How to calculate the intercept of an indifference curve in an Edgeworth box? Consider an exchange economy with two goods (Good 1 and 2) and two individuals ($A$ and $B$):

$A$'s utility function is $u_A(x_{A_1}, x_{A_2}) = 2x_{A_1} + 5x_{A_2}$
$B$'s utility function is $u_B(x_{B_1}, x_{B_2}) = 3x_{B_1} + 7x_{B_2}$
$A$'s initial endowment is $(\omega_{A_1}, \omega_{A_2}) = (4, 6)$
$B$'s initial endowment is $(\omega_{B_1}, \omega_{B_2}) = (10, 2)$

The core condition requires:

$$
2x_{A_1} + 5x_{A_2} \geq 2\omega_{A_1} + 5\omega_{A_2} = 2 \times 4 + 5 \times 6 = 38
$$

and

$$
3x_{B_1} + 7x_{B_2} \geq 3\omega_{B_1} + 7\omega_{B_2} = 3 \times 10 + 7 \times 2 = 44
$$

The line with  equation $2x_{A_1} + 5x_{A_2} = 38$ hits the left boundary at:

$$
(x_{A_1}, x_{A_2}) = (0,38/5), ~~~~(x_{B_1}, x_{B_2}) = (14, 2/5)
$$

The line with equation $3x_{B_1} + 7x_{B_2} = 44$ hits the left boundary at:

$$
(x_{A_1}, x_{A_2}) = (0,54/7) ~~~ (x_{B_1}, x_{B_2}) = (14, 2/7)
$$

I don't understand how these intercepts have been calculated.

I've used the MRS and endowment point to calculate the $(x_{A_1}, x_{A_2})$
intercepts correctly:

$$x_{A_2} = -\frac{2}{5}x_{A_1} + \frac{38}{5}$$

But get an incorrect $(x_{B_1}, x_{B_2})$ intercept:

$$
x_{A_1} = 14, ~~ x_{A_2} = 2
$$

Please can someone enlighten me? No worries if you can't.

Alex

In an edgeworth box model the total amount of goods must be constant. In your problem this translates to

\begin{eqnarray}
x_{A_1} + x_{B_1} &=& \omega_{A_1} + \omega_{B_1} = 10 + 4 = 14 \tag{1}\\
x_{A_2} + x_{B_2} &=& \omega_{A_2} + \omega_{B_2} = 6 + 2 = 8 \tag{2}\\
\end{eqnarray}

So let's consider the first intercept

$$
(x_{A_1}, x_{A_2}) = (0, 38/5) \tag{3}
$$

which you properly derived. If you replace these values in Eq. (1) you get

$$
0 + x_{B_1} = 14 ~~~\Rightarrow~~~ x_{B_1} = 14 \tag{4}
$$

and if you replace in Eq. (2) you get

$$
\frac{38}{5} + x_{B_2} = 8 ~~~\Rightarrow~~~ x_{B_2} = \frac{2}{5} \tag{5}
$$

So there you have it

$$
(x_{A_1}, x_{A_2}) = (0,38/5), ~~~(x_{B_1}, x_{B_2}) = (14,2/5)
$$

You can do the same for the other intercept, I will leave that for you to complete


Expansionary fiscal policy in a low mobility economy I am reading the CFA Level 2 Economics section and I came across this statement:

  In emerging markets, capital flows may be restricted. In that case, impact of trade balance on exchange rate (goods flow effect) is greater than the impact of interest rates (financial flows effect). In such a case, expansionary fiscal policy or monetary policy leads to increases in net imports, leading to depreciation of domestic currency

My question is: how can expansionary fiscal policy which results in an increase in interest rate cause depreciation of currency?

Where do you see that this expansionary policy is itself causing interest rates to rise?

If capital flow restrictions are damping inflationary pressures then the increased stock of money minus the decrease in buying power might cause an increase in imports. This increase in imports increases demand for foreign currency and decreases demand for domestic currency. This method of exchange subverts the capital flow restriction and the depreciation follows.


How to compute elasticity of substituion in general? We know that the elasticity of substitution is defined as
$$
e=\frac{d \ln(x_2/x_1)}{d \ln(MRS_{12})}=\frac{\frac{d(x_2/x_1)}{x_2/x_1}}{\frac{d(MU_1/MU_2)}{MU_1/MU_2}}
$$
When we compute ES for CES functions, MRS is function of $x_2/x_1$, so we can let $z=x_2/x_1$ and do the math easily.
But for other utility/production functions, such as quasilinear $u(x_1,x_2)=2x_1^{0.5}+x_2$, what am I supposed to do?
I believe ES will be depending on $(x_1,x_2)$. So maybe the question can be asked as
"What is ES of $u(x_1,x_2)=2x_1^{0.5}+x_2$ at $(x_1,x_2)=(1,1)$?"

The formula you already have there is a general formula for elasticity of substitution, but I can see that it might be difficult to apply to your problem here given that $MU_{x_2}=1$. There is also another way how formula for elasticity of substitution can be expressed. You can use 'partial derivative formula' (e.g. see Sydsaeter et al. EMEA pp 430) which is the inelegant 'monstrosity' given below. For elasticity of substitution between $x_2$ and $x_1$ it will be given by:
$$\sigma_{x_2x_1} = \frac{−F_1^′F_2^′(x_1 F_1^′ + x_2 F_2^′)}{x_1x_2[(F_2^′)^2F_{11}^{''}
 − 2F_1^′F_2^′F_{12}^{''}+ (F_1^′)^2F_{22}^{''}]}, \text{ for }  F (x_1, x_2) = c$$
So in your case:
$$\sigma_{x_2x_1} = \frac{−x_1 (x_1^2 + x_2)}{x_1x_2[1^2\cdot 1
]}= \frac{-x_1^2-x_2}{x_2}$$
More specifically for $(x_1, x_2) = (1,1)$: $\sigma_{x_2x_1} = -2$


Why do people think a stock should have a certain price based on the company's revenue? Stock investment comes part and parcel with discussions about quarterly earnings, P/E ratios, and a host of other considerations designed to measure the "intrinsic value" of a stock and whether it "should" go up or down, or predict future prices based on whether the company is growing/shrinking.
Considering only stocks that don't offer dividends:
Why do investors care about P/E ratio, revenue, or any other company revenue/growth metric? If a stock is worth what people are willing to buy/sell it for, why are investors making their buy/sell decisions based on metrics that don't affect anyone outside the company?

If the price is too low (relative to any metric, be it earnings, growth, etc.), then anyone can profitably launch a takeover/acquisition bid.
Example. A company has 1B shares each priced at \$1 (so market cap is \$1B), pays no dividends, and earns \$100B (profits) per year. Then one could buy up all 1B shares for \$1B, own the company entirely, and enjoy \$99B in profits in just the first year alone.


Clearing price in a double auction market I have been reading a paper on energy markets and I have stumbled upon double markets and clearing prices, which got me quite confused (bare in mind, I am relatively new to this topic). Quote from the work (Chapter 3, C):

  The order book market design is implemented via a double auction market with discrete market closing times that results in a single clearing price in every trading period. .... The lowest bid price that can still be served given the aggregated supply determines the market clearing price.

The way I understand this model is that there will be only 1 price, which every buyer is going to purchase the product for. For example:

Buyers:

Buyer 1: bid price = 30 cent
Buyer 2: bid price = 25 cent
Buyer 3: bid price = 20 cent
Buyer 4: bid price = 15 cent

And the ask prices of the sellers per item:

Sellers:

Seller 1: ask price = 25 cent
Seller 2: ask price = 20 cent

From what I understand is, that there would be just one clearing price and Buyers 1 and 2 will both purchase an item from Seller 1 and 2 for 20 cent, instead of 30 and 25 cent. Have I understood the concept of the double auction correctly, or will Buyers 1 and 2 purchase their items for 30 and 25 cent from the respective sellers?

In your example, the market clearing price is $25$ as there are two buying bids at that price or higher and two selling bids at that price or lower, and no other price achieves this match

So Buyer $1$ and Buyer $2$ both pay $25$ and Seller $1$ and Seller $2$ both receive $25$

If you want actual examples, you could look at the shares of Tottenham Hotspur Limited (the football club) on Asset Match and the Auction results (almost every month) in the right hand column.  The orders are shown cumulatively but it is easy enough to decipher the actual bids at each price.  For example in June 2019 they looked like this

  Cumulative  Actual           Actual   Cumulative
   wanted     wanted   Price   offered   offered
    11900         0     250p      875        875
    11900         0     260p      500       1375
    11900      7900     265p     9842      11217
     4000      2500     270p    16314      27531
     1500      1500     275p     1384      28915

The market clearing price was $265$ covering $11217$ shares as this is where the cumulative supply and demand curves cross.  The successful trades included all those shares offered at $250$ and $260$ and $265$, and all those wanted at $275$ and $270$ plus $7217$ of the shares wanted at $265$.  All successful transactions were settled at $265$, though the Assetmatch would have then charged a small fee for arranging the deals


What is value in the context of microeconomic analys for case of monopoly profit maximization I'm trying to refresh my microeconomics knowledge. And I have some "blind spots" I just can't fix.

Let's say we have a monopoly on the market. It's usual goal is to maximize it's profits. The point where $MR=MC$ will profit maximizing condition.

What is value in this context?
I mean, the good $Q$ is being Demanded by customers so value concept should be assigned to it, right? Is there a "value curve" or "marginal value curve" for such charts? Or value is utility, or benefit?

I'm confused about the usage of those terms.

The demand curve represent the marginal value that consumers put on a good. That is, the marginal value for the $Q$-th unit of the good is the height of the demand curve at $Q$.

The total value from consuming $Q$ units of the good is therefore the area under the demand curve from $0$ to $Q$.

The net value (i.e. net of cost) from consuming $Q$ units of the good is consumer surplus, which equals total value (defined in the previous paragraph) minus total cost (represented by the sum of the two shaded rectangles in your graph).


Tactical voting when the voting rule is unknown The Gibbard-Satterthwaite theorem implies that, in every non-dictatorial voting system with 3 or more candidates, there is a preference profile in which some of the voters can gain by lying about their preferences. However, usually this gain requires that the voters know the voting rule.

For example, consider a voting system with 3 candidates, A B and C, and 12 voters with the following preferences:

3 voters prefer A>B>C;
4 voters prefer B>C>A;
5 voters prefer C>A>B.

Consider the following two voting rules:

plurality - in which C is elected;
Instant-runoff - in which B is elected (after A is eliminated in the first round).

Consider the 5 C>A>B voters, and assume all other voters are truthful:

In plurality voting, they should of course be truthful so that their favorite candidate C wins.
But in instant-runoff voting, they can gain by lying and saying that their best candidate is A, since this will prevent the election of their worst option B.

So without knowing the voting rule, these voters cannot know whether lying about their preferences will help them or harm them.

The situation is different with the 3 A>B>C voters:

In plurality voting, they can gain by lying and saying that they prefer B, as this will prevent the election of their worst option C;
In instant-runoff voting, although they won't gain from lying, they also won't lose.

So even without knowing the voting rule, these voters can know that voting for B will either help them or at least not harm them.

For the sake of this question, assume that all voters are truth-biased. This means that, if they are not sure whether lying will help them or harm them, they will be truthful. They will only lie if lying may help them and may not harm them. So in the above example, the C>A>B voters will be truthful and the A>B>C voters will lie (assuming the B>C>A voters are truthful).

MY QUESTION IS: Is there a collection of reasonable (non-dictatorial, monotone, etc.) voting rules, such that, in all preference profiles, no truth-biased voter will want to lie?

In other words: we look for a collection of voting rules so that, for every preference profile and every group of voters, there exists a voting rule in our collection where their best response (when all other voters are truthful) is to be truthful.

You use the term 'deterministic' several times to refer to Gibbard-Satterhwaite, and a related question might specify preferences over risk for voters, and then ask whether there's a non-deterministic voting rule for which truth-telling is incentive compatible. I think this paper, by Gibbard from 1977, is relevant to that question.

As for the question you actually asked, if I understand you correctly, 'truth-biasedness' seems pretty strong. A voter misreports only if both (a) there are no voting rules under which misreporting would hurt her and (b) there is at least one voting rule under which misreporting would help her. So what's wrong with the following?

Say you have 3 voters, and consider 3 voting rules, one for each voter. Voting rule $i$ is: "Choose voter $i$'s most preferred alternative, unless the other two voters both prefer the same alternative and it is not the same as voter $i$'s most preferred alternative."

If the other two voters report truthfully, then a truth-biased voter can't gain from deviating: If voting rule $i$ is in effect and the other two voters differ in their most preferred alternative, then she cannot gain from misreporting because she gets her favorite alternative. If the other two voters both prefer the same option, then regardless of the voting rule that option will be chosen. In the former case there is one voting rule under which misreporting hurts her, in the latter case there are no voting rules under which misreporting helps her.


What fraction of new businesses die out within a year? Is there a simple way to figure out how many new businesses appear and disappear each year in the US economy?
It seems a key question to figure out how the economy is changing over time, although I suppose the data is potentially messy...

The Business Dynamics Statistics (BDS) of the Census provides annual measures of business dynamics (such as job creation and destruction, establishment births and deaths, and firm startups and shutdowns) for the economy and aggregated by establishment and firm characteristics. The use of the LBD as its source data permits tracking establishments and firms over time. In particular, BDS provides information on Establishment openings and closings and Number of startups and firm shutdowns.

The following figure is based on BDS and from Haltiwanger, John, Ron Jarmin, and Javier Miranda, (2009) "Business Dynamics Statistics: An Overview".

Note: SUSB means Statistics of U.S. Businesses from Census firms as well.


Pros and Cons of Elasticity of Demand Represented as an Absolute Value I've been reading quite a bit about elasticity of demand. There seems to be an argument among texts as to whether elasticity of demand should be represented as negative or as an absolute value. The argument for one method over the other depends on the text, but generally boils down to "because this is how we do it." I'm looking for a more meaningful discussion about this topic.

What are the pros and cons of using the negative? Of the absolute value?

Elasticity of demand is almost always assumed to be negative. It is assumed that there is an inverse relationship between price and quantity demanded. If you want to buy 2 hamburgers for $5 each you aren't suddenly going to want to buy 3 hamburgers if they now cost $10 each. If this isn't the case it means that consumers aren't rational which blows up 99% of the models economics has to offer.

Because the elasticity of demand is always negative it can be assumed that if I say X is the elasticity of demand I mean X is negative because elasticity of demand is always negative. If I say -X is the elasticity of demand you can still assume that it is negative because a) I said it explicitly, and b) it is always true.

At this point it's just a matter of preference and doesn't matter either way, I just wanted to explain why it really doesn't matter since someone who understands what elasticity of demand means will understand that it will always be negative in almost all scenarios.

Personally, I think that explicitly saying that the elasticity of demand is negative is a better choice since I can imagine some fringe scenarios where a product being expensive leads to that product being sold more often, (I think of caviar as an example for these types of products, where consumers buy it precisely because its expensive) but for most economic models the assumption holds.


How can I compare degree of stability (or persistency) in two dynamic systems/models? Let's say I have two dynamic VAR models for two countries. What is the best way to compare persistency or degree of stability in the two models. Use eigenvalues of the two systems?

The most straightforward way is to examine the coefficients of your VAR model, since the persistence is broadly understood in econometrics as a system dependence on its own past (see Verbeek (2008): a guide to modern econometrics).  A simple VAR model is given:
$${\displaystyle y_{1,t}=c_{1}+a_{1,1}y_{1,t-1}+a_{1,2}y_{2,t-1}+e_{1,t}\,} \\
{\displaystyle y_{2,t}=c_{2}+a_{2,1}y_{1,t-1}+a_{2,2}y_{2,t-1}+e_{2,t}.\,}$$
Now, in very similar fashion as with AR models how persistent the variable is will be given by how much it depends on its own past (lags). For example, persistence of $y_1$ can be gauged by coefficient $a_{1,1}$. The larger the coefficient the more persistent the series is.


How interest rate affects currency I am quite new to economics. I was reading about changes in interest rates and its effect on currency value.

The fact is as interest rates increases, the currency value also increases and vice versa. However I want to understand the reason.

At first, I thought following: As interest rate increase, people borrow less, spend less, so cost of goods decreases, value of currency increases.

However when I read in investopedia, it says following:

  Generally, higher interest rates increase the value of a given country's currency. The higher interest rates that can be earned tend to attract foreign investment, increasing the demand for and value of the home country's currency. Conversely, lower interest rates tend to be unattractive for foreign investment and decrease the currency's relative value.

Q1. Now I dont understand what does it mean by increasing the demand for and value of the home country's currency. What is it meant by demand for currency by foreign investors?

In another article it says:

  The rise of interest rates in a country often spurs inflation, and higher inflation tends to decrease the value of a currency.

But on the same page, it says:

  Generally, higher interest rates increase the value of a given country's currency.

Q2. Why these two different statements are there?

If I understand it correct, the word "spurs" here means increases inflation. But this confuses me.

My understanding is:

interest rate increases, people can borrow less, spend less, economy slows, inflation decreases, currency value increases
interest rate decreases, people borrow more, spend more, economy grow, inflation increases, currency value decreases

Q3. Are these understanding correct in general (though I understand the relation is not that straight forward and there are other factors too that affects currency value / inflation)?

Its important to keep in mind that the exchange rate is a "price for currency" and just like any other price it is determined by supply and demand. The main question now is what determines supply and demand for currency?
There are two main models that tell us how exchange rates behave based on the two main forces driving demand (and supply) for currency.
One factor is trade of goods (the goods market). If foreigners buy our goods they need our currency, so they demand our currency and higher demand ceteris paribus (all else staying constant) leads to a higher price and the value of the domestic currency increases. Based on such considerations in the goods markets we have the model of Purchasing Power Parity (PPP). However empirically it does not always hold and in reality it is mostly expected to hold in the long run.
Answer to Q1: Beyond the goods market discussed above, the second main factor is the capital market and that is what Investopedia is referring to. This gives rise to the model of Uncovered Interest Rate Parity, called UIP (there is also a "Covered Interest Rate Parity Model"). This says that if interest rates are higher in the domestic country compared to the foreign country, then foreign investors would like to invest in our country to get the higher returns. To do so they need our currency. So they buy it (demand it) and therefore as long as supply of currency doesn't increase (the central bank printing more money) the price and value of a currency must increase. Also note that there's no reason to expect the central bank to change the supply in a floating exchange rate regime, which most countries have (i.e. there is no attempt to intervene in the exchange rate to keep it fixed).
Answer to Q2: It is not necessarily true that a higher interest rate should increase inflation in general. However increasing the interest rate can decrease inflation. Your understanding of inflation is correct. The second part of the second quote you gave, that higher inflation decreases the value of the currency, however is correct. This is due to the first model we discussed, the PPP. The idea is that inflation makes goods more expensive and therefore our goods have less foreign demand, which leads foreigners to have less demand for our currency (they buy less of our goods so they need less of our money to buy our goods) and less demand for the currency reduces the value of the currency.
Answer to Q3: I believe this follows from the general discussion above.


Interaction term significant, joint hypothesis not I am trying to find out if some channel is important in the transmission of shock x1 to outcome variable y.
For this, I am running a regression in which y is on the LHS and x1 on the RHS, once alone and once interacted with a variable x2 that differentiates between observations where the channel can exist and where it cannot.
I am getting that the interaction term is significantly different from zero, but when I test whether beta_x1+beta_interaction*[mean of x2]=0, I get that the H0 is not rejected, and when I test whether beta_x1=0, that is also not rejected.
What would you suggest, should I conclude that the channel is important on the basis of this?

Looking at what you wrote, your regression has the form:
$$
y_i = \beta_0 + \beta_1 x_{1,i} + \beta_2 x_{1,i} x_{2,i} + \varepsilon_i
$$
Here $x_2$ is a dummy taking the value $1$ for a subsample of observations and $0$ otherwise.
Then:
$$
E[y_i|x_{1,i} = x_1, x_{2,i} = 0] = \beta_0 + \beta_1 x_{1}.
$$
and
$$
E[y_i| x_{1,i} = x_1, x_{2,i} = 1] = \beta_0 + (\beta_1 + \beta_2) x_{1}.
$$
There are various hypothesis that you can test:

$H_0$: there is no (mean) effect of $x_1$ on $y$ for the subset where $x_{2} = 0$. This amounts to a test of $\beta_1 = 0$.
$H_0$: there is no (mean) effect of $x_1$ on $y$ for the subset where $x_{2} = 1$. This amounts to a test of $\beta_1 + \beta_2 = 0$.
$H_0$: the (mean) effect of $x_1$ on $y$ is the same for the subsets where $x_2 = 1$ and $x_2 = 0$. This amounts to a test of $\beta_2 = 0$.

I am getting that the interaction term is significantly different from zero,

This is a test of point 3. that the (mean) effect is different for the two subgroups.

when I test whether beta_x1+beta_interaction*[mean of x2]=0, I get that the H0 is not rejected

You should not multiply $\beta_2$ with the mean of $x_2$. To test for 2, you should conduct the hypothesis test that $\beta_1 + \beta_2 = 0$.

when I test whether beta_x1=0, that is also not rejected.

This is a test of 1. which indicates that you cannot reject that there is no (mean) effect for the subgroup where $x_2 = 0$.
Remark 1: Hypothesis tests are a bit strange in the sense that they can contradict each other. For example it is possible that you do not reject $\beta_1 = 0$ and $\beta_2 = 0$ but you do reject $\beta_1 + \beta_2 = 0$.
Remark 2: related to this, notice that the tests are not independent. So if you test all three hypothesis, you have the mutliple testing issue (cfr wiki link) in the sense that the probability of rejecting at least one of the three is (likely) bigger than the nominal value of the test.


Is it proven that prestige gained from sports victories helps the country economically? Most of the world's governments support their professional sports teams, both through direct monetarily contributions and through numerous sports schools for children. One of the main rationales for that support is that victories in international competitions help the country gain 'prestige'.

But what exactly is the practical benefit of this 'prestige'? Does it help the country grow economically by attracting tourists or investment? Or perhaps it's merely a matter of national 'pride', without any monetary gains?

I'm looking for academic research on this topic or official statements by government institutions.

There is research into this topic but it's not proven.

There's too much variability to consider.

Take the '04 Detroit Pistons (it's a City, I know, but the premise scales). In 2004 the Detroit Pistons were underdogs to the Los Angeles Lakers. Economically, LA was in a much better place than Detroit but Detroit scrapped it's way to a victory (and a return to the finals but a loss the next year to the San Antonio Spurs (Go Spurs Go)). Detroit's victory may have led to sales growth in player's jerseys (Richard Hamilton and Ben Wallace for instance) but the sports victory did not save the city from it's demise and subsequent bankruptcy.

I believe the economic benefits of professional sports victories are more cosmetic than practical. A real estate agent may have a few more selling points in an economic transaction but the gains are usually temporary as it's hard to have back-to-back victories in professional sports...

Controversially, the theory MAY ACTUALLY apply to collegiate sports and the economic prowess of a university. Ever been to University of Georgia or Alabama? Those walls aren't lined with money from their journalism schools, I can tell you that much.

It'd be hard to prove that professional sports wins tie to economic success given how many other exogenous factors there are to economic success but there's data available to analyze this question (specifically, GDP growth and World Cup/Olympic Cup/World Title Events).

I don't know if governments are tossing up grant money for this research though.


How is freelancing viewed under Marxism? How does Marxism view freelance workers? Since a freelancer is the owner of their means of production, are they still viewed as exploited by the bourgeoisie? Could freelancing exist in a Marxist society?

Marx addresses this about two-thirds of the way through Section 1 of the Manifesto. In the standard English edition of 1888, it reads:

  The lower strata of the middle class - the small tradespeople,
  shopkeepers, and retired tradesmen generally, the handicraftsmen and
  peasants - all these sink gradually into the proletariat, partly
  because their diminutive capital does not suffice for the scale on
  which Modern Industry is carried on, and is swamped in the competition
  with the large capitalists, partly because their specialized skill is
  rendered worthless by new methods of production. Thus the proletariat
  is recruited from all classes of the population.

So his basic argument is that, sure there might be small business owners (freelancers in this example), but that because of 1) inability to compete against large firms ostensibly taking advantage of economies of scale and 2) rapid development of technology, they become obsolete and are driven to the proletariat.


Why does a reduction in money demand lead to a rightward shift in the LM curve? In my textbook, it says Y must rise to restore money market equilibrium as the justification.

If the demand for money falls as the supply remains constant, there is excess supply of money. It is equivalent to an increase in the supply while the demand stays constant.


Plim of ols estimator Suppose you are given 2 models.
Model of 1 has $y$ as the dependent variable and $x$ as the independent:
$$y = \beta_0  + \beta_1 x + \epsilon$$
Model 2 has $w$ as the dependent variable and $x$ as the independent variable
$$w = \lambda_0 + \lambda_1 x + u,$$
such that both models have their own disturbance term.
Then you are given a fitted model in which $y$ is dependent on $w$.
$$y = \phi_0 + b w + e$$
Now the question is to find plim of $\hat{b}$.
I tried making $x$ the subject from model 1, plugged the $x$ in model 2 and then plugged $w$ (model 2) in fitted. Now when I took $Cov(xy)$ after all this substitution my fitted model $y$ doesn't have and $x$. I can't further solve for $plim$.

Here is what I think should be the answer based on your problem description. Otherwise this is hopefully still helpful for you to solve the problem.
I star by considering the model equations
$$(1) \ \ \ y = \beta_0 + \beta_1 x + e_y $$
$$(2) \ \ \ w = \lambda_0 + \lambda_1 x + e_w, $$
and then I manipulate equation (1) to get
$$(1b) \ \ \ y = \beta_0 + \frac{\beta_1}{\lambda_1} ( \lambda_1 x) + e_y, $$
from equation (2) I then find
$$(2b) \ \ \ w -\lambda_0 - e_w=  \lambda_1 x,$$
which I insert in (1b) to get
$$y = \beta_0 - \frac{\beta_1}{\lambda_1}\lambda_0 + \frac{\beta_1}{\lambda_1} w - \frac{\beta_1}{\lambda_1} e_w+ e_y,$$
I then define $b_0 :=\beta_0 - \frac{\beta_1}{\lambda_1}\lambda_0$ and $b_1:=\frac{\beta_1}{\lambda_1}$  and $u :=  - \frac{\beta_1}{\lambda_1} e_w+ e_y$ to get the estimation model
$$y = b_0 + b_1 w + u$$
where I know the probability limit of $\hat b_1$ is
$$var(w)^{-1}cov(wy) = b_1 + var(w)^{-1}cov(wu),$$
where I note that $cov(wu) = cov(w,-(\beta_1/\lambda_1) e_w+ e_y) = -\frac{\beta_1}{\lambda_1} var(e_w)$.
I assume that $cov(x,e_w) = cov(x,e_y) = cov(e_w,e_y) = 0$.
Here is a small test code in R
N <- 1000
beta <- 1
lambda <- 2
x <- rnorm(N)
e_y <- rnorm(N)
e_w <- rnorm(N)
y <- 1 + beta*x + e_y
w <- 1 + lambda*x + e_w

model <- lm(y~w)

W <- cbind(rep(1,N),w)
bias <- -(beta/lambda)*solve(t(W)%*%W)%*%t(W)%*%e_w
coef(model)[1] - bias[1,1]
1 - (beta/lambda)*1
coef(model)[2] - bias[2,1]
beta/lambda


Leontief preferences and 2nd welfare theorem Does the 2nd welfare theorem hold with Leontief preferences?  If not, which of the assumptions does not hold?

Hint:

  Second Welfare Theorem: Suppose that for every individual $i = 1,...,N$ the utility function $U^i(c_i)$ is continuous, locally non-satiated, and quasi-concave. If $\left\{c_1^P,...,c_N^P\right\}$ represents a Pareto optimal allocation in which $c_i^P >> 0$ for every $i = 1,...,N$, then there exists a set of prices, $p^E \geq 0$ and $p^E \neq 0$ and a set of transfer payments, $\left\{\tau_1,...,\tau_N\right\}$ such that:

  $\left\{c_1^P,...,c_N^P\right\}$ is feasible

  $$\sum^N_{i=1}c_i^P \leq \sum^N_{i=1}\omega_i^P$$

  For every individual $i = 1,...,N$, the consumption bundle, $c_i^P$, solves:

  $$\max_{c_i} U^i(c_i) \ s.t. \ p^E \cdot c_i = p^E \cdot \omega^i - \tau_i$$

  and $\sum^n_{i=1}\tau_i = 0$

Or in other words, for any efficient (Pareto) allocation, there exists a price vector such that the price vector and optimal bundle represent a quasi-equilibrium with transfers.

Also note that you need preferences to be convex and locally non-satiated and the production set must be convex. So now what happens when $U_i(c_i) = \min \left\{\frac{c_1^P}{\alpha_1},...,\frac{c_N^P}{\alpha_N}\right\}$? It is indeed continuous, locally non-satiated and quasi-concave.


Why do some businesses choose scarcity as their business model instead of raising the price to meet the demand? Here are some examples of what I'm talking about:

Mass events such as Burning Man, the Olympics, and the World Cup sell out tickets very quickly which forces fans to resort to scalping or using bots if they want to secure a spot
Concerts of popular artists sell out very quickly which creates a massive scalping market
Limited editions of clothing suffer from automated bots buying up and reselling almost all of their stock in a matter of seconds
Popular restaurants sometimes require making a reservation several days in advance or don't take reservations and have everyone wait in line for a long time
Daycares in Canada and the US frequently have waiting lists of several years which forces parents to sign up for one as soon as they conceive

I'm sure there are more examples of such practices that I'm not aware of. All of them could have addressed the difficulty of obtaining the product through some form of dynamic pricing - as demand goes up you increase the price, as demand goes down you decrease it. Various forms of auctions could also be used to determine the price, if required. This is how the world of airlines operates these days - planes are almost never sold out, but you might find that a ticket costs 10x the original price if you buy one right before departure.

What's the name for such business policies in economic theory?
Why would a business choose to follow such practices?
Can this strategy actually result in higher profits over the long term or are businesses losing money by not using dynamic pricing?

Your question is somewhat ill-posed as stated, because none of your examples are good instances of businesses creating artificial scarcity.  Each of them are businesses that face real capacity constraints, whether it be building space and fire-code restrictions or an attempt to manage a sort of tragedy-of-the-commons demeaning of the service.

But you are right in wondering why these businesses don't run their prices up until demand meets capacity. It's basically down to a choice by the business whether to ration through pricing, or ration through queueing.

Queueing is viewed, rightly or wrongly, as a more "fair" means of rationing, since (in the case of non-essential goods) everyone has the same endowment of hours in the day. To the extent that this is true, it's a means to distribute the good or service equitably in a cross-class sense.

It is also a more robust business model in terms of revenue stability, as it leaves much of the "clearing house" work in the respective markets to consumers themselves.  One alternative would be to continually monitor the market and adjust prices to keep patronage at or near existing capacity, which is a tricky balancing act that entails potentially high information and menu costs.

Another, obviously, would be to expand the enterprise - but economies of scale must be present.  Even then there are associated costs and risks - expansion can serve to dilute a brand, and very few restaurant franchises receive Michelin stars.  The market for event space is extremely fraught politically, and the subject of a lot of recent academic interest.

Scalping is an example of arbitrage that takes advantage of the inherent inefficiency of queueing.  One can argue that tickets sold in advance of an event must be priced below their value, with the difference being a combination of a risk premium the venue-owner pays to be assured of a full house well in advance and a risk discount that event-goers demand because of the non-zero possibility of their attendance being disrupted at the last minute.  Flesh-and-blood scalpers make money off of the rapid market shifts that arise due to the resolving of this uncertainty for both parties, and it could be argued that this leads to a more efficient market.

Of course, software breaks this model entirely, and so I wouldn't make that argument today.  But it's certainly true that whatever value scalpers have captured historically was money that even large monopolies like Ticketmaster were not especially inclined to capture for themselves, suggesting that the costs of doing so exceeded the expected benefits.


Risk and Information Does anyone know of some papers that look at how risk preferences affect demand for information (or related topics about the connection between risk and Information)? I took an information economics class a while ago and misplaced the syllabus.

I can remember that some classical models predicted that higher risk aversion leads to lower consumption for information. My professor remarked that this seemed pretty counter-intuitive, and might be a result of a fundamental mis-specification in modeling information. Thoughts? I'd also be interested in experiments that look at this problem empirically. Thanks!

The classic paper on preferences over the timing of information revelation is Kreps and Porteus (1978). This seems to capture at least a little, if not most, of what you seem to be describing, so you should definitely have a look.

Strzalecki also has a nice paper connecting Kreps-Porteus to the various modern approaches to preferences under ambiguity.


Concave production function implies convex cost function Let's assume we have an increasing production function $f:\mathbb{R^+} \to \mathbb{R^+}$

Now, assume this production function is concave and that the price of input z is fixed (this is a single-input and single output case). I want to show this implies the corresponding cost function $C^f(w,q)$ is convex.

My thoughts:

let $z,z' \in \mathbb{R^+}$ where W.L.O.G $z'>z$ and let $f(z)=q$ and $f(z')=q$

Since $f$ is concave, we take $\alpha \in [0,1]$  $s.t$:

$$f(\alpha z +(1- \alpha)z') \geq \alpha f(z) +(1- \alpha)f(z')$$

let $\alpha z +(1- \alpha)z'=z''\in \mathbb{R^+}$ where by necessity $z\leq z'' \leq z'$

Since cost of $z=w$ is fixed at some $w \in \mathbb{R^+}$

we can rewrite our cost function as $C^f(q)$ which is convex if for $\alpha \in [0,1]$:

$$C(\alpha q +(1- \alpha)q') \leq \alpha c(q) +(1- \alpha)c(q')$$

Now, since $f$ is concave, it cannot be the case that $f$ experiences increasing returns to scale. Then $f$ has constant returns to scale or diminishing returns to scale.

Then:

Since $z''$ is clearly feasible then we have that:

$$C(w,q'') \leq w*z''$$
$$=\alpha w*z + (1- \alpha) w*z'$$
$$= \alpha c(w,q) + (1- \alpha) c(w,q')$$

Does this look correct?

Given the fixed input price $w$, the cost function can be written as
$$
C(q)=f^{-1}(q)\times w
$$
where $f^{-1}$ is the inverse of the production function $f$. From the discussion here, one can conclude that the inverse of a concave strictly increasing function is convex. Thus, $C(q)$ is convex as well.

Going back to your approach, you might like to have this clearly stated. Let $q''=\alpha q + (1-\alpha)q'$, $f(z)=q$, $f(z')=q'$, and $f(z'')=q''$ Then
$$
\begin{align}
f(z'')&=&q''\\
&=&(\alpha q + (1-\alpha)q')\\
&=&\alpha f(z)+(1-\alpha) f(z')\\
&\leq&f(\alpha z +(1-\alpha z'))
\end{align}
$$
Then $f(z'')\leq f(\alpha z +(1-\alpha z'))$ implying that $\alpha z +(1-\alpha z')\geq z''$ since $f$ is (strictly) increasing. Hence,
$$
z''w=C(q'')\leq \alpha C(q)+ (1-\alpha) C(q')
$$


Suggested model for dependent variable of different groups I want to test the impact of X on Y. The dependent variable Y is being employed. Now, I want to see if the impact of X is different for those employed in agriculture (A) and non-agriculture (N) sectors. What is the right model to do this?
Do I need to include some interactions?
Or should I define separate dependent variables for A and N? How do I define those variables? Which one of the following:
1- Create a dummy variable for group A (N) which takes value 0 for group N (A) and also not-working group
2- Create a dummy variable for group A (N) which takes value 0 for group N (A) and drop the observation for not-working group
3- Create a dummy variable for group A (N) which takes value 0 for not-working group and drop the observation for group N (A)

For individual $i$, let $Y_i$ and $X_i$ be the relevant variables and let $D_i$ be the dummy for agricultural sector: 1 if in agriculture and 0 if not.
Then you can run the following regression:
$$
Y_i = \alpha_0 + \alpha_1 D_i + \beta_0 X_i + \beta_1 X_i\times D_i + \varepsilon_i.
$$
Assume that $\mathbb{E}[\varepsilon_i|D_i, X_i] = 0$.
Then if a person is not employed in agriculture, we have:
$$
\mathbb{E}[Y_i|X_i = x, D_i = 0] = \alpha_0 + \beta_0 x.
$$
On the other hand for a person employed in agriculture, you obtain:
$$
\mathbb{E}[Y_i |X_i = x, D_i = 1] = (\alpha_0 + \alpha_1) + (\beta_0 + \beta_1) x.
$$
So you only need to create one dummy. The value of $\alpha_1$ give the difference in agriculture and non-agriculture employment when $x = 0$. The value of $\beta_1$ gives the difference in the marginal effect of $X$ on $Y$ between agriculture and non-agriculture.


Can anyone give me some reference on Mundell-Fleming model estimated empirically? In virtually all texts of intermediate Macroeconomics$^1$ the Mundell-Fleming model is taught. But his estimate is not addressed in the classical texts of econometrics. I've always wanted to read some reference, but my searches have not worked

1: "Most open macroeconomy models in the textbooks are variations of the Mundell-Fleming model." Ohno Lecture notes: Mundell-Fleming Model with a Floating Exchange Rate

First, you don't estimate the "model", but its parameters. You can then try tests that check if the specification is correct and if you do want to test the "model".

There are different approaches to estimation. In this nice article the author uses a VAR model to estimate the parameters of the Mundell-Flemming model for the Australian economy.

http://cms-content.bates.edu/prebuilt/huh.pdf?origin=publication_detail


Inflation and economic growth Noticeable works about the impact of inflation on economic growth are dated back to the 90s.

For example, Barro (1995):

  the impact effects from an increase in average inflation by 10 percentage points per year are a reduction of the growth rate of real per capita GDP by 0.2-0.3 percentage points per year and a decrease in the ratio of investment to GDP by 0.4-0.6 percentage points.

He also shows outliers there:

Bruno and Easterly, “Inflation Crises and Long-Run Growth” (1998), reiterate that extreme situations matter for growth:

  growth falls sharply during discrete high inflation crises, then recovers rapidly and strongly after inflation falls.

Since after these papers, no highly cited paper on topic appeared. Though there's Acemoglu et al., “Institutional Causes, Macroeconomic Symptoms” (2003), which is relevant in another sense.

In a recent survey (2012), the Bank of England mentions without a reference that

  The consensus seems to be that
  above a threshold of around 3%–4%, inflation imposes welfare
  costs, while the plausible gains from reducing inflation below
  about 2% are unlikely to outweigh the advantages of a positive
  inflation target.
  There is even less guidance in the literature on the optimal
  level of inflation in developing and emerging countries,
  though Balassa-Samuelson effects imply that optimal
  inflation in these countries should be a little higher than in
  industrialised countries.

Apart from cross-country evidences, rare country studies are available. The IMF on India (2014):

  Our findings suggest that, on average, there is a negative long-run relationship between
  inflation and economic growth in India. We also find statistically-significant inflation-growth threshold effects in the case of states with persistently-elevated inflation rates of above 5.5 percent.

Does the current academic consensus remain with Barro's 1995 paper? Are there any new estimates of the impact of inflation, threshold levels of inflation, and changes in inflation on long-term economic growth?

Macro regressions, especially annual ones, have in general two flaws:

They have small sample problems and
They have no proper identification

In order to circumvent problem #1, people often assume that the DGP process behind different countries are the same, increasing observations from perhaps 60 to 600.

In order to attack #2, many people add timing assumptions. However, this is still no clear identification, these are still assumptions.

To see the issue: Imagine high inflation at $t-5$, and low growth at $t$. Using a standard timing assumption, the former caused the latter. However, we like to think about agents as forward looking. Can we be certain that expectations w.r.t. the latter didn't influence the former?

Especially because of #2, this type of regressions have lost popularity. Also, there is not really much more to do.

tl;dr: No important new results that I know of.


HHI and concentration I calculated the HHI index for Chile exports and got values ranging from 0.09 and 0.13. We know that Chilean exports are very concentrated (around 40% of the exports are copper related goods) and the index might be misleading. I used HS 6 digits with the Customs data and Comtrade data. I am really puzzled and appreciate any help. Thanks.

At the HS6 level, there are thousands of product codes (I believe around 5,000) so if you're just computing the HHI using product codes, then actually it's pretty surprising you've received such a large number! However, for the interpretation of your result you should keep in mind that you've computed the export HHI of Chile using HS6 product codes, which definitely do not correspond to a more common, yet harder to define, notion of "commodities".

For example, there are many product codes that can be said to be copper related, and refer to various forms of smelted and refined copper. For instance, the HS6 code (in the HS1992 nomenclature) for copper ore is 260300, but there are dozens of product codes for refined copper and related products (i.e. 740110, 740120, 740200, etc.). Do you want to treat all these as separate products? It depends on the question you want to ask.

For instance, if you wanted to ask what the export HHI of Chile is for commodities, then you would need to define what a commodity is, and which HS codes you want to aggregate into commodities such as "nickel", "copper", etc.. and then compute the HHI based on the export shares of these groupings. There are pre-existing groupings of commodities, but the "right" aggregation will depend on your question.


How can a "producer face a limited market as regards sales and yet a highly competitive market as regards price"? Kaldor (1972):

it is evident that the co-existence of increasing returns and competition—emphasised by Young and also by Marx, but wholly excluded by the axiomatic framework of Walrasian economics—is a very prominent feature of de-centralised economic systems but the manner of functioning of which is still a largely uncharted territory for the economist. We have no clear idea of how competition works in circumstances where each producer faces a limited market as regards sales and yet a highly competitive market as regards price.

I don't understand the last sentence. Could someone explain and also provide concrete examples of how it might be possible that a "producer faces a limited market as regards sales and yet a highly competitive market as regards price"?

Could someone explain and also provide concrete examples of how it might be possible that a "producer faces a limited market as regards sales and yet a highly competitive market as regards price"?

I believe an example would the Bertrand duopoly. In Bertrand duopoly you have only two firms so all sales are made just by two firms, but we know that in Bertrand duopoly, thanks to competition, the optimum price will be exactly equal to marginal costs like in perfect competition.
For example, assume that there two firms competing on price. Their demand is given by:
$
q_1=  D_1(p_1,p_2) =
\begin{cases}
 D_1(p_1)/2, \text{ if } p_1 =p_2 \\
 D_1(p_1), \text{ if } p_1<p_2\\
      0, \text{ if } p_1>p_2
\end{cases}
$
the marginal costs of will be given by $MC$. In such case the firm's best responses will be given as in the picture below (taken from wikipedia). As can be seen from the picture the best responses intersect exactly where prices equal marginal costs so in such situation you get prices that are equivalent to perfectly competitive prices, even though the sales are made on duopoly market.


Competition Data across Countries I am looking for data sources that measure competition across countries. The variable I'm looking for could be any type of Concentration Ratio, Lerner Index, Herfindahl Index or Markup.

The data does not need to be by industry for each country. It could be an "average" for each. Otherwise data for any specific industry, besides banking and finance would also be welcome.

If a cross-country dataset is not available, data for U.S. states would also be appreciated. Panels are obviously preferable, but a cross-section will do as well.

I'm aware that the World Bank has such data on the financial industry. I am also aware that there are some estimates of markups for several OECD countries, but the number of countries is usally is very small.

Does anyone know where to find such data?

Depending of the accuracy you're looking at (stylized facts or estimated parameters), private database like http://go.euromonitor.com/passport.html may help you to support your theory. Some institutions grant access to them. Some industries (e.g. tobacco) have their info widespread.

A (non-exhaustive) list: https://www.insead.edu/library/databases


What is the danger of (China's) investment-led growth as opposed to consumption-led growth? I keep reading that China must switch to consumption-led growth or productivity-led growth, that investment-led growth is 'dangerous.'

I understand that it is probably not sustainable in the sense that returns on capital will start to fall after awhile. But what else is the danger?

From the Chinese perspective, it's "dangerous" because high investment for so many years, particularly when driven by state incentives or by state-owned firms might induce mis-allocation of resources, high indebtness levels and excess capacity (some might say even voluntary, for example dumping in steel to hurt developed countries' industries). For instance, this paper states that:

  The main  objective  of  management  in  Chinese  state-owned  and  state-
  dominated  firms  has been  to  maximise  not  profits  but  the  growth  of  investment  and  output.  The  reward  to such  bureaucrats  takes  the  form  of  prestige,  power  and  the  accompanying  perks  of commanding an organisation; the reward being greater the larger the organisation.

Another reason is that investment is more volatile than consumption. However, if investment is supported importantly by state-owned enterprises, this might not apply well to China, which by the way have not had a recession in decades).

From a western perspective, high investment (and low consumption) contributes to a high trade balance surplus and therefore to a high current account surplus, which might be good for the central bank of China (accumulation of reserves) aiming to keep the Yuan relatively low to foster the competitiveness of the export sector, but is bad news for the rest of the world. The latter would benefit from higher consumption of the Chinese population (via Chinese imports and rest of the world's exports). The same story is told of Germany, which would help other countries (mainly European partners, because of same currency) by rebalancing its economy from exports toward more consumption.

Additionally, note that some economists have blamed China (among others) for the Great Recession (e.g. here or here), partly because of their voracious reserve accumulation policies, a core element in the export-led Chinese development strategy. Thus, a more rebalanced global economy might be good for the world economy as a whole, decreasing the likelihood of another recession.


How are petro states able to maintain gasoline subsidies without black market export smuggling? I don't understand how petro states can have crazy low gasoline prices without smugglers exporting the gasoline and selling it elsewhere.

For example, in Venezuela the domestic price of gasoline is about 5 cents per gallon (compared to the current US retail price of around $2.10 per gallon). In other words, the US retail price is about 40 times the Venezuelan price. That is a pretty big incentive for a smuggler. There are other countries which have similar subsidized prices.

How does Venezuela prevent smugglers from just loading up trucks with gasoline and exporting it? They don't even have to ship it out of Venezuela. They could truck it across the border into one of the neighboring countries and sell it there or export it from the neighbor. Venezuela must have some mechanism for controlling who is receiving the cheap gas and preventing them from exporting it, what is it?

As a second question along the same lines, how do they prevent people from converting the oil into a different product and then exporting that product. So, for example, oil can be converted into polypropylene pellets. A person could take the (virtually) free oil, convert it into polypropylene and then export the polypropylene. How do they prevent this from happening?

There has been rampant smuggling from Venezuela to Colombia - see links below. This is the basis for my question.

http://www.wsj.com/video/colombia-black-market-gas-trade-/BC14C5B7-69A0-4A0E-84B2-5377A7FDF79B.html

http://www.wsj.com/articles/venezuela-pays-price-for-smuggling-1402271308

http://www.wsj.com/articles/venezuela-to-reopen-colombia-border-1470962864


Universal Basic Income In 2017 some countries have adopted the Universal Basic Income as an alternative to Welfare Payments, my question is, is it economically feasible by governments?

In my view, this is not a well defined question since it isn't very clear what you mean by 'feasible':

If you mean 'are developed countries in principle able to pay for a UBI?', then the answer is trivially yes.
Perhaps you mean 'politically feasible'? Obviously, that depends on the political constraints on redistribution, attitudes towards 'handouts', etc. - though I'm not sure this is the appropriate forum to discuss such issues.
Perhaps you mean 'A Good Thing'? Well, that's not really what feasible means...


What are possible solutions when promoting competition is not applicable? Usually, more competition means lower prices and higher quality as less effective businesses go out of business. However, it appears that it's not always the case. When there're a lot of health insurance companies, each of them has relatively little bargaining power with service providers (hospitals) and, as a result, prices are significantly higher compared to a hypothetical government-funded single-payer system. Is there any free-market solution? What libertarian scholars (they exist, don't they?) would suggest?

There's another example, social networks. Facebook was selling user private data without them realizing it but never went bankrupt or lost a lot of users. It's evident to me that it's due to its oligopolistic nature. You can't nationalize Facebook or do something similar to what is proposed for health care by American presidential candidates like Bernie Sanders. You also can't promote the creation of many new tiny Facebooks because the social network user wants to have all their friends, family members, colleagues, favorite celebrities, etc. available in one place so people would unwittingly gradually monopolize "the social network market" back by opting for the network with more users than its competitors.

Are there any studies that found any umbrella solutions (preferably, ones that don't involve socialism) for cases when simply promoting competition doesn't work?

There is one universal "solution" to monopolism without government intervention.

Just allow the monopoly to do its worst. It will give very strong incentives to find ways to satisfy needs of potential clients of the monopoly in ways that would diminish market force of the monopoly. Basically it's bet that human creativity will eventually tame (or even kill) the monopoly. The most radical example of such creativity is a creation of an invention that makes the whole monopoly obsolete. Another example of creativity: It's also possible that different people buy services/goods of the monopoly for different reasons, so there would be strong incentives to develop imperfect substitutes for different categories of potential clients of the monopoly. Of course there are many more other ways to outsmart the monopoly, I just gave some abstract examples of it.

Real life example: US shale oil boom as response to monopoly of OPEC


Meaning of innovation in the wealth creation process Is there a formal definition or measure of wealth that captures the notion that with improving technology "life gets better"?

A stupid example of what I mean would be the invention of the iPhone. I know that with the iPhone new markets were and new profit possibilities were created and in that sense the economy got richer. That effect could be measured by let's say the GDP.
But apart from that I can now watch Netflix on the bus or text people everytime, everywhere. So personally my life got a whole lot more pleasant.

Also is there an accepted connection between innovation and "wealth" in the sense that I described above?

Cheers,
FL

The extra benefit to you, beyond what you pay for your iPhone and for your Netflix subscription, is called consumer surplus and in theory this could be aggregated across all consumers who take advantage of this innovation

It is difficult to measure:  again in theory it could be done by judging how much more individuals would be willing to pay until they were indifferent between purchasing or not purchasing


Circular Flow with Inventories I´m trying to fully understand the basic circular flow and the equivalence among production, income and expenditure, but considering the accumulation of inventories (still the most basic version, without financial sector or government).

When there´s the hypothesis that the firms sell everything they produce, the equivalence among product, expenditure and income is obvious, but what if the firms don´t sell everything and inventory (either planned or unplanned) is formed?

Product Y is the value of everything that is produced even if it isn't sold. All of the output is consumed either by the household sector or there is accumulation of inventories which is interpreted as an investment done by the firms, so that Product = Expenditure. So far, so good, but this value must turn into income (wages, since the model considers just work as a production factor) and now there is less income than product (because less output was sold, which leads to lower wages) and the equality between product and income doesn't hold anymore. Would inventory somehow generate this missing piece of income? Is it impossible to maintain the model as simple as this and still keep the equivalence? If not, what´s the minimum amount of information necessary to add?

Also, if it´s true that a flow of real goods in one direction must accompany a flow of money in the other direction in this simple model, is there an interpretation for the "acquisition" of inventories that fit in this idea or it should be abandoned?

EDIT. Some additional thoughts:

As I understand, the idea of circular flow contains 3 direct causalities (which are equalities):
1. Production -> Income
2. Income -> Expenditure
3. Production -> Expenditure
All of these happen in the same period of time. The next causality connects 2 different periods and it is not necessarily an equality. The production here is the level of production of the next period:
4. Expenditure -> Production (a behavioral relation and not an identity like the previous ones)

"3" analyzes the destiny of the values of all produced goods. Everything that is produced ends up with someone. If there´s inventory, the "trick" that considers unsold goods also as an expenditure (by the firms) leads to the equality Y = C + Inventory. There isn't a monetary counterpart in the "acquisition" of inventory by the firms, so it really seems just an exception to balance the identity.

"2" analyzes what people do with their incomes. If inventory is formed, it means the workers didn't spend everything and there's some savings S inside their houses. They're the only ones who receive income, so that wages are the only form of income. Income = C + S. Comparing with the previous equation, it makes sense that the value of inventory is the same as the amount of money under the mattresses of the household sector.

Now I´m struggling only with "1", which seems like a philosophical relation and not mathematical like the others. The factors of production "turn into" a finished good. The firm begins the period with a plan to produce N items and spends a certain amount to achieve that. The resultant payment of the factors acts as a definition of "value of production" Y? Is payment of factors in some sense the same thing as "costs of production"? Is the equality production=income a tautology?

About "4", without creation of money, it seems that in this simple example the production has an upper limit because just a certain amount of income can be paid. So, the production of the next period can only be lower. In this next period, if workers decide to spend their savings, the production can raise again later.

The statement

  and now there is less income than product (because less output was sold, which leads to lower wages)

misses that the workers are paid to work a certain number of hours in production, and that production happened, so current wages are unaffected.

Meanwhile, the firm’s income is unaffected by the inventory build, since it is a form of investment, and thus the wages used to produce the inventory are effectively capitalised on the balance sheet.

Incomes might only fall in subsequent periods, as production is lowered in response to the unplanned growth in inventories.

As such, there is no real mystery to be explained.


Game theory - Write a maximization problem (with restriction) I have a problem with finding a way how to solve this example: We have the company, which has two types of customers indexed as $H$ and $L$. We assume: $θ_H > θ_L$. Quantity$(Q)$ of $H$ indexed customers is in population. Payout of type of the customer$(i)$, which buys products($x$) for a price($p$) is $U_i=θ_iv(x)−p$. Company determines quantity and price for that quantity for every type of a customer ($x_i,p_i$). Costs of the company are $C(x_h,x_l)=x_h+x_l$. Company does not know type of the customer and maximizes its profit.

  Find maximization problem which company solves (with restriction). Solve this example with $v(x)=\ln x$.

Here is the maximization problem solved by the company :

\begin{eqnarray*} \max_{x_h, p_h, x_l, p_l} & p_h + p_l - x_h - x_l \\ \text{s.t} &  \theta_hv(x_h) - p_h \geq 0 \tag{IR$_h$} \\ &  \theta_lv(x_l) - p_l \geq 0 \tag{IR$_l$} \\ &  \theta_hv(x_h) - p_h \geq \theta_hv(x_l) - p_l \tag{IC$_h$} \\ &  \theta_lv(x_l) - p_l \geq \theta_lv(x_h) - p_h \tag{IC$_l$}\end{eqnarray*}

Now we solve the above maximization problem for $v(x) = \ln x$. Given that $\theta_l < \theta_h$, it is easy to see that only IC$_h$ and IR$_l$ will be binding in optimum, and we can rewrite the optimization problem as :

\begin{eqnarray*} \max_{x_h, p_h, x_l, p_l} & p_h + p_l - x_h - x_l \\ \text{s.t} &   \theta_l\ln x_l - p_l = 0 \tag{IR$_l$} \\ &  \theta_h\ln x_h - p_h = \theta_h\ln x_l - p_l \tag{IC$_h$} \end{eqnarray*}

Substituting the constraints in the objective, we can rewrite the objective as follows :

\begin{eqnarray*} \max_{x_h, x_l} & \ \ \theta_h\ln x_h + (2\theta_l-\theta_h)\ln x_l - x_h - x_l  \end{eqnarray*}

Further assuming $\theta_h + 1 < 2\theta_l$, and solving the problem yields the following:

\begin{eqnarray*} x_h^* & = & \theta_h \\  x_l^* & = & 2\theta_l-\theta_h \end{eqnarray*}
Consequently,
\begin{eqnarray*} p_l^* & = & \theta_l \ln(2\theta_l-\theta_h) \\  p_h^* & = & \theta_h\ln \theta_h + (\theta_l-\theta_h)\ln (2\theta_l-\theta_h) \end{eqnarray*}


Deducing the Total Cost function $MC = (TC)'(q) = 3q^2 - 40q+220, \quad  where \quad  1 \leq q \leq 20 $

The task is to deduce a function of $TC$, if for the production of the first item we need 291 monetary units, and to write out the cost value if $q$ = 8 units.

I have found that $TC = q^3-20q^2+220q$, but i can't understand how to use that 291 monetary units for finding the cost value

The total cost was 291 m.u. for 1 unit given $MC(q) \equiv \frac{dC(q)}{q} = 3 q^2 - 40 q + 220$.

First, the area under the Marginal Cost gives the Total Variable Cost, $TVC(q)$. To find this area, we will integrate the Marginal Cost:

$$
\begin{align}
TVC(q) &= \int_0^q\frac{dTVC(q)}{dq} dq = \int_0^q (3q^2 - 40 q + 220) dq\\
&= \left. \left(q^3 -20q^2 +220q  \right) \right|_q - \left. \left(q^3 -20q^2 +220q\right)  \right|_0\\
&= {q^3 -20q^2 +220q}
\end{align}
$$
Now, you have to use the additional information of 291 m. u. to find the Fixed Cost. The Total Cost equals the Variable Cost plus the Fixed Cost (which does not depend on q):
$$\begin{align}
TC(1) = TVC(1) + FC &=  291\\
1^3 -20 \cdot 1^2 + 220 \cdot 1 + FC &= 291\\
FC &= 90
\end{align}
$$

Hence, for the 8 units:
$$
\begin{align}
TC(8) = TVC(8) + FC &= 8^3-20 \cdot 8^2 + 220 \cdot 8 + 90\\
&= 1082
\end{align}
$$


Calculating Market Concentration without sales data I want to calculate market concentration (HHI and C4) but I don't have sales data. Is it accurate to use the share of establishments of each firm as a proxy for market power?

Could you list some references that use this or a similar method?

Why not using the number of workers? And simply replacing sales (or output) by workers in the HHI or C4 indices. I saw this in the literature, but where? May be in a report of the German "Monopolkomission"...

EDIT: I found an example for France. The share $C_{10}$ of the production of the 10 biggest firms is very correlated with their share in total employment (at the sectoral level). The correlation coefficient is about 0.96. Note, however, that their production share often tend to be higher than their employment share, maybe due to increasing returns to scale.
Source: Insee, GR2 – Concentration des groupes : part des 4 ou 10 premiers groupes (NES 114 postes)
https://www.insee.fr/fr/statistiques/2381764?sommaire=2381775&q=concentration


If I had a new economical theory, how could I share it with academical environments? I call it “algorythmic economy” If I had a new economical theory, how could I share it with academical environments? I call it algorythmic economy.
I have made this same question on Quora.
https://www.quora.com/unanswered/If-I-had-a-new-economical-theory-how-could-I-share-it-with-academical-environments-I-call-it-algorythmic-economy
I am still writting the paper, and my intention is to prepare a proof-of-concept software to show easily demos to children, for them to not be lied anymore about wealthness.
Further than opinions, what I ask for is how can I share the paper and the software to truly interested people, with a genuine interest in the very deep nature of Economics.
Thank you.

Might be better for Academia:SE, but I'll give my two thoughts anyway.
The primary means of academic discourse is through peer-reviewed journal publications. Therefore, the simple advice is to write a paper and try to publish it in a (serious) economic journal. Here is a list of journals in decreasing order of reputation. There are different rankings used in the profession, but the broad classification of what constitutes a top 5 or an A-journal is not overly disputed in my opinion. Please do try to publish in an Economics journal. A lot of physicists or computer scientists publish papers claiming to revolutionize or reinvent Economics in non-economic journals like Nature of Science, probably get non-economists as reviewers and publish their claims without reference to the previous similar work in Economics.
As side-conversations during the publishing process you may also think of presenting at conferences, workshops, have private conversations / e-mails with academics in the field, or discuss your research on Twitter.


Because Sunk Costs can encode information, should Sunk Costs really be ignored? Source: p 286, Principles of Economics (7 ed, 2014) by N Gregory Mankiw

  [1.] Economists say that a cost is a sunk cost when it has already been committed
  and cannot be recovered. Because nothing can be done about sunk costs,
  you should ignore them when making decisions about various aspects of life,
  including
  business strategy.

Source: Is the Sunk Cost Fallacy Actually Smart Business? (2013 May 5), based on the research of Sandeep Baliga and Jeffrey Ely. I have not read the paper itself as it appears to need graduate-level Microeconomics and Real Analysis.

  [...] [2.] “We call it the ‘theory of the second best,’” he says. “The more you can remember, the better it is, and you don't have to commit this fallacy at all. But if it's a common feature of human beings that they do forget stuff, then the sunk cost fallacy is an optimal response to that forgetfulness. Sunk costs can encode information about decisions you made in the past, and if that's the case you should take them into account, because if you didn't, you'd make even worse decisions.” [...]

I know that Mankiw's book is for first-timers to microeconomics, but 1 appears to oversimplify the subject of Sunk Costs. Is 2 correct? And does 2 refute 1?

I do understand 2's subtlety: 2 means that Sunk Costs should motivate you to try to determine  the reasons for the past decision, which may or may NOT justify resuming a past action; 2 does not mean that high Sunk Costs oblige you to resume a past action thoughtlessly and always.

It's all about the precise idea these authors are trying to communicate:

A) Mankiew is explaining that we are sometimes too stuborn: we sometimes make a bad investment and then feel some vindication in making another bad investment that might rescue the first one, even though we know it's a bad investment on its own. In abstract terms that can be stated by saying that sunk costs should not be taken into account when evaluating whether to increase an investment in a project. Say you put in 100 dollars in a project (A) and got nothing back but you think if you only put in another 100 you will at least get you original 100 back. However, there is another project (B) that pays you 101 if you put in 100. We have the tendency to try to rescue our bad investment and put our money in project A again, but project B pays us a higher return, and we should go for project B.

B) Baliga and Eli are explaining that although, as Mankiew says, you should not use sunk costs in your calculation of whether a new investment is good or bad, it makes sense to keep track of sunk costs from an informational perspective. If you tend to forget what you did or how well it turned out, then recording your sunk costs in a notebook might help you figure out which were good investments previously and might be good in the future too, or not.


Would a car that was produced last year but bought this year be accounted for in the GDP? The equation for the GDP is: $$C+I+G+(X-M)$$
If consumers are buying new cars produced last year...would those still be included in the GDP?

GDP is actual production. Since the car was produced last year, it adds to last year's GDP.  Since it wasn't sold, it would show up in inventory investment (which seems to be included in I in your equation). This year, when the car is sold, inventory investment goes down and consumption goes up by an equal amount, so there is no effect on GDP.
Pop quiz: analyze this example using the income approach to GDP.


Derivation of Arrow-Pratt risk aversion measure This is a question about the derivation of Arrow-Pratt relative risk aversion measure $R(w)=-\dfrac{U^{''}(w)}{wU^{'}(w)}$.

I have an own way to derive it, but I really want how did the authors themselves come up with it.

I do not own the book "Essays in theory of risk-bearing" (1971), where this has been done, and neither does the library in my university, so I can't settle this question on my own.

All I can read in online reviews is that measure was designed to stay stable under positive affine transformations, and that it's a measure of the curvature since it has the second derivative in the denominator, but that still does not answer the question of why and how the authors actually derived it.

Any help would be appreciated.

Please find below the pages which may interest you.

Arrow, K. J. Essays in the Theory of Risk-Bearing, North-Holland Publishing Company, 1971

I let the admin delete this post if the few extracts are not allowed...


Economic and Statistical Significance Of Coefficient I want to know If I am comprehending these terms correctly
Summarizing the difference between economic and statistical significance of coefficients (Describing the terms, process of assessing each with formulas)
Statistical Significance is driven from a large estimate or small standard error where we look at t-tests or p-values to determine whether or not to reject a null hypothesis. While Economic significance looks more at the magnitude and sign of the estimated coefficient, if the numbers turn out to be so small then the x variables do not really affect the y variable.
The process of assessing with formulas For Statistical significance wouldn't assessing the process with formulas just include the formulas to calculate t-test and p-values to determine if we can or cant reject the null. Such as the t*, critical values, p-value
For Economic significance isn't it =0+11+....+. and dealing with 2?
Question 2 Why one does not necessarily mean the other?
(For Whoever marked my last one as a duplicate I don't see why, My question asks about Statistical Significance and Economic while the other one just talked about economic, and I looked at his question and feel maybe it could answer 10% of my question) If whoever first commented could respond again, the answer was so helpful I wanted to show my friends but got burdened this morning waking up to seeing the post was gone.
The previous question got "duplicated" by this "Is there any standard measure of economic significance?" post.

Statistical significance refers to situation where we can say the coefficient is statistically significant at some level based on test statistics (in regression $t$-statistics given by $\hat{\beta}/(s.e.(\hat{\beta}))$) and corresponding $p$-value.
Economic significance indeed depends on the magnitude of the coefficient. As pointed out in this question by KennyLJ sometimes rule of thumb when measuring economic significance is to look at if one standard deviation change in $x$ would result in 'sufficiently large' (which could be 1/2 of standard deviation or also 1 standard deviation change in $y$ - this is very context and field dependent - what is economically significant simply requires good knowledge of wider economic literature).
For example, if we would estimate regression of  daily wages ($w$), measured in ${\\\$}$, on education $(E)$, measured in years of education:
$$w_i = \beta_0 + \beta_1 E_i + e_i $$
and if we would estimate that $\hat{\beta_1} = 0.01$, and this estimate would be statistically significant at $1\%$ due to $t\text{-stat}=10$, we would say the coefficient is statistically significant but economically insignificant because if one extra year of education on average increases daily wages just by ${\\\$}0.01$ and that is nothing. Even if the coefficient is statistically significant from economic perspective it might as well be just zero. However, if $\hat{\beta_1} = 20$ meaning that on average one year of education increases daily wage by  ${\\\$}20$, it would be both statistically and economically significant because having extra $20$ dollars per day thanks to one year of education is non-trivial.
Next the estimated wage $\hat{w_i}= \hat{\beta_0} + \hat{\beta_1} E_i$ would be just that  - an estimated/predicted value by the model given what $E_i$ is. Since the predicted value is derived from estimates of $\beta_0$ and $\beta_2$ it can tell you about statistical significance of the result only as much as just looking at the betas individually.
Lastly $R^2$ is measure that tells you what amount of variation in the sample can the model explain. For example, $R^2=0.25$ would tell you that your model can explain. This is important to take into consideration but again does not tell you about economic significance of the result. For example, it is possible to have results where  betas are for all practical perspective very close to zero, but there is so little variation in the data that they are significant and you get excellent fit (high $R^2$), but that would not necessarily made the result economically significant if the magnitude of the effect is relatively miniscule.


What are some famous examples of infant industries that failed? The Japanese and Korean car and steel industries are often touted as examples of successful infant industries.

I'm trying to find some famous examples of failed infant industries. (They don't seem to show up easily on a quick Google search, so it would perhaps seem like there are not many such examples?)

Malaysia's Proton cars (if you want a specific example ), but overall the Malaysia Automobile industry failed. Currently, only the locals drive Malaysian cars.


Stag Hare inefficient Nash Equilibrium and level-K thinking Two players $i,j$; both have two strategies $\{h,s\}$.
The payoffs vector of $i,j$:
$u(h,h)=(5,5)$ (if both players choose $\{h\}$ then $i$ receives 5 and $j$ receives 5)
$u(h,s)=(10,0)$
$u(s,h)=(0,10)$
$u(s,s)=(15,15)$
The Nash equilibria include $(s,s)$ and $(h,h)$. Experimental evidence suggests that with communication, most people will realize $(s,s)$.
However, when information is incomplete, it could be rational for one player to play $h$ if one of the following conditions hold:

The player believes that hare is attractive enough for the other (this is discussed in a textbook); or, more generally if the player is a level-k thinker (k>0)
If the player is a max-min decision maker.
If the player is picking a Nash Equilibrium such that that his profit cannot be sabotaged by the other.

I wonder if the level-k results and/or the third interpretation ("non-sabotagable" NE) is reasonable or covered by literature.

Level-k reasoning in the stag hunt game is analyzed in
Gracia-Lázaro, Carlos, Luis Mario Floría, and Yamir Moreno. "Cognitive hierarchy theory and two-person games." Games 8.1 (2017): 1.
The idea that playing $s$ guarantees its payoff is discussed in
Aumann, Robert "Nash equilibria are not self-enforcing, in ‘‘Economic Decision-Making: Games, Econometrics and Optimization’’(JJ Gabszewicz, J.-F. Richard, and LA Wolsey, Eds.)." (1990).
The stag hunt game is due to Aumann.
Related to that is the idea of risk dominance of Harsanyi and Selten in their 1988 book "A general theory of equilibrium selection in games." The stag hunt is pretty much the leading example. It formulates the idea that this Pareto inefficient equilibrium is less risky to play.
It should be noted that the game has a third equilibrium in mixed strategies.


Demand curve is same as Marginal Benefit curve? Demand curve is same as Marginal Benefit curve  [Source: Microeconomics by Pindyck & Rubinfeld, Chapter 10, Section 5 - Monopsony]. I have only seen intuitive explanations for this statement. Can anyone prove it mathematically?
I am confused because for example is the curve is P = 10 - Q, then for Q = 1 to Q = 2, the total utility level changes for BOTH the first consumed product and the second one but the term "marginal benefit" seems to capture only the change due to second item consumed.

Nuance matters:
In the comments under 1muflon1's answer the quote given is

The demand curve represents marginal benefit. The vertical distance at each quantity shows the mount consumers are willing to pay for that unit. Willingness to pay reflects the benefit derived from each unit.

So the actual claim is not that the demand curve is the same as the marginal benefit curve, but that it represents it in some way. To be even more precise, the inverse demand curve represents marginal benefit. The demand and inverse demand curves are often conflated as these mappings are represented by the same graph.


Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences? According to a textbook, a monotone increasing but nonlinear transformation of a utility function might not represent the same preferences. Why is it so?

An example of such preference would be appreciated.

One reason I could think of is regarding convexity of the function (and hence risk aversion). For example, $u(x) = x$ is risk neutral, but $v(x) = \ln(u(x)) = \ln(x)$ is risk averse.

See also this.


How does US (its economy, banks, industry) profit from dollar being the "standard currency"? How does US (its economy, banks, industry, "finance industry") profit from dollar being the "standard currency"? I am not seeking "ideological" explanations, but explanations of the mechanisms involved, of the kind of "how things work", better backed by actual numbers. Could one recommend some honest, preferably not ideologically coloured, accessible reference which discusses such mechanisms?

Some major benefits include:

Seigniorage on currency acts as a source of government revenue, allowing for lower taxes and higher spending. One paper (Neumann (1992)) puts this at about \$15 billion a year.
Lower borrowing costs on public and private debts due to greater demand for financial assets denominated in the currency, particularly credit risk-free assets. A McKinsey report (An exorbitant privilege? Implications of reserve currencies for competitiveness (2009)) estimates that this lowered the "...US borrowing rate by 50 to 60 basis points in recent years, generating a financial benefit of $90 billion".
Because households consume many non-tradable goods and services and earn income denominated in local currency, households naturally have hedges on the fluctuation of local currency. Increasing the scope of dollar denominated goods and assets increases the strength of this hedge, reducing currency risk in consumption, trade and finance. For example, Euro-ization is thought to have increased GDP on in the Eurozone by 0.4 percent per year (about 40 billion Euros) from the reduction of transaction and hedging costs (Emerson, Gros, Italianer, Pisani-Ferry, and Reichenbach(1992)).
More liquid capital markets, because there are many more buyers and sellers of dollar denominated assets.
Deeper capital markets, because liquid and cheap capital encourages the raising of capital

You many also be interested in the book Exorbitant Privilege (Eichengreen (2012)) which includes an extensive discussion of this topic.


What are the justification of using 1990 or 2010 as benchmark in studies? Normally, many international studies and documents using multiple-of-10 years (for example 1990, 2010) as the benchmark year.
For example: Dong,2019, p.899 used 1990 as the benchmark to calculate the Export Market Leniency Laws variable as discussed here, or WorldBank converted GDP to $USD 2010 as discussed here.
I have some justifications for this usage:

These numbers look round and are convenient. If you used the benchmark as 1991 or 2011, the readers will think you had some reasons to omit 1990 or 2010, you will be questioned about cherry-picking data.

Multiple-of-10 years do have an advantage in the USA and some other countries because these are the census years, so the macro-level data would be up-to-date and better in demographical.

Could you please justify these ideas and offer me some more reasons for these choices?

First, something that was not explicitly mentioned in your question is that in both cases you refer just to indexation, so answer will also be given in context of indexation.
Second, your premise is false. Datasets & research do not use just multiples of 10 but also multiples of 5 often. For example, for HICP Eurostat choose year 2015 as base year. Moreover, you will occasionally see other numbers as well.
There is no reason to choose round numbers or multiples of 10 or 5 other than round numbers and multiples of 10 or 5 are aesthetically pleasing.

Choice of base year in any index does not matter analytically, it only changes visuals. Analysis won't be affected by converting GDP into 2009 or 2010 or 2011 etc dollars. As long as whole analysis uses the same dollars for everything there will be no change.
Only time when choice of base year in index matters is when you are doing a visualization. For example, if you want to know how productivity in Russia increased since fall of USSR (in 1991), you could choose base year 1991 making productivity index in 1991= 100 which makes it easier to see if productivity declined or increased just by looking at the number itself (although even if you would choose year 1990 a correct comparison would take no more than few extra seconds of your time). Even here it is context depended as the graphs will look almost identical.

Most of the reasons you state are false except the first one:

These numbers look round and are convenient.

This is actually correct reason in most of these cases. For some reason people like numbers that are multiples of 10 or 5, why this happens is question for psychology not economics.

If you used the benchmark as 1991 or 2011, the readers will think you had some reasons to omit 1990 or 2010, you will be questioned about cherry-picking data.

This is false. If choice of index would make actually a difference for an analysis then choosing 2010 would be equally questionable and people could equally accuse you of cherry picking. In any case where choosing different year would actually affect data analysis, the choice of year needs to rigorously justified or your research will be sooner or later questioned.

Multiple-of-10 years do have an advantage in the USA and some other countries because these are the census years, so the macro-level data would be up-to-date and better in demographical.

Again false.

Most countries around the world do not even conduct censuses in round years. See here database for dates of all censuses around the world. For example, the Netherlands where I live conducts census every 10 years with years ending with 1 (i.e. 1991, 2001, 2011, 2021), yet the Netherlands does not indexes its statistics with years ending with 1. For example, as you can see here CBS (Statistical office of the Netherlands), indexes CPI with year 2015 (following Eurostat). You will not see virtually any indexes in year ending with 1 in any research produced by Dutch research centers such as Centraal Planbureau or De Nederlandsche Bank, even when research is only done on Dutch level without any international comparison.
You can still combine all census data with GDP, CPI or whatever you want being indexed or expressed in dollars from any year you choose. For example, if you want to regress real GDP on population, trying to see if larger population leads to higher GDP, and you have census from round years (e.g. 2010, 2020...) you can still choose to express everything in 1997 dollars or 1998 dollars. It literally does not matter. Only thing that does matter is that once you choose some base year you should express all dollar quantities in that base year and not use let's say consumption in 2005 dollars if income is expressed in 2010 dollars.

To really drive this point home, below I extracted from Fred dataset Consumer Price Index for all Urban Consumers. I made 2 graphs. In one of the graph the benchmark year is 2007 in the other one the benchmark year is 2010. I removed title from the graph telling you which index uses which year as a benchmark. Can you see any difference, can you tell which one is indexed to 2007 and which to 2010?


If a fluctuating cryptocurrency becomes the new world coin, would it stop fluctuating? An often mentioned criterium for money is that it should be a unit of account. It could be argued that cryptocurrencies don't satisfy this requirement.

The argument is that businesses like bakers would adjust their prices all the time, which is not acceptable. I.e. it fails to be a unit of account.

Suppose that suddenly a cryptocurrency would be the only coin that's accepted in this world.

Would this mean that it stops fluctuating, as there's nothing else to exchange the coin into, and thus becomes a unit of account?

Your question is very similar to "if we were back on the gold standard, what mechanisms exist to regulate inflation/deflation".

The question is a difficult one because it brings into scope the role of banks and credit and how they would fit into the world. Crypto-systems (in the sense of cryptocurrencies) don't address credit today.

You'd likely see the world separated into two categories of 'user':

Those who manage their own wallets
Those who do not

For the second category banks would continue to exist. Cold wallet storage, data centers and the like. Those banks would still be licensed to issue notes on the basis of the 'digital gold' they hold, so we'd be back to square one with banks being literally issuers of notes with cryptocoin as the new gold.

The value of the trustless gold, and its trust based proxy, would be regulated by the same mechanisms that existed under the old gold framework: trade imbalances result in cross border settlements of gold influx/egress that adjust bank exposure to circulating 'paper'. This results in credit interest rate adjustments, which accelerate or brake the economy depending.

So yes in short international trade would act as a mechanism for adjusting things and tending towards some regulation of the currency value. Similarly central banks would adopt policies to manage the availability of coins. I don't know what policies, but we should never underestimate the power of states (eg now under C19) to simple dictate that coins be donated/given/taxed etc to a central authority.


Isolating single campaign effects over a sales series I'm trying to wrap my head around the concept of advertising effectiveness and hit a wall when I tried to measure the quantitative effect of an advertising campaign on the sales tendency of a business.
As far as I know, this is an econometrics question, since I have isolate the effect of said campaign from past and future campaigns, but also from distribution, macro effects, competitor activity and random effects.
Can you point me to a paper or a textbook that deals with this kind of problem?

You might take a look at the Causal Impact R package and accompanying paper.


How does FRED Quarterly Real Gross Domestic Product and USA GDP growth rate match? https://fred.stlouisfed.org/series/ND000334Q
From this not seasonally adjusted data, Q2 GDP merely dropped 1-4305/4674=8% QoQ? What makes this number to be so different from the 32.9% decline they published today supposedly calculated form the seasonally adjusted GDP data?
https://fred.stlouisfed.org/series/GDPC1

As Fred dataset clearly states the second series in quarterly series at an annual rate where the $32.9\%$ change is calculated just as the difference from preceding quarter. The annual rate change from preceding quarter is calculated differently than quarter-on-quarter rate. You can review the formulas fred uses here. Most of the discrepancy between the numbers can be attributed to that.

the seasonal adjustment is done by Fed using algorithms not by calculating quarter-on-quarter value so a discrepancy might creep already just from different method of seasonally adjusting the data although that should not be excessive.


Utility and consumption tax If I have a model with taxes on consumption denoted $\tau$ should I write the utility function as $u(c)$ or $u((1-\tau)c)$? Thanks

U(c).

Taxes are an adjustment on your income/resource and show up on your budget constraint.

U(c) just measures the utility you get from consuming c.

As an aside, consumption taxes should not be 1-t.

Example: Investment = F - (1+t)C = Net Savings.

If you wrote (1-t), it would mean, Investment = F -C + tC. Higher is the tax rate, more is the investment or budget left over for investment, ceteris paribus - which does not make sense.

EDIT

The answer by @Henry got me thinking about the following.

If a model is proposed where a consumer purchases C units of consumption goods taxed at rate t, such that the consumer will have to give away tC units in taxes and ultimately will consume (1-t)C, the analysis is based on tangible goods. In the budget constraint of the consumer it will read as :

Investment = Output - Price * C

since the consumer will have paid for C units and then ultimately consumed (1-t)C units due to the tax.


Looking for a term that explains market participants that lie about their participation to gain access to said market I'm Looking for a term that explains the behavior of a market participants that will lie or exaggerate how much or what they offer in order to gain access to a market that would otherwise be inaccessible.

This is simular to the concept "bait and switch" but the goal here isn't adverse-deception, its to overcome a barrier of entry.

For example, participant X wants to penetrate a market but monopoly protections prohibit entry. X can enter the market under the pretense of selling a different product and finds a way to disguise their new product to steal market share from the monopoly.

Another example, Company Y wants to start manufacturing widgets, but suppliers only contract with companies who are a part of the big widget alliance. Big Widget alliance only accepts companies who produce at a certain quantity. Y then pretends to have a certain output to gain access to the market.

Another example (but might be a different concept), is when participant Z is known as a gizmo buyer but they actually are in the market exclusively to sell gizmos.

What about a meme agent? (e.g. an agent mimics the qualities of another agent to "fool" regulators, competitors, consumers.)


How to calculate expected revenue in reverse auctions (procurement) I'm trying to find the correct formula to calculate de expected revenue of a reverse auction, properly, a second-price sealed-bid procurement auction to identify the lowest cost supplier.

Prices are private, independent, and uniformly distributed between 50 to 100. no bidder will go below 50. And the number of bidders are 10

We know that it does not matter whether we use a first-price or a second price auction - the expected final price is the same.

The formula E(p)=(n-1)/(n+1) stems from the fact that it is the valuation of the (n-1)th bidder that determines the expected price.

Now, this is a reverse auction, so the expected price stems from the ordering of bids.  In a reverse auction, the price is not dependent on the value of the (n-1)th bidder, but on the second bidder. So we get that instead,
E(p)=2/(n+1).

Hint: In second price sealed bid, it is optimal to bid your own valuation for the good. So in a reverse auction, it is optimal for each person to bid their lowest possible price they are willing to supply at. Intuitively, if one individual deviates from that strategy, it doesn't increase their chance of winning the auction or increase their chance at getting a higher priced contract, since the price they supply is based on other contractors' bids.

So the expected revenue is going to be the average value of the second lowest bidder amongst ten bidders. Try to set up an integral to describe the distribution and go from there.

For a normal second price auction (not reverse):

$F(x)$ is the probability that the price will be less than or equal to some given $x$, and $f(x)$ is the corresponding density function.

$$F(x) = \frac{x-50}{50}; \quad f(x) = F'(x) = \frac{1}{50}$$

Probability that second highest bid is $x$, with $n$ bidders:

$$h(x,n) = n(n−1)f(x)(1−F(x))F(x)^{n−2}$$

Expected value of $x$ (the price):

$$\int^{100}_{50} x h(x, n) dx$$

So you can easily apply a similar logic to your reverse auction. Set up $F(x)$ so that it represents the probability that the price will be greater than or equal to some given $x$.


Sources to know about latest research I wanted to keep myself aware of the latest research news and trends etc. in economics. What are some good sources (newsletters, magazines, websites etc.) for that?

I did find one from Nature. How comprehensive is it? If it is not that comprehensive, what sources shall I read from to have a comprehensive summary of latest developments?

The National Bureau of Economic Research is a good source for the latest in economic research: https://nber.org/

You can also go to Brookings institute:  https://www.brookings.edu/

Federal Reserve Board:  https://www.federalreserve.gov/econres.htm


price elasticity: Linear regression low r square I faced an interview question for a job where interviewer asked me suppose your r square is very low (between 5 to 10%) for a price elasticity model.

How would you solve this question? Anything that a typical econometrics guy would do?

Edit: I have posted this question in stats.stackexchange.com forum for understanding this problem from the perspective of model diagnostics and feature engineering

I would raise two issues about the dataset to which the regression line was fitted:

The range of prices in the dataset.  If the datapoints all lie within a very narrow range of prices, then even small variation (whether real or due to measurement error) in the associated quantities can lead to a low coefficient of determination $R^2$.  In terms of the formula:

$$R^2 = 1 - \frac{\text{Residual sum of squares}}{\text{Total sum of squares}}$$

a narrow range of prices tends to result in little of the total sum of squares being explained and most of it being residual, resulting in a low $R^2$.  Note that it is assumed here that the regression takes price as the independent variable and quantity as the dependent variable.

The number of datapoints.  If the number is small, then, even within its range of prices, the dataset may happen to be unrepresentative of the distribution of points within the population of interest. This can result in the squared residuals calculated from the dataset being on average either much smaller or much larger than is representative of the population.  Thus it is possible that $R^2$ has been correctly calculated from data which is not representative of the population.