texts: Why doesn't Costco simply raise prices and nix the membership fee?

texts:
I know little about the field of economics. I realize this question may be too rudimentary for this forum but I am sure someone here can explain this.

My question concerns Costco, which is a wholesale retailer that sells groceries, as well as electronics, clothes, and home goods. To even enter the store, one must have a Costco membership.

My question is simple: What purpose does the Costco membership fee serve? More specifically, why doesn't Costco get rid of the the whole "paid membership" idea, open its doors to anyone and everyone, and raise its prices to make up for the lost revenue?

Costco basically offers two different memberships, the standard membership with an annual fee of \$55 and the Executive membership costing \$110. The primary benefit of the Executive membership is that members receive 2% cash back on every Costco purchase (which is in addition to whatever cash back your credit card is earning for you). Thus, it only makes sense to purchase the Executive membership if one's yearly spending at Costco exceeds \$2,750 per year.

This is Costco's defense:

  "Costco's membership fee provides a means of covering part of our operating costs and overheads thereby reducing our prices on the products we sell. This way the more members we have, the lower our prices and the more you buy, the more you save."

If Costco did not require a membership fee, Costco would generate more revenue from a significant increase in customers. Costco could raise prices slightly on every item to compensate for the loss.

If Costco is indeed making the smart decision economically by requiring a membership fee, then why don't more stores adopt this model?


texts: Mathemtical Economics Question regarding Profit Maximization

texts:
I'm studying Mathematical Economics and there's this question that I'm unable to understand.

Q. Suppose a firm faces a demand curve for its product $P = 32 - 2Q$, and the firm's costs of production and marketing are $C(Q) = 2Q^2$. Find the following:

(f) What would the competitive price and quantity be, assuming $C(Q) = 2Q^2$ represented the industry cost function?

Actually the question has 5 more parts but I was only stuck on this last one (f). In the other parts I calculated Profit formula, price and quantity that maximize total revenue and the price and quantity that maximize profit (if by any chance these are related to the last part)

Any help will be appreciated!


texts: Solow-Swan production function- What is '$L$'

texts:
If $L$ represents the amount of labour in the Solow-Swan production function:

$Y/L$=$f(K/L)$

how can $Y/L$ equal 'per-capita income' if $K/L$ is the capital/labour ratio?

I thought per-capita income was income divided by the entire population.

Thanks.


texts: Because Sunk Costs can encode information, should Sunk Costs really be ignored?

texts:
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.


texts: How is Comparative Advantage a superset of Absolute Advantage?

texts:
Source: 'The Theory of Comparative Advantage - Overview', Prof Steven M. Suranovic

  Advantageous trade based on comparative advantage, then, covers a larger set of circumstances while still including the case of absolute advantage and hence is a more general theory.

Please explain this? What's the intuition, which I prefer over a formal proof?


texts: Term for the phenomenon when an undesirable but competitive strategy dominates

texts:
For example, in some sports, the use performance enhancing drugs is considered undesirable, but it is difficult or impossible to be competitive unless you use performance enhancing drugs.  So, the use of performance enhancing drugs becomes this sort of undesirable dominant strategy that is a struggle to control.

Other examples abound.  Is there a succinct term in the economics field for such phenomena?


texts:
Why is Pakistan repeatedly defaulting?

2008 - Pakistan seeks USD9 billion IMF bailout to avert crisis
2013 - Saudi Arabia come to Pakistan’s Rescue with USD15 Billion Energy Bailout Deal
2014 - Saudi Arabia loaned Pakistan USD1.5bn to shore up economy
2015 - IMF approves USD506 million for Pakistan under bailout programme
2017 - China bails out Pakistan with USD1.2bn loans

What is the fundamental problem with Pakistan's economy?


texts: Through the Slutsky equation I know that if the good is inferior the marshallian demand function is steeper than the hicksian demand but I cannot understand why the Compensating variation is higher than the equivalent variation. Is this because the increase in utility shifts the hicksian to the left instead of shifting it to the right (in a graph with prices as y and demand as x)?


texts:
I am considering the idea of "Harry Browne's permanent portfolio". I seen a few versions of this strategy where the different parts consists of funds which in turn have some costs associated with them.

Then why not just buy one ETF(which only contains the corresponing asset) for each of three parts consisting of government securites and gold and for the last forth just a large stock fund for the stock part?


texts: Optimal taxing in case of negative externalities

texts:
Suppose an individual $i$ has the utility function

$U= f(x(i)) - k$(sum of all $x$ with index not equal to $i$)

Where $x(i)$ denotes the miles driven by $i$, and $k$ is a positive constant.

The function $f$ is such that $f(0)=0$, and has a negative double derivative. It crosses the x axis once after increasing at $x=0$.

We're asked, that if a social planner taxes individuals on basis of $t$ dollars per mile driven, how will such an optimal tax change as we increase the number of individuals? It is given that the planner maximizes sum of all utilities.

I started out by finding the best response of individual $i$, which is
$f'(x)=t$. Hence every person has the same best response, so miles driven by everyone are the same. Hence maximising utility of any person will suffice.

Max. $f(x) - f'(x)*x - k(n-1)x$

Which gives me $x=(n-1)k/f''(x)$

I don't know how to proceed further.


texts: Differentiating a conditional expectation: RBC models with uncertainty

texts:
Is the following true? \begin{equation}\frac{\partial}{\partial X_{t+1}}E_t(f(X_{t+1}))=E_t(\frac{\partial}{\partial X_{t+1}}f(X_{t+1}))\tag{1}\end{equation} where $f$ is some affine function (e.g., $f(x)=a+bx$), $E_t(X_s)=E(X_s|I_t)$ denotes the conditional expectation of $X_s$ given information $I_t$ in time period $t$, and where $X_s$ denotes the value of some variable $X$, say financial asset holdings, in time period $s$, such that $X_s$ is unknown (i.e., stochastic) given information at time periods $0\leq t<s$ but known otherwise.

Edit 3: I think we should view $X_{t+1}$ as a function of information in time period $t$, i.e. $X_{t+1}=X_{t+1}(I_t)$. This hinders $(1)$ from being zero (see Alecos' comment below). If this is the right way to look at the problem (see "Edit 2" below; I do not know how to look at the problem, that's why I'm asking!) then $(1)$ may be written in detail as \begin{equation}\frac{\partial}{\partial X_{t+1}}E(f(X_{t+1}(I_t))|I_t)=E(\frac{\partial}{\partial X_{t+1}}f(X_{t+1}(I_t))|I_t).\tag{1'}\end{equation}

I often notice that $(1)$ (or $(1')$) seems to be used when studying real business cycle models with uncertainty where the Lagrange method is applied (this framwork is outlined in e.g. Gregory C. Chow's Dynamic Economics: Optimization by the Lagrange Method).

For example, we may have a situation where we have to differentiate \begin{equation}-\lambda_t A_{t+1}+E_t(\lambda_{t+1}(1+r_t)A_{t+1})+\Phi\tag{2}\end{equation} w.r.t. financial asset holdings $A_{t+1}$ in time period $t+1$, where $\lambda_t,\lambda_{t+1}\geq 0$, $r_t\in\mathbb{R}$ and $\Phi$ are independent of $A_{t+1}$ (i.e., they are not functions of $A_{t+1}$), and seem to use $(1)$ to arrive at the conclusion that the partial derivative of $(2)$ w.r.t. $A_{t+1}$ is \begin{equation}-\lambda_t+E_t(\lambda_{t+1}(1+r_t)).\tag{3}\end{equation}

I neither understand if $(1)$ is used to justify the implication from $(2)$ to $(3)$, nor if $(1)$ is true, within the framework mentioned in the parenthesis above, but know of other treatments which begin by discussing measure theory and stochastic processes (e.g., Lecture notes for Macroeconomics I: Chapter 6), and then deriving similar, but not exactly analogous, first order conditions to that derived by using fact $(1)$ and the Lagrange method.

Edit 1: I was asked to post a reference. The reference is lecture notes written by my lecturer. It says the following. If we have a representativve household's maximization problem $$\max_{\{C_t,A_{t+1}\}_{t=0}^{\infty}}E_0\sum_{t=0}^{\infty}\beta^tu(C_t)$$ subject to the budget constraint $$C_t+A_{t+1}=Y_t+(1+r)A_t,\quad\forall t\in\mathbb{Z}_{\geq 0},$$ then we want to investigate the first order conditions for the Lagrangian\begin{equation}\mathcal{L}=E_0\left[\sum_{t=0}^{\infty}\beta^tu(C_t)+\sum_{t=0}^{\infty}\lambda_t[Y_t+(1+r)A_t-C_t-A_{t+1}]\right].\tag{4}\end{equation} One first order condition is the partial derivative of $\mathcal{L}$ w.r.t. $A_{t+1}$: $$-\lambda_t+E_t[\lambda_{t+1}(1+r)].$$ (To be exact he writes that the above is a first order condition for the Lagrangian $\mathcal{L}$. I've interpreted that as meaning that he partially differentiates $\mathcal{L}$ w.r.t. $A_{t+1}$.)  My question is then: Why is that true?

Edit 2: I've also used the following reference: Chapter 5. Real Business Cycles. See equation $(5.7)$. How does the author derive that equation? Does he differentiate inside the conditional expectations, as expressed by me in $(1)$?

Edit 4: To be more exact, $I_t$ may capture the value of e.g. output $Y_t$ (compare with the budget constraint above).


texts: How important are new guns to organized crime in North America?

texts:
I keep reading two things (I can provide examples if needed). They both seem true to me and it also seems like most people agree with them.

There are tons and tons of guns in North America (example). Many of them are owned by organized crime groups or are "available" to them through the secondary market (example, example, example [p5,p8,p12]).

North American organized crime groups obtain (often steal) and manufacture tons of new guns every year, many of them for their own use rather than resale (example, example [p5,p8,p12]).

Assuming you agree with these, I'm wondering how they fit together.
More specifically, how important is the flow of new guns to organized crime groups? How much are they just diversifying their sourcing. How much do they really "need" all of the new guns to stay up-to-date or replace old stock, dispose of incriminating weapons, etc? How much is it just another revenue source? Is it even possible to get a good idea about this given the limited availability of information and the diversity of circumstances across the continent?


texts: Are IV and 2SLS estimation methods the same?

texts: As far as I understand two-stage least squares method (2SLS) is the generalization of instrumental variable (IV) method. What is the difference between these two estimation techniques? Can we use those interchangeably?


texts: How to build a Social Accounting Matrix from an Input-Output Table?

texts:
I built an Input-Output table (IOT) with the industryXindustry format because I thought it was a building block to build a social accounting matrix (SAM). But now I realize that I can't transpose the data from the IOT into the SAM because the SAM requires an industryXcommodity format and does not support industryXindustry or commodityXcommodity flows.

So the question is, how am I supposed to transfer data from the IOT to the SAM? They are supposed to be one of the main sources of information to build a SAM...

Many thanks!

Sarah


texts: If a utility function is quasi-concave, can we say that the IC curve associated with it is convex?

texts:
Let's say we have an utility function, $ U(x,y) = \sqrt{x \cdot y} $. The indifference curve associated with this is convex, while the function itself is quasi concave (because it satisfies $ f_{xx} f_x^2 - 2 f_{12} f_1 f_2 + f_{yy} f_y^2 $).

So, can we say that an utillity function is quasi-concave if the indifference curve is convex (and vice-versa)?


texts:
How can I distinguish between those factors that affect supply elasticity and those that shift it?  I am trying to make two regressions, one with the determinants that affect its elasticity and the other with the determinants that shift the curve. However, it seems that many of the factors are common, for example, the number of producers or technology. Any ideas?
Thanks in advance!


texts: Why is there a positive risk-free interest rate?

texts: I've been told that the interest rate is the price needed to be willing to take on the risk associated with lending. This is why personal loans have higher interest rates than bank deposits, for example. So why is there a positive (as opposed to zero) risk-free rate? It is usually assumed that government bonds are risk-free, yet they have a positive return. If there is no risk, how can there be a positive rate?


texts: Convex rationalization when the budget sets are segments?

texts:
Backgroud:
SARP can be defined on general budget set.

SARP: Assume for all $B$ the choice $c(B)$ is only one element. If $x_i,x_{i+1}\in B_i$, and $x_i = c(B_i)$, for all $i\in \{1,N-1\}$, then $x_1=c(B_1)\notin B_N$.

I learnt that, if the budget is this: $B_i=\{x\mid p_ix\leq p_ix_i\}$, then, SARP implies that the finite data is rationalized by convex preferece.
Motivation: most real life problems have more complicated budgets. For example, if the agent is allocating her money between risky security and riskless cash, then her budget will be a segment rather than a triangle.
My question: Let $y^i$ and $z^i$ be two points, and $\overline{ y^iz^i}$ is the segment connecting $y^i$ and $z^i$.
Let $B^i=\overline{ y^iz^i}$ be the segment budget set.
Let the data be $(x^i,B^i)^{i\in\{1,2,...,n\}}$ where $n$ is a natural number.
Can we still have a convex rationalization of the data?
That is, we are trying to find an Axiom, similar to SARP, such that the following two conditions are equivalent:

The data satisfies the Axiom,
The data is rationalized by a convex preference.

If we could also get monotonicity, then it will be better. The focus is on convexity of preference.
My try: I've gone through the paper "Revealed preference analysis for convex
rationalizations on nonlinear budget sets". However, this paper requires that budget set $B$ is monotone, and a segment budget set is not monotone.
Any comments, long or short, will help. Any related reference will help, too. Thanks in advance.


texts: What makes statistics economical reports so varied and different?

texts:
Search for Iran's GDP in Google, and what you will see is an image representing GDP of Iran, compared to other neighbor countries. It gives us the value of 393.4 billion USD (2015).

Now in that page simply open some results. From Wikipedia, from World Economics, and other sources. You see values from 300 to 1.3 trillion Dollars.

Values are not coherent with each other. As an engineer who is not an economist but understands figures and diagrams, I think these values are so varied that they can not be used in researches as reliable information.

I'm working on a proposal, and I need information that can be trusted. What makes such a bold and universally known economical value so varied across data sources?


texts: how to calculate Leontief demand functions from first order conditions of a CES function when sigma tends to 0?

texts:
This question is NOT about how to approximate a CES function to a leontief function.
Knowing that:
$i= good (\begin{array}{*{20}{c}}
{1}&{or}&{2}
\end{array})$
$j= firm (\begin{array}{*{20}{c}}
{1}&{or}&{2}
\end{array})$
I have this optimization problem:
$\begin{array}{*{20}{c}}
{\begin{array}{*{20}{c}}
{\mathop {Maximize}\limits_{{Z_j},{Y_j},{X_{i,j}}} }&{\pi _j^z}
\end{array} = p_j^z{Z_j} - \left( {p_j^y{Y_j} + \sum\limits_i {p_i^q{X_{i,j}}} } \right)}&{(0.1)}
\end{array}$
subject to
$\begin{array}{*{20}{c}}
{{Z_j} = \min \left( {\frac{{{X_{1,j}}}}{{a{x_{1,j}}}},\frac{{{X_{2,j}}}}{{a{x_{2,j}}}},\frac{{{Y_j}}}{{a{y_j}}}} \right)}&{(0.2)}
\end{array}$
In the book that I am following, they arrive at the following first-order conditions:
$\begin{array}{l}
\begin{array}{*{20}{c}}
{{X_{i,j}} = a{x_{i,j}}{Z_j}}&{\forall i,j}&{(1)}
\end{array}\\
\begin{array}{*{20}{c}}
{{Y_{j}} = a{y_i}Z}&{\forall j}&{(2)}
\end{array}\\
\begin{array}{*{20}{c}}
{{Z_j} = \min \left( {\frac{{{X_{1,j}}}}{{a{x_{1,j}}}},\frac{{{X_{2,j}}}}{{a{x_{2,j}}}},\frac{{{Y_j}}}{{a{y_j}}}} \right)}&{\forall j}&{(3)}
\end{array}
\end{array}$
Then in a footnote they say the following: "we cannot solve this profit-maximization problem by simply applying the Lagrange multiplier method because the Leontief-type production function $(0)$ is not differentiable.To derive the intermediate input demand function $(1)$ and the composite factor demand function $(2)$, we have to use a constant elasticity of substitution (CES) function, which is a generalized functional form of the Leontief-type function, and derive these first-order conditions. When the elasticity of substitution in the CES function tends to zero, the derived first-order conditions approach the expressions of $(0)$, $(1)$ and $(3)$."
What I understand from the bolded part above is that you first solve the optimization problem represented by the equations $(0.1)$ and $(0.2)$ but using a CES function instead of $(0.2)$.  I approach the problem as follows:
Knowing that:
$\begin{array}{*{20}{c}}
{\sigma  = \frac{1}{{1 - \rho }}}& \wedge &{\rho  = \frac{{\sigma  - 1}}{\sigma }}
\end{array}$
The problem is:
$L({Z_j},{Y_j},{X_{i,j}}) = p_j^z{Z_j} - \left( {p_j^y{Y_j} + \sum\limits_i {p_i^q{X_{i,j}}} } \right) + {\psi _i}\left[ {{{\left( {\frac{{X_{1,j}^\rho }}{{a{x_{1,j}}}}+\frac{{X_{2,j}^\rho }}{{a{x_{2,j}}}}+\frac{{Y_j^\rho }}{{a{y_j}}}} \right)}^{\frac{1}{\rho }}} - {Z_j}} \right]$
Later, I understand that once you get the optimal demands with the first order conditions of this problem, then you evaluate what happens to these when sigma tends to 0 and these functions should approximate $(1)$ and $(2)$. I already solved this problem, but  I don't know how from the first-order conditions of the above problem we arrive at equations (1) and (2). Can someone please tell me how to do this?
This is the first order condition:
${X_{1,j}} = {Z_j}{\left[ {\frac{1}{{a{x_{1,j}}}} + \frac{1}{{a{x_{2,j}}}}{{\left( {\frac{{p_2^q}}{{p_1^q}}} \right)}^{\frac{\rho }{{\rho  - 1}}}}{{\left( {\frac{{a{x_{2,j}}}}{{a{x_{1,j}}}}} \right)}^{\frac{\rho }{{\rho  - 1}}}} + \frac{1}{{a{y_j}}}{{\left( {\frac{{p_2^y}}{{p_1^q}}} \right)}^{\frac{\rho }{{\rho  - 1}}}}{{\left( {\frac{{a{y_j}}}{{a{x_{1,j}}}}} \right)}^{\frac{\rho }{{\rho  - 1}}}}} \right]^{( - )\frac{1}{\rho }}}$


texts: statistical discrimination VS taste based discrimination

texts: Given the progress in the literature on economics of discrimination. What is the reason for still believing in the dichotomy taste-based VS statistical discrimination. I think the first theory is just a specific case of statistical discrimination, where information on discriminated workers' productivity is weighted by the discrimination coefficient (which basically is just a scaling factor). Any attempt to disentangle the two types of discrimination is pointless. Or?


texts: Does savings lead to investment in physical capital?

texts:
In the introductory macroecon textbook I'm reading, it's made clear that savings=investment.  Mathematically, this makes sense to me.  However, I'm having trouble understanding the qualitative implications.

After looking through other similar questions, it's clear that this is due to an accounting identity where inventory accumulation due to savings is counted as investment.

But, I stumbled across this blog post, https://mainlymacro.blogspot.com/2012/01/savings-equals-investment.html, that claims savings eventually equals investment in capital (S=DK).  From what I understand, the author of the post is saying that savings will lead to inventory accumulation, DS, which will eventually lead to output (Y) decreasing.  The output must decrease for the firm to avoid losing money.  Decreasing output will lead to income decreasing, and therefore savings further decrease to the point where savings equal DK, or investment in capital goods.

Why does the eventual decrease in savings cause savings to equal investment in capital goods (S=DK)?  Am I correctly interpreting what the author of the post is saying?


texts: Finding restrictions on parameters for a demand function

texts:
I have a question that asks:
Let $x_1$ be the quantity of a good 1, $p_1$ the price of good 1, $p_2$ the price of good 2, and
$M$ is income. Let
$_1(_1, _2, ; ) = _1^_2^^$ Where $$, $$, $$, and $$ are parameters.
If this is a demand function, what restrictions does this impose on the parameters?
I am a bit confused if my understanding of the question is correct, currently what I've gone and done is impose the restriction $x_1 p_1+x_2 p_2≤M$, and then sub in $_1^_2^^$ for $x_1$, resulting in $Ap_1^α p_2^β M^γ (p_1 )+x_2 p_2≤M$. I have then gone and rearranged for the various parameters, resulting in:
$A≤(M-x_2 p_2)/(p_1^(α+1) p_2^β M^γ )$,
$α≤ln((M-x_2 p_2)/(Ap_2^β M^γ ))/ln(p_1 ) -1,Ap_2^β M^γ$,
$β≤ln((M-x_2 p_2)/(Ap_1^(α+1) M^γ ))/ln(p_2 )$,
$γ≤ln((M-x_2 p_2)/(Ap_1^(α+1) p_2^β ))/ln(M) $
I'm not really sure if my approach is correct at all, as this seems more of a maths rearranging formulas answer rather than something related to economics. I was wondering if anyone could help me get on the right track if this is wrong. Thanks


texts: Game theory: SPNE and simultaneous move games, Interpret it in a tree

texts:
Question:

And the solution:

It says in the question, that Franco can eat half or almost all.
And after that, Francisco can choose to give the whole roll to the ducks or eat the rest of it.

I don't get the matrix in the solution.

If Bob eats all. We're looking at the top row. And therefore Francisco can choose to accept, or feed the ducks. I don't get it where he can (Accept, Accept).. Like, what. Accept first that Bob eats almost all, and then eat the rest of the whole roll?
Still on the first row, where Bob eats almost all. (Accept, Feed) does that mean that Francisco accept that Bob eats the whole roll, and then feed the ducks? (*)

Beacuse this is a simultaneous move, which means Bob and Fransicso dosen't know what either the other know.

So if we talk about the first rows in the matrix again, does it mean that
- If Bob choose to eat almost all, then Fransicso - whitout knowing Bobs move - that he have to think "ooh I don't know if Bob is gonna acceptet, but if he do I can either choose (Bob eats all => I accept, I eat all)
- If Bob eats all, => I accept, I will throw the roll to the ducks.

Is it like that I should think? when it comes to this simultaneous move. And the first list (*) is how I should think if it was a sequential move?


texts: One Week U.S. GC REPO Bid Rate Exceeds Ask Rate

texts:
I have recently downloaded a time-series of one-week U.S. Generalized Collateral Repurchase Agreement Rates from Bloomberg (Ticker: USRGCY1Z CURNCY). While looking through the data, I noticed that the bid rate exceeds the ask rate a vast majority of the time. Intuitively, this does not make much sense to me since normally the bid rate is the rate at which a bank is willing to borrow and the ask rate represents the rate that is applied when lending money.

This can be found here: https://financial-dictionary.thefreedictionary.com/Interbank+Bid+Rate

When considering the nature of a GC Repo contract, which is fully collateralized, might the reason be that the collateral (mostly high-quality bonds) are in such high demand that banks "charge" a premium when borrowing?

I am very grateful for any thoughts or hints, thank you in advance!


texts: What are the mathematical constants used in economy formulas?

texts:
For the calculation of the taxes, the rate is the coefficient of proportionality.
This coefficient is constant because

  It is the value of the ratio between a quantity and another that is constantly repeated in a set of values.
  It is a constant value which is in direct proportional functions or reverse, quadratically proportional or inverse

Other examples of this type in macroeconomic, finance, commercial.. ?

P.S - I refer both type of constants: specific fixed numeric value and as constants in economic theory


texts: How does excessive consumption in an area decrease tax revenue?

texts:
Source: p 156, Urban Geography (2009; 3rd ed) by Michael Pacione

  The main ideological battle is between pro-growth
  and anti-growth factions. The pro-growth ideology
  proclaims that more development results in increased
  population, greater aggregate sales, more local tax
  revenues and more local jobs, owing to increased local
  spending. Benefits therefore flow to those who need
  employment and those in favour of lower taxes.
  The
  anti-growth ideology emphasises the other side of the
  coin: development brings more people to an area than
  local institutions can service, thus any $\color{darkred} { \text { downward trend
in taxation  }   }$  is overcome in the later stages of growth
  by the need for $\color{green} { \text { greater fiscal expenditure  }   }$.

1. How does excessive consumption in local institutions cause a $\color{darkred} { \text { downward trend
in taxation  }   }$? Excessive consumption ought to be boost tax revenue?

2. The last sentence seems to contradict the  anti-growth ideology. Please clarify? I am guessing that the anti-growth ideologues want to avoid $\color{green} { \text { greater fiscal expenditure  }   }$; so why do they reject a growth (or overgrowth) in consumption?


texts: How does keeping the value of the dollar by foreign US bondholders makes their exports more affordable?

texts:
How does this work?

  In February 2018, China owned \$1.18 trillion of U.S. debt. It's the
  largest foreign holder of U.S. Treasury securities. The second largest
  holder is Japan at \$1.06 trillion. Both Japan and China want to keep
  the value of the dollar higher than the value of their currencies.
  That helps keep their exports affordable for the United States, which
  helps their economies grow. That's why, despite China's occasional
  threats to sell its holdings, both countries are happy to be America's
  biggest foreign bankers. China replaced the United Kingdom as the
  second largest foreign holder on May 31, 2007. That's when it
  increased its holdings to \$699 billion, outpacing the United Kingdom's
  $640 billion.

Source:
Article - Who Owns US National Debt


texts: Adding a non-binding constraint to the objective function

texts:
I am dealing with a constrained optimization problem found in Tirole's Theory of corporate finance. My question is not related to the details of this model, but just to provide some context, we are solving for the optimal contract to secure outside financing in a setting with costly state verification. $y(\hat{R})$ is the probability of no audit when income $\hat{R}$ is reported. Audits cost $K$ to the lender. $w_0(\hat{R},R)$ is the reward for the borrower in case of no audit, and $w_1(\hat{R},R)$ in case of audit.

The objective function is:
$$\max\limits_{y(\cdot),w_0(\cdot,\cdot),w_1(\cdot,\cdot)}\left\{\int_0^\infty w(R)p(R)dR\right\}$$

It is subject to the incentive constraint for the borrower to report the true income $R$:
$$w(R)=\max\limits_{\hat{R}}\{y(\hat{R})w_0(\hat{R},R)+(1-y(\hat{R}))w_1(\hat{R},R)\}$$
and to the break-even constraint for lenders who provide $I-A$ to the entrapreneur.
$$\int_0^\infty[R-w(R)-[1-y(R)]K]p(R)dR\geq I-A$$

My question relates to the following.
The author argues that, since the second constraint binds at equilibrium, it can be added to the objective function. The problem is then equivalent to minimizing the expected audit costs:
$$K\left[\int_0^\infty[1-y(R)]p(R)dR\right]$$
subject to the two above constraints.
I don't understand why we could add the binding constraint to the objective function and find an equivalent problem subject to the same constraints.
Is there a general optimization principle that I missed along the way?
Thanks!


texts:
I'm trying to rework Mankiw, Romer, Weil (1992) with fresh data.

From their paper:

n: workforce growth rate

  We measure n as the average rate of growth of the working-age population, where working age is defined as 15 to 64.

s: rate of savings

  We measure s as the average share of real investment (including government investment) in real GDP...

Y/L: output per worker

  ...and Y/L as real GDP in 1985 divided by the working-age population in that year.

They also assume...

  ... that g+δ=0.05

As for human capital:

  We use a proxy for the rate of human-capital accumulation (Sh) that measures approximately the percentage of the working-age population that is in secondary school. We begin with data on the fraction of the eligible population (aged 12 to 17) enrolled in secondary school, which we obtained from the UNESCO yearbook. We then multiply this enrollment rate by the fraction of the working-age population that is of school age (aged 15 to 19).

Considering the latest version of the Penn World Tables, should I use emp and the corresponding growth rate for n, rgdpo/emp for Y/L, and hc for human capital (Sh)? What about s? I'm a little perplexed as MRW include government investment.

Excerpt from the PWT 9.0 legend for convenience.

Real GDP, employment and population levels

  rgdpe Expenditure-side real GDP at chained PPPs (in mil. 2011US$)

  rgdpo Output-side real GDP at chained PPPs (in mil. 2011US$)

  pop   Population (in millions)

  emp   Number of persons engaged (in millions)

  avh   Average annual hours worked by persons engaged

  hc    Human capital index, based on years of schooling and returns to education; see Human capital in PWT9.

Current price GDP, capital and TFP

  ccon  Real consumption of households and government, at current PPPs (in mil. 2011US$)

  cda   Real domestic absorption, (real consumption plus investment), at current PPPs (in mil. 2011US$)

  cgdpe Expenditure-side real GDP at current PPPs (in mil. 2011US$)

  cgdpo Output-side real GDP at current PPPs (in mil. 2011US$)

  ck    Capital stock at current PPPs (in mil. 2011US$)

  ctfp  TFP level at current PPPs (USA=1)

  cwtfp Welfare-relevant TFP levels at current PPPs (USA=1)

National accounts-based variables

  rgdpna    Real GDP at constant 2011 national prices (in mil. 2011US$)

  rconna    Real consumption at constant 2011 national prices (in mil. 2011US$)

  rdana Real domestic absorption at constant 2011 national prices (in mil. 2011US$)

  rkna  Capital stock at constant 2011 national prices (in mil. 2011US$)

  rtfpna    TFP at constant national prices (2011=1)

  rwtfpna   Welfare-relevant TFP at constant national prices (2011=1)

  labsh Share of labour compensation in GDP at current national prices

  delta Average depreciation rate of the capital stock

Shares in CGDPo

  csh_c Share of household consumption at current PPPs

  csh_i Share of gross capital formation at current PPPs

  csh_g Share of government consumption at current PPPs

  csh_x Share of merchandise exports at current PPPs

  csh_m Share of merchandise imports at current PPPs

  csh_r Share of residual trade and GDP statistical discrepancy at current PPPs


texts:
My question is simple: in theory, why should we expect the total quantity that firms want to sell to be (at least approximately) equal to the total quantity that consumers want to buy?

As I understand it, the standard explanation is something like this. If supply were greater than demand (for instance), then there must be some 'frustrated' sellers who cannot sell all of the units that they want to sell. Instead of paying the market price, buyers could therefore pay a lower price to these sellers while still buying all the units that they want to purchase. This pushes the price downwards, a process that continues until supply equals demand.

I find this kind of explanation unsatisfying for two reasons:

In the standard framework of competitive equilibrium, agents choose quantities (and view prices as fixed). And yet, the disequilibrium adjustment story here relies on price setting.
The explanation is highly informal. As a result, it is unclear what assumptions are necessary for it to hold and when we should expect supply to equal demand.

I would be very grateful if anyone could improve on this explanation.

Edit: what I am looking for is a rigorous story explaining why:

If the number of units that producers want to sell exceeds the number that consumers want to buy, the price will fall.
If the number of units that consumers want to buy exceeds the number that producers want to sell, the price will increase.

This is a very fundamental assumption in economics so I think deserves a good answer on economics SE (apparently, not everyone agrees, judging by the recent downvotes!)

The puzzle (for me) is how this can happen in an environment when everyone views the price as given (i.e. the standard model of perfect competition).


texts: Under the gold standard, how did the redemption of gold work in practice?

texts:
For example, in the US:

  In 1834, the United States fixed the price of gold at $20.67 per ounce, where it remained until 1933. (EconLib)

Does this mean that anyone with US\$20.67 could walk up to any bank in the US and demand an ounce of gold? Conversely, could anyone with an ounce of gold demand US\$20.67 in paper money from any bank?

Or were the rules of redemption more restrictive than that?


texts: would CPEC leave at least 10000 people jobless?

texts:
Some Indian newspapers quote a Netherlands based Russian analyst Yoana Barakova and say that CPEC will leave at least 10000 people jobless in Pakistan's Gilgit-Baltistan province.

The Indian media industry has a credibility crisis (plus here and here). Also, I know that India has a strong antagonistic attitude toward both Pakistan and China, and hence it is natural that their newspapers will print anything which has an anti-Pakistan whiff. The press conference seems to be administered by Indians. So, it is hard to trust their newspapers especially when it comes to any news related to either Pakistan or China.

Can anyone reflect on this analysis of Yoana Barakova and tell if the analysis is correct? Iow, would CPEC really leave at least 10000 people jobless? If YES, why?


texts: Does immigration help to sustain welfare in rich European countries?

texts:
There is a lot of discussions about immigration and its effect on economies lately in Europe, so I'd like to ask a question. Is it true that immigration helps to sustain welfare in rich European countries? For example, in the case of pensions, since life expectation is increasing and natality rates are decreasing in the richest European countries, the ratio of people receiving a pension to that of active workers (who pay those pensions with their taxes) is increasing. Since immigrants usually have a higher natality rate, they should help counteract this effect.

However, often people counter this argument by saying that immigrants receive much more money from welfare, than they return through taxes, for various reasons:

unemployment is much higher among immigrants than among natives
there are many irregular immigrants who still receive healthcare (if they go to an emergency room), but who don't pay taxes
etc.

Especially (but not only) in Denmark, this constant grievance has reached incredible levels. It seems to me baseless racism, but I'm not an economist, so I'd like to know:  are there studies which prove that the contribution to welfare from immigrants is a net positive? Are there studies that indicate that by blocking immigration, rich European countries would risk not being able to pay pensions in the future?


texts: The new Keynesian IS curve: What determines output?

texts:
The New Keynesian IS curve can be described by the following (log-linearisation around the steady-state):$$y_t=E_t(y_{t+1})- \frac{1}{\theta}(i_t - E_t\pi_{t+1}-\rho)$$
where $\displaystyle\frac{1}{\theta}$ is the intertemporal elasticity of substitution in consumption, $\rho$ the discount rate,  and the remaining terms have their usual interpretation.
In the book Dynamic Macroeconomics, by Alogoskoufis, in chapter 16 (page 461), the author states:

Recall that this is nothing more than the Euler equation for
consumption, supplemented by the assumption that all output is
consumed, and the same relation was derived in the new classical model [it's eq. 14.10]
of chapter14. However, in contrast to the new classical model, where
output is determined by aggregate supply, in this model, because of
staggered pricing, output is determined by aggregate demand. Thus, it
is the IS curve that drives output ﬂuctuations.

I do not understand in what way is the output being determined by aggregate supply in the free price setting, nor by the aggregate demand in the sticky prices one.


texts: Deadweight Loss Due to Taxes Represented on a Graph of the Market?

texts: Let's say a market is operating at equilibrium, with MSB=MSC, and a tax is imposed on the market. This would shift the supply curve to the left and cause a deadweight loss represented by the triangle on the graph. However, somewhere in a different market, the demand for a substitute good would increase and the surplus in that market will increase. Does that mean that some of the deadweight loss in the original market is canceled out by the increase in surplus in the new market?


texts:
For rebasing annual price index, we divide all price indices by the value of the new base year.
With quarterly price indices, there is not a single base year with the value 1.00. In the base year, there are 4 quarters and none of their values is 1.00. I calculated the average of 4 quarters, it is still not 1.00, something around 0.87.
How can one rebase the quarterly price index to another quarterly base year?


texts: I do not understand the notion risk premium. Let us suppose that John goes to the city by car, but he is thinking about not paying for the parking. If he is caught in the act he must pay the fine. How to interpret the risk premium for this game (not paying the parking)?


texts: Why does immigration boost the economy? (or does it not...?)

texts:
I'm a novice at macroeconomics, and trying to understand the effect of immigration (from developing nations) on the economy of a developed nation. Specifically, I am considering the effect when the nation itself does not have full employment.

So, from what I have read, immigration is a positive thing for the economy in general. The increase in workforce capacity means that production can increase, therefore exports increase, and therefore the economy grows.

However, what if the nation does not have full employment? In this case, there is already a section of society (let's say 5%) which is available to work. This would suggest that there are actually not enough jobs around, and so any immigrants arriving will also not have any jobs. If there had been any jobs for the immigrants to take, then employment wouldn't be at the 5% level. Despite this however, all developed nations have at least some level of unemployment, yet immigration is still beneficial. Why is this?

My suggestions are the following:

Immigrants from developing nations tend to be happier to take on unattractive jobs, which citizens of the developed country may refuse to do. Therefore, whilst the citizens remain unemployed and live off benefits, the immigrants will take on "newly created" jobs which would otherwise not have existed, boosting the economy.
The 5% unemployment rate is actually due to people who are sick / disabled / otherwise unable to work. Therefore, assuming the immigrants are able to work, again there will be new jobs created which would otherwise not have existed.
Higher immigration creates more competition for jobs, causing wages to decrease and allowing companies to pay their employees less. Therefore, the nation's companies make more money, and this causes the economy to grow.

Are any of these correct, or reasonable suggestions? Or are there any other thoughts? Thanks!

Alternatively, is my hypothesis that immigration typically boosts the economy not, in fact, correct?!


texts: Creation of Money - Hypothetical Situation II

texts:
Continuation off this line of questioning. If I issue an IOU, it would need to be fungible, transferrable, etc in order to be considered "money." Understood - My follow up questions are:

Remaining agnostic as to whether or not my Note Payable is money: Say my friend takes out a cheaper loan because he uses my Note as collateral. So his interest rate 10% => 7%. While it may not technically be money (not all collateral is), its silhouette remains. Thus, has my IOU not increased the money supply? How is this conceptually treated?
Let's assume my IOU IS money because I'm heavily trustworthy, etc. For example, ABS, MBS, some CDOs (effectively) trade as information-insensitive debt. How much of the Monetary Supply is created Endogenously (in private situations like this), vs. Exogenously (by the Fed, etc) ?


texts: Autocorrelation function of a random walk process

texts: What is the intuition behind the result that the autocorrelation function of a random walk process $y_{t}=y_{t-1}+e_{t}$ tends to 1 as $t\rightarrow 0$? Thank you.


texts: Do we really need accurate utility functions?

texts:
Knowing that a utility function's primary purpose it to be used as a tool to rank consumption bundles, I was wondering:

  "do we really need to be concerned with accurate identification utility functions or would simple structural assumptions do?"

The main argument against this would be that by using misspecified  utility functions we would end up with inaccuracy in estimation of demand.

But in terms of using it as an tool to index consumer welfare, does it really matter?


texts: Can we make any general statements about the impact of a single-payer healthcare system on an economy?

texts:
The topic of single-payer healthcare is enjoying a moment in the limelight in the US. A significant chunk of the population supports such a system, and more than a few presidential candidates have stated they do as well. As sweeping economic policies go, this one seems to be easier to analyze than many, given that there are a number of countries using such (or very similar) systems, including other Western democracies.

My main questions are as follows:

Does the theory and evidence indicate that single-payer improves the financial well-being of patients, and if so, how are those improvements distributed (how do the benefits differ at different income levels, e.g.)?
How does it affect the medical industry generally? Is there merit to the claims opponents of single-payer often make that it reduces innovation and technological advancement within the sector? How does it affect employment and wages of medical staff?
Beyond the obvious (higher taxes), what are the implications of such a massive government spending program?

I have no particular background in economics, but I imagine that this question will generate very different answers from different economic schools. I'd appreciate several perspectives, if possible!


texts: Textbook for macroeconomics (advanced undergrad)

texts:
I find that many contemporary macroeconomics textbooks are too applied, filled with examples, case studies and intuitive illustrations, often at the expense of quantitative rigour and therefore the depth of the understanding they convey.

Is there a canonical, quantitative textbook for central macroeconomic concepts and models? This should be preferably readable at an advanced undergraduate level.


texts:
William Quinn et al. in their Boom and Bust (Cambridge University Press) describe the causes of the Railway stock market bust in 1840s England.

The outflow of gold due to problems with the harvest prompted the Bank of England to increase its interest rate from 2.5 to 3 per cent on 16 October and then to 3.5 per cent on 6 November. Some commentators have suggested that the decline in railway share prices was attributable to these rises in the Bank of England rate – the Bank was in essence pricking the bubble.

My question is, how could bad harvest season make the Central bank to increase in key rate? From the description, it seems that the anything but the decrease in economic activity was needed. Also, how the increase in the key rate could could have made a contribution to the declining prices? At least in theory.


texts: Why should small open economies avoid interest rate policies?

texts: I've been taught that small economies open to capital flows should avoid manipulating interest rates because increasing interest rates will mean capital inflow which causes currency appreciation. Overall, interest rate policy causes exchange rate volatility. But why is the case for small economies? Why is the US or China less susceptible to this theoretical argument?


texts: Do wages differ in two perfectly competitive labour markets?

texts: I understand that within a single labour market, the wages would be the same between two workers as firms and workers are both wage takers, but what about when there is more than one perfectly competitive labour market: if the labour market for jobs A and B are both perfectly competitive, would the workers in A earn the same as the workers in B, provided that the two jobs are not the same?


texts: Fixed vs pegged exchange rate: What's the difference (if any)?

texts:
I am told very firmly by an economist that a pegged exchange rate is NOT the same thing as a fixed exchange rate. So what, if any, is the difference between the two?

Addendum: Here's one webpage about the difference. I am looking for simple explanation of the difference and ideally also some good and simple contrasting examples.

Add2: Robert Mundell has a lengthy classification here, but it seems to me that his distinction is not one of kind, but merely one of degree.


texts: Question about violating the zero conditional mean assumption

texts:
Question for y'all with a background in econometrics.

Does the zero conditional mean assumption rely on complete randomness in a trial when doing regression analysis?

For example, if I was testing the effect of a free training program on wage, and the men in the trial were randomly given x amount of months of training, but the women were not assigned randomly, would that be a violation of a ZCM? I am struggling to make the connection between randomness and ZCM at all, but it was pointed out to me by someone that it is in fact influential.


texts: Why did the EUR/USD go down immediately when the Fed cut interest rate?

texts: I was following the Fed’s decision on interest rates. I thought if there is an interest rate cut, the EUR/USD will go up but contrary to that it went down on 07/31/2019 immediately after the decision to lower interest rates. Some sites claim that the Fed didn't cut enough (50 basis points) as opposed to the actual cut of 25 basis points. I have been following the news for almost 3 months and no one expected a 50 basis point cut. Is there something I am missing?


texts:
Why do we just assume that the β is symmetric for a stock? Could it not very well be the case that the β has a larger leverage (covariance with the market) for example 1.2 in a bear (baisse) market and a lower leverage (covariance) e.g. 0.8 in a bull (hausse) market for an individual stock, or the other way around? This would mean that the stock drops more than the index when the index drops and gains less than the index when the index gains. Of course this is neither a rational investment compared to index nor is it by definition a covariance, but it looks from numbers and graphs that several stocks or investments do not have the same β during a bull/ gaining market compared to a bear dropping market, it will drop more than the market when the market drops and not even outperform the market when the market gains.
Or is that something that would be explained by the alpha value of the CAPM, meaning that the alpha is some individual characteristic of the company?


texts: Does inflation equal change in M1 or M2?

texts:
According to monetarism, inflation can be predicted precisely by the change in money supply and GDP growth.
Does "money supply" here refer to M1 or M2, i.e. does it include debts created by private banks?


texts: Why the historically narrow asset class purchases from QE

texts:
Let's begin by mapping out some context by assuming the following goals of implementing QE:

prevent dire systemic liquidity concerns
reach inflation targets
manage expectations in the private sector

If I'm not mistaken, the vast majority of QE has been government debt securities. However, in principle, any asset class could be bought under by issuing central bank liabilities.

Question

If my understanding is correct that any asset class can be bought by issuing a liability (central bank money), then why have we only seen government debt securities be purchased historically? Would a broader range of asset purchases not help the Fed with the goals of QE as listed in the above bullet points?


texts: Linear Probability Model Instead of Logit in Fixed Effects Regression

texts: In our panel data analysis we estimated a fixed effects linear probability model (LPM) instead of a fixed effects logit regression because our sample size was quite small (600 individuals) and the fixed effects logit decreased our number of observations hugely (to less than 200 at times), while our LPM kept much more observations. Likewise, our logit wouldn't converge as we had to include region indicators and very few people moved such that we had issues of small numbers in cells in logit. Is there a stronger way to explain/justify this, or a preference for linear probability models over logits more generally in panel data with fixed effects? We completed our analysis in Stata.


texts: Is there a difference between settlement price vs market delivery price or are they the same thing?

texts:
I've been learning about Futures Contracts on Khan Academy (The finance related forum on there is quite old and no one has replied to my questions in the past) and the instructor has used the term "market delivery price" in the first few videos and "settlement price" later on.

I assume they are the same thing, right? From my understanding, both terms mean "both the buyer and seller are agreeing on a price on a future date for the commodity".

If this is the wrong place to post this, please let me know and direct me to where it should be posted. Thank you so much for your time, everyone!


texts: Are there any books on economy of the medieval England?

texts: I would like to learn more about how the medieval economy in the UK worked. Are there any economists that research medieval society in the UK? Are there some good books on this?


texts: Solve the Ben-Porath Model (Optimal Control Problem)

texts:
Suppose we have a Ben-Porath style human capital investment model, in which the representative agent maximize her lifetime earnings: $$V(h, a)=\max \int_{a}^{R} e^{-r(t-a)}\left[ w h(t)(1-n(t))-px(t)\right] d t$$ s.t. $$\dot{h}(t)=z_{h}(n(t) h(t))^{\gamma_{1}} x(t)^{\gamma_{2}}-\delta_{h} h(t)$$, where the constraint is the human capital production function.
I try the current Hamilton and obtain the FOCs: $$w h(t) n(t) = \mu(t) \gamma_{1} z_{h}(n(t) h(t))^{\gamma_{1}} x(t)^{\gamma_{2}}$$ $$px(t)=\mu(t) \gamma_{2} z_{h}(n(t) h(t))^{\gamma_{1}} x(t)^{\gamma_{2}}$$ $$\dot{\mu}(t) =r \mu(t)-\mu(t) \left[\gamma_{1} z_{h}(n(t) h(t))^{\gamma_{1}} x(t)^{\gamma_{2}} h(t)^{-1}-\delta_{h}\right]-w(1-n(t))$$ $$\dot{h}(t)=z_{h}(n(t) h(t))^{\gamma_{1}} x(t)^{\gamma_{2}}-\delta_{h} h(t)$$ $$\mu(R)=0$$.
I have no idea how to solve this analytically and get the the optimal solution and the value function, which should be $$V(h, a)=w\left\{\frac{m(a)}{r+\delta_{h}} h+\frac{1-\gamma}{\gamma_{1}}\left[\frac{z_{h} \gamma_{1}}{r+\delta_{h}}\left(\frac{\gamma_{2}}{\gamma_{1}} \frac{w}{p_{w}}\right)^{\gamma_{2}}\right]^{1 /(1-\gamma)}\times \int_{a}^{R} e^{-r(t-a)} m(t)^{1 /(1-\gamma)} d t\right\}$$ and $$n(t) h(t)=\left[\frac{z_{h} \gamma_{1}^{1-\gamma_{2}} \gamma_{2}^{\gamma_{2}}}{r+\delta_{h}}\left(\frac{w}{p_{w}}\right)^{\gamma_{2}}\right]^{1 /(1-\gamma)} m(t)^{1 /(1-\gamma)}$$, where $m(t)=1-e^{-\left(r+\delta_{h}\right)(R-t)}$ and $\gamma =\gamma_{1}+\gamma_{2}$.
Update: I find that Christopher Taber's slide solves this problem. I follow his approach and get the $n(t)h(t)$ exactly the same as above. I then try to use the $n(t)h(t)$ to solve the differential equation of $h(t)$ given some certain $h(a)$, and get $$\begin{aligned} h\left(t\right)= e^{-\delta_{h}\left(t-a\right)} h(a)+\frac{r+\delta_{h}}{\gamma_{1}}\left[\frac{z_{h} \gamma_{1}}{r+\delta_{h}}\left(\frac{\gamma_{2}}{\gamma_{1}} \frac{ w}{p_{w}}\right)^{\gamma_{2}}\right]^{1 /(1-\gamma)}  \times \int_{a}^{t} e^{-\delta_{h}\left(t-s\right)} m(s)^{\frac{\gamma}{1-\gamma}} d s \end{aligned}$$. I then try to use $n(t)h(t)$ and $h(t)$ to get $V(h,a)$. However the result is quite messy and I fail to get the $V(h,a)$ as above.


texts: How to get details on all the models used for evaluating ACA?

texts: I am trying to track down the models and the underpinnings/details for them for models that may have been used to evaluate the ACA/Obamacare.  I am aware of Gruber's (proprietary) model, and am thinking that the Urban Institute's HIPSM model may have been used, but not sure if there are others.  Even for those two, it seems I'll need to do a good bit of research to figure out what's in them and how they work.


texts: log-linearize a forward looking variable (P/D) with recursive expression

texts:
I can solve the model in dynare but I need your help with the following problem: How does one derive a log-linearized expression for a forward-looking variable around the steady-state? For example, the price dividend ratio can be defined as
$\frac{P_t}{D_t} = E_t [M_{t,t+1}\frac{D_{t+1}}{D_t}(1+
\frac{P_{t+1}}{D_{t+1}})]$
The goal is to derive the relation between $\frac{P_{t+1}}{D_{t+}}$ and shocks / state variables at $t+1$, assuming that at $t$ the system is in steady state so $\frac{P_t}{D_t}$ is the steady state value C.
If we ignore the expectation and log-linearize it, I  get
$\log C = m_{t,t+1} + \Delta D_{t+1} + \log(1+\frac{P_{t+1}}{D_{t+1}})$
and clearly one can solve $\frac{P_{t+1}}{D_{t+1}}$ analytically (assuming that $m$ and $\Delta D$ are known functions of shocks/state variables).
But, isn't ignoring expectation imposing that the equality hold state by state, instead of on average?
Please advise, thanks!


texts: Constancy of current value Hamiltonian and numeric computations

texts:
I am playing with a simple, continuous time optimal growth problem to learn optimal control. The social planner chooses $c_t$ to maximize:
$$\int_0^\infty e^{-\rho t}u(c_t)dt$$
where
$$\dot k_t=f(k_t)-c_t,$$
$u$ is CRRA, $f(k_t)=k_t^\alpha$ and $k_0$ is given.

This has straightforward solution with optimal trajectory $(k_t,c_t)$ converging to stationary point $(k^*,c^*)$.

Numeric computations using a Python implementation of Ben Moll's MATLAB algorithm yield appropriate looking consumption-capital diagrams:

where the dashed vertical line represents the stationary point.

The optimization algorithm uses an approximation where, roughly speaking, there is a discrete guess for the value function, its derivative is approximated using its first difference and then approximate consumptions and costates are computed to update the value function.

The problem I am running across is when I try to evaluate the property that the current value Hamiltonian evaluated at the optimal $k$, $c$ and $\lambda$ should be constant. Following is a plot where values of $\mathcal H(k,c(k),V'(k))=u(c(k))+V'(k)[f(k)-c(k)]$ on the vertical axis depend on $c(k)$, the approximated optimal consumption and $V'(k)$, the first difference in the approximated value function.

As I understand from Chiang (1992), $\mathcal H$ should be constant but this is clearly not reflected in my plot -- all of my other plots are spot on. Am I making a mistake in my plot of the optimized current value Hamiltonian or is there some approximation error that is being magnified in my plot?


texts: Meaning of UK Employment Change Index - 3 Months Average

texts:
I am trying to understand the meaning of an economic index which is measured in the following way:

The value for month n is determined by calculating the average of the last 3 months (n, n-1, n-2) and subtracting the average of the previous (non-overlapping) 3 months (n-3, n-4, n-5).

I wonder if anyone has an idea as to how to isolate a certain month (that data is not published) or how to better "understand" the meaning of the value of a specific month - the economic meaning (difference between one month and another) is not that clear to me.

Thanks, Tom


texts: How is freelancing viewed under Marxism?

texts: 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?


texts:
I have an Euler equation $ (\frac{ c_ {t+1} }{c_t})^\sigma = \beta (1+r)$,where $c_t$ is the t period consumption,r is interest rate and $\beta$ is discount rate, and a budget constraint $\sum _{t=0}^\infty \frac{c_t}{(1+r)^t}=\sum _{t=0}^\infty \frac{y_t}{(1+r)^t}$, where $y_t$ is income.

My question is how to substitute Euler equation into budget constraint to get the following equation?

$c_t\sum_{j=0}^\infty\frac{[\beta(1+r)]^\frac{j}{\sigma}}{(1+r)^j}=\sum _{t=0}^\infty \frac{y_t}{(1+r)^t}$


texts: Has the "dismal theorem" practical implications?

texts:
The so-called "dismal theorem" asserts that we do not appropriately account for catastrophic scenarios which have very small probability of occurrence. It has been studied in details by Martin's Weitzman, notably in his article "Additive Damages, Fat-Tailed Climate Dynamics, and Uncertain Discounting".

The articles of Martin Weitzman rely on a large dose of mathematics, and my skills do not allow me to get everything, nor of course to question the reasoning and deductions of Weitzman. His conclusion is broadly that "The take-away message here is that reasonable attempts to constrict bad-tail fatness can leave us with uncomfortably big numbers" (p19)

I would like to know if there are actually any practical implications from this dismal theorem. In particular concerning climate change. I thought so until @Dole pointed out that the dismal theorem could also be used to justify trillions of dollars in investment in a anti-asteroid defense system. I would appreciate any insight on the conditions to apply this theorem, if it can ever be used. Any relevant literature would also help me.


texts:
I am trying to understand the fact that, given that the uncovered interest parity holds, a rise in dollar interest rates will cause the dollar to appreciate. Is this a good intuition?

Uncovered interest parity (UIP) is defined as ${R_F=R_$}+{({E_{F/$}}^e-{E_{F/$}}^c)}/{E_{F/$}}^c$ where $$ $$ $R_F$ is the annual return of foreign currency, $$ $$ ${R_$}$ is the annual rate of return (the interest rate) for holding dollars in a bank, $$ $$ ${E_{F/$}}^e$ is the expected exchange rate (how many foreign currency units could be bought with one dollar) in one year's time, and $$ $$ ${E_{F/$}}^c$ is the current exchange rate (also per dollars). $$ $$

Example. Supposing ${R_$}$ is 4%, ${E_{F/$}}^c$ is 0.67, ${E_{F/$}}^e$ is 0.69, the rate of return for holding foreign currency $R_{F}$ is 7%. But now, a rise in dollar interest rates (${R_$}$ is now 8%) it means I fix the rate of return on dollars at 7% and see how ${E_{F/$}}^e$ changes. Is that the correct intuition? I use this approach and get that ${E_{F/$}}^e$ is 0.66, which means the foreign currency appreciated, but that means the dollars didn't appreciate, which contradicts my original claim...


texts: The Sonnenschein-Mantel-Debreu results, what are the implications for macroeconomics?

texts:
I have always wondered why such a negative result such as Sonnenschein–Mantel–Debreu theorem (SMD) theorem is usually ignored or disregarded by practitioners, specially in macro.

The result roughly says that there is no deep empirical implications of the rationality assumptions when aggregated because the aggregate demand itself only inherits Walras' law and homogeneity of degree zero. The lack of empirical implications can be translated to the lack of identification and so we cannot hope to recover the underlying preferences from an aggregate demand setup as much of the cross-country empirical macro or calibration macro seems to try. For additional discussion of the importance of the SMD theorem, see this piece.

In sum what are the implications of the SMD theorem for macroeconomics.


texts: Self-selection bias during the course of experiments

texts:
Suppose you are running a randomized experiment to assess the effect of $X$, say some training program for unemployed people, on $Y$, say the chance of finding a job in the coming year. Suppose also that $X$ takes time : maybe it lasts for several month.

Because you randomize, you do not need to worry about self-selection bias initially. But during the course of $X$, some people will likely realize that $X$ is beneficial to them, and others may realize that they are wasting their time.

As a result, one might expect that among people who drop from the program, there is a higher proportion of agents for which the treatment effect would have been smaller. This might induce an over-estimation of the treatment effect.

My questions are :

Is this kind of bias discussed in the literature on randomized experiments?
Does it have a canonical name ?
Do researcher try to control for this, and if yes, how?


texts:
In last years I have read a lot about "Smart contracts".

But I cannot understand why we need bitcoin for this?
The old-fashioned US Dollar are not used in Smart Contracts?


texts: Competitive equilibirium of max utility functions

texts:
Apologies in advance if my terms aren't exact, I'm learning "Mathmatical Economoics" in the hebrew language and some of the terms don't translate well.

I was given the following question:
Two sellers are a part of an exchange market with two goods, each has the utility function $u(x,y)=\max(x,y)$. Assume the first seller starts with two units of product $x$ and one unit of $y$.

Find $(a,b)$ s.t seller two starts with $a$ units of $x$ and $b$ units of $y$, for which there is a competetive equilebrium.

Any guidence will be of great help! Thanks in advance


texts: How to solve a variation of Merton's optimal portfolio problem?

texts:
Does anyone know how to solve the following problem?

I have tried to solve this  but I'm lost since I have never dealt with a Stochastic Dynamic Programming problem with many variables.

$max_{c_{t},\phi_{t}}\ E_{0}[\sum_{{t=0}}^{\infty}\beta^t\ln(C_{t})]$

$s.t. \ W_{t+1}=(W_t-C_t)[\phi_tR_{t+1}+(1-\phi_t)R_f]$ with $W_{0}$ given

$R_{f}$ represents the gross return of a riskless asset and $R_{f}=(1+r)$ and $R_{t}$ is the return of a risky asset. $R_{t+1}$ is an $i.i.d.$ random variable with unkown cumulative distribution $F$.

I am supposed to solve the exersice using dynamic programming (bellman equation) by finding the optimal policy functions.  I need to prove that the optimal share of the risky asset, $\phi_t$, is constant.

I am also given a guess for the value function which is $V(W)=F+Gln(W)$.


texts: Is the standard of living of poor & middle class people higher than in the past?

texts:
I really hope this is not opinion based.  I am just looking for numbers, links, straightforward proof if possible that the lifetime we are in now, this decade, most of us are living better than in the past since the cost of living has increased and so has income inequality.

Are more people on welfare than any time in history for instance?


texts: What is the significance of the findings in Nagel's 1995 paper on Learning Theory?

texts:
This post concerns the findings in Nagel (1995). It is a bit outdated but nevertheless still relevant. She examines the Guessing Game, and how individual study-subjects behave in repeated games.
In her paper, she explains the behavior of the study-subjects in two different ways;

Behavior based on $\bar{X}$ from the previous games.
Behavior based on individual experience, under the umbrella term Learning-Direction Theory.

Where $\bar{X}$ is the average guess.

She formalizes her claim in the second explanation, in the following way;
\begin{equation}
    \text{a}_{it}=
    \begin{cases}
    \frac{X_{it}}{50}, \text{for } t = 1\\
    \frac{X_{it}}{\bar{X}_{t-1}}, \text{for } t = 2,3,4
    \end{cases}
\end{equation}
Where $a_{it}$ is called the adjustment factor. She then goes on, to define the optimal adjustment factor that comes from retrospective reasoning;
\begin{equation}
    \text{a}_{opt,t}=
    \begin{cases}
    \frac{p\bar{X}_{t}}{50}, \text{for } t = 1\\
    \frac{p\bar{X}_{t}}{\bar{X}_{t-1}}, \text{for } t = 2,3,4
    \end{cases}
\end{equation}
where $p$ is the factor used to adjust the mean. Ie. Guess $\frac{2}{3}$ of Mean.
This claim, is merely a descriptive model that explains how the study-subjects learn. And how they eventually adapt.
She finds empirical support from the experiments she makes.
This claim, insofar, is rather simple to grasp and is an important finding.

What I do not understand, is the importance of her first claim. In essence, what she finds is that there is a tendency, as the game is repeated, that the average guess moves towards equilibrium with differing rates depending on $p$.

How is this even an important finding? This is already the predicted Nash-Equilibrium, albeit, it is reached later than expected.


texts: How can nominal interest rates be negative?

texts:
It used to be (and perhaps still is) standard to teach in economics classes that the nominal interest rate cannot possibly be negative. So why have some nominal interest rates gone negative?
This includes not just interest rates on electronic reserves but also on government bonds.
Interest rates (1990-2020) of 10-year government bonds for Switzerland:

Germany:

Denmark:

Sweden:

Related questions:
The Swiss 10-year interest rate fell to as low as -0.975% in August 2019. I believe this means that if someone bought Fr 100M of these bonds, then in 10 years' time, they'd have lost Fr 9.75M and get back only Fr 90.25M.

Is it possible/plausible that the cost of storing Fr 100M in cash for 10 years exceeds Fr 9.75M (about US$11M)?

And even if storing cash were really so costly, why don't the holder(s) of Fr 100M have alternatives to buying Swiss government bonds? For example why aren't there banks that would gladly take those 100M as deposits at say -0.5% interest rate?


texts:
In economic theory we know that with the use of some calculus, Hotellings Lemma and Sheppards lemma we can derive a given firms supply function and in term its Profit function.

With data of a given firms costs, can we in fact get an accurate estimate of its profit function and supply function?


texts:
In the econ literature, what is the convention when it comes to (not) hypenating some common terms like:

first(-?)best, second(-?)best,...
best(-?)response?
...

The Economist suggests that "There is no firm rule to help you decide which words are run together, hyphenated or left separate" so I thought people here could be more aware of the conventions in econ than people, say, at http://english.stackexchange.com.


texts: Effects of an expected increase in the inflation rate on the market for loanable funds

texts:
I am supposed to answer a question in my economics class and was wondering if someone could explain it out for me. The question is,

  What is the effect of an increase in the expected inflation rate on the loanable funds market?

This question goes against what I was taught. I was taught about the Fisher Effect where the real interest rate is not effected by changes in expected inflation and that the quantity of loanable funds does not change with this rise in effect inflation. So, my instinctive answer upon reading the question would be to answer no effect on quantity or real interest rate and that there would be a rise in nominal interest rate. However, this was a multiple choice question and that wasn't even close to one of the answers.

I think I got the answer right by saying

  It decreases the demand for loanable funds, thereby increasing the nominal interest rate.

All of the answers involved a shift in the demand curve for loanable funds. My question is if anyone could explain to me why there would be a shift in the demand curve instead of what we would expect based on the Fisher Effect?


texts: A reference for most used utility functions in macroeconomic problems of intertemporal optimization

texts:
I'm looking for a reference with the most used utility functions in macroeconomic problems of intertemporal optimization. The reference should preferably include a list of properties of those functions, and of why they are usually used.

Any help would be appreciated


texts: Will periodical increasing and decreasing cryptocurrency supply peg cryptocurrency to dollar effectivelly?

texts: As far as I understand, in order to make cryptocurrency pegged to USD we need somebody to take the risks of exchange rates. So, if ratio CRYPTO to USD is at a given time 1CRYPTO:1,1 USD, then we increase cryptocurrency supply by 10% and it will return to 1:1 parity? And conversely, if at a given moment ratio is 1.1 CRYPTO: 1 USD, we decrease money supply by 10% and ratio will return to 1:1, is that right?? Increasing and decreasing amounts of cryptocurrency in existence in response to price fluctuations can effectively peg 1 crypto: 1 USD or not??


texts: More direct way to derive indirect utility function from expenditure function

texts: I have this general form for a expenditure function $e(p,u)=f(u)\cdot g(p)$ where $f(u)$ is increasing monotonic. How can I derive a functional form for an indirect utility function from this expenditure function?


texts: How do you define the market cap of an ETF?

texts:
I'm hesitating between these 2 solutions:

The conventional calculation:

MCAP = #shares * SharePrice

Perform the weighted average of the MCAP of each stock in the ETF

MCAP = sum(iStockWeight * iStockMCAP)

Thanks for your help.


texts:
I have data on "share in labor employed in manual occupations" for two years (i.e. 1980 and 2005) and looking to create the following dependent variable:
change in the share of labor employed in manual occupation over the period 1980-2005
Which is the appropriate method based on the definition in bold above?

Share in 2005 - Share in 1980

(Share in 2005 - Share in 1980)/(Share in 1980)

My best guess: given that I am dealing with "shares", method 1 would be appropriate.


texts: The second welfare theorem without monotonicity

texts: Are there non monotonic preferences that are strictly convex and continues but the second welfare theorem does not hold for them?


texts: Why do banks loan at APR < 6%, when they can invest that principal in ETFs?

texts:
I screenshot the picture beneath from HSBC HK's website. Scroll down a quarter of the way, and click on 'Rates' to download that PDF. I ask just about loans under my green horizontal line.

Canadian ETFs with MERs < 0.15% like  XUS (iShares Core S&P 500 Index ETF) can probably outstrip an APR of 6%.

Thus why would a wealthy bank loan at APRs < 6%?
Conversely, why don't they charge more than 6%? Why not charge the opportunity cost of loaning, that is, the APR gained from investing in a relatively safe ETF like XSP?

Furthermore, HSBC probably has PhDs in math like James Simons who can invest in alternative investments that can yield a higher rate of return for the same risk.


texts: Use Lag Operator to find Lifetime Budget Constraint

texts:
The budget constraint is

$c_t + \tau_t + s_{t+1} =w_t(1-l_t) +(1+r_t)s_t$

And assume

$\underset{t \longrightarrow \infty}{lim} \ \displaystyle{\frac{s_t}{\Pi_{i=1}^{t-1} (1+r_i)}} = 0$

Lag Operator $L$ is defined as $L \cdot x_{t+1} = x_t$

How can I get lifetime budget constraint using the Lag Operator?

Many Thanks!


texts: Incomplete and Intransitive Preferences: Reference Request

texts:
I've had the opportunity to read this blog post on incomplete and intransitive preferences and would like to cite it in a informal presentation. However I cant seem to find the author.

The main site seems extremely old, though I find this essay extremely insightful for someone at my level any guidance for who the author is appreciated.

The site link: https://cruel.org/econthought/essays/get/intransitive.html


texts: Intuition behind Real Money Demand and Real Money Supply

texts:
Standard undergraduate textbooks begin with an exposition of the  money market with the following equilibrium condititon:

$$\frac{M^{s}}{P}=L\left(R,Y\right)
$$

In the above, the LHS is what is defined as "Real Money Supply", and the RHS is defined as "Real Money Demand". My question is the following: does the fact that we divide the LHS by the price level render these two quantities in units of goods? Intuitively, I think these quantities represent the number of goods that can be bought for a given amount of nominal money. What are the units of these quantities?


texts: Charging a minimum increment on the second price in online advertising auctions

texts:
Many ad servers running GSP auctions tend to charge a $0.01 increment on the second price. I was wondering if there was any theoretical basis for this, or is it just a way for ad servers to make a little extra money at the expense of advertisers?

Although it probably wouldn't have much effect on incentives in practice, it seems that doing this breaks incentive compatibility in a true Vickrey auction, and breaks the equilibrium properties of a GSP auction.

I have heard the case made that this is a tie breaking rule, in which case what do you do when two bidders bid the exact same amount? You can't charge $0.01 extra because it would exceed their maximum bid. In which case this doesn't address the breaking of incentive compatibility.

Thanks


texts: How should one determine the proper number of lags in a time series regression?

texts:
I am using time series data in economic model estimation. I want determine proper lag for Error Correcting Model (ECM) model for example. I can check AIC, SC and HQ criterion for determine proper lag. But I am not sure about max lag that I must start with it. What is max lag for annual, quarterly and monthly time series.

Is max lag would be changed if I used another econometric approach for example ARDL, VAR or VECM?


texts: How does one derive the elasticity of substitution with implicit functions?

texts:
I would like to derive the elasticity of substitution. I'm aware that such a thread with a very straightforward explanation already exists, but my case is slightly different and I'm not sure how to differentiate the functions involved.

But let me first introduce you to my problem. I have to derive the elasticity of substitution
$$\sigma = \frac{f_1 f_2(f_1z_1+f_2z_2)}{z_1z_2[2f_{1,2}f_1f_2-f_{11}(f_2)^2-f_{22}(f_1)^2]}$$
where I have the following production function $y^0 - f(z_1,rz_1)=0$ for which $r$ is defined the following: $r=\frac{z_2}{z_1}$.

As I have already mentioned this problem is already perfectly solved in this thread: How does one derive the elasticity of substitution?

But now comes the clue in my specification, where I do not now how to proceed: I have to express $z_1$ as function of $r$, such that $z_1=g(r)$. The marginal rate of substitution can thus be expressed as follows $$MRTS_{21}=\frac{f_1(g(r),rg(r))}{f_2(g(r),rg(r))}$$
How can I derive the differential of $f(g(r),rg(r))$, which is the first step in the derivation of the elasticity of substitution. I somehow should use the theorem of implicit functions, but I'm not sure how..

I hope someone can explain this differential to me!

Cheers


texts: An explanation of the formula for the present value of an annuity

texts:
I'm reading a book that gives three formulas. In all of these formulas:

$x$ is the amount of money to be received in the future
$n$ is the number of years
$r$ is the interest rate.

The first is the present value of a lump sum: $PV = x / (1 + r) ^n$. Pretty self explanatory. Suppose I wanted $100$ dollars in $20$ years and could invest money at a $5\%$ rate of return, what amount of money would I have to invest today to have $100$ dollars in $20$ years? $100 / (1.05) ^{20} = 37.69$. Alternatively, if I have $100$ dollars today and it depreciates at the rate of $5\%$ a year for $20$ years, it would be worth $37.69$ dollars in $20$ years.

The second formula is the formula for the present value of a perpetuity: $PV = x / r$ ($x$ is the amount of money to be received at the end of each year forever. So getting $100$ dollars at the end of each year forever would be the same as getting $2000$ dollars today, assuming I can invest that at the rate of $5\%$ per year.

The third formula appears to combine the two: the formula for the present value of an annuity: $PV = (x / r) - ((x / (1 + r) ^ n) / r)$ ($x$ is the amount of money received at the end of each year for $r$ years).

Notice that the left hand side is exactly the formula for the present value of a perpetuity. The right hand side is the present value of a lump sum divided by $r$.

I'm trying to understand the third formula. How would someone derive it? Why do we subtract the present value of a lump sum from the present value of a perpetuity? I understand intuitively that an annuity must have a lower present value than a perpetuity. If $r = 20$, there needs to be some way to indicate that payments stop after $20$ years. I'm just not sure how this is incorporated into this formula.


texts: Can small countries use a foreign currency as their official currency?

texts:
Having one of the "big currencies" (US-Dollar, Euro, Japanese Yen) is of several advantages:

Tourism: There is a huge amount of people who can directly use it (317*10^6 US citizens, 337*10^6 people in the Eurozone, 128*10^6 Japanese).
Trade barriers: I guess trade might also get easier, at least for small companies.
Reliability: Citizens and companies can probably trust more in the value being stable of those 3 currencies than smaller ones.
Security:  I'm not too sure about the Dollar / Yen, but Euro bank notes have quite a lot of security mechanisms which make the forgery of banknotes harder.

Especially for small countries, I would guess having one of those big currency would have the advantage of not having to pay for producing the bank notes / coins.

So why do contries like Seychelles (Seychellois rupee), São Tomé and Príncipe (São Tomé and Príncipe dobra), Cape Verde (Cape Verdean escudo) ... have their own currencies? Can you give one example which shows the effect if such a country took one of the big currencies?

Are countries not allowed to use another countries currency officially?


texts: Has any progress been made on the Pacman Conjecture on Finite Time Horizons?

texts:
The Pacman conjecture states that the optimal strategy for monopolistic durable goods manufacturers is to set price high and slowly drop it (i.e. eating their way down the demand curve).

Empirically this seems to hold as it's the strategy employed by virtually all intellectual property producers (book publishers, movies, video games, software, etc). Microsoft has gone so far as to charge over \$100 at the time of release for pre-orders, and nothing for the same title 12-18 months later on Xbox Live. (I know, I know, the plural of anecdote is not data, but given the trend at brick and mortar retailers as well, I feel safe making the assertion).

Is this a function of the lack of spoilage/storage costs (i.e. IP lasts forever in the US [practically], and has almost no marginal cost to reproduce), such that it wouldn't work with cars, and if so, why are the same model year cars frequently sold at substantial discounts after their initial release.

It seems to have been going on long enough that literally every car buyer should be aware they can get the same car substantially cheaper in six months, yet people continue to consume both large physical durable goods and IP-related goods almost immediately upon their availability.


texts: Why do people think a stock should have a certain price based on the company's revenue?

texts:
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?


texts:
Is it possible for a social choice rule to simultaneously violate the condition of non dictatorship and weak pareto property?
Non dictatorship is when there is no individual such that if he prefers x over y, then so does the society irrespective of what the society feels.
And Pareto property is that if all individuals prefer x over y, then so should the society. It is about how society preserves total agreement.

I don't think it's possible because of the following reason.
Now, if we have dictatorship and rest all also agree with him, then society is essentially preserving that opinion (so Pareto property satisfied).
On the other hand, if Pareto property is not satisfied, ie total agreement of x preferred over y by each individual doesn't not lead to society choosing x over y, this means there is no individual such that if he prefers x over y, then society prefers x over y. So non dictatorship is satisfied.
Please see if this line of thought is correct.


texts: Non parametric and parametric tests of martingale?

texts:
A martingale is a model in which the expectation for the next value is equal to the presently observed value, even given knowledge of prior values, ie

$E(X_{n+1} |X_1, X_2, ..,X_n)=X_n$

What tests for testing if a time series is a martingale are available? I am particularly interested in non-parametric tests. Is there any relation with conditional moments literature?


texts:
The classical supply and demand theory states that prices and quantities of a given good (in a perfectly competitive market) are determined by the supply and demand of that good, a shift in the demand curve, for example, would change the equilibrium prices, but how exactly does that work, can't imagine a firm owner saying 'Ok guys, the supply curve for our product shift to the right, time to raise prices"

I can grasp how a price above the equilibrium would go down (the producers would not sell, so they lower the price because less profit is better than no profit)

But how can an increase in demand drive prices up?


texts: Are state owned enterprises really inefficient?

texts:
The typical right wing/free market argument, that leads to privatisation of government assets is that the government assets will be far more efficiently managed when in the hands of profit seeking capitalists, rather than being owned by the government.

Certainly it's fair to say that government departments are inefficient - a department that is directly funded by the government can't go bankrupt, so long as the government keeps funding it.

However, for a SOE the company still needs to stand on its own right, the SOE doesn't receive funding directly from the government.

The SOEs management structure is exactly the same as a privately owned company, except that the government is choosing who the board of directors is.

So the question is, unless the government is electing a board of directors that have different priorities to profit seeking capitalists, how is it that a SOE would be less efficient than a privately owned company?

Is there any research showing that SOEs are less profitable than privately owned companies?


texts: Oligopoly kinked demand graph doesn't make a sense to me

texts: Hello, so in class I learned about the kinked demand curve in oligopoly. Our teacher said that under the sticky price, the demand is inelastic. However, I don't understand how the demand can be inelastic when the marginal revenue is still positive.


texts:
I lost a 100 dollars bill in the laundry (it was destroyed).
I clearly lost 100 dollars.
Where are they now? Who won 100 dollars?


texts: Was there resistance, historically, to the idea that human behavior deviates from rational decision making theory?

texts:
I have edited this question considerably to narrow the focus.

A recent New York Times article was published on the Nobel Prize for Economics. The article discusses that Nobel laureate Richard Thaler was responsible for a push to account for human behavior in economic models:

  ...He showed that people depart from rationality in consistent ways,
  so their behavior can still be anticipated and modeled.

What is the historical context of resisting including these data in older models and what has influenced the paradigm shift?

More broadly, I am most interested in the question of why there was resistance historically in economic models when there is empirical evidence (cognitive neuroscience, psychology) going back for decades indicating that humans, in certain contexts, make decisions that may deviate from various definitions of "rational" choice. If this is not out of scope for this site (as pointed out in the comments) I would also like this to be a part of the answer to my question.


texts: Diminishing returns and economies of scale

texts: I was wondering whether these are contrary as one effectively says production becomes cheaper as production increases. To increase production you may need to upgrade from a standard machine to high capacity (like if a seemstress wanted to go from making friends clothes to a small buisness) which would cost alot more to produce more (diminishing returns). I know they are uneven but I'm I going wrong somewhere? Is diminishing returns an advantage of smaller buisnesses?


texts: Market price, output that maximize the price and level of firm profit after applying a license fee

texts:
I'm currently working on a problem that says the following :

At first we had a number N of firms in perfectly competitive industry,the exercice gives us the total cost and the Market Demand with p as the market price . After studying this case ( Consumer surplus, market equilibrum and firm profit ) the exercice adds the following :"The government decides that each firm in the industry must pay a license fee of 12 per period, whether they produce an output or not " and from this we should find the market price and what output maximizes firm profit and level of firm profit.
I don't know how to interpret the license fee, is it a tax? the only exercises i've seen so far are with a per unit tax applied to the producer .


texts: Reference recommendation on the causal relationship between family size and children's educational attainment, or the quantity-quality trade-off

texts:
I am currently reading both Poor Economics and Factfulness, and two seemingly contradictory statements jump out at me.

From Factfulness, and I am kind of taking this statement out of context, but it suggests that there is a quantity-quality trade-off between family size and children's educational level (independent of whether the mother is more educated):

  Educated mothers decide to have fewer children and more children
  survive. More energy and time is invested in each child’s education.

  Rosling, Hans. Factfulness (p. 69). Flatiron Books. Kindle Edition.

However, from Poor Economics, the authors also discuss studies on the same issue, and seem to suggest that there is no relationship at all:

  Of course, these three studies alone may not be the last word, and
  there is certainly a need for more research, but for now, our reading
  of the evidence, contrary to what Sachs argues in Common Wealth, is
  that there is no smoking gun to prove that larger families are bad for
  children.

  Banerjee, Abhijit. Poor Economics: A Radical Rethinking of the Way to
  Fight Global Poverty (p. 110). Perseus Books Group. Kindle Edition.

I understand that more research needs to be done on the "quantity-quality" trade-off. Poor Economics provides reference to the three studies it examined that found no trade-off, while I found a few studies online that supports the trade-off.

All the references I have seen so far are single-country studies. Is there a cross-country studies, across wide cultural and income regions, that can shed more light on this family-size effect? what are some of the latest development in this research?


texts: The Principle of Optimality and the Bellman Equation

texts:
Given (1) and (2), is it possible to show the existence of a Bellman equation (3), using Bellman's Principle of Optimality?

$$\ max \Sigma\beta^s U(C_t)$$

Subject to the following resource constraint:

$$C_t + K_{t+1}= F(K_F, E_F,S_t)$$

Where:
$$E_t = F_E(K_E,E_2,R_t, R_{t+1})$$
$$S_t = \Sigma(1-d)E_t$$
$$R_{t+1}=R_t -E_t$$
And the Bellman equation is given:

$$V_t (K_t,R_t,E_t)= max_{C_1,K_2,E_1,E_t} {U(C_t)+\beta V_{t+1}(K_{t+1},R_{t+1},E_{t+1}) + \lambda_2 (F_2 (K_2,E_t-E_1)-E_t)}$$

This problem is taken from eq. (27) and eq. (39) of the following textbook: https://are.berkeley.edu/~traeger/pdf/KarpTraegerDraft.pdf.
The specified parameters in the model are:

Consumption $C_t$
Capital $K_t$
The energy sector $E_t$
The carbon stock $S_t$
The finite resource $R_t$

Would genuinely appreciate being able to see how this is conducted on this type of model.


texts: Value representation theorem for countable set

texts:
How can we prove the following:  if a relation $R$ is a weak order on a set $X$ and $X_\sim$ is finite, then there exist a function $v:X\to \mathbb{N}$, which is a value representation of preference relation $R$.

Here I know the construction of the function $v$ when the range is the set of real numbers (as $X_\sim$ is countable). But,I am confused  when the range of $v$ is the set of natural numbers.

Could anyone please help me?


texts: How to show that a homothetic utility function has demand functions which are linear in income

texts:
A homothetic utility function is one which is a monotonic transformation of a homogeneous utility function.

I am asked to show that if a utility function is homothetic then the associated demand functions are linear in income.

In general if $H$ is monotonic and we compose it with a function $g$ which is homogeneous we get $H(g(x,y))$ which is homothetic and so the ratio of derivatives of $H$ with respect to $x$ and $y$ is the same as the ratio of the derivatives of $g$ with respect to $x$ and $y$ since the outer function cancels out. This means all income expansion paths are rays from the origin and the slope of indifference curves (level sets) have the same slope along the income expansion path.

My question is how does one show generally that the demand functions are linear in income? If you don't have the functional form of the utility function then what can you substitute into the budget constraint to solve for $x$ or $y$ as functions of prices and income only?

All you know is that the negative ratio of derivatives is equal to $p_1/p_2$ but you can't substitute anything into the budget constraint for $x$ or $y$ since you only have general partial derivatives.

The only way I can think to do that is take the inverse of the derivative of the inner (homogenous) function g in order to solve for $x$ (or $y$).


texts: Mean Variance Optimization in a Utility Maximization Framework

texts:
I'm struggling to gain a broad understanding of Mean-Variance utility theory as it relates to finding the efficient frontier of a group of assets which each have some return and variance.

The typical mean-variance utility function is given by

$U(x) = E(r) - \frac{\alpha}{2}Var(r)$

where $\alpha$ is some risk aversion parameter. The generally accepted way to find the efficient frontier is to minimize the following equation (https://en.wikipedia.org/wiki/Modern_portfolio_theory):

$Var(r) - q E(r)$

where, here, $q$ is a risk tolerance parameter - increasing the value of $q$ pushes us out onto the frontier.

At first, I thought that the equation to be minimized was just the negative of the utility function, but the negative of the utility function is

$-U(x) = \frac{\alpha}{2}Var(r) - E(r)$

I understand that the $\frac{1}{2}$ is simply a quadratic programming construct, but I don't know how we can change the risk aversion parameter, $\alpha$, to a risk tolerance parameter, $q$, and slap it onto $E(r)$. This makes me think that I am missing  something significant in this framework as it relates to utility, indifference curves, and the frontier. Hoping for some clarification.


texts: Why is elasticity not constant on a straight line graph?

texts: There are different zones of elasticity on a graph, but if we are to imagine a negatively sloped, straight line on a price v quantity graph, we find that elasticity differs based on where we look on the graph. Why is this the case, rather then elasticity being constant?


texts: What are some different methods for pricing electricity?

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

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

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

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


texts: Where to start, to know the cost, in hours of work, necessary to produce one more car (or any other good)?

texts:
Let's say I want to buy a car. It costs that, so I can know that, for example, I have to work 3 months to pay for it. But does the car really needs three months of human work to be build?

What is the real cost of a car in terms of human work? More specifically : What is the marginal cost of a car in terms of human work?
What does it take build just one more car? And I don't want to include the cost of building the factory, the R&D, or other similar things.

As a first approximation, I could take its cost, and divide by the average hourly wage in the country. But this would include profit, taxes and other things unrelated to just building the car. And it would not take into account that the raw materials have been extracted and processed in an other country, with higher or lower hourly wages.

This is how I would try to find out :
Consider the car factory as a black box : we don't care what's going on inside, we just care about input (work, energy, parts, raw materials...) and output (cars, by products, garbage, pollution...).

We divide the input by the number of cars produced, and get a first partial answer :
To build one car we need :

X hours of work
Y tons of steel
Z kWh of electricity
...

and we repeat these steps, recursively, with the steel factory, the power plant, etc. until we get to the raw material/mining industry.

We unfold the tree :

X hours of work
Y tons of steel

N hours of work
M tons of dirt
...

Z kWh of electricity

P hours of work
Q tons of coal
...

...

So in the end, we know there is X + N + P + ... hours of work in that car (and some free natural resources).

And what about the same question for a t-shirt? A loaf of bread?

I realise it takes a lot of work to answer this question. It probably involves analysing a big part of the world economy, maybe the factories are reluctant to give this type of information, and by the time you're done, the processes may have changed so much that you have to start over again.

But still, I think it's an interesting question, and I feel it would help everyone to understand the world.

Has anyone ever attempted this? Is there a book? A database? A Ph.D thesis? A paper?
Or maybe the question should be reformulated?