Concept of Utility in demand systems I have seen that researchers use different utility function in demand systems estimation such as Stone Geary. What is the role of these utility functions? What are utility function other than stone Geary?

The utility function taken for estimating demand systems depends on several parameters:

The nature of theoretical models and definitions of the variables used in these models are quite different from the nature of data that is available to us for estimation. Standard microeconomic theory tells us that demand is obtained as a result of some form of utility maximization. Naturally, therefore, the structure of demand function would depend heavily on the structure of utility function used to specify the consumer's preferences. Therefore, when we are trying to estimate a demand system, we look at the data we have at hand and the structure of the data, the variables available etc. give us an idea of what kind of demand system would be suitable, and hence, what kind of utility function we should start with.

Sometimes, the nature of analysis we would like to conduct can only be done only with a particular demand system. And therefore, it is natural to start with a utility specification that yields that particular demand system. On other occasions, we might just want to "keep things easy" and therefore choose utility functions which yield "tractable" demand functions.  Stone-Geary is a good example of this. Stone Geary utility function yields what is known as the "linear expenditure systems". The analysis can then be carried out in terms of "product-wise expenditures", which is usually what is available to us in the form of data. CES-utility function is another such example.

Aggregation is also an important consideration. We might want aggregate the demand system and be able to say something about the properties of a more macro kind of economic entity. In that case, we don't really have many options, since aggregation requires very strict requirements. We then stick to some usual homothetic utility function (like Cobb-Douglas or Stone-Geary).

Finally, there are demand systems which have all the above listed nice properties. This is indeed what is usually done these days. Deaton and Muellbauer's (Linear/Quadratic - approximated) Almost Ideal Demand System (AIDS) is the state of the art demand system, inspired by the work of Stone and Geary on expenditure systems, as well as Gorman's work on aggregation. It's "easy" to estimate, requires lesser assumptions, has nice(est) aggregation properties, and can be made to fit usually available household-level survey data.

Hope it helps.


Existence of utility representation of a rational but discontinuous preference This is related to Do discontinuous preferences imply no continuous utility function?

I think the title of the above-linked question is phrased in such a way that obscures a subtly different but more interesting question which the OP also hinted at in the body. I'd like to ask that explicitly here.

  Does there exist a rational but discontinuous preference relation that is representable by a (potentially discontinuous) utility function?

In other words, if $\succsim$ satisfies completeness and transitivity but violates continuity, can we still find a utility function to represent it?

From known results, the answer does not seem obvious.

We know that continuous utility representation exists if and only if preference is complete, transitive, and continuous. But this doesn't tell us what happens when preference is not continuous.
We know that utility representation does not exist for some discontinuous preference (e.g. the lexicographic preference). But can this conclusion be generalized?

Finally, I want to note that the requirement for $\succsim$ to violate continuity means we're ruling out finite (and countable?) domains.

I think a basic problem is that any utility function defines a preference, and discontinuous utility functions can be used to define discontinuous preferences. Hence there are many discontinuous preferences that can be represented by utility functions.
An example:

Let $U(x,y)$ be a continuous utility function that maps from $\mathbb{R}^2$ to $(0,1)$. This latter may seem arbitrary, but the strictly monotononicaly increasing function $\frac{x}{x+1}$ maps from $\mathbb{R}_{++}$ to $(0,1)$, so it should be fine. Also define a closed set $H \subset \mathbb{R}^2$. Let
$$
\hat{U}(x,y)
=
\left\{
\begin{array}{ll}
U(x,y) & \mbox{if} (x,y) \notin H \\
\\
U(x,y)+1 & \mbox{if} (x,y) \in H.
\end{array}
\right.
$$
Obviously $\hat{U}(x,y)$ is not continuous and neither are the preferences defined by it. (The boundary of $H$ is prefered to anything outside $H$.) But the way these preferences were generated seems fairly general. So a large class of discontinuous preferences exists for which there is a utility representation.

Future question: How 'large' is this class, what measure can be used?

EDIT: As @NicolasPinto points out in his answer it is also necessary to specify that $H$ is such that
$$
\exists x \in H, \exists y \notin H: y \succ x,
$$
so $H$ is not the upper contour set of some point,
otherwise $U(x,y)$ and $\hat{U}(x,y)$ would in fact represent the same continuous preferences.


Real GDP explanatory variable In order to make an econometric model for explaining the evolution of the US Real GDP, does it make sense (from an economic point of view, not from a statistical one) to include CPI (as a proxy for inflation) among the regressors?

You are not very clear on whether your model is uniequational or a system of equations (e.g. a VAR). I will assume the former is your case.

There are several approaches to estimating Real GDP. One approach is via estimating a production function (i.e. a supply side approach). Here, you need information on factors of production, like hours worked, education level, physical capital, etc. It would make little sense to use inflation as a regressor in this approach.

An alternative method is to focus on the demand side, by which you are interested in explaining the determinants of GDP sub-components like consumption, government spending, etc. This approach is in my opinion the most common among specialised institutions like central banks and etc. For example, Atlanta Fed, OECD, NIESR UK, researchers at the Bank of Canada.

The latter type of models are normally very complex, and go beyond the one equation system. As such, some of them do include inflation as one of the variables (both as independent and dependent variable), because inflation is expected to affect real wages and thereby consumption (for example, see the documentation of the Atlanta Fed model here.

Now, if you only have one equation, and are using the demand side approach, I would include inflation as long as other included variables are also nominal (like retail sales). Alternatively, you can redefine every variable as real, and not include inflation. This is a more restrictive scenario though, as you are imposing extra restrictions (which, in fact, you can test).


Marginal Product of Capital in the Solow Model In the classic form of the Solow Model:

$$ Y=K^\alpha (AL)^{1-\alpha } $$

Describe circumstances in which the marginal product of capital could rise over time, at least for a temporary period.

I've calculated:

$$ MPK = \frac{dY}{dK} = \alpha K^{\alpha -1}(AL)^{1-\alpha } $$

The thing is, I thought one basic assumptions of the Solow Model was diminishing marginal returns, so how could there ever be a case when MPK is increasing?

According to your calculations MPK is not increasing in $K$. The Solow model assumes $0< \alpha < 1$, thus $\alpha - 1 < 0$ and $K^{\alpha - 1}$ is decreasing in $K$.


What has caused the recent 25% unemployment rate in Spain? The unemployment rate in Spain has recently been fluctuating around 25%.

What has caused this?

Here's an explanation from Paul Krugman. You can read more about this in Krugman's book End This Depression Now!.

Since joining the Euro, Spain has experience large capital inflows—money flowing into Spain, mostly from Northern Europe. These inflows caused a boom in investment, coupled with an increase in prices of virtually everything (including labor) relative to other Eurozone countries.

One consequence of this is that the recession in Spain has been exacerbated by the fact that high costs of production (especially high labor costs) made the Spanish economy less competitive so that the country wasn't able to rely on exports to substitute for the reduced domestic demand.

In order to remedy this situation, Spain needs to become more competitive (i.e. for labor costs to fall relative to those in other countries). Normally, this would happen automatically: as a country exports less, demand for its currency from importers (and hence the currency's value) falls so that its products become cheaper for foreigners. However, the fact that Spain is in the Eurozone means that it can't devalue its currency—it doesn't have one of its own!

Instead, Spain must rely on 'internal devaluation', i.e. reducing the wages of its workers relative to those elsewhere in the Eurozone. This is problematic because workers are typically reluctant to accept a pay cut (so-called downward nominal rigidities). Thus, the way that the economy adjusts is to have a sufficiently large share of the workforce unemployed that people are prepared to accept jobs on significantly lower wage than they might have expected in the pre-recession years.

It should be noted that this line of reasoning is not without controversy. For one, a significant share of macroeconomists do not believe the nominal rigidities story.


When shall I use bootstrap standard error? There are many papers use bootstrap standard error when they do econometrics.

My question are:

why do we need bootstrap standard error?
when to use it?

Normally, you use bootstrapping when you cannot derive a formula for the variance-covariance matrix of your estimator. Since you do not have this formula, you cannot obtain the standard errors of parameters, and so your econometric analysis is very limited. In these cases, using bootstrapping is the only option available. This is common in complex, non-linear models.

Similarly, you do not need them for those cases where you can derive robust, close-form formulas for the standard errors (as in OLS, or linear panel data models, or most of models found in most of textbooks). In this cases, you already have a formula which is asymptotically efficient, and bootstrapping would be redundant, and probably counterproductive if done incorrectly.

Notice that bootstrapping is not only useful for obtaining the standard errors of parameters. You can also bootstrap full tests. For example, you can bootstrap the Hausman test that compares RE versus FE. To go this way would imply a longer answer.

For a quick and hands-on introduction, check Cameron and Trivedi (2010), Chapter 13.


How to linearize the following difference equation? I'm doing economic modelling where $x_t$ is the intertemporal cash-flow variable. I need to solve the following recurrence relation

$$x_{t+1}=\frac{x_{t+8}}{x_{t+1}}$$

My problem is that I don't exactly know how to linearize this function. Maybe I should introduce a new variable $y_{t} = x_{t+1}$ and get

$$y_{t}^2={x_{t+8}}$$

Could you help me out with the correct linearization technique, please? I'm looking forward to your answer.

We have the recurrence relation

$$x_{k+1} = \frac{x_{k+8}}{x_{k+1}}$$

If the denominator is nonzero, this recurrence relation can be rewritten as follows

$$x_{k+7} = x_k^2$$

Assuming positivity and taking the logarithm of both sides, we obtain a linear recurrence relation

$$\ln (x_{k+7}) = 2 \ln (x_k)$$

Shifting,

$$\ln (x_{k+1}) = 2 \ln (x_{k-6})$$

Let

$$\eta_k := \left( \ln (x_k), \ln (x_{k-1}), \dots, \ln (x_{k-6}) \right)$$

be a $7$-dimensional state vector. In matrix form,

$$\eta_{k+1} = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 0 & 2\\ 1 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 1 & 0\end{bmatrix} \eta_k$$

Hence, we need $7$ initial conditions. We recover $x_k$ via $x_k = \exp( \mathrm e_1^{\top}\eta_k )$.


Continuity of preferences Let $\succsim$ be a transitive and reflexive relation on a metric space $X$ with closed upper and lower contour sets. If $\succsim$ is not complete, does it hold that: for all converging sequences with $x_n\succsim y_n$ for each $n\geq 1$ and $x_n\to x$, $y_n\to y$, we have $x\succsim y$? I think that without the completeness of $\succsim$ this cannot hold, but I failed to provide an example.

Giskard is right lexicographic preferences would make the job being dicsontinuous, but the problem is to find relations with closed contour sets. Maybe an idea would be to start from constructing a preference relation  for which the only possible upper and lower contour sets are $X$ and $\emptyset$. In that case, you take the indiscrete topology, and all nets (or generalized sequences) converge to all the points in $X$. Anyway, I have not been able to construct such a relation yet.


What are the economics behind web spam? In this question, I'm referring to "web spam" on search engines (not email spam), such as placing misleading keywords on one's web page so that a pornographic site, for example, would get a lot of traffic that isn't necessarily related to what the site has to offer.

I am interested in understanding the dynamics, or rather, the economics behind this kind of activity, preferably with some numbers as examples or as data.

Links to studies are also appreciated.

I used to work for a major online advertising network, and it's pretty much an open secret in the industry that a substantial portion of ad impressions are either bot-generated, scams to exploit misleading search engine results, or both.  There are typically several layers of "middlemen" involved between the company whose products are being advertised and the websites running the ads, and everybody has a financial incentive to keep their mouths shut about the rampant fraud involved.

The basic economics is this:  an unscrupulous website joins an advertising network (which often have insufficient resources dedicated to their review/approval process for new websites joining their network) and then either purchases botnet traffic (at a lower price than they're receiving in ad revenue) or tries to pull in search engine traffic through misleading search terms, for as long as they can get away with it.  They're typically caught fairly quickly, but by that time they may have made several hundred (or several thousands) of dollars in profit.  Then they register a new scam website and repeat the process.  Remember:  websites are typically paid for the ads that appear on their website, even if nobody ever clicks on them.

Since nobody in the entire industry is really interested in exposing this aspect of the business, it may be difficult to find actual studies.  I'll take a look though, and would suggest that "fraud in online advertising" is the appropriate search phrase.

Update: It looks like the Wikipedia article on Ad Fraud has a number of references that may serve as a good starting point.  An online search turns up a good number of results as well, although many of them appear to be marketing material for software that claims to help prevent/stop ad fraud.


what is the Relationship between Zero nominal interest rates and liquidity traps So I'm reading mankiw"s principles of economics and I'm in the chapter about the influence of monetary and fiscal policy on Aggregate demamd.
The part about nominal Interest rates and liquidity traps left me confused and I didn't really understand what it meant. Can anyone elucidate the role of short run interest rates and their effect on the economy?
More specifically, can anyone explain this particular paragraph:

"Some economists have suggested that the possibility of hitting the zero lower bound for interest rates justifies setting the target rate of inflation well above zero. Under zero inflation, the real interest rate, like the nominal interest, can never fall below zero. But if the normal rate of inflation is, say, 4 percent, then the central bank can easily push the real interest rate to negative 4 percent by lowering the nominal interest rate toward zero. Thus, moderate inflation gives monetary policymakers more room to stimulate the economy when needed, reducing the risk of hitting the zero lower bound and having the economy fall into a liquidity trap."

The paragraph that you included likely assumes that nominal rates won't go below zero, and therefore that $r_n$>=0 at the zero lower bound. This has been challenged by unconventional monetary and exchange rate policies (i.e. the EU, Switzerland). This likely leads to a few assumptions under classical economic frameworks:

-The Money Demand curve is not horizontally asymptotic at $r_n$=0

-If it is assumed that there is rate mobility below a zero nominal rate (it can go lower and lower with market manipulation), $\frac{d\left(r_n\right)}{d\left(Q_{md}\right)}$≠0 where $r_n$<0. Logically, a -0.41% rate affects consumers differently than does a -0.68% rate (remember that this is effectively the risk free rate; risk premiums will yield positive rates that can be interpreted using classical liquidity preference theory)

This tool has been used for different reasons. Switzerland isn't using negative nominal rates to escape a liquidity trap, but to keep the Franc from appreciating and sending their trade deficit through the roof. The EU on the other hand has resorted to this unconventional monetary policy to try to stimulate growth and avoid a deflationary spiral. They hope to incentivize banks to lend money at the negative rate plus a risk premium rather than be charged to hold money as reserves by the ECB. Consequences exist for these policies, however. Because consumers would rather hold money as cash than lose it in a negative yielding savings account, the money supply of the banking system weakens, and rates can rise back up. Due to its only recent implementation, negative interest rates are likely still considered experimental at best.

Anyways, the paragraph argues that an above zero inflation target allows more policy flexibility, as $r_r$=$r_n$ when inflation equals zero. This effectively gives borrowers cheaper "real" lending while lenders still gain a rate on their assets above holding money as cash (and therefore no bank runs or contracted money supply). Again, this paragraph is either assuming that the ZLB equals zero, or that negative nominal rates are not sustainable. Mankiw would probably argue that a higher inflation target (which leads to generally higher nominal rates in equilibrium), would've given the EU a better ability to manipulate aggregate demand with a "target" lower bound of 0% nominal interest.


Infinitely repeated games and real-world situations? I do understand the gist of what infinitely repeated games are in that T=$\infty$ ; that is the stage game is played each period for an infinite number of periods.

In his book "Strategy", Watson makes the following claim:

  Although such a game may not seem realistic at first (people do not
  live forever), infinitely repeated games are useful for modeling some
  real-world situations.

With reference to the part in bold, could you elaborate?

Thanks.

In most situations it is not clear when a game ends, it is just clear that at every point in time there is a probability that this is the last period of them game.

Just try to say what is this $T$ for the life of a human? 150 years? Even if you are 150 years old there is a (probably small) chance that you will survive another year. And the next year? There is also another chance to live another year, and so on.

As long as there is no fixed endpoint to the game, infinitely repeated games are, in my opinion, more realistic as long as there is some chance of ending the game included (i.e., as a discount rate).

Infinitely repeated games are also a way to resolve some problems backward induction (for example in the Chain-store paradox). You really have to know that there is a very last situation to use backward induction.


Calculate average annual inflation The price index in the year 1993 is 60.
The base at 2012 is 100.
The annual nominal interest rate between 1993 and 2012 is 66% on average.
What is the average annual inflation between 1993 and 2012?
I know that
Inflation = $\frac{X_{t+s}-X_t}{X_t}$x$ 100$
where $X_{t+s}$ is the current year and $X_t$ is the year being compared.
However, when I use this formula with $X_{t+s}=100$ (since it is the base of the index) and $X_t=60$, I just get the annual nominal interest rate of 66.6666%.
What did I do wrong here?


What effect has the 30% increase in money supply from Feb-June of 2020 had? I commented on a previous question that this is probably a better one. Old question
Generally speaking, how has the increase in money supply resulting from the CARES act stimulus package affected the macroeconomic state of the US? Everything I've found to date is "Well, it hasn't, really" which just seems absurd. There's been a 30% increase in the M1 money supply, and a nearly 18% increase in M3. Did it actually just offset the decrease in velocity of the price level equation P=(MV)/Y to "maintain balance"? What if consumer and business confidence skyrockets for X reason next month, thousands of M&A deals go through, homes are bought and sold, etc etc and velocity to 2007 levels by end of year (I know unlikely, just trying to understand implications with an extreme).
If there's simply more background reading I need to do, links are always welcome.
Reference:
30% increase in M1
18% increase in M3
EDIT:
This article was published Bloomberg this morning.

Excluding volatile food and fuel costs, the so-called core CPI --
viewed by policy makers as a more reliable gauge of price trends --
rose 0.6% from the prior month, the biggest jump in almost three
decades, after a 0.2% increase in June. On an annual basis, core
inflation measured 1.6%, a four-month high, following 1.2% in June.

This is more or what I was expecting to see, and while it obviously isn't a direct causal relationship to the stimulus, is it safe to make that connection? If not, why not?

I pretty much agree with the answer that Brian provided except for:

As for the effect of monetary aggregates, there are any number of reasons to expect that their changes will have no observable linkage to activity.

This is not a conventional view hold by mainstream economists, although to Brian's credit he points that out by saying:

Nevertheless, some economists still attach significance to monetary aggregates, one of them will have to offer an explanation.

Even though using 'some' as a synonym for mainstream of the profession is a bit strange.
Mainstream View on Significance of Money Supply:
The conventional view is that changes in money supply actually matter for what the inflation is. For example, this holds true for virtually all general equilibrium macro models presented in Advanced Macroeconomics from Romer which is classic graduate macro textbook. You will find the same views expressed in virtually any undergraduate macro textbook as well. However, there are two caveats:

As shown by Krugman (1998) in his influential paper its not just money supply what matters. It is also the expectations of money supply that matters! Any expansion of money supply that is precieved as being only temporary and promptly reversed will have only limited impact on inflation and inflation expectations at the best.
There are certain situations, a prominent example of such situation would be when interest rates are at zero lower bound (ZLB),  where inflation becomes unresponsive to money supply. The reason for this is that at zero lower bound peoples willingness to hold cash becomes infinite as money themselves carry implicit zero nominal interest and hence if central bank would try to push for negative interest rates people would just soak up all the extra cash by hoarding it.

However, even despite the above caveats mainstream economists generally do believe that money supply affects inflation because ZLB is not a 'normal'state for an economy to be in - at least not historically. Moreover, also even though peoples expectations of money supply expansion can be fickle and central banks that are know as 'inflation fighters' might initially not have enough credibility in their commitment to permanently increase money supply, this obstacle is very situational and it is agreed by conventional economists that if central bank is really committed to monetary expansion the expectations eventually adjust.
For example, in 2019 the IGM forum- which is arguably the best poll for discovering what top mainstream economists think as it interviews a cross-section of top mainstream economists of diverse political beliefs, gender and age showed that in response to Q: "Countries that borrow in their own currency can finance as much real government spending as they want by creating money?" which is arguably a proxy to whether M matters for inflation, as the biggest problem with increases in M is that it leads to inflation,  26% disagreed, 57% strongly disagreed and 7% had no opinion and once the responses were weighted by confidence 24% disagreed and 76% strongly disagreed.
Furthermore, of course just because mainstream economists claim there is a relationship that does not mean there has to be one - that would be fallacy of arguing from authority, but my point here is to represent the conventional/mainstream view. Of course, mainstream academia is also not a monolith I am sure that there are mainstream economists who might hold different views but I believe it is fair to say that if they exist they are in minority.

View of the Bank of Canada (BOC) on Money Aggregates:
Furthermore, Brian misrepresents the official view of Canadian central bank presented on their website. However, I do not want to insinuate he does that on purpose because I think he is valuable user and even though I disagree with him here I actually hold him in high regard and I am sure he would never do that purposefully, rather I believe its due to erroneous assumption that absence of the series is evidence for their views on role of money supply which is fallacy.
In fact the same page that Brian provided link to BOC states:

For further discussion of uncertainty as well as the information and analysis used to inform monetary policy decisions at the Bank of Canada, see Jenkins and Longworth1 (2002) and Macklem2 (2002).

Hence the website does not offer all details. Now if you open both of those papers you will see that actually money supply matters:
For example in Macklem, Tiff, "Information and Analysis for Monetary Policy: Coming to a Decision." Bank of Canada Review, Summer 2002: 11-18 we will find:

The economic model used in the staff projection
focuses on the links from interest rates to spending by
households and firms. Information on various holdings
of money and credit provide yet another view of what consumers and firms are doing and planning to do. In
order to spend, consumers and firms need money or
credit, so the evolution of the monetary and credit
aggregates provides clues to spending plans. In practice, these aggregates are also affected by portfolio
shifts and other purely financial developments, so, as
with other high-frequency indicators, the challenge
for the staff is to separate the genuine signals about
economic activity and inflation from volatility related
to other factors. Regular contact with financial institutions provides useful insight into the particular developments that appear to be affecting the growth of
money and credit at the time. Information is also
obtained on credit spreads in bond markets and on
any changes in the conditions under which banks are
lending to businesses and households as indicators of
changes in credit quality and availability.
The staff in the Bank’s Department of Monetary and
Financial Analysis assemble this information to provide an overall view from the financial side of the
economy on the outlook for output growth and inflation, as well as on the risks surrounding this outlook.
Based on this analysis, they also make a recommendation to the Governing Council on the setting of the target overnight interest rate at the next fixed announcement date.

Next in Jenkins, Paul and David Longworth, "Monetary Policy and Uncertainty."Bank of Canada Review, Summer 2002: 3-10.

Second, it [The BOC] examines data on monetary and credit
aggregates, as well as information on credit spreads
and overall credit conditions. The purpose is to assess
the behaviour of financial intermediaries, the financial
conditions of households and of the business sector,
and the implications for demand and inflation pressures in the economy.

The emphasis and comments in [] are mine.
Hence unambiguously BOC takes monetary aggregates into account and believes they have some impact on  inflation. Or to be more precise it at least shows that they claim to do that (nobody can of course see what is in their heads).
We can only conjecture why BOC does not list money supply separately on the website but mentioned it in the papers. My best guess is that BOC does not list it because money supply is generally less useful for short-term forecasting, certainly not as useful as augmented New Keynesian Philips curve for example (which is based on output gap that is listed there).  However, forecasting ability of a aggregate has no implications for underlying relationships. Even nonsense variables can be useful for forecasting because they happen to co-vary with the variable you want to forecast in some way and vice versa - this is well accepted in literature on forecasting.
For example, according to Economic Forecasting and Policy from Carnot, Koen and Tissot certain types of forecasting models are built:

... models are based solely on the statistical properties of the series under consideration, irrespective of any interpretation or causal relationships informed by economic theory...

The authors also state that such models can often provide relatively better forecasts than the structural (i.e. theory/underlying economic relationship based) models. Also you will find this caveat in pretty much any text on forecasting even outside economic profession.  Hence whether money supply is used for forecasting or not in itself tells us nothing about what the actual relationship is or whether institution using such forecasts thinks what the actual relationship is (also note forecasting should not be confused with empiricism or statistical estimation of some empirical models).
However,  it is actually a common mistake that even many very intelligent people make all the time to assume that if there is some fundamental relationship between two variables they should be good at forecasting or vice versa. Nonetheless, any such assertions are simply just a fallacy and as a consequence one cannot generally judge underlying economic relationship simply from forecasting models central banks/professional forecasters use let alone from the variables they use for forecasting.


How do I calculate price elasticity of demand using historical price and quantity data? I work for a company that produces retail items and I am tasked with calculating the price elasticity of demand for a subcategory that shall remain unnamed. I have 5 years of monthly market data that shows market price as well as ounces sold. My independent variables include IV estimated prices, monthly income spent on non-durables (national Fred data), ounces sold of a related subcategory, and 11 dummy variables for the 12 months of seasonality. The model is Log-Log.

My idea was to control for everything that would be a supply side factor and then use the coefficient of price as my demand curve slope. Of course, the demand curve is always changing, but in aggregate I would assume a relatively steady demand curve. It would at least be better than simply calculating dQ/dP. The problem is my coefficient for price is positive. Also, even though the R-Square is around 70% and the F-Stat is significant at the 99%+ level, my individual parameters are mostly not statistically significant.

The problem is, I am looking at monthly data for an entire subcategory. The volume sold and weighted average prices continue to rise and I am not sure how to isolate demand. Any ideas would be greatly appreciated.

Regarding the IV price estimator to remove endogeneity, I ran the stage 1 regression with the cost of raw materials as my X and price as Y. This price estimator has an R-Square of .91. The cost of raw materials has a correlation of .11 versus .32 when run against quantity.

You've fallen into a really common pitfall -- the spurious regression. The parameters you chose to include can't be chosen 'willy nilly' by throwing data into a regress command. Ultimately this can't be answered in so little words, without data, while maintaining accuracy.

That said I can try to answer your question as a reference point. Before even attempting this I couldn't emphasize enough caution. Just remember that a model that's almost correct -- for practical purposes is 100% wrong.

So it seems you've settled on a linear log-log specification. I would do a quick Google Scholar search on papers forecasting consumer demand for a product similar to the one of interest. The functional form along with parameters you choose to include must be derived from theory. You'd be able to just copy their equation and just modify it to your data. Otherwise, you're doing blind statistics. This is the main reason you're getting inconsistent signs.

What you're trying to do is specify a derived demand for the category of goods you're focussing on. Your general model is going to look like this:

$ logQ_t = \alpha + \beta_llogP_t + X'_t\gamma + \epsilon$

where:
Q sales    P selling point
  X vector of factors other than selling price
$\epsilon$ random component in demand

Have you included any economic indicator parameters? This would be things like GDP, income, population growth, unemployment, interest rates... etc. Depending on the good -- for your purpose -- there's usually theory providing necessary parameters regardless of statistical significance. I would do this first. Add some macro indicators and re-check the F-statistic for the model. Your model would then provide not only own price elasticity of the good, but you'd get an income elasticity, as well as cross-price elasticities for competing/complementing goods. If your company has spent money on advertising this would be necessary to include as well. Have you added dummy variables for the 'category' of the good itself? And trend variables? Lags of seasonal effects, their quadratic effects? Interaction effect variables?

Any cursory approach would lead to omitted variable bias over your misspecified parameters. On most circumstances you'll have to verify the multiplier effect isn't changing through time.

Have you checked for normality, autocorrelated errors?

This is as broad and general a reference I can think to give you. The functional specification here might be better calculated through an autoregressive form. But this is beyond the scope I think.

I'm not sure as to your level of econometric/demand analysis so I kept things devoid of much math. I hope this was somewhat helpful. It was great intuition to stop what you're doing when you saw incorrect signs. Keep to that rule of thumb.


Are there any countries in which post-dated cheques are commonly used in trade? I am reposting from the Personal Finance & Money Stack Exchange because my question was flagged as being about economics and off-topic.

The post-dated cheque is the most common payment instrument for internal commerce in Turkey. According to the data published by The Banks Association of Turkey, ₺784 billion (equivalent to \$208 billion in December 2017) worth of payments were processed through cheques, most of which are believed to be post-dated. To compare, Turkey's total exports were worth ~$150 billion in the same year.

The reason for me asking this question is: I have been hearing from numerous people that the usage of the post-dated cheque as a financial instrument is unique to Turkey. That is obviously not true; there are other countries that allow post-dating cheques, e.g. Canada.

However, the argument is that the majority of payments are made with post-dated cheques, which could indeed be unique to Turkey. In Turkey, when someone writes you a post-date cheque, you can use that cheque to pay someone else. The process is described by most as minting money on-the-fly. Used as legal money, cheques change hands frequently, and you can find yourself paying for property using a cheque written by someone you don't personally know. Only when the date comes can the cheque be cashed in by its n^th holder, realizing its value promised to its 1st holder. This highly exaggerates the number given above (₺784 billion) which does not reflect how many times a cheque was used in payment.

This essentially forms a network of trust that operates in parallel to the banks. The reason I have been told is that the banks are owned by the holding companies of Turkey, and their operational capabilities outside the financial domain make them competitors to every other company. Thus a businessman in Turkey has an excuse not to disclose his financial/business history to banks; it's like leaking information to your competitors. So instead of taking out a loan, they write post-dated cheques. Again, I am relaying what I have been told.

Given the situation in Turkey, are there any other countries with similar financial habits? Or do the countries listed in Wikipedia (Australia, Canada, India, Serbia etc.) see only limited use?

Iran is another similar case, however in Iran use of post-dated cheques are mainly due to difficulties that a businessman will face if he wants to use bank loans.
For example banks usually have a well-known precondition for extending loan to firms and households which is providing sufficient liquid collaterals.
For finding more theoretical elaborations you can search for "access to credit" literature which tries to elaborate why banks do not have sufficient incentive to provide credit to some people.


Will major economies be able to repay their debt? According to The Economist, lots of major economies are in debt to the extent of it consuming most of the countries' GDP. And the whole system almost seems to resemble a Ponzi scheme at a macro level. I'm sure this is a gross simplification of how things work and I'm no economist by any measure. But at some point, wouldn't the debt of these countries grow beyond the expectation that it will ever be paid off? How is it there is so much worldwide debt without the whole system ready to implode?

Whether a country's debt is sustainable is a difficult question to answer. Bohn developped a framework for answering this question and the cited paper is a summary of much of its findings.

Henning Bohn, 2005.
"The Sustainability of Fiscal Policy in the United States,"
CESifo Working Paper Series
1446, CESifo Group Munich.

Bohn proposes to estimate a fiscal reaction function to model a country's fiscal policy. He concludes that for a country's fiscal policy to be sustainable, it is sufficient that its primary balance is a (linear) increasing function of its lagged debt-GDP .

$pb_{it}= \alpha_i + \beta_i d_{it-1} + \delta_i X_{it} \ \ \ \ \  \beta_i>0$

($X_{it}$ is a vector of control variables)

There are however some problems with this framework. If for example does not exclude an ever increasing debt limit, which seems counter-intuitive. Some of these problems are resolved in Ghosh et. al. 2011 and non-linearities in a fiscal reaction function are added and they introduce the concept of fiscal space.

Atish R. Ghosh & Jun I. Kim & Enrique G. Mendoza & Jonathan D. Ostry & Mahvash S. Qureshi, 2011.
"Fiscal Fatigue, Fiscal Space and Debt Sustainability in Advanced Economies,"
NBER Working Papers
16782, National Bureau of Economic Research, Inc.

Yet, there are still some drawbacks to this approach. Japan is a country that has almost reached its debt limit but financial markets doe no seem to response to this fact. Therefore this framework as evolved from estimating these fiscal reaction functions to stochastic debt simulation. Celasun, Debrun and Ostry wrote a seminal paper on this procedure.

Oya Celasun & Xavier Debrun & Jonathan David Ostry, 2006.
"Primary Surplus Behavior and Risks to Fiscal Sustainability in Emerging Market Countries: A "Fan-Chart" Approach,"
IMF Working Papers
06/67, International Monetary Fund.

They for example calculate the probability that a country's debt-GDP ratio increases more than 10% in comparison to a baseline-year. But again, this does not answer some fundamental questions. If for example the indebtedness of a country does increase with 10% in 5 years, does this mean that fiscal policy was insustainable?

It should be clear now that determining the sustainability of a country's debt is difficult. In the end, it really all comes down to the fact that a country's fiscal policy is sustainable as long as institutions and individuals are willing to buy their debt instruments.

edit:
To answer your comment, I think the easiest concept to understand, it the one of fiscal space so I will try to explain that:

Assume a country's fiscal policy looks the following:

$pb_{t}= \alpha + \beta_1 d_{t-1}+ \beta_2 d_{t-1}^2 + \delta X_{it} $

In which $\beta_1>0>\beta_2$. This thus implies that a country's primary balance initially increases as debt increases to offset the debt accumulation but will decrease after a certain point, called fiscal fatigue. This fiscal fatigue implies a limit to the debt ratio a country could pay back. To see this, you have to look at the debt dynamics, (r-g) equals the interest rate-growth differential:
$\Delta d_t= (r-g) d_{t-1} -pb_t$

This equation explains how an increase in primary balance could counter debt accumulation. The debt limit, lets call it $d^m$ is the highest debt ratio for which the primary balance sufficies to hold the debt ratio constant. ($X_t$ is ignored):

$(r-g) d^m = pb= \alpha + \beta_1 d^m + \beta_2 d^{m2}$

After $d^m$, the primary balance will never be high enough to hold debt constant due to fiscal fatigue. Lenders to the government know this and thus will never buy debt securities after this point, causing a country to default.
 Fiscal space is now simply the difference between a country's current debt ratio and the debt limit and thus is a measure of the amount of fiscal maneouvrability a country has left before it will default.


(Microeconomics) Why must fims always lower prices when there is excess supply? This may seem like a basic question but it has been really bothering me for a while. I understand what excess supply is, and my question is regarding the firms' response to it.

All economics texbooks state that when there is excess supply

"there will be a downward pressure for firms to lower prices to the new equilibrium point".

I think this statement is not always true. I don't understand why firms always receive pressure to lower prices when there is excess supply.

For instance, if price elasticity of demand (demand elasticity) for the market is inelastic, lowering prices to get to the new equilibrium may actually lower the total revenue for the firm compared to the original price(where there was excess supply). In this scenario, I believe frims can definitely choose to simply maintain their prices at the excess supply level and ignore the stock that results from it, because the Total Revenue is higher compared to when firms lower the price to get to the new equilibrium.

So the question I wish to ask is, when there is excess supply, why are prices always lowered to the new equilibrium point where the quantity of demand increases and the quantity of supply decreases?

Why is there always a 'downward pressure' when, depending on the elasticity of demand, maintaining the price at the excess supply level can result in higher Total Revenue for the firm compared to when the price is lowered to the new equilibrium?

Every economics textbook I searched states that firms will always lower prices when there is excess supply, but I really don't get it, especially learning later on about Total Revenue, elasticity of D, etc in the later chapters of Microeconomics. As stated at the beginning, no matter how much I put my thought into it I could not come up with an answer. I would sincerely appreciate it if someome could give me a clear answer on this. :D

You are absolutely right. In many markets, especially consumer markets, which people often think of, firms are not forced to lower prices. If a bakery produces to much bread one day, it might make a bigger profit if it keeps the price and throws away the breads they have not sold at the end of the day. That is because its limited competition.

What many forget to tell you when they teach microeconomics, is which markets microeconomic models is designed to model. It is market with perfectly competition (infinitely many suppliers and consumers) and where everyone have perfect knowledge about prices. Think if big international markets of standard products, like crude oil, flower, rice and stocks.

If you are a farmer wanting to sell rice on an international exchange (normally you will just sell directly to a distributer), you are to small to affect the market. Your only option is ether to sell a tiny amount below the spot price (the last transaction), or choose not to sell at all (something you probably don't want to do). If there are more sellers than buyers, the price is pressed downwards. This downward price pressure will continue until prices are either so small that buyers want to buy more, or the price is so low that some producers don't want to sell anymore.

If you did not understand the last paragraph you should probably read up on how stock/commodity market auctions work.


What are the recent advancements in building a unified theory of bounded rationality? It seems that bounded rationality models focus on explaining a particular psychological bias, in a very specific way. In particular, its seems that the state of the art consensus is that one size does not fit all. The prevalence of framing effects makes this issue very difficult, but is there any way to think of a general approach to modelling bounded rationality.
Is it regret minimization, or random choice, or rational inattention?

The term bounded rationality was introduced by Herbert Simon. He wrote

  "The term, bounded rationality, is used to designate rational choice
  that takes into account the cognitive limitations of both knowledge
  and cognitive capacity. Bounded rationality is a central theme in
  behavioral economics. It is concerned with the ways in which the
  actual decision-making process influences decisions."

This passage seems to focus only on incomplete information, limited information processing time, limited knowledge -and not on any "psychological biases" like framing effects and the like. But the passage is complemented by a last phrase

  "Theories of bounded rationality relax one or more assumptions of
  standard expected utility theory"

which suddenly opens the content of the term to anything. So "bounded rationality" has come to signify "deviations from strict rationality in any way", making it rather impossible to arrive at a general, all-encompassing, or even most-encompassing, modeling approach, that at the same time, will be specific enough so as to be operational.


Sensitivity/continuity of optimal solution Suppose for every $y$, $f(x,y)$ is strictly convex in $x$. $f(x,y)$ is continuous in $y$ and let $\mathcal X$ be compact (in my problem, $\mathcal X$ is an interval). Can anyone suggest any theorems or references for the problem of whether $x^*(y) = \text{argmin}_{x \in \mathcal X} f(x,y)$ is continuous in $y$?

As no one has answered, I will give this a try.

To begin with, together with compactness, and of course nonemptiness, of $X$, which you have assumed, you need $f(x,y)$ to be continuous in $x$ in order to ensure, via Weierstrass extrem value theorem, that $$\theta(y)=\text{argmin}_{x\in X}f(x,y)\tag{1}$$ exists for any $y$. It is good, as you do, to assume strict convexity in $x$, for this gives us a unique solutions to the minimization problems, and thus $(1)$ is a singleton.

Under these assumptions, I will try to show that $(1)$ is continous in the following sense, where I am essentially using the definition of continuity in terms of limits of sequences. The fact that the argmin is a set makes it complicated to directly apply the notion of continuity of function which seldom, in elementary calculus, maps elements to some set of sets.

Theorem. Consider a nonempty compact set $X\subseteq \mathbb{R}$ and a continuous function $f:\mathbb{R}^2\to\mathbb{R}$. Furthermore, suppose that $$\theta(\bar{y})=\{z|z\text{ minimizes }f(x,\bar{y})\text{ over }x\in X\}$$  is the singleton $\{\bar{z}\}$ (to ensure this, assume strict convexity in the first argument of $f$). Then, for sequences $z_n\in \theta(y_n)$, where $\{y_n\}_{\mathbb{N}}$ is a sequence converging to $\bar{y}$, we have $z_n\to \bar{z}$.

Proof. I will give a short proof. It is by contradiction, and is a variant of the proof of Lemma 6.3.2. in Nonlinear Programming: Theory and Algorithms, 3rd Edition, 2006, by Bazaara et al.

So suppose $z_n\to\bar{z}$, $z_n\in \theta(y_n)$, and suppose $|z_n-\bar{z}|>\epsilon>0$ for all $n\in I$ where $I$ is some index set. Since $X$ is compact and $z_n\in X$, the sequence $\{z_n\}_I$ has a convergent subsequence $\{z_n\}_{I'}$ with limit $z_0$ in $X$. By assumption, $|z_0-\bar{z}|\geq\epsilon>0$ and thus $z_0\neq \bar{z}$. In addition, for $\{y_n\}_{I'}$ it holds that $$f(z_n,y_n)\leq f(\bar{z},y_n)\tag{2}$$ since $z_n$ minimizes for $y_n$, but $\bar{z}$ does not minimize for $y_n$ necessarily.

Now, use continuity of $f$ in both of its arguments, and take the limit over $I'$ in $(2)$, to get that $$f(z_0,\bar{y})\leq f(\bar{z},\bar{y})\tag{3}.$$ But as $z_0\neq\bar{z}$ and $\bar{z}$ minimized $f(x,\bar{y})$, it follows that $z_0$ is another, distinct minimizer of $f(x,\bar{y})$ over $X$. Hence, $\theta(\bar{y})$ is not a singleton. But this contradicts the fact that $\theta(\bar{y})$ was a singleton. QED.

Reference suggestion. The Theorem of the Maximum. This theorem is more general and "provides conditions for the continuity of an optimized function and the set of its maximizers as a parameter changes". It involves the concept of a multivalued function (note that the assumption of the argmin being a singleton simplified the proof of the theorem above).


How to calculate inflation rate in order to perfom VAR model? For an assignment I need to perform a VAR model on the three variables real GDP, short term interest rate and inflation. While for the first two variables I have not any problem, I am struggling to understand how to obtain a reliable "inflation" time series to be used for the  model.

An expression I found on "Vector Autoregressions" by James H. Stock and Mark W. Watson is:
$$
\pi_t = 400 \ln \left(\frac{P_t}{P_{t-1}}\right)
$$
where $P_t$ is the chain-weighted GDP index.
However, I don't understand the reasoning behind this expression (why 400?) and I'd prefer to avoid using the chain-weighted GDP index since is an index I don't know very well.

I'd like to start from the GDP deflator. I tried with some reasoning to obtain an useful expression and I came to the conclusion that maybe a good variable is:
$$
\pi_t = \frac{DEF_t -DEF_{t-1}}{DEF_t}
$$

Is that correct? Which is the best series to use as inflation for the VAR model?

Stock and Watson use log approximation and quarterly data. Premultiplying the log approximation by 400 could be due to data being quarterly.

Your second method is fine too.


Search and Matching model with 2 agents? I would like to know if you know any model with Search and matching framework (Mortenses-Pisarides style) with 2 types of workers (like Ricardian and rule of thumb consumers for exemple) ? I would like to see such a model featuring different wages, hours worked and unemployment rates between the 2 consumers. In the end I would like to implement such a framework to a DSGE model with Ricardian and rule of thumb consumers. Thank you.

I am not sure if this is exactly what you are looking for, but this paper has model that sounds like what you want:
Shimer, Robert, 2006. “On-the-job search and strategic bargaining, ”European EconomicReview50, 811—830.
Have a look at this one too:
Shimer, R. (2007). Mismatch. American Economic Review, 97(4), 1074-1101.


Is there any economic explanation why industrialization first occured in Britain? I am asking this question because historians often consider pre-industrialization Britain to be a poor and backward country relative to other European powers/states such as Spain, France, Italian city-states, or Habsburg empire.
Maybe this is a naive view, but I would expect that it would be the richest countries places where people would have the most time/resources to spend on science and industrialization. I get that people's attitudes and culture could play (Weber's protestant ethic) a role but I also don't see that big differences among European countries, and Germany was culturally similar to UK but industrialized relatively late. So was the UK just lucky or was there some economic reason why UK was ripe for industrialization?

A detailed and thoroughly researched analysis of why Britain industrialized first and other countries only later may be found in Robert Allen's The British Industrial Revolution in Global Perspective.  The following quotes are from my own summary of his arguments in a blog post.

Had I been asked beforehand for answers to these questions, I might have listed the following features of 18th century Britain:

Large and accessible coal deposits.
Ingenuity of its inventors, exploiting the scientific knowledge of the enlightenment.
Relatively good governance by the standards of the time.
Rural land reform (enclosure) facilitating higher food production to support growing cities.

According to Allen, however, 1 and 2 were not unique to Britain, and 3 and 4 are dubious.  His analysis focuses instead on relative prices.  And his main conclusion is this: in 18th century Britain, a combination of relatively high wages and cheap energy from coal made it profitable to substitute steam power for labour, even though the steam engines of the time were very inefficient.  Allen presents detailed evidence showing that the wages of labourers in 18th century Britain were much higher than those in most of Europe, India and China, and comparable only with those in the Netherlands and parts of North America.   Only Britain had significantly exploited coal at that time, and the price of energy in British coalfield regions was the lowest in the world.

How had this situation come about?  The reasons are complex and Allen’s explanation goes back several centuries.  Prominent in his account are: Britain’s success in exporting woollen cloth, supported by improvements in sheep farming; its economic gains from mercantilism and empire; the growth of London beyond the point at which its energy needs could be met at reasonable transport cost by wood; the development (via what Allen terms ‘collective invention’ by London builders) of houses designed to be heated by coal; and the consequent stimulation of coal mining around Newcastle, from where London was supplied by ship.

The power obtained from steam engines per ton of coal increased tenfold between 1730 and 1850.  Steam power became profitable at progressively lower wage / coal-price ratios, and around 1850 was rapidly adopted in other European countries and the US.  These countries had not been without coal deposits, inventors or entrepreneurs, but profitability at their prices determined the timing of adoption. Since moreover they were able to adopt the latest and most efficient technology, they did not need to waste resources repeating Britain’s long experimentation with early steam engines.


Elasticity with perfectly inelastic / elastic demand When a change in price results in an infinitely large response in quantity demanded, demand is perfectly elastic. The perfectly elastic demand curve is horizontal. At price P, consumers will buy a quantity Q. If there is an increase in price, quantity demanded drops to zero due to the existence of perfect substitutes. However, when price drops, how will the PED remain infinity? Wouldn't consumers demand as much, if not more, of the product?

In the title you ask about perfectly inelastic demand; in the text it is about perfectly elastic demand. I guess you want to know about the latter. So you can skip one of the paragraphs.

Let us define PED as this absolute vale
$$\varepsilon_p = \left| \frac{d Q / Q}{dP / P} \right|,$$
(otherwise it is a non-positive value, this is just a convention).

In general, both perfectly elastic and inelastic demand are defined in the limit. As always, the math gets a little fishy when $\infty$ is involved (or if you want to divide by zero). To stay sane, it helps to think of an "infinite quanity" as it is used in economics as "very, very, very large approaching infinity" or as "as much as possible". Similarly, think of a good with an "infinite price" as a good that "nobody can buy".

With perfectly inelastic demand, price changes do not affect demanded quantity $q$.
As an example, think of a life-saving drug. How must the price change that you demand $q'<q$ instead of $q$? Well, you always demand $q$ - it doesn't happen. How can we express "it doesn't happen"? We can say that you would only consume less than $q$ if the price becomes some number that is larger than any real number. Now think about a limit approaching this benchmark case of a vertical demand curve, some sequence of very steep declining lines. Then for any $dQ/Q<0$ it must be that $dP/P$ approaches infinity. Similarly, for a demanded quantity $q'>q$, i.e., $dQ/Q>0$, "the good has to be thrown at you". For a meaningful sequence approaching the perfectly inelastic demand, you have to ignore the restriction that prices are positive -- it must be that $dP/P \rightarrow - \infty$. Hence, $\varepsilon_p \rightarrow 0$.
Alternatively, don't think in limits, but ask the reverse question. Instead of "how must the price change that my demanded quantity changes", ask "how do I change my demanded quanity if the price changes"? The answer is, not at all: $dQ/Q =0$ for any $dP/P$, making the PED always zero.

With perfectly elastic demand, an arbitrarily large quantity can be sold at some market price $p$. As an example, think of a \$100 bill or a (hypothetical) perfectly competitive market. "Arbitratily large" does not mean infinity, which is not a real number.
Again ask, how does the price have to change that my demanded quantity changes? By definition, any quantity is demanded at price $P$. That is, the price does not have to change at all. Hence, $dP/P=0$ for any $dQ/Q$. Then $\varepsilon_p$ is not well-defined (you divide by zero), but you can think of a sequence of very flat declining lines that approach the horizontal demand such that $dP/P\rightarrow 0$ and $\varepsilon_p \rightarrow \infty$.
You can again also ask the reverse question: how does demanded quantity change when the price changes. For this just consider the limit again (and ignore the restricion to positive quanitites). If a \$100 bill is offered at \$99.99, demanded quantity goes to infinity. If a \$100 bill is offered at \$100.01, demanded quantity goes to minus infinity -- you would want to sell your bills. That is, $dQ/Q \rightarrow  \mbox{sign}(dP/P) (-\infty)$ and $\varepsilon_p \rightarrow \infty$.


Why are cost functions often assumed to be convex in microeconomics? Why are cost functions typically assumed to be convex in producer theory of (introductory) microeconomics?
For me this goes against the intuition of economies of scale. There are fixed costs (FC) which contribute to concavity of the cost function. There are also variable costs (VC) which may be concave, linear or convex. If we are on the concave part of VC, total costs (TC) must also be concave due to both FC and VC being concave. If we are in the linear part of VC, TC are again concave due to the concavity of FC. And if we are in the convex part of VC, TC may be either concave, linear or convex depending on the relative influence/weight of FC and VC on/in TC. However, even in the case where TC is convex, the producer does not have to operate that way. It can rather operate multiple copies of its production facility each at the level where TC is concave or linear to ensure the TC added over all production facilities is never convex.*,** This makes the assumption of convex costs suspect for me.
I do see one reason why convexity could occur, though. It is if resources are becoming scarce and the producer is big enough to influence the prices in the input markets. However, the producers are assumed to be small in perfect competition, yet their cost functions are assumed to be convex. This appears contradictory to me. So what am I failing to see?
*The fact that FC are incurred with each copy of the production facility might or might not make this a poor strategy depending on the relative weight of FC and VC.
**I think I borrowed the idea for this argument from Varian "Microeconomic Analysis". In 3rd edition, Section 5.2 "The geometry of costs" p. 68 it says:

In the long run all costs are variable costs; in such circumstances increasing average costs seems unreasonable since a firm could always replicate its production process. Hence, the reasonable long-run possibilities should be either constant or decreasing average costs.

The cost function is also shown to be concave in the subsequent section 5.4 "Factor prices and cost functions".

Edit: Thank you for all the great answers! It seems we can have different plausible stories with opposite implications. So far it seems one can plausibly argue for both convex and concave costs. The crux of the matter becomes the assumptions needed to make one story more plausible than the other. Thus the question is, what are the assumptions taken to make convex costs plausible (and concave costs implausible) in introductory microeconomics?

There are several reasons:

Didactic Reasons: Other users seem to have missed it but in your question you specify you are talking about "(introductory) microeconomics" [emphasis mine].
Well the most prosaic answer is simply that it is much easier to solve
cost minimization, or various other models when costs are assumed to
be convex.
This in itself is sufficient reason to construct problems with convex cost functions in introductory microeconomic courses. Demand and supply are not linear, yet in most textbooks and introductory problem they will be assumed to be linear. In addition, in real life demand can be sometimes even upward sloping if a good is a Giffen good, and supply can actually be downward sloping (e.g. some labor supply in some special cases depending on people's preference between consumption and leisure). Yet introductory textbooks typically show downward sloping demand and upward sloping supply (e.g. see Mankiw Principles of Economics that discusses these concepts but only briefly, or more narrowly micro introductory books such as Frank Microeconomics & Behavior).
This is to a great degree for didactic reasons. It is much better for students to first master basics with simple models and when it comes to learning about costs having nicely behaved convex cost functions with single minimum makes learning easier than having to teach cost minimization with concave cost curves. Hence, even if empirically most cost curves would be concave not convex it would be very bad teaching practice to start with concave functions (or just go for full blown realism where cost functions might be piecewise, have different concavity/convexity at different points, be ill defined somewhere etc).

Because of Decreasing Returns to Scale - This was covered in great detail by Bayesian, but let me add more arguments and also rebuff some of your arguments in the question.
First, it is not unreasonable to assume that costs are convex in a long-run. In a world of scarcity firm cannot forever increase its demand for factors of production without affecting costs of these factors or inputs as well, their prices will rise eventually (ceteris paribus). We have crystal clear evidence that wages rise in tight labor markets, or that generally speaking shift in demand to the right (ceteris paribus) rises prices.
You argue that in perfect competition models firms are assumed to be small, but that is not a good argument in this case. This is because firms are assumed to be too small in terms of their output being able to affect market price of their output so price of output can be taken as given (See Frank Microeconomics and Behavior pp 337). Perfect competition does not require price of inputs to be taken as given. In fact, firm might operate on perfectly competitive market while facing just monopolistically competitive factor market (where the firm is consumer not producer).
Next, you argue that thanks to fixed costs one firms could just continuously invest in a new factories, but this argument should be false. A fix cost by definition cannot vary with output. If firm increases output by building new factory, the cost of factory ceases to be fixed costs. In fact fixed costs primarily exist in short-run as in a long-run most costs are variable (see Mankiw Principles of economics pp 260). In a long-run as you try to build more and more factories you run into the same problems of scarcity of land, capital and labor and thus bid up their prices. In fact this is nicely visualized and explained in the Mankiw textbook with the picture below:

Empirically, we observe that many industries have decreasing returns to scale (although constant returns to scale are common as well), and increasing returns to scale are rare (although not completely uncommon). See for example: Basu & Fernald, 1997; Gao & Kehrig 2017.
Introductory texts by their nature will not deal with specific cases but more general ones. Most introductory textbooks again do not spend too much time on Giffen goods not just because modeling them would be difficult for 101 students but also because they are not very often seen (although, I am not claiming non-convex cost functions are as rare as Giffen goods).

On the Aesthetics: I think Giskard raises a valid point that there are probably many economists who assume convex costs just for mathematical elegance. However:

I think Giskard slightly exaggerates the problem and is bit too cynical about it. For sure there are economists who value mathematical elegance uber ales, but there is increasing trend in share of empirical papers (see Angrist et al 2017), even in microeconomics, and I think that a reasonable non-cynical explanation for the small share of micro empirical papers is that until very recently there was always lack of good micro data (in addition this is also due to breakdown, you can see the share of industrial organization empirical papers (that also heavily use cost functions) is quite high).

Empirically, most industries do not exhibit increasing returns to scale. While non-convex functions are definitely real (especially along some points of cost curve), empirical evidence does show that decreasing returns to scale (although constant returns to scale as well) are quite common (e.g. see Basu & Fernald, 1997; Gao & Kehrig 2017), but I think Giskard has definitely valid point that some modelers will ignore empirics for sake of mathematical elegance.

Lastly, but not least, I think mathematical elegance can explain why such assumption features heavily in some published theoretical work, I don't think it can explain why it is featured in introductory micro texts. Is really quadratic cost function $c=q^2$ mathematically elegant? I don't think so but that is probably the most commonly used cost function you will ever see in intro texts.

Regarding the Varian quote. Varian on page 67 states that he will first cover situation with fixed factor costs and later move to variable factor costs. Hence, unless I am misreading Varian I think the statement on the page 68 is made under assumption of constant factor prices. However, the explanation above by Mankiw does not assume that.


US economy stagnant growth Why US growth is stagnant even though unemployment is significantly low . Not only US but all developed nations are facing this problem. Is limited population the cause of this , I mean lower human resources.

Not necessarily. One has to distinguish between (output - I just assume that you mean output, i. e. gdp) growth and per capita growth.

In (very) simple terms: Growth is the result of either population growth, capital accumulation (more investment) or technological progress.

So one reason for the low US growth could be limited population growth and looking at the data this is a possibility (Population Growth Rate US)
Another possibility might be the "unusability" of technical progress. While a lot of research is done and we discover lots of new things not everything can be used in the production progress and is therefore not reflected in gdp growth.

One way to check this possibility is to development a new measure of technical progress - I think Daron Acemoglu and some coauthors are working on a new index. Another possibility is that this technical knowledge is just worthless. Consider the internet rush around 2000 which was at that time considered as technical progress which would increase the productivity of the whole economy... Well most of this was wrong and this technical progress did not lead to an increase in productivity - an argument often used by Robert Solow.

So the question: "Why is a nation not growing" is pretty difficult and not easy to answer or even understand.


How to estimate market risk using only publicly available data? How can I calculate market risk for the US Stock Market (NYSE or NASDAQ) using only freely accessible data? I'm only interested in the market risk of the whole economy not of different industries, companies or sub-sectors.

Somebody suggested to me to download market index data and construct the volatility as a measure of market risk. But I can't find a proper explanation how I do this.

Thank you.

p.s. Is the following procedure correct?:

I get data US Stock market (for example https://fred.stlouisfed.org/series/SP500) calculate the growth rate and in the last step I compute the variance of the growth rate to get the market risk?

This paper on Fluctuations in Uncertainty may be helpful and relevant.

  The  volatility  of  the  stock  market  or  GDP  is  often  used  as  a  measure  of  uncertainty  because  when  a  data  series  becomes  more  volatile  it is  harder  to  forecast.

Computing the variance or standard deviation of the growth rate of a variable is quite a common procedure to get volatility figures.

The above figure shows the VIX index of 30-day implied volatility on the Standard & Poor's 500 stock market index. The  VIX  index  is  traded  on  the  Chicago Board Options Exchange. It is constructed based on the values of a range of  call  and  put  options  on  the  Standard  &  Poor's  500  index  and  represents  the  market's  expectation  of  volatility  over  the  next  30  day.

Other  common  measures  of  uncertainty  include  forecaster disagreement, mentions of "uncertainty" in news,  and the dispersion of productivity shocks  to  firms. Check Bloom's web page and his Economic Policy Uncertainty Index


Budget constraint hyperplanes This question relates to a specific paper by Eric Budish, published in 2011 in JPE, but I've tried to put all relevant information in this question. On page 1072, he defines budget constraint hyperplanes as follows:

  Let $H(i,x) = \{\mathbf{p}:\mathbf{p} \cdot x = b_i \}$ denote the
  hyperplane in $M$-dimensional price space along which agent $i$ can
  exactly afford bundle $x$. As prices cross $H(i,x)$ from below, bundle
  $x$ goes from being affordable for $i$ to being unaffordable for $i$.

$\textbf{p}$ represents a price vector for the $M$ goods, which, importantly, are indivisible. $b_i$ is agent $i$'s budget. I think the rest is sufficiently self-explanatory. My confusion is with this subsequent statement:

  Importantly, the number of such hyperplanes is finite because the
  number of agents and the number of bundles are finite. This is an
  advantage of having only indivisible goods.

This I don't see. For example, suppose $M=2$. Then aren't all $\textbf{p}=(\alpha b_i, (1-\alpha)b_i)$ such that $\alpha \in [0,1]$ hyperplanes meeting that definition, and thus I have infinitely many?

Having said that, a hyperplane is the set of those price vectors, not each of the vectors, so maybe the full set of price vectors I've just described together define just one hyperplane? I suppose my issue is understanding what a hyperplane is in this setting, and how the indivisibility gives us just a finite set of hyperplanes to work with. Any guidance would be very much appreciated.

The set $\{\mathbb{p}:\exists \alpha \in (0,1), \mathbb{p}_1=\alpha b_i, \mathbb{p}_2=(1-\alpha)b_i\}$ coincides with the hyperplane $\{\mathbb{p}:p_1+p_2=b_i\}$, therefore you are not finding extra hyperplanes by doing this and varying $\alpha$.

More generally, if you fix $x=(x_1,x_2)$ and $b_i$, you obtain one hyperplane characterized by the equation $\{\mathbb{p}:p_1 x_1+p_2 x_2=b_i\}$. Since there are finitely many such $x$ (and $b_i$ is given), there are finitely many such hyperplanes.


How do you calcualte Yield To Maturity, given only the coupon rate and current required rate of return? Suppose today a 10 per cent coupon bond sells at par. Two years from now, the required return on the same bond is 8 per cent. What is the YTM?

^That's a question I've been asked and have literally no clue about how to calculate the YTM.

My understanding is: YTM is the anticipated return on a bond if held to maturity. If I buy a fresh bond at say \$90 and the par value is \$100 at 10% coupon rate, the YTM will be 10/90 = 11.11%. So for this question, If I buy a bond on the secondary market at par value, the YTM should equal the coupon rate no? If so, how does rrr affect YTM?

I'm so confused, send help.

The yield-to-maturity is similar to an internal rate of return, so the calculations need to take into account the timing of cash flows. So your example calculation 10%/.90 = 11.11% does not work. (That is known as a simple interest convention, which I think is sometimes used in the Japanese bond market.)

The calculation form depends upon the coupon frequency of the bond. For an annual coupon, if we denote the yield as y, then the price of the bond equals (convention of \$100 equals par):
$$p = \sum_{i=1}^8 \frac{10}{(1+y)^i} + \frac{100}{(1+y)^8}.$$

However, I do not know what “required return” in the question refers to (a true internal rate of return?). You would need to find the price of the bond using that “required return,” and then work from the price equation to get the yield.


Key Performance Indicators I am reading some book about strategic management.

First, I must tell you that my native language is not English.

My question is:

In the book, they divided Key Performance Indicators into three groups:

1) indicators of competence (or indicators of competency)

2) indicators of profitability

3) indicators of effectiveness (or indicators of efficiency)

Did someone heard about this distribution (division) of KPIs and what is the exactly translation of indicators?

I gave my best to translate correctly on English. If somebody heard of this division could you write the name of the books or articles on English where can I further read about it.

Key Performance Indicators are important elements of a company that can be used to asess a firm's current core competencies and business model. They are based on of key result areas. Here is my interpretation of the three indicators and some examples (There are many more):

Competency: A firm's business strategy and it's competitive advantage

Example: Retention, Value (Quality/Price), R&D Investment

Profitability: A overall indicator of market performance

Example: ROI, Gross Margin, EBITDA

Effectiveness: The implementation of a firm's strategy

Example: Market Share, Sales, New Market Segments

You may notice that the examples can be related to other indicators, because the indicators are a broad overview of the firm.


Intuition - Why does elasticity vary along a curve? Source: p 96, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw

  Even though the slope of a linear demand curve is constant, the elasticity is not.
  This is true because the slope is the ratio of changes in the two variables, whereas
  the elasticity is the ratio of percentage changes in the two variables.

  [Source:] Elasticity along a straight line demand curve varies from zero at the quantity axis to infinity at the price axis. ... At the midpoint ... elasticity is equal to one, or unit elastic.

Please explain the above intuitively? I ask NOT for a formal proof.

Think of it this way. A yacht costs $\$0.01$. How much do you demand? Then double the price. Now how many would you demand?

Then consider something closer to a market price. Something in 6 or 7 figures I guess. If you've got some money, you might buy one at the market price. But then if that price doubles, wouldn't that affect your demand a lot more than the 1 to 2 pennies change?

Simply put, as you go up the demand curve, the same percentage change in price is a much bigger absolute movement in price.


Does an instant settlement system (such as blockchains) eliminate the possibility for short selling? My understanding is that a short sell is possible because you can sell positions you don't have and then buy at a later point to cover your position (with the price hopefully being more favorable) to settle the trade.

In an instant settlement system (blockchains are the obvious examples, such as Bitcoin or Ethereum) would it be possible to have perform a short sell? Is there some other means of achieving the same thing?

Imagine:

I borrow 1 bitcoin from you and agree to pay you back $(1+r)$ bitcoin in a month.
I immediately sell the bitcoin you lent me.
One month from now, I buy $(1+r)$ bitcoin and pay you back.

If I can conduct those transactions, I can short sell bitcoin.


Gali (2015) Chapter 8 Symmetric Steady State In Chapter 8 (small open economy) of Gali's 2015 version of Monetary Policy, Inflation, and the Business Cycle, he often performs log linearisations around a symmetric steady state like below:

My questions are:
1. What exactly is a symmetric steady state,
2. How do we know that it exists
3. How do we know that $P_H = P_F = P$ in steady state? (I know from S=1, that I can infer that $P_H = P_F$, but I'm confused about whether S=1 is the cause for $P_H = P_F$ or a consequence of $P_H = P_F$).

Thank you very much for your time in advance!

The steady state is "symmetric" in the sense that terms of trade with all other countries are equal to $1$, with respect to the home country. It would be non-symmetric if for some of them terms of trade were not equal to unity.

Is there anything in the model that precludes this steady state from existing? Usually not. Then it is feasible, i.e. it exists. Whether it is an attractive, stable steady state, is another matter.

$S$ is the ratio of two price levels. Logically then, it is a derivative measure of these two, so the price levels are the underlying forces.


Reference request: Gender wage gap / Minority wage gap Disclaimer: I am neither a social scientist nor an economist. I hope the ESE is the right place to ask this question.

Disclaimer 2: I do not intend to spark an ideologically driven discussion here. Please keep any non-professional opinions to yourself.

Recently I have been exposed to discussions about the "gender wage gap" and similar concepts (such as race wage gaps), mostly through popular media. As always with scientific topics in popular media, and especially in this particularly politicized case, people tend to throw about contradicting studies, misinterpret studies, claim the other side's studies are false due to not adjusting for one variable or another.. you know what I'm talking about. Reporting on the subject tends to be poor, probably due to ideological reasons (e.g. here and here).

I want to look at the facts myself. Luckily I am a mathematician, so I believe to be able to handle the statistics and methodology questions in such papers. Also I don't really have a horse in this particular political race, so I think I can look at it from a reasonably neutral position.

Could you please provide links to the more relevant literature regarding this issue, or that is in some way relevant to the issue? Preferably papers that are particularly transparent regarding their ways of data collection and interpretation, and if possible even provide their raw data (is that common in economics / social sciences?).

If you have an opinion on the issue, which you probably do, please try to provide literature supporting your opinion, as well as the best literature you know of that attempts to refute your opinion. If you are not a cargo cult scientist, which I assume you are not, then this should be possible. Do feel free to indicate where you think that literature went wrong.

Edit
X-post, because I didn't know where to post (sorry).

There are a lot of possible places to start when looking at the literature on gender or racial wage discrimination/differentials. Preferably, it'd be good to look at the literature on labor supply as a whole (e.g. Mincer equation, work-leisure tradeoffs etc.), but we could be here all day discussing papers related to modelling wages in general (I am happy to provide some if you would like.) I will do my best to summarize the theoretical and empirical literature I give reference to below. Let us look at differentials.

Becker (1973), A Theory of Marriage: Part I was some of the earlier work on family economics, where men and women would tend to pick each other for marriage based on their relative strengths. To put it roughly, though people tend to like marrying others who are the same height, race, education level, etc., the theoretical model set up by Becker predicted that because families care about work (employment), leisure, and household production, there'd end up being some sort of division of labor so that all these needs were met.

Mincer and Polachek (1974), Family Investments in Human Capital: Earnings of Women and others would build off of this earlier body of work when looking at the effects of education and work training on wages. This paper in particular argued that the expectations of market activity, particularly regarding raising children, would affect how much women would pursue education or work training, and would effect how employers would want to pay women over time. If women are more likely than men to leave the workforce to spend time raising a child, then their wage-age profile will change. Intuitively, even before a child is born, women might get paid less because future expectations of productivity affect wages and individual investment into skills.

Becker (1971), The economics of discrimination is a gigantic book written as a lot of the basis for modelling economic discrimination. There's a lot to sift through and I'm not super well-read in that area, but the gist of the model set up here is you can distinguish between prejudice which is where employers may have a preference for certain type of worker that shows up in the utility function, and discrimination, which is the explicit unequal treatment of equals; that is, unequal outcomes. Although there may be prejudice from employers, depending on the search model used, if there are enough jobs by non-prejudiced employers, we may not see any discrimination in outcomes.

Even after controlling for confounding variables that could affect the wage gap between women and men, or between races, there is some discrimination in outcomes on the basis of race and gender.

Dougherty (2004) Why is the rate of return to schooling higher for women than for men? uses the Oaxaca decompositions in E. Sommer's answer to look at why the rate of return to education seems to be higher for women than for men. In this paper, one theory looked at was that better educated women are more willing/able to compete with men to push back against gender discrimination, hence why it seems the rate of return is higher. The paper has some support for this finding.

Lang and Lehmann (2011) Racial Discrimination in the Labor Market: Theory and Empirics notes that while taste/preference frameworks combined with search models are able to explain a lot of differences between wages and unemployment duration, these models are not so good at showing differences in unemployment rates themselves. Statistical models (employers have some sort of imperfect information that leads to discriminatory outcomes through, for example, self-confirming stereotypes) can explain magnitudes of wage differences well, but not much about employment. This paper tried to combine elements of the two approaches.

This above article is a particularly good one to look at (and should not be too much of a problem to sift through if you have a good math background). I don't think I can do justice trying to summarize the breadth of their results here in a reasonable amount of time, so check it out on your own if you like.

There are a lot of good articles in labor economics that look at gender and racial discrimination but those are a few I've picked out to give some brief summaries on. Some of the ones I've not mentioned, but which are important to the literature are listed below. Just because I chose not to summarize them does not mean the below articles are particularly less important. I just have my own time constraints. My presentation of the existing literature is also not comprehensive, but hopefully a good starting point for others.

Hope some of these resources prove useful to you and future users.

Further Reading

Oaxaca-Blinder Decomposition:

Blinder, Alan S. "Wage discrimination: reduced form and structural estimates." Journal of Human resources (1973): 436-455.
Oaxaca, Ronald. "Male-female wage differentials in urban labor markets." International economic review (1973): 693-709.

Labor Supply/Compensating Differentials:

Oaxaca, Ronald L., and Michael R. Ransom. "On discrimination and the decomposition of wage differentials." Journal of econometrics 61, no. 1 (1994): 5-21.
Rosenzweig, Mark R., and T. Paul Schultz. "The demand for and supply of births: Fertility and its life cycle consequences." The American Economic Review 75, no. 5 (1985): 992-1015.
Henderson, Daniel J., Solomon W. Polachek, and Le Wang. "Heterogeneity in schooling rates of return." Economics of Education Review 30, no. 6 (2011): 1202-1214.
Goldin, Claudia, Katz, Lawrence F, and Kuziemko, Ilyana, “The Homecoming of American                         College Women: The Reversal of the College Gender Gap”, Journal of Economic                             Perspectives 20(4), 2006, 133-156
Blau, Francine D., and Lawrence M. Kahn. "The US gender pay gap in the 1990s: Slowing convergence." ILR Review 60, no. 1 (2006): 45-66.
Mobius, Markus M., and Tanya S. Rosenblat. "Why beauty matters." American Economic Review 96, no. 1 (2006): 222-235.
Lang, Kevin, Michael Manove, and William T. Dickens. "Racial discrimination in labor markets with posted wage offers." American Economic Review 95, no. 4 (2005): 1327-1340.


How to Calculate Marginal Utility Imagine a scenario where an agent is faced with two purchasing options, each with an individual utility function. Let us say option $A$ offers $m$ units of $P$ per £, and option $B$ offers $n$ units of $Q$ per pound. Additionally, utility is linear with respect to $P$, but not so for $Q$. How do I find out when the marginal utility of $A$ is greater than $B$?

Let's assume our agent purchases positive quantities of $x$ and $y$. The utility maximization problem (without constraints on purchasing non-negative quantities) is:

\begin{equation}
 \begin{array}{*2{>{\displaystyle}r}}
 \mbox{maximize (over $x, y$)} & u(x,y) \\
 \mbox{subject to} & p_x x + p_y y \leq w
 \end{array}
\end{equation}

The Lagrangian is:

$$ \mathcal{L}(x, y, \lambda) = u(x,y) - \lambda(p_x x + p_yy - w)$$

Assuming $u$ is concave and differentiable, the problem is a convex optimization problem (in the jargon of optimization problems), and Slater's condition holds, hence the first order conditions are necessary and sufficient for an optimum. The first order conditions are:
$$ \frac{\partial \mathcal{L}}{ \partial x} = \frac{\partial u}{\partial x} - \lambda p_x  \quad \quad  \frac{\partial \mathcal{L}}{ \partial y} = \frac{\partial u}{\partial y} - \lambda p_x = 0 $$

Combining both equations (taking out lambda) we have:

$$\frac{\partial u / \partial x}{p_x} = \frac{\partial u / \partial y}{p_y} $$

This gives you the classic microeconomic theory result that the marginal rate of substitution is the ratio of prices. From here can you answer the question?

(Note: as you may have noticed, I slipped into your question a few more assumptions: eg. an assumption that the agent actually buys positive quantities of Option  A and Option B.)


why did the 2008 financial crisis happen inspite of banks having 85% insurance on deposits in U.S.? I read What Happened in 2008?  which gives some idea and similar things are happening in India. Seems India's 2019/2020 is similar yet different as millions are educated unemployed. While I can understand people having losses who had mortage, what about those who didn't have any mortage or loans. Did they escape ? From what I have been reading 85% of the money invested in a bank account upto some agreed amount is insured. Although I don't know whether that 85% figure insured amount was agreed after or before the 2008 financial crisis.

At the end, my question is simple, did people who had no loans of any sort, did they escape the 2008 financial crisis, or were they also caught in unexpected ways ?

Yes, most of the loans were insured - this is called a credit default swap (CDS) that an insurance company insures a bank loan in case of a default (i.e. when a borrower cannot repay, the insurer pays the bank).  Banks and insurance companies were making an unprecedented amount of money through this practice.

However, when the housing bubble burst, too many loans defaulted to the point that the insurance companies could not pay the banks.  Then the banks were going bankrupt unless they were bought out.  For instance, Lehman Brothers, which reportedly had relatively more mortgage-related assets, had to declare bankruptcy as the federal government or no other bank would bail it out. (words are that people in finance did not like Lehman Brothers which is one of the reasons why it was not bailed out)

The 2008 financial crisis (people now call it the Great Recession) froze all economic activities so virtually few were able to escape it.


fixed an marginal cost calculation issue I'm trying to solve a question that is quite difficult for me. I did part of the question but, bit difficult to decide the exact answer for the below question.

After coming up with an innovative idea for a new product, you paid 4000
to an industrial designer to draw the blueprints and found a factory in China that agreed to produce the product for you for $3 per unit (the price includes the shipping cost from China to you).

Since this is a totally new and unique product, you have no idea how the demand for it would be. Therefore, before you start pricing the product and ordering large amounts from the Chinese factory, you decide to run an experiment (or a pilot study): you talk to Target and they allow you to sell your product at 11 different Target stores for 11 different prices (a different price at each store). These stores are located in areas whose residents have similar average income, so you can be certain that price (and not income) is the only factor varying among these stores.

After 2 weeks, Target sends you the sale numbers for your product.

Price   Quantity Demanded
4   221
5   210
6   185
7   162
8   144
9   122
10  102
11  81
12  61
13  46
14  25

What they are asking is to measure the total fixed cost and the marginal cost.

Can 4000 be decided as the fixed cost? If so how the marginal cost can be calculated? I believe the variable cost is 3$. This 4000 should be only the initial fixed cost. How can I calculate the marginal cost.

The marginal cost is 3. Marginal costs do not depend on the fixed cost, and when your variable costs are constant, then the marginal cost and the variable cost are the same. Note that your total cost is $C=FC+3q$ and the marginal cost is always the derivative of your total cost, in this case, $3$.

As for the fixed costs, 4000 is definitely part of it, but maybe also the forgone profits from selling the goods in the various stores at sub-optimal prices, as pointed out by another response. Other's have pointed out that if you calculate the variable profits for each price, 9 gives the largest profits, so in all the other stores that you made less profits, the lost profits should probably be added to the fixed cost.


The Difference between investment and savings in CA identity Mathematically speaking the current account is defined as:
$$\text{CA}=S-I$$

where $S$ is savings and $I$ is investment.

We know for a closed economy $S=I$ so $CA=0$. practically speaking for an open economy what is the difference between these two terms?

Yesterday I gave an example of an economy based on grains of wheat where the real domestic activities were

Plant wheat grains, grow them and harvest them, getting more grains as a result
Consume wheat as food
Store unconsumed wheat for future planting or consumption

In an open economy there are two further possibilities

Send wheat grains abroad (e.g. exports)
Receive wheat grains from abroad (e.g. imports)

So saving represents the excess of production of wheat grains over consumption, while investment represents a combination of planting grains for future production and increasing stocks of grain.

In this open economy, you then get the macroeconomic tautology that the increase in stocks must be equal to production plus imports minus the sum of consumption and use for planting and exports.  Rearrange this and you get that saving (production minus use for consumption) minus investment (use for planting plus increase in stocks) must equal exports minus imports (in effect the balance of trade or, if you take into account other foreign income, the current account balance), i.e. $S-I = X-M$ or $CA=S-I$

You may then want to translate this into monetary terms using the price of wheat, or in a more complicated economy the price of all the stuff involved, but the key is to recognise this is about stuff measured in monetary terms rather than about money


How Does Production Possibility Curve Shift (Partially)? Textbook:

"Suppose that a new pizza assembly line improves the pizza production process and that the development of the new assembly line does not require the use of more of society's resources.

Although the ability to produce wings has not changed, the new pizza making technology causes the production possibilities frontier to expand outward from $PPF_1$ to $PPF_2$.

It is now possible for society to produce more of both because the improvement in pizza making technology allows a redeployment of the labor force that also increases the production of wings."

My question:

I understand that improvement in pizza making technology will allow the same amount of workers to produce more. But why is it assumed that workers can be allocated to make more wings?

If for example, at point A, we produce 200 wings and 70 pizzas with 10 workers making wings and 10 workers making pizzas. Why at point B, do we produce 220 wings and 80 pizzas? I think it could be 200 wings and 80 pizzas because how do you know that its not still 10 workers making wings and 10 workers making pizzas (just more efficiently)?

Perhaps in order to produce 80 pizzas you don't need 10 workers but just 8 and the extra 2 workers can now produce wings.


Is saying that the demand is elastic or inelastic too oversimplified? As we know that elasticity varies from infinity to zero as we move along a linear demand curve, then is it correct to label any demand curve elastic or inelastic as a whole?

From your Q I am not sure if you are asking solely for linear demand functions or demand functions in general.
When it comes to demand functions just in general  actually, we do not a priori know that "elasticity varies from infinity to zero as we move along a linear demand curve"  there is a class of constant elasticity demand functions for which price elasticity of demand is always the same. For example:
$$P  = Q^{1/\epsilon}\implies Q= P^\epsilon$$
will have constant price elasticity. Since price elasticity is given as:
$$e_p= \frac{dQ}{dP} \frac{P}{Q}$$
In the above case the elasticity would be simply equal to $\epsilon$, as:
$$\frac{dQ}{dP} \frac{P}{Q} = \epsilon P^{\epsilon-1}\frac{P}{P^{\epsilon}}= \epsilon$$
The constant price elasticity functions are relatively popular in the literature and for these functions it clearly makes sense to label them as elastic or inelastic based on value of $\epsilon$.
However, even for a linear demand functions where price elasticity of demand changes along the function it would be reasonable to say that one demand curve is more inelastic relatively to some other demand curve, respectively being more or less elastic over some range. In such situations however the terminology might often be abused and demand function simply termed 'inelastic' - this happens especially in many undergraduate texts and I suppose you could call it an 'oversimplification'.