipment that is owned by landlords and rented to tenants.

Blanchard, Macroeconomics (2017, p. A-3):

Residential investment (...) is the purchase of new houses or apartments by persons.

Mankiw, Macroeconomics (2015, p. 27):

Residential investment is the purchase of new housing by households and landlords.

Hubbard & O'Brien, Macroeconomics (2017, p. 255):

Residential investment is spending by households and firms on new single-family and multi-unit houses.


Data of Inflation and unemployment for a Panel Data I am looking for data of Inflation and unemployment to run a Panel Data of a Philips Curve.

Can anybody help me with some website/source that I can find data like these?

In my mind I would need too many countries (60 is enough) with this information through, for example, 2010 until 2019. Is it possible to obtain these data?

Many thanks

For unemployment rates, check the ILO. For inflation rates, see the World Bank


What will happen if the government not print money? I already post this question in Money.SE, but I need to transfer the question in to this site because it's off-topic...

As I said in my previews post.

I start researching the reason why the government can't print more money to resolve its dept and I found this answer
"Why can't the government just print more money to resolve its debts?".

Its says the reason why the government can't just print more money to resolve its dept is the inflation... "The more money printed, the lower its value".

Then another question popup in my mind. What if the government not print money anymore? Does the value of money increase?

It causes unemployment to increase. Policy makers usually have to make a choice between inflation and unemployment. More money means inflation and less money means less investment, less job and more unemployment. If money becomes valuable then people will prefer to keep it in bank instead of creating jobs.


When a demand function is split, how do we algebraically change function For example, in tacit collusion for a Bertrand situation, demand would be split between the two colluding firms. How would the reflect upon the demand function?

For example D = 100 - 2Q, and for simplicity sake MC = 0.
I though to divide D by 2, D* = 50 - Q.

This does not make intuitive sense to me, as how does splitting the demand function change the slope?

The Bertrand case you mention is a little special because it induces a discontinuity in the demand function. Suppose that market demand is $D(P)=1-P$, zero marginal cost, and that all consumers buy from the low priced firm (and split equally in the event of a tie).

If the two firms try to collude around a price $p=0.5$ (with quantity $0.25$ each) then each firm's demand curve will look like this:

Mathematically, a firm's demand will be: $Q_i(p_i,p_j)=0$ if $p_i>p_j$; $Q_i(p_i,p_j)=D(p_i)/2$ if $p_i=p_j$; and $Q_i(p_i,p_j)=D(p_i)$ if $p_i<p_j$.

More generally, it is possible for the slope of a firm's residual demand curve to differ from that of the market demand curve. It all depends on how consumers are allocated across the two firms. The relevant material on rationing rules can be found in Section 5.3 of Tirole's The Theory of Industrial Organization.


Why do low-income earners tend to spend more? I am reading an article in the Economist.
It is discussing the China's unbalanced economy especially the lower household consumption proportion in GDP than the global average. The writer thinks the poor social safety net in China plays a part in curbing the household consumption.
Then follows the below sentence.

As low-income earners have a higher propensity to spend, the lack of
support weighs on consumption more generally.

I don't quite understand why low-income earners have a higher tendency to consume.
I can't find any other supporting details in the article as if the writer takes it as a common sense.
Anybody could help to shed some light on it?
Thanks.

Marginal propensity to consume  is the proportion of an aggregate raise in pay that a consumer spends on the consumption of goods and services, as opposed to saving it. If someone gets extra income $\\\$1000$ and consumes  $\\\$750$ of this additional income their marginal propensity to consume is 0.75.
The marginal propensity to consume is higher for poor people since they have to devote higher share of an income to necessities. Suppose that person needs to spend at least $\\\$500$ a month for their living expenses. Now in such situation if a poor person would get a $\\\$500$ of income per month (relative to situation when the person would have nothing) they will have marginal propensity to consume 1 whether such person likes it or not as all additional income they get will be spend on these necessities. Person whose income would increase $\\\$1000$ (again relative to 0) will have to have at least marginal propensity to consume 0.5 and person with income increase of $\\\$10000$ (again relative to 0) at least marginal propensity 0.05. Of course, the richer people wont consume only necessities but the point is that as peoples incomes decrease the necessities become higher share of their budget.
At the same time as people get richer they spend a smaller proportion of their income as they already enjoy a high standard of living and thus are able to devote more of their income to savings.  You can read more about this in Blanchard et al Macroeconomics: a European perspective or any other macroeconomic textbook.


Applications of Trig functions in Economics? Are there any applications of trig functions (ie $\sin(x)$, $\cos(x)$,$\tan(x)$) in economics?

The main property of trig functions is their cyclicality. Then one would think that they could be ideal in time series analysis, to model "fluctuations around a trend". I believe that the reasons they are not actually used in such a setting are

1) They are deterministic functions, so they do not allow for fluctuations to be stochastic

2) If the researcher wants to create a model that produces up and down fluctuations (oscillations) around a trend, he would want to obtain that property from the behavioral and other assumptions of the model. If he were to use a trig function, he would a priori impose on the model the sought theoretical outcome.

Instead, one opts for difference-differential equations. There we obtain oscillations (damped or not) if some characteristic roots are complex -and then the trig functions appear, but as an alternative representation, not as buidling blocks.


How can I solve for total money spent if I use a non-constant MPC? Background

Today in my macroeconomics class my teacher taught us three concepts.

The first is very simple: consumption $c$ is a linear function of national income $y$. Mathematically, $$c = My + b$$

We will call $M$ the marginal propensity to consume, and refer to it accordingly as MPC. MPC can also be thought of as the fraction of income that is spent rather than saved. So MPC is going to be some number less or equal to one but greater than or equal to zero ($0 \leq M \leq 1$).

The second concept we learned is also quite simple. As income $y$ increases, MPC decreases.

The third concept is a little bit more complicated. Let Person 1 has $5$ dollars. Let MPC be universally constant and equal to $\frac{3}{4}$. Now, since MPC $= \frac{3}{4}$, Person 1 spends $\frac{3}{4}$ of his or her income on Person 2. So Person 2 has an income of $\frac{3}{4} * 5 = 3.75$ dollars. Person 2 will now spend $\frac{3}{4}$ of his or her income on Person 3. And so on to infinity. I instantly recognized this as the sum of a geometric series: $$5*\sum_{n=0}^\infty\left(\frac{3}{4}\right)^{n} = 20$$
This makes sense, but only when disregarding the second concept (MPC decreases as $y$ increases). When I asked about it my teacher said that since calculus isn't a prerequisite for the class we won't go any further in depth; we'll just let MPC be a constant to simplify things in an introductory-level macroeconomics class. So I thought about the problem for a while today and realized that if we did account for MPC decreasing as y increases, or in this case, MPC increasing as $n$ increases, then we could write the total money spent as an infinite series of kind of infinite product (??). My model can be found below.

The Main Question

I just finished Calculus III last fall so I've never formally learned anything about infinite products. I'm not even sure if these are infinite products since many of them are finite. Anyways, can the following infinite series that I came up with be solved for convergence? If so, how can I figure out the number it converges too? Long explanations will be appreciated. Keep in mind I have a very coarse knowledge of mathematics beyond Calculus III.

$$\sum_{i=0}^{\infty} \left(\prod_{n=0}^{i} \frac{n + 2}{\sqrt{n^2 + 5n + 7}}\right)$$

Perhaps it would be better if I knew how to solve the infinite product first.

Also, I came up with the function $\frac{n + 2}{\sqrt{n^2 + 5n + 7}}$ as a model of MPC because I figured MPC should start around $\frac{3}{4}$ and increase asymptotically towards $1$ as $n$ approaches $\infty$.

Does any of this make economic sense or am I missing a major concept?

I don't know that the distribution you claim is wrong but it strikes me as having a couple of very undesirable features. For one, virtually the entire population all of the has >0.99 MPC, which seems very high for a distribution you think is centered around 3/4. For another, if you think that the income shocks in your model are transitory rather than permanent, my reading of the literature is that these are way too large. But that's all separate from your question about estimating things conditional on the actual MPC distribution and ordering.

Ordering from low to high MPC seems to take a strong stance on how trade works in the economy. Again, I don't know that is wrong but it doesn't strike me as true. If we think that MPC is caused by income then this is akin to saying the richest guy get the money first, spends some it at the second richest guy's store and saves the rest, he spends the spending of guy 1 at the third richest guy and so on. The economy strikes me as less neat than that and so a random ordering makes more sense to me in the absence of evidence about where high vs. low MPC people spend their money.

I tried messing around with simulations (in Python) to see how well we could approximate these random chains of consumption. In general, experimenting a few parameter values with uniform, beta, and your distribution above, distribution doesn't matter so much in determining total consumption effect. Using the geometric or arithmetic means of the MPC distribution give nice approximations of actual total consumption effect from the random chains of consumption.* On the other hand, if you order the households by MPC from high to low or low to high this makes a huge difference in the resulting total consumption effects.

* - That said, I explicitly ruled out distributions of MPC where MPC can be zero (or less). If that happens the geometric mean will be zero and the resulting approximation using the geometric mean quite poor.

Code:

# Python 3.x code for stack exchange question
# http://economics.stackexchange.com/questions/3123/how-can-i-solve-for-total-money-spent-if-i-use-a-non-constant-mpc
import numpy as np

# Parameters
households = 5001
sims = 10000
initial_shock = 5

# Alternative marginal propensity to consume populations
MPC_vec_lin = np.linspace(0.01, 0.2, households)
MPC_vec_beta = np.random.beta(2, 5, size=households)

# THis is the function Gragas asks for
nvec = np.arange(0,households)
MPC_vec_gragas = (nvec + 2) / np.sqrt(nvec**2 + 5*nvec + 7)

MPC_vec = MPC_vec_gragas

# Calculate geometeric and arithmetic mean MPC from the population
approx_geo_mean = np.mean(np.log(MPC_vec))
approx_long_run_eqiv_MPC = np.exp(approx_geo_mean)
avg_MPC = np.mean(MPC_vec)

# Assuming that all households had the same MPC (@ geo / arithmetic level), what is the total effect?
approx_total_shock_with_geo = initial_shock / (1 - approx_long_run_eqiv_MPC)
approx_total_shock_with_mean = initial_shock / (1 - avg_MPC)

print('Initial shock size:', initial_shock)
print('Approximate total effect with geometric mean:', approx_total_shock_with_geo)
print('Approximate total effect with arithmetic mean:', approx_total_shock_with_mean)

# Simulating many possible orderings, what is the total effect for each ordering?
total_shock_vec = np.zeros(sims)
for i, item in enumerate(total_shock_vec):
    MPC_vec_random_order = np.random.choice(MPC_vec, replace=False, size=households)
    random_products = np.cumproduct(MPC_vec_random_order)
    total_shock = np.sum(initial_shock * random_products) + initial_shock
    total_shock_vec[i] = total_shock
# Compare resulting average and std. of total effect from simulations
print('Average total effect from simulations:',  np.mean(total_shock_vec))
print('Std Dev of total effect from simulations:',  np.std(total_shock_vec))

# Conclusion, mean and geomean do a very nice job of approximating the resulting total effect without knowing the
# general specific ordering. However, the worst and best total effect ordering (low to high and high to low) are
# quite different.

MPC_vec_low_to_high = MPC_vec.copy()
MPC_vec_low_to_high.sort()

MPC_vec_high_to_low = MPC_vec_low_to_high.copy()
MPC_vec_high_to_low = MPC_vec_high_to_low[::-1]

product_low_to_high = np.cumproduct(MPC_vec_low_to_high)
total_shock_low_to_high = np.sum(initial_shock * product_low_to_high) + initial_shock

product_high_to_low = np.cumproduct(MPC_vec_high_to_low)
total_shock_high_to_low = np.sum(initial_shock * product_high_to_low) + initial_shock

print('Maximum effect ordering effect size:', total_shock_high_to_low)
print('Minimum effect ordering effect size:', total_shock_low_to_high)

Results:

Initial shock size: 5
Approximate total effect with geometric mean: 6023.35708426
Approximate total effect with arithmetic mean: 6154.37897874
Average total effect from simulations: 5999.77721767
Std Dev of total effect from simulations: 642.715838738
Maximum effect ordering effect size: 16675.8496051
Minimum effect ordering effect size: 777.157515589


Deriving Equation for Engel Curve I have a utility function of $U = B^{.67}Z^{.33}$ with Income $Y$, Price of Good B is $P_b$ and price of Z is $P_z$ I now need to derive an engel curve for this. I have no idea where to start.

It is quite simple. The engels curve is the change in demand for a good as a function of income, keeping prices fixed

Solve the constrained maximisation problem
$$
\max B^{0.67}Z^{0.33}-\lambda(P_bB+P_zZ-Y) \Leftrightarrow \\
B=\frac{0.67Y}{P_b} \\
Z=\frac{0.33Y}{P_z} \\
\lambda = \frac{0.5303709372}{P_z^{33/100}P_b^{67/100}}
$$

Fix prices at some level. I choose 1 for simplicity. Then the engels is simply
$$
Y=\frac{1}{0.67}B \\
Y=\frac{1}{0.33}Z
$$


Unusual perfect complements utility function min{ax+y, x+2y} What's the graph for this utility function? How can it be represented graphically?

Is this function perfect complements? I do not fully understand that in the question attached in the picture, the slope cannot be a fractionnary number since the goods are perfect complements.

You can solve this question by breaking the Utility function into 2 parts.

Use U(x,y) =

i) 6x+y if 6x+y < x+2y

ii) x+2y if x+2y < 6x+y

This would simplify into the Utility Function

U(x,y) =

i) 6x+y if 5x < y

ii) x+2y if 5x > y

When you graph the function you'll get 5x=y as the line of kinks. When 5x>y, that is, to the right of the line of kinks, the corresponding IC will be have a slope -(1/2) since it lies on the line x+2y. Points to the left of line of kinks correspond to the line 6x+y and have the slope -6.

Given point (8,9) clearly lies to the left of the line of kinks in the area where 5x>y, therefore this point lies on the Utility line x+2y having slope -(1/2)


Are US federal reserve notes money, or merely currency? I have heard from my friend that US federal reserve notes (aka dollar bills) are not actually money, but merely currency. He told me that money and currency are different, and that money is currency with some extra properties. That is, all money is currency, but not all currency is money. What is the truth of this? Is it the case federal reserve notes are merely currency, and not money as is usually thought?

Federal notes are both money and currency.
Currency can have two meanings:

In context of foreign exchange rate currency might simply refer to a system of money in common use in a particular country. That is, when discussing foreign exchange all USD, GBP, RMB etc are considered currencies.
Outside foreign exchange, currency means notes and coins in circulation. However, again currency is still money.

Money is more broad term in economics for a thing that serves as medium of exchange, unit of account and store of value (see Mankiw Principles of Economics 8 ed. pp 604). Consequently, money can be viewed as a sort of 'umbrella' term that encompasses currency but also much more.   That is all currency is money but not all money is currency. For example, money on deposit account will be considered money but not currency. Checks are also money but not currency. In addition, broad money will include also assets that can be easily converted to traditional money such as treasury bills.
However, most of money does not have special extra properties vis-a-vis currency. There is little practical difference between money in your wallet and money on your deposit account. Sure deposit accounts with debit cards might be more convenient (take less space, most cards now have contactless pay etc) but economically they are not special.  This being said when discussing broad money, such as T-bills, you could justify saying they have extra properties as well.


Is printing money to pay government expenses regressive or progressive taxation? Lets say that the government decides to pay some of its expenses by printing money*. This (according to some schools of thought) effectively increases the inflation rate and devalues the value of the country's currency. So the government skims off a little bit from the whole country's money & the money everyone had is worth a bit less.

So we have a weird indirect form of taxation.

Would this form of taxation be:

Regressive  (taxing the 'poor' disproportionately)
Progressive (taxing the 'rich' disproportionately)

*Not actually printing, but you get what I mean.
*Lets assume the amount created is below the amount which would trigger hyper-inflation.

It rather depends on what happens to wages and interest rates, a ceteris paribus issue, and who you identify as "rich" or "poor": for example current workers borrowing to buy a house tend to be richer than the unemployed but poorer than those with large savings.

If wages fail to rise then existing workers may lose from this with their pay falling in real terms (while new workers resulting from the increased expenditure could gain)
If interest rates fail to rise then existing holders of money may lose with the value their assets falling in real terms (while existing borrowers may gain as they have to repay less in real terms)

If both rise to reflect the impact of inflation, it is much harder to identify who is bearing the cost

Incidentally, the extent to which moderate unfunded increases in government expenditure actually affects inflation is an empirical question and the evidence is not conclusive


Why does HDI use log-transformed data for income index? For calculation of HDI, the Income Index used is $\mathrm{I_{income} = \dfrac{ln(Income) - ln(min Income)}{ln(max Income) - ln(min Income)}}$. Why is the log transformed income used here? World Bank has answered that it is to emphasize the diminishing returns to the standard of living but I don't get how log-transform can reflect diminishing returns.
I know that log-transform is generally used to reduce skewness in the data and a log-transformed independent variable does reflect diminishing returns in a linear regression model but for calculating HDI, we take geometric mean and don't perform multiple linear regression.

Decreasing returns to standard of living means that if you add a certain amount $\delta$ to the income of a low income person, then the increase in her standard of living is bigger than if you would give the same amount to a high income person.
Let $SL(x)$ be the standard of living for a person with income $x$.
Take a person with income $x$ and a person with income $y > x$, and let us add an amount $\delta$ to the income of both persons. Then we should have that:
$$
SL(x + \delta) - SL(x) > SL(y + \delta) - SL(\delta).
$$
The left  hand side is the increase in the standard of living for the poor person. The right hand side is the increase in the standard of living for a rich person.
Dividing by $\delta$ and taking the limit for $\delta \to 0$ gives:
$$
\frac{d SL(x)}{dx} > \frac{d SL(y)}{dy}.
$$
The left hand side is the marginal return to the standard of living for a person with income $x$ and the right hand side is the marginal return to the standard of living for person with the higher income $y$.
Decreasing marginal returns means that this marginal return decreases when income increases. So it is lower for the higher value $y$ compared to the lower value $x$.
A function with a decreasing slope is called a concave function. So what you want in the end is a function that is

Increasing, i.e. $SL(x)$ increases with $x$
concave, i.e. $dSL(x)/dx$ decreases with $x$.

One (popular) function that satisfies these two conditions is the natural log function. Note that $d \ln(x)/dx = 1/x$ which indeed decreases with $x$.
The function that the world bank uses:
$$
SL(x) = \frac{\ln(x) - \ln(x_{min})}{\ln(x_{max}) - \ln(x_{min})},
$$
is just a linear transformation that makes sure that:

$SL(x_{min}) = 0$
$SL(x_{max}) = 1$.

So the function is:

increasing
concave
between 0 and 1


The Fed Lowered Interest Rates, Are they going to buy Bonds? I originally asked this question on personal finance/money because I didn't know that this exchange site existed. link to same question at person finance/money.  Someone on that site mentioned that it might be off topic, so I thought I would try here.

The Fed just lowered interest rates yesterday by 0.25%. I haven't heard anyone mentioning a resurgence of quantitative easing (QE).

Is the Fed going to start buying bonds in order to influence the interest rate? If so, where can we find the dollar amount of bonds they are buying and over what time frame?

There have been no such announcements as far as I know. The press release from the Federal Reserve mentions the following implementation details:

Decrease in interest rate on required/excess reserve balances to 1.80 percent
Repo operations for up to an aggregate amount of $75 billion
Decrease in the primary credit rate to 2.50 percent

My guess is that if these efforts do not have enough of an effect, then quantitative easing might resume soon as hinted by Powell:

  "It is certainly possible we will need to resume the organic growth of the balance sheet sooner than we thought," Powell told reporters during a press conference. - CNN


In the US, do high wages in regions like New York and California offset the high cost of living? It's well understood that the cost of living in New York City vastly exceeds the cost of living in, say, rural Louisiana.  It is also well understood that wages in New York City vastly exceed those in rural Louisiana.  My question is: who comes out ahead?

To clarify, let me offer a thought experiment (not sure if this is valid or not, I'm no economist).  Imagine we have two individuals: one in rural Louisiana with a low cost of living and low wage ("Lou" for short), the other in New York City with a high cost of living and a high wage ("Nue" for short).  Imagine that both Lou and Nue earn exactly the median household income for their respective region.  They live in virtually identical homes (paying the local rent).  They drive virtually identical cars.  They have the same number of children.  They have the same healthcare plan, and so on.  Now imagine that each day Lou and Nue both go to the mall, and buy the exact same items as one another (paying the local price).  Let's imagine they are spending very quickly, far more quickly than either can afford.  Who runs out of money first, Lou or Nue?

A follow up question: is there a single number which tracks this quality I'm trying to describe?  It seems like median income divided by local CPI would just about do it, but that's purely based on my own untrained intuition.

TL;DR Wages offset the high cost of living in most states.  In NY and CA specifically, wages are insufficient to offset the high cost of living.  In New York City specifically, wages do not even come close to offsetting the high cost of living.

Having now researched this a bit, I can give a very concrete answer to the Lou/Nue hypothetical, and I think a pretty decent answer to the general idea.  Let me just say up front, I am not an economist, I'm taking a best guess based on the data published by real economists.  These are layman's conclusions, and, as BKay pointed out, can't possibly capture the complexity of the real world.  That said...

Nue runs out of money first.  Here's why:

The regional price parity (RPP) in NYC is 136.  That means, a purchase which costs \$100 for an average American will cost \$136 for an average resident of NYC.  The median income in NYC is \$50,711.  This is 97% the national median income.  This means that a days work which pays \$100 for an average American pays \$97 dollars for an average resident of NYC.

The regional price parity in Louisiana is 91.  A purchase which costs \$100 for an average American will cost \$91 for an average resident of Louisiana.  The median income in Louisiana is \$40,462.  This is 77% the national average.  This means that a days work which pays \$100 for an average American pays \$77 dollars for an average resident of Louisiana.

In addition to Lou and Nue, also let us consider Medie.  Medie earns exactly the national median income, and her cost of living is exactly the national average, i.e. RPP = RWP = 100.  (Sidebar: to the extent that such a person exists, they probably live in Pennsylvania, which comes the closest to conforming to both wage and price averages).  So let's compare a hypothetical wage and price for Medie, Lou, and Nue:

Medie earns \$100 per day
Apples cost \$1 each in Medie's home town
Medie can buy 100 apples per day

Lou earns \$77.81 per day
Apples cost \$0.91 each in Lou's home town
Lou can buy 85 apples per day

Nue earns \$97.63 per day
Apples cost \$1.36 in Nue's home town
Nue can buy 71 apples per day

Note, this effect only holds for New York City proper.  If you compare New York State with Louisiana, they are dead even.

To answer the question more generally, all other things being equal it pays to be in a high wage, high cost of living state, though there is major regional variation.  To try and answer this more fully, let's look at the data BKay supplied above, and expand the hypothetical from the original question.  Regional Price Parity data is fairly easy to come by (i.e., "for every dollar spent by an average american, how many dollars must a person from region X spend to get the same result?").  Regional Median Wage data is also pretty easy to come by.  From the Regional Median Wage we can trivially calculate Regional Wage Parity (i.e. "for every dollar earned by an average American, how many dollars can a person in region X expect to earn?").  This is a term I'm making up, so I know it's not exactly scientific, but I think it give a good gestalt for the situation.  This gives us:

$$
\frac{Regional Wage Parity}{Regional Price Parity} = HowMuchStuffYouCanBuy
$$

"How much stuff you can buy" is really the figure that this question is trying to get at.

The state with the highest "apples per day" value is New Hampshire (126) followed by Virginia (123).  As I said, New York and Louisiana do the worst.  DC and Georgia conform exactly to the national average.  Here are these value's graphed:

Note, while local wages seem to predict well for this "how many apples" measure, prices do not seem to predict at all.  Goes to show, cheap != affordable.

Here's the raw data I used for this if you want to play around with it:

+----------------------+-----------------------+----------------------+------------------+
|        State         | Regional Price Parity | Regional Wage Parity | How Many Apples? |
+----------------------+-----------------------+----------------------+------------------+
| Louisiana            | 91.40%                | 77.81%               |               85 |
| New York             | 115.40%               | 99.14%               |               86 |
| New Mexico           | 94.80%                | 83.12%               |               88 |
| Mississippi          | 86.40%                | 77.30%               |               89 |
| Arkansas             | 87.60%                | 78.39%               |               89 |
| Montana              | 94.20%                | 84.35%               |               90 |
| Kentucky             | 88.80%                | 80.21%               |               90 |
| North Carolina       | 91.60%                | 83.45%               |               91 |
| Florida              | 98.80%                | 90.60%               |               92 |
| Tennessee            | 90.70%                | 83.27%               |               92 |
| South Carolina       | 90.70%                | 83.53%               |               92 |
| West Virginia        | 88.60%                | 81.89%               |               92 |
| Nevada               | 98.20%                | 91.10%               |               93 |
| Alabama              | 88.10%                | 83.07%               |               94 |
| California           | 112.90%               | 109.39%              |               97 |
| Arizona              | 98.10%                | 95.31%               |               97 |
| Hawaii               | 117.20%               | 115.16%              |               98 |
| Maine                | 98.30%                | 97.09%               |               99 |
| Ohio                 | 89.20%                | 88.24%               |               99 |
| Delaware             | 102.30%               | 101.61%              |               99 |
| District of Columbia | 118.20%               | 118.01%              |              100 |
| Georgia              | 92.00%                | 92.23%               |              100 |
| Indiana              | 91.10%                | 91.93%               |              101 |
| Michigan             | 94.40%                | 96.26%               |              102 |
| Oklahoma             | 89.90%                | 91.71%               |              102 |
| Idaho                | 93.60%                | 95.86%               |              102 |
| Pennsylvania         | 98.70%                | 101.48%              |              103 |
| Illinois             | 100.60%               | 103.93%              |              103 |
| Texas                | 96.50%                | 100.33%              |              104 |
| Vermont              | 100.90%               | 105.73%              |              105 |
| Oregon               | 98.80%                | 103.97%              |              105 |
| Kansas               | 89.90%                | 96.16%               |              107 |
| Rhode Island         | 98.70%                | 106.07%              |              107 |
| Missouri             | 88.10%                | 95.00%               |              108 |
| New Jersey           | 114.10%               | 124.36%              |              109 |
| Alaska               | 107.10%               | 118.71%              |              111 |
| South Dakota         | 88.20%                | 98.39%               |              112 |
| Wisconsin            | 92.90%                | 104.50%              |              112 |
| Washington           | 103.20%               | 116.72%              |              113 |
| Wyoming              | 96.40%                | 109.30%              |              113 |
| Colorado             | 101.60%               | 116.78%              |              115 |
| Iowa                 | 89.50%                | 103.26%              |              115 |
| Massachusetts        | 107.20%               | 123.79%              |              115 |
| Nebraska             | 90.10%                | 105.34%              |              117 |
| Connecticut          | 109.40%               | 128.66%              |              118 |
| Utah                 | 96.80%                | 115.15%              |              119 |
| North Dakota         | 90.40%                | 107.59%              |              119 |
| Minnesota            | 97.50%                | 117.62%              |              121 |
| Maryland             | 111.30%               | 134.28%              |              121 |
| Virginia             | 103.20%               | 126.95%              |              123 |
| New Hampshire        | 106.20%               | 133.56%              |              126 |
+----------------------+-----------------------+----------------------+------------------+

Sources:
Wage data (Direct XLS Download)
Price Data (PDF)


Why does fiat money have value? Or as Tobin (1992) put it: "How Can Money Have Positive Value in Exchange?"

Money, however, is an embarrassment to value theory. According to standard theory, something can have positive value only if it generates positive marginal utility in individuals’ consumption or positive marginal productivity in the making of goods and services that do generate marginal utility. The embarrassing puzzle is sharpest for fiat money. All of its value comes from the fiat that makes it money. Fiat money has no intrinsic non-monetary source of value. It cannot be eaten or worn or be used in any other way that generates utility for consumers, except a few numismatists. Nor can it contribute to the production of things that consumers do value. It can be produced at zero social cost. Yet it is a scarce commodity for any individual agent. Why is it worth anything at all? That the institution of money is of value to the society as a whole as a public good does not automatically give it value to individuals in market exchanges.

Is there today any consensus answer to the above question?

The answer, that can be found in greater detail in the following book

Rudolf Richter, Money — Lectures on the Basis of General Equilibrium Theory and the Economics of Institutions, Springer, 1989.

is quite simple. One has to create a positive marginal utility to the user. How one can achieve this aim? One has to create a positive demand for fiat money, which can be accomplished that taxes can only be paid with fiat money. Then it has a positive marginal utility, and the trick is done.


Where/What should I search to find the big companies annual paid salary information? I want to know how much salary paid by apple in 2017 to whole employees. Also the details of other payments of the company(How much they paid for raw materials for example). Also like to know these information about other big companies.

But my study field isn't economics and my English isn't well enough to know where and what should I search?

I will be happy if you guide me!

I believe there is no comprehensive source of the information collected in a standardized way that you are looking for.

If you want to have info on a single company only, I guess your best bet is to look at the companies' annual reports. Companies disclose a lot of information about their operations there.

Some newspapers certainly did investigations on the topic and collected (spuriously, I guess) some info on that. Try to check the Wall Street Journal, the Financial Times and the Economist for the starter.

If you look for the aggregated statistics by countries, try to search the web-site www.statista.com and the works done by scientists like Gabaix and Branco Milanovic. They both did much of empirical work in inequality and could gather much info on that. No guarantee they published their datasets free of charge.


Solving a Cournot Equilibrium, the case of Q=q1+q2, Q(q1,q2)=q1+q2 I am struggling with the differentiating between when to use $ Q=q_1+q_2$ and $Q(q_1,q_2)=q_1+q_2$

For a 2 player cournot game,
given
$$ P=a-bQ, with \ MC's \ c_1 \neq c_2   $$

I find the following:

FOC
 $$  q_{i}^* = \frac{a-c_i}{2b} - \frac{q_j}{2}  $$

which leads to me to a equilibrium value of $$q_i^{eq}= \frac{a-2c_i+c_j}{3b} $$

when using $$P=a-b(q_1+q_2)$$

$$ \textbf{HOWEVER} $$

The supplied answer is $$q_i^{eq} = \frac{2a+c_j-2c_i}{3b} $$

with FOC

$$ q_{i}^* = \frac{a-c_i}{b} - Q  $$

where the answer uses

$$P = a-bQ(q_1,q_2) $$

When am I supposed to use the different Q's? as all my lecture notes follow the method I used, and there are other questions which look identical and use $Q=q_1+q_2$ but there is obviously a time to use $Q(q_1,q_2)$.

First point: you write "I am struggling with the differentiating between when to use $ Q=q_1+q_2$ and $Q(q_1,q_2)=q_1+q_2$". But these are the same thing: both define $Q$ as a function of $q_1$ and $q_2$. It's just that the second expression makes this functional dependence explicit by writing out the arguments, whereas the first does not. This is purely an issue of notation and has no bearing on the solution.

Let's start by writing out the profit function and computing the first-order condition:

$$\Pi=[a-b(q_i+q_j)]q_i-c_i q_i$$

$$\frac{\partial\Pi}{\partial q_i}=0 \iff a-b(q_i+q_j)-bq_i-c_i=0\iff q_i=\frac{a-bq_j-c_i}{2b}.$$

This is the FOC that you got in your solution (just slightly rearranged). So far, so good!

Let's repeat those same two steps but writing the profits in a slightly different way

$$\Pi=[a-bQ]q_i-c_i q_i$$

$$\frac{\partial\Pi}{\partial q_i}=0 \iff a-bQ-b\underbrace{\frac{dQ}{dq_i}}_{=1}q_i-c_i=0\iff q_i=\frac{a-c_i}{b}-Q.$$

This is the FOC from the solution you were given. But note that $Q=q_i+q_j$. Making this substitution gives

$$q_i=\frac{a-c_i}{b}-Q=\frac{a-c_i}{b}-q_i-q_j$$
$$q_i=\frac{a-bq_j-c_i}{2b}.$$

In words: your answer, and the provided solution have exactly the same first-order condition. So we can be confident that both are correct at least this far, and the discrepancy must be coming from the next step.

Now we need to solve the system of first-order conditions for equilibrium. We have

$$q_i=\frac{a-bq_j-c_i}{2b},\ q_j=\frac{a-bq_i-c_j}{2b},$$
$$q_i=\frac{a-b\frac{a-bq_i-c_j}{2b}-c_i}{2b}.$$

Solving this last equation for $q_i$ yields
$$q_i^{\text{eq}}=\frac{a-2c_i+c_j}{3b}.$$

This is your answer. It is unclear where the answer in the solution came from, but the most likely situation is that there is an algebra error in the final step of computation of the solution.


Why do exports include only hard products? Looking at country lists by exports.
Diving into exports always shows things like gas turbines, computer hardware, petrolium -- all physical things.
None show things like exporting services: financial services, engineering consulting, licensing software. I would imagine that would be a considerable component in countries like UK. In some countries medical tourism might bring considerable revenue.
If traditional export metric is for hard products only is there a metric that encompasses service export as well? And is there any data on account balance (export - inport) of countries with services included?

Found a fairly nice one from OECD. It includes combined trade in goods and services as a percentage of GDP. It is also possible to drill into goods only (which seems most commonly presented in the public domain) or services only data.


Features of the set of Bayes Correlated Equilibrium in a single-agent decision problem with uncertainty I would like your help to better understand the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty The notion of BCE is provided in this paper for a generic $N$-player game.

Consider the following single-agent choice problem under uncertainty.

Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{V})$. First, let nature draw a realisation $v$ of $V$ from $P_V$.
Then, let the decision maker choose an action $y\in \mathcal{Y}$, with $\mathcal{Y}$ finite, without observing $v$. Upon the decision has been made, the decision maker gets a payoff $u(y,v)$.

Before choosing an action, the decision maker can receive some signal to refine her prior about the state of the world.

Now, I want to use Theorem 1 in Bergemann and Morris (2016) to characterise the set of optimal strategies under minimal assumptions on the amount of information that is processed by the decision maker. To do that, I introduce the notion of one-player BCE.

A one-player BCE of the game described is a probability distribution $P_{Y,V}\in \Delta(\mathcal{Y}\times \mathcal{V})$ such that:

1) $\forall v \in \mathcal{V}$
$$\sum_{y\in \mathcal{Y}}P_{Y,V}(y,v)=P_V(v)$$

2) $\forall y\in \mathcal{Y}$ and $\forall \tilde{y}\neq y$
$$
\sum_{v\in \mathcal{V}} [u(y,v)-u(\tilde{y},v)] \times P_{Y,V}(y,v)\geq 0
$$

Let $\mathcal{P}$ be the set of BCE.
Let
$$
\mathcal{Q}\equiv \{P_Y\in  \Delta(\mathcal{Y}): P_Y(y)\equiv \sum_{v\in \mathcal{V}}P_{Y,V}(y,v) \text{ }\forall y \in \mathcal{Y}, P_{Y,V}\in \mathcal{P}\}
$$

Questions:

1) Is $\mathcal{Q}$ convex? I guess it is because $\mathcal{P}$ is convex. Could you confirm?

2) Let $ \mathcal{B}\equiv \{b\in \mathbb{R}^{|\mathcal{Y}|}: b^Tb\leq 1\}$ be the unit ball in $\mathbb{R}^{|\mathcal{Y}|}$. Let us stack in a $|\mathcal{Y}|\times 1$ vector the image set of every probability distribution $P_{Y}\in \mathcal{Q}$. With some abuse of notation, let us still denote any such a vector by $P_{Y}\in \mathcal{Q}$. Does
$$
\max_{P_Y\in \mathcal{Q}} b^T P_Y
$$
exists $\forall b\in \mathcal{B}$? I guess the answer to this question depends on the features of $\mathcal{Q}$. For example, if $\mathcal{Q}$ is compact, then the maximum above exists. Could you help?

Yes,  $Q$ is convex and closed precisely because $P$ is and Q is its image under a continuous function. Therefore, $Q$ is compact.

The function you are maximizing is continuous as well, so the maximum must exist.


Preferences exhibiting local nonsatiation I'm self studying my way through Varian's Microeconomic Analysis right now and am having trouble answering this question:

Consider preferences defined over the nonnegative orthant by $(x_1, x_2) \succ
(y_1, y_2)$ if $x_1+ x_2 < y_1+ y_2$. Do these preferences exhibit local nonsatiation?
If these are the only two consumption goods and the consumer faces positive
prices, will the consumer spend all of his income? Explain.

The solution manual says the preferences are locally non satiable except at (0,0) but I don't know why that is.

any help would be greatly appreciated.

Since we are working in $\mathbb{R}_+$ you can't go below (0,0). So consider the point (0,0). Are we guaranteed a point around it that is preferred? So using the notation you used, let $(x_1,x_2)=(0,0)$, then any other point $(y_1,y_2)$ where $y_1$ or $y_2$ is positive will be worse than $(0,0)$. So we have a satiation point at $(0,0)$.

Now consider anywhere else. We can also go lower by reducing either coordinate so there is always a better point until we reach both points =0.


What is the assumption behind "indifference curve does not cross"? If only weak-ordering and continuity is assumed, "ICs" can definitely intersect.

If we assume Monotonicity or convexity in addition to weak-ordering, then we can get "no cross of IC".

But those two assumptions are argueably too strong. In some real world scenarios they are violated.

Are there any weaker assumptions for the "IC cannot cross"?

If only weak-ordering and continuity is assumed, ICs can definitely intersect.

This is not true. First, if you're speaking of indifference curves, you'd already be assuming either local non-satiation or monotonicity.

Let's speak of indifference sets instead. The analogue of two sets, $I_1$ and $I_2$, "crossing" each other can be formalized as $I_1\ne I_2$ and $I_1\cap I_2\ne \varnothing$.

Take two alternatives $x_1,x_2\in X$ and define two indifference sets as follows:
\begin{align}
I_1:=\{x\in X:x\sim x_1\}\quad\text{and}\quad I_2:=\{x\in X:x\sim x_2\}.
\end{align}
WLOG, assume that $x_1\succ x_2$, so that $I_1\ne I_2$. If we allow $I_1$ to "cross" $I_2$, then $I_1\cap I_2$ must be non-empty. Let $\bar x\in I_1\cap I_2$ be an element in the intersection. By the transitivity of the indifference relation $\sim$, we have $x_1\sim \bar x$ and $\bar x\sim x_2$, implying $x_1\sim x_2$. But this is contradictory to our assumption that $x_1\succ x_2$. The contradiction therefore suggests that transitivity, a property of the weak ordering, is violated.


Empirically estimating TFP Suppose we assume that production function has a Cobb-Douglass form:
$$Y=A\times K^\alpha\times L^\beta,$$ where $Y$ is output (GDP), $A$ is Total Factor Productivity and $L$ is labor. By log-linearizing the production function we have:
$$y=a+\alpha k+\beta l,$$ where $y=log(Y)$, $k=log(K)$ and $l=log(L)$. Hence, the model that we empirically estimate can be written as:
$$y_t=a+\alpha k_t+\beta l_t+\epsilon_t,$$
where $\epsilon$ is the error term. Suppose applying OLS we have the estimated parameters, i.e. $\widehat{a}$, $\widehat{\alpha}$ and $\widehat{\beta}$.
Question Does only $\widehat{a}$ refer to $TFP$, or the $TFP=\widehat{a}+\epsilon$? As far as I know, $\epsilon$ is also called Solow residual. Please elaborate.
Thanks!

The total factor productivity (TFP) would be $a+\epsilon_t$ where $a$ is the average TFP and $\epsilon_t$ (where Solow residual is technically actually $\Delta \epsilon$) tells us how TFP varies across time. Let me explain:
First, the $A$ should also be function of time in time series model as technology can change (I doubt you want to impose restriction that technology has to be constant and if so then having time varying residual would not make sense) so actually the production function should look like this:
$$Y_t = A_t K_t^{\alpha} L_t^{\beta}$$
Hence log linearizing would give us:
$$y_t = a_t + \alpha k_t + \beta l_t,$$
where lower case letter denote logs $ \ln X =x$. Now when you make mistake is in specifying your OLS. The $a_t$ actually is the residual. Since we can only observe $k_t$ and $l_t$ we cannot include $a_t$ in regression and it will be the residual because it can be calculated as:
$$y_t - \alpha k_t - \beta l_t = a_t, a_t \equiv TFP$$
So actually $a_t$ is the residual $\epsilon_t$. So the specification would be:
$$y_t = \alpha k_t + \beta l_t + \epsilon_t.$$
However, the above specification is unnecessarily restrictive as it forces TFP to have 0 mean (although we  can always rescale any variable to have zero mean this could bias $\hat{\alpha}$ and $\hat{\beta}$). As a result we can add a constant term $\beta_0$ to the above regression.
$$y_t = \beta_0+ \alpha k_t + \beta l_t + \epsilon_t.$$
In this case TFP ($\ln A_t$) would be $\ln A_t = \beta_0+ \epsilon_t$ where $\beta_0$ represents the average factor productivity and $\epsilon_t$ would be the deviation from the average over time (see Van Beveren, I. (2012). Total factor productivity estimation: A practical review and sources cited therein - the source talks about panel data applications but I think the basic explanation holds up even in pure time series even if time series has its own issues that require attention). Also as mentioned at the beginning if you want to assume TFP is constant $A_t=A$ then $\epsilon_t=0, \forall t$.
Lastly, Solow residual is actually defined in growth terms so actually it is $\Delta \ln A_t = \beta_0 +\epsilon_t - (\beta_0 + \epsilon_{t-1}) = \Delta \epsilon_t$, since Solow residual is defined as productivity growth (see Barro & Sala-i-Martin Economic Growth 2nd ed. pp 434-435).
PS: if you actually are going to perform the estimations on a time series you should take into account that all series will most likely be $I(1)$ and estimate the whole model in first differences where the interpretation of constant would be average rate of growth of TFP. In the above I did not explored this issue in order to avoid unnecessarily adding more confusion.


CES utility function in an Edgeworth box Two consumers have the CES utility function $x_1^\beta +x_2^\beta$, for $0<\beta<1$, their initial endowments are $w^1=(1,0)$, $w^2=(0,1)$ Draw the Core of this economy in an Edgeworth box. Note and verify that the demand of the CES utility function is $x_i^*(p,pw)={\dfrac{p_i^{(s-1)}}{(p_1^s+p_2^s)}}$$pw$, where $s={\dfrac{\beta}{\beta-1}}$
I have drawn the IC of the CES function, that I guess are the similar to this in a sense in order to find the core. https://dismaldocket.files.wordpress.com/2013/02/pareto-set.jpg
For the finding the demand I was looking at equating their MRS=$\dfrac{\beta x_1^{\beta-1}}{\beta x_2^{\beta-1}}$ = $\dfrac{p_1}{p_2}$
by substituting this to the budget equation I get that $x_1^*$=$\dfrac{w \cdot p_1}{p_1^2+p_2^{\beta/(\beta-1)}}$
However I most probably have done miscalculations or am completely sidetracked :). Any suggestions is more than welcomed.

There seems to be some confusion in the expression for $x^*_i$ in the question that whether $i$ is for consumer of for the good. Assuming $i$ is for consumer:
Let $x^*_i = (x_1^i,x_2^i)'$ be the equilibrium bundle for consumer $i$.
Since utility function is same for both, from MRS we have:
\begin{align}
\frac{x_1^i}{x_2^i}=\bigg(\frac{p_1}{p_2}\bigg)^{s-1} \tag{$i=1,2$}
\end{align}
Budget constraint for $i$:
\begin{align}
p_1x_1^i+p_2x_2^i&= p_iw  \\
x_2^ip_2 \Bigg(\bigg(\frac{p_1}{p_2}\bigg)^s+1\Bigg)&=p_iw \tag{using MRS}\\
x_2^i \bigg(\frac{p_1^s+p_2^s}{p_2^{s-1}}\bigg)^s&=p_iw \\
x_2^i &=\frac{p_2^{s-1}}{p_1^s+p_2^s}p_iw
\end{align}
So,:
$$x^*_i(p,pw) = \Bigg(\frac{p_1^{s-1}}{p_1^s+p_2^s}p_iw,\frac{p_2^{s-1}}{p_1^s+p_2^s}p_iw \Bigg)$$
The question can be solved further, for $p_1/p_2$ using the constraint: $x_j^1+x_j^2 = 1$


Which are commonly used economics dictionaries? Do economic dictionaries distinguish between different interpretations of terms in different economic schools of thought, or are there different dictionaries for different schools of thought?

For most part different 'schools of thought' do not have different definitions of terms. New Keynesian definition of GDP is the same as Keynesian definition of GDP or Neoclassical definition of GDP or any other 'school of thought' that you can think of. Marginal utility also has the same definition across economics.  This is because terminology is not about interpretation but about definitions and most of the time it makes sense for people to agree on one definition so everyone can understand each other.
This is because in a modern context distinguishing among schools is much less useful than in past (save for classification) since nowadays any idea that can get empirical support will eventually be accepted. For example, it is no longer even valid to say that modern mainstream is just neoclassical synthesis (neoclassical economics + New Keynesian economics) since now it comprises of behavioral economics, institutional economics etc. In fact even historically mainstream economics always absorbed ideas from everywhere (you will find Austrian influences in theories on prices, Marx is why we use $K$ for capital etc.) although less so than in the present.
When terms have different definitions it is usually not across 'schools of thought' (although there might be some exceptions) but across sub-fields. For example, the definition of technology is more narrow in the growth theory than in microeconomics.
Good economic dictionaries are:

The New Palgrave Dictionary of Economics (this is probably the most comprehensive one)
The Economist: Economics A-Z
Oxford A Dictionary of Economics

The above provide reasonably well overview of definitions used in economics. Most textbooks, especially undergraduate ones, will have 'glossary' at the end where you can find terminology as well.


When was the supply and demand model first used? Who created the supply and demand model in economics or when was it first used?

The Wikipedia page about the supply and demand model has a History section.

According to Hamid S. Hosseini, the power of supply and demand was understood to some extent by several early Muslim scholars, such as fourteenth-century Syrian scholar Ibn Taymiyyah, who wrote:

  "If desire for goods increases while its availability decreases, its
  price rises. On the other hand, if availability of the good increases
  and the desire for it decreases, the price comes down."

Antoine Augustin Cournot first developed a mathematical model of supply and demand in his 1838 Researches into the Mathematical Principles of Wealth, including diagrams. However, John Locke (1691), Adam Smith (1776) and David Ricardo (1817) also used this model.


Macroeconomics, the circular flow of income and profits I'm really confused about the concept of the circular flow of income. Specifically, I'm confused about the following situation:

Imagine a simple economy where households don't save their income, so they spend it entirely on goods/services.

Now imagine there is only one firm in the economy producing a single good, say chocolates. Let's assume the firm has $5000 in total at first (obtained from all households, none of whom have any income at the moment).

Let's say the firm buys raw materials from households and pays households their wages, and let's assume altogether it costs the firm all \$5000. And now the firm decides to sell all chocolates produced at a price such that in total, the prices add up to \$6000, so that the firm earns \$1000 in profit.

But here I find a problem: no one can buy all \$6000 worth of chocolates because only \$5000 is in the economy at the moment. So firms can only sell a total of \$5000 worth of chocolates and thus never earn any profit.

Where did I go wrong? Did I go wrong? I'm assuming I did because to me the result I got is nonsensical.

The firm broke the circular flow of income in your example; profits went into a black hole.

Imagine that the firm instead distributes all profits to the owner, who spends all proceeds.

The firm gets \$6000 in revenue, pays \$5000 in wages, and pays \$1000 in dividends. The wages and dividends are enough to provide the revenue.

I am ignoring the issue of the initial money holdings. There is a number of ways these transactions can be supported: credit, or the \$1000 dividend was paid out revenue as it came in.

In order to respect the initial money holdings, and have sales of \$5000, what happens is that the firm has excess inventory (with a sales value of \$1000). That is, the workers could not afford to buy all of the output. The firm would be profitable, but with zero cash flow. Since the cash used to pay the workers returned to the firm, it would be able to then pay a dividend out of profits. That dividend could then be used by the owner to buy the remaining inventory.

It is not obvious how the firm can forecast its profits exactly in this fashion, but that would be covered up in an economic model by solving for all flows simultaneously. If all cash flows are settled simultaneously, we actually cannot see how the money flows work; we only see the net movement.


Minimalist example of voter profiles yielding different outcomes Let the set of alternatives be $\left\{a,b,c,d\right\}$.

Let there be $n$ types of voter profiles, each type with a different strict ordering over the set of alternatives.

The number of voters belonging to the profile types need not be the same, let us denote these by $v_1,v_2,...,v_n$.

What is the minimal number of $n$, for which you can construct the voter profiles in such a way that the plurality rule (a.k.a. first-past-the-post), simple run-off (election with two rounds) rule, elimination rule and the Borda count all yield different outcomes? (Assume non-strategic voters. Outcomes should not be ties.)

EDIT:
Plurality rule has one round of voting and whoever has the most votes wins.  Example: United Kingdom parliamentary elections

The simple run-off rule has two rounds of voting. The two candidates with the most votes in round 1 advance to round 2. In round 2 voters vote for their favourite remaining candidate, and whoever has the most votes wins. Example: French presidential election

The elimination rule is similar to the run-off rule but has three rounds (number of alternatives minus one). In each round the candidate with the least votes is eliminated (figuratively). Others proceed to the next round.  Example: Academy award (Oscar) vote

Minimalist guesses ("here are some profiles with $n = 4$") are fine, ideal solution would provide a proof that $n$ is minimal.

First, let me state that this is a beautiful problem!

Here is a proof that $n=4$. To prove that $n \leq 4$, consider the following example:

$m+4$ voters have preference $a \succ d \succ b \succ c$
$m+3$ voters have preference $b \succ d \succ c \succ a$
$m+2$ voters have preference $c \succ d \succ b \succ a$
$m$ voters have preference $d \succ c \succ a \succ b$

where $m \geq 2$. I leave it to you to check that $a$ is selected by the plurality rule, $b$ by the simple run-off, $c$ by the elimination rule and $d$ by the Borda procedure.

Now, let us prove that $n>3$. The cases $n=1$ and $n=2$ are trivial, so let us assume $n=3$ and write $v_1,v_2,v_3$ for the number of voters in  the three voter profiles. Without loss of generality, let us assume that $v_1 \geq v_2 \geq v_3$, that $a$ is selected by the plurality rule, that $b$ is selected by the run-off election, that $c$ is selected by the elimination rule and that $d$ is selected by the Borda count.

The outcome of the plurality rule shows that $a$ is most preferred by voters of group 1 (since it wins with no ties). If $a$ were also preferred by voters of group 2, $a$ would win the run-off election, which is a contradiction. Thus $a$ is most preferred by voters of group 1, $b$ is most preferred by voters of group 2, and $v_1>v_2 \geq v_3$, the latter inequality being strict if $b$ is not most preferred by voters of group 3. But then it is clear that both $a$ and $b$ survive the first two rounds of the elimination rule, i.e. that $c$ and $d$ are eliminated, which is a contradiction.


What are the most used approximations in economics? As I progress in my self-study, I'm tired of having to search for several different approximations techniques used in economic textbooks. Sometimes the authors don't even tell the reader they are using an approximation, they just assume the reader is already familiarised with the approximation.

Because of this, and to try to help me, and my fellow students of economics, I ask the following. What are the most used/useful approximations (and techniques) used in economics?

My wish is that anyone whether studying alone or not, can come to this question, as they'll be sure that it will have at least some approximation related to what they want. Any help would be appreciated.

Here's an example:

I've read today that «$\frac{\Delta m_{t+1}}{m_t}=\frac{\Delta M_{t+1}}{M_t}-\frac{\Delta P_{t+1}}{P_t}$.»

Well this is not an equality but an approximation, for if $z=\frac{x}{y}$, then $\frac{\Delta z}{z}\approx \frac{\Delta x}{x}-\frac{\Delta y}{y}$

There are four categories of approximations used in economics.  Unfortunately, none of them are economic approximations, but rather mathematical or statistical approximations.  As such, they do not appear in the economic literature, so much so as in the mathematical literature.  You are not seeing in the economic literature because students should be exposed to the content by mathematicians.

The difficulty comes from the type of math used in economics.  There are two ways you could look at calculus.  One is that it is the study of change.  The other is that it is the study of approximations.  All of calculus is a set of approximations, though if you will mentally agree that $\lim_{n\to\infty}\frac{1}{n}=0$ then you can get "exact" answers.  Imagine, however, that the smallest unit is a penny, then you cannot go to zero and now you have an approximation if a penny is the smallest possible size.  The question economists have to answer within the profession is whether or not the difference has a large enough impact to matter.

It is rare in economics for anything to be anything except an approximation.  There are some categories though to these approximations.

The first category can be thought of as either equilibrium approximations or local approximations.  Mathematicians would use the phrase "local approximations."  The main one of these is the Taylor expansion, though there are others.  In classes, I have to be very careful when I teach undergraduates because they often substitute their own mental approximations for the actual ones in work.  While it is wonderful that they are trying to work problems through from first principles, its usually the ones who didn't study the answer in the book and who are panicking.

The second one can be thought of as functional approximations.  The actual functions in the real world are discrete and usually created by the separate functions of many different firms.  While there are certain mathematical properties created by the topology of the problem.  We know that certain types of problems are forced to have a certain general form, but the specific form will be unique to the real world problem.  As an example, a taxi company needs one driver per cab.  If you add cabs but no drivers then no revenue gain is created.  Likewise, if you add cab drivers but no cabs, you get not revenue gains.  Indeed, in both cases you can take losses from paying the cabies and the costs for the cabs such as insurance.  So the production function, which is a Leontief production function is assumed to be present almost all the time, ignoring cabbies who quit, or wrecked cabs resulting in a temporary mismatch between workers and cabbies.

There is also the issue that utility functions are ordinal and any function that preserves preference ordering is equally valid.  This is not an approximation so much as an arbitrary choice for convenience.

The third category could be thought of as model approximations.  For example, using game theory, is an arbitrary choice as a way to model something.  The use of a general equilibrium method versus a model that is sub-game perfect will create different approximations in the end.  Of course the goal is for empiricism to judge between the modeling methods, but for your purposes they should both be thought of as approximations.

Finally, all of statistics is a form of approximation.  The danger is to believe statistical models and all economic models are statistical models.  They can be excellent or poor.  Statistical significance is not enough, it needs economic significance, that is "what is the effect size."  Likewise, how sensitive is the statistical model to the data and to reality.  You can easily create a statistical model that is not at all robust.  That will make your approximations very fragile.

There isn't a list.  The most common are Taylor expansions, finding the slope, $\hat{\beta}$ in models as an approximation of the derivative, and production functions.  The best way to tell you are dealing with an approximation will always be seeing $\Delta$ in a problem.  If you see $\Delta$ then you are dealing with an approximation of $\mathrm{d}$.  Although $\mathrm{d}x$ is really an approximation of $\Delta{x}$, economics always solving inverse problems so in economic practice $\Delta{x}$ is an approximation of $\mathrm{d}x$.