texts: Why does competition work for capitalism?

texts:
As far as I know, capitalism is based on competition:
If two(or more) companies produce similar products that compete against other, these companies are in a competition.
Because the objective of a company is to earn as much money as possible, the company will try to maximise the selling of their product. However, because normally there are more than a single company, every company has to sell their best possible product for the lowest price without making enough profit. That leads to a situation where the consumer gets a very good product for a very fair-realistic price.

My problem here is, that this only works if every company only can make the decision about what price they make for what quality once. Like in the prisoner's dilemma.
The prisoner (the company) will (usually; if he is sane) make the decision to betray his member (->Game Theory).
The point is the ideal strategy changes if this 'game' will be repeated forever (is identical to a situation where nobody knows, when the game ends). The strategy any sane prisoner would take is to not betray his gang-member, however, if his member betrays him he will betray him, too, until his member does not betray him anymore.
Because this is a simplified version of a real competition, real companies should act like the prisoners: make a high price until the competitor make a low price. However, no company would make a low price because although they would make better profit in short term, the company would make better in longterm if they made the unspoken deal with the other companies.

So why is it not like this in real world, or is it like this and I haven't noticed that yet?


texts: Nominal Growth rate above Nominal Interest Rate

texts:
I'm reading Ray Dalio's "An In-Depth Look at Deleveragings", and at one point he's talking about central banks providing liquidity and credit support, and he states:

  "This produces relief and, if done in the right amounts, allows a
  deleveraging to occur with positive growth. The right amounts are
  those that a) neutralize what would otherwise be a deflationary credit
  market collapse and b) get the nominal growth rate marginally above
  the interest rate to tolerably spread out the deleveraging process."

I'm not sure I understand point b here. Could someone explain the interplay between nominal growth rate and nominal interest rate, and how they affect the deleveraging process?

Thanks!


texts: Why wasn't the wage of the entrepreneur included in explicit costs?

texts:
I was solving an economic problem (I was calculating explicit and implicit costs) and noticed one interesting thing:
In the said problem, the entrepreneur set himself the wage of 10 000 rubles AND in the solution said wage was NOT included in explicit costs. But his old wage (before he started his own business) was included in implicit costs(By the way, his old wage was 12 000 rubles).
This puzzles me because although he owns the business, he's also its employee. And if he is his own employee, his wage must be accounted as a wage of any other employee. I don't think that an accountant would make an exception for him. Besides, if he decreased his own wage, then expenses of his business would decrease and consequently, its profit would increase.


texts: Game theory for showing interest and availability when dating

texts:
The more cynical (or perhaps realistic) of us would argue that there's a fair amount of game theory going on in the dating game.

For example a classic ploy is 'Don't ring for three days, because you don't want to come across too keen'.  Of course this rule is now widely considered obsolete (as would be natural in any game).

A fairly straight forward hypothesis I would put forward is:

Everybody in the dating game is looking to get hitched with their highest possible value match.
By conveying unconditional interest in the other partner, you let them know that they can safetly 'get you' and so it's safe to pursue higher value mates knowing that they can score at least as highly as you.
Therefore, the smarter strategy is to not let your dating interest know how available you are for them, so that they are incentivised to make commitments to you.

Now I know, this seems like a deeply cynical and flawed way of thinking. I'm not looking for a social criticism of this thinking. Rather I'm interested if there have been any studies carried out, where by the attractiveness of someone is assessed according to the availability they've communicated, etc.


texts:
Let $x \in [0,1]$ denote some state (e.g. market share).
Let $i \in \{1,2\}$ denote an agent (e.g. firm).
Im considering a model where payoffs $F_i(x)$ are perfectly invertible in the sense that the payoff functions can be mirrored along the line $x = \frac{1}{2}$ with $F_1(x) = F_2(1-x)$. Take $F_1(x) = x$ and $F_2(x) = 1 - x$ for instance.
Is there a fixed term for these kind of games. It has somewhat a zero sum flavor, because preferences are perfectly opposing. Firm one wants increase its market share, and firm 2 wants to decrease the market share of firm 1 in the same manner.
I can think of Hotelling or a linear city. But is this the most generic characterization?
Or, even better, is there a mathematical term for this kind of functions which are mirrored along a fixed line?

Edit: Example Consider the following advertising differential game defined by $(x,u_1,u_2) \in [0,1] \times \mathbb R_+ \times \mathbb R_+$
\begin{align}
&v_1(x_0) = \max_{u_1}\int_0^\infty{e^{-t}(x - u_1^2/2)dt}\\
&v_2(x_0) = \max_{u_2}\int_0^\infty{e^{-t}(1 - x - u_2^2/2)dt}\\
\text{s.t.}\quad & \dot x = u_1 - u_2
\end{align}
$x$ is the market share of firm 1, and $u_i$ is the respective advertising effort.
A stationary feedback Nash equilibrium $(\phi_1(x), \phi_2(x))$ solves a coupled system of Hamilton-Jacobi-Bellman equations
\begin{align}
&v_1(x) = \max_{u_1}\{x - u_1^2/2 + v'_1(x)(u_1-\phi_2(x))\}\\
&v_2(x) = \max_{u_2}\{1 - x - u_2^2/2 + v'_2(x)(\phi_1(x)-u_2)\}
\end{align}

It turns out that $(\phi_1(x), \phi_2(x)) = (1,-1)$ is the unique Nash equilibrium with associated values
\begin{align}
&v_1(x) = x - \frac{1}{2}\\
&v_2(x) = \frac{1}{2}-x\\
\Longrightarrow \quad &v_1(x) = v_2(1-x).
\end{align}

How would one characterize the class of games in general? Symmetric antagonistic?

I may propose the following definition:

  Let $(\phi_1(x), \phi_2(x))$ solve
  \begin{align}
&v_1(x) = \max_{u_1}\{F_1(x,u_1,\phi_2(x)) + v'_1(x)f(x,u_1,\phi_2(x))\}\\
&v_2(x) = \max_{u_2}\{F_2(x,\phi_1(x),u_2) + v'_2(x)f(x,\phi_1(x),u_2)\}.
\end{align}
  A differential game is symetrically antagonistic if
  \begin{align}
v_1(x) = v_2(\overline x - x) \quad \forall x \in X
\end{align}
  where $\overline x := \max X$.


texts: Best texts on cash usage and share buybacks in companies

texts: What would be a good reference for how companies utilise their cash to conduct share buybacks. I am trying to understand how share buybacks affect the valuation of a company.


texts:
came across a problem set that I had no clue how to tackle, but looks painfully simple.

It's a market for electricity where households utility is represented by:

U(E) = aE - 2mL2 (Household Utility)
C(E) = wE + FC (Firm cost function)

Where E is quantity of Electricity and L is daylight available at the households, and FC is a fixed cost, with a,m,and w being constant variables. The problem required deriving the Demand and Supply Curves and then getting the Competitive Equilibrium values for price and quantity as a function of the variables.

Typically, with a two good market, I would derive the marginal utility and equate them over their prices to obtain a value for one good and substitute that into the income constraint to get the demand as a function of one good. However, I can't work this out at all! Daylight doesn't have a price and I'm at a loss for how to derive demand. Similarly with Supply, if I take MC = w, would the supply curve simply be w?

Thanks for all of your help!


texts: Did capitalism exist before the 18th century?

texts: Were there capitalistic economies before the 18th century?


texts: Utility Functions: Implying endless consumption?

texts:
Do utility functions imply that if a consumer's income infinite, his consumption should also be infinite? The reason why I'd think this is the case is based on my basic understanding of utility functions.

Recall your cobb-douglas style utility function:

$$U(x_1...x_n)=\prod_{i=1}^nx_i^{\alpha_i}$$

where $0<\alpha_i<1$ and $\sum_{i=1}^n\alpha_i=1$

If our consumer is utility maximizing he should spend all of his income in a given period or even over multiple periods.

A practical application would be to answer the question of whether or not consumption growth in consumption (C) in the GDP equation can grow holding the number of consumers in an economy fixed as argued on the my answer Can an economy grow without its population growing?.

Thank you to   Kenny LJ for inspiring this question.


texts: Is "technical chart analysis" for stock development something that is scientifically supported?

texts: I assume the answer is "no" because if you can predict the development of a stock then people would get very rich. However there are so many YouTube channels and web sites where people talk about things like Elliot Waves and other theories.


texts: Job-finding rate in an urn-ball model with types

texts:
Setup Say you have two types of workers, high and low. The share of low-types among the unemployed population is $P$. I want to find the job-finding rate for these types.

Matching Matching is through an urn-ball model: Each unemployed has one single ball (application) that he tosses at random into an urn (vacancy). Each vacancy will then have $ x \in [0, \infty)$ many applications, mixed from both types. The vacancy will pick a high type (at random) whenever there is one, otherwise it will pick randomly among the whole (low-type) pool of its applicants. Denote by $g(x)$ the probability mass function of a vacancy having $x$ many  applications.

Job-finding rates The average pool job-finding rate of each pool is equal to the likelihood of a specific unemployed of that pool of finding a job.

Consider the matching-rate of the low-types: Denote $P(M)$ probability of a specific low-type matching, $P(x_h = 0)$ the probability of a vacancy unconditionally having zero high-types. Then, the low-type's job-finding rate is

$$ P(M) P(x_h == 0| M) \frac{1}{E[x | x_h == 0 \wedge M]}$$

A specific low-type will only find a job if

he matches
everyone where he matched was of the low-type (no high-type matched)
and then, with the inverse rate of people that on average matched wherever he matched (if there's 10, he has a 1/10 chance of getting the job)

That's at least what I thought. Denote $P(M) = 1$, people toss a ball that always lands in one urn. Say $g(x) = 1/4$ for $x\in [0, 3]$: The tossing is in a way that applications are equally distributed over vacancies with boundaries 0, 3.

I think that

$$ E[x | x_h == 0 \wedge M] = \sum_x P(x | x_h == 0 \wedge M) x \\
= \frac{1}{P(x_h == 0 \wedge M)}\sum_x P(x \wedge x_h == 0 \wedge M) x$$

Where we can rewrite

$$ P(x_h == 0 \wedge M) = \sum_x P(x_h == 0 \wedge M \wedge x)\\
= \sum_x P(x_h == 0 | \wedge M \wedge x)$$

As I said, $P(M) = 1$, and $P(x_h == 0 | \wedge M \wedge x)$ is the binomial chance of drawing $0$ high-types out of $x-1$ applications with probability $1-P$. All sums start at $x=1$.

With the numerical example I gave, and $P=0.5$, I have

E[x | x_h == 0 \wedge M] = 1.57
P(x_h == 0| M) = 0.583

and the total job-finding rate of the low-type is roughly 0.371

Is this the best way to proceed? I'm somewhat worried that my number is not clean (and I can't really represent it as a rational number), while the problem as I've set it up is pretty symmetrical.

Check using corner-case When I set $P = 1$, the job-finding rate of the low-type becomes $0.5$. I think that's wrong, because 1/3 of applicants get a vacancy with 1 applicant, 1/3 with 2, and 1/3 with 3. That means, they have a 1/3(1+1/2 + 1/3) chance of matching, which is 11/18, roughly 0.6 - and not $0.5$.

Is there a different test I could do, or a different (simpler?) way to calculate the job-finding rate of the low type? Is my expression just blatantly false?


texts: Reliable US yearly population and netmigration estimates by state from 1970 up to today

texts:
I am looking for US data on population and net migration by state and year from 1970 up to recent years (2015, 2016, 2017)?

Is there a reliable, clean and integrated/compatible source?

For 2010 to 2017 I found this US Census State Population Totals and Components of Change: 2010-2017 website. Is there anything similar for previous periods?

Other sources I considered that are not adequate:

Net Migration   Patterns for US Counties: only decennial
Census::CPS Historical Migration/Geographic Mobility Tables: does not disaggregate by state


texts: In what contexts are stable markets sub-optimal?

texts:
My understanding is that market stability is a good thing, because it allows more reliable estimates of profits (revenues minus expenses) and expected return-on-investment related to new investments.
But in a recent article about Goldman Sachs' 4th quarter losses, with a 75% in commodities trading revenue as the greatest factor.
In the a BBC article, the firm reportedly framed the losses as:

Goldman has blamed the problems on unusually calm markets, which can dampen demand from clients looking to take advantage of fluctuation.
Executives have pledged to improve the business, which accounts for a large portion of the firm's overall revenue.
Investors, however, are growing impatient.
SOURCE: Goldman posts first quarterly loss in six years (BBC)

See also: Goldman’s Commodity Revenue Drops 75% to Lowest on Record
- In which contexts are stable markets sub-optimal?

I'd also be interested in information how firms and governments can work to destabilize markets to create profit opportunities.


texts:
Find Pareto optimal allocations and the core for the following economies
Consider an exchange economy with two agents and two goods. Let consumption sets are the nonnegative orthant. Agent 1’s utility is represented by $x+y$ and agent 2’s utility is $xy$. Endowments are (e,0) for agent 1, and (0,e) for agent 2 with  > 0.
When I find MRS and equalize them, I am going to find $x_2=y_2$  This is interior point (contract curve. ). By feasibility constraint, $x_1=y_1$.
Its core is given as follows. Why?

How can we find (determine) core? What it’s appropriate calculation to find core? For example, why we assume $e/2$?


texts: Balanced Growth Path (Qualifier Question)

texts:
$\textbf{Full disclaimer:}$ I am studying for my candidacy exams and this question is from one of the exams last year.

$$max\;\sum_{t=0}^\infty \beta^t \frac{c_t^{1-\gamma}}{1-\gamma}$$Subject to the following constraints:
$$c_t+i_t=y_t$$
$$y_t=A_tk_t^\alpha$$
$$k_{t+1}=(1-\delta)k_t+i_t$$
$$ln(A_{t+1})=ln(A_t)+\mu$$
$$c_t,k_{t+1}\geq 0$$
(b) Compute a balanced growth path in which capital, consumption and output grow at constant rates. On the balanced growth path
(i) What is the growth rate of capital?
(ii) What is the growth rate of consumption?
(iii) What is the growth rate of output?
(iv) What is the ratio of capital to output?
(v) What is the ratio of consumption to output?

$\textbf{My work:}$
Combining the constraints we get:
$$c_t=A_tk_t^\alpha+(1-\delta)k_t-k_{t+1}$$
Taking two terms from the objective function we get:
$$...+\beta^t\bigg(\frac{\big(A_tk_t^\alpha+(1-\delta k_t-k_{t+1}\big)^{1-\gamma}}{1-\gamma}\bigg)+\beta^{t+1}\bigg(\frac{\big(A_{t+1}k_{t+1}^\alpha+(1-\delta k_{t+1}-k_{t+2}\big)^{1-\gamma}}{1-\gamma}\bigg)+...$$
Differentiating w.r.t  $k_{t+1}$ and substituting consumption back in we get:
$$c_t^{-\gamma}=\beta\bigg[\alpha \bigg(\frac{A_{t+1}k_{t+1}^\alpha}{k_{t+1}}\bigg)+(1-\delta)\bigg]c_{t+1}^{-\gamma}$$
$$\implies \frac{c_{t+1}}{c_t}=\bigg[\beta\bigg(\alpha\bigg(\frac{y_{t+1}}{k_{t+1}}\bigg)+(1-\delta)\bigg)\bigg]^{\frac{1}{\gamma}}\qquad(1)$$
I also derived:
$$\frac{k_{t+1}}{k_t}=(1-\delta)+\frac{c_t}{k_t}-\frac{y_t}{k_t}\qquad(2)$$
$$\frac{y_{t+1}}{y_t}=e^\mu\bigg(\frac{k_{t+1}}{k_t}\bigg)^\alpha\qquad(3)$$
My train of thought is the following:
$\frac{k_{t+1}}{k_t}=\frac{c_{t+1}}{c_t}$ because if $\frac{k_{t+1}}{k_t}>\frac{c_{t+1}}{c_t}$ we would not satisfy the transversality condition because we would have capital in the "last" period which means we cannot be maximizing consumption. If $\frac{k_{t+1}}{k_t}<\frac{c_{t+1}}{c_t}$, we would eventually not be able to maintain constant consumption. Using that and the fact that the ratio of output to capital will be constant over time, equating equations (1) and (2) yields the following messy results:
$$\bigg(\frac{y_t}{k_t}\bigg)^\gamma+\alpha\beta\bigg(\frac{y_t}{k_t}\bigg)=\bigg((1-\delta)+\frac{c_t}{k_t}\bigg)^\gamma+\beta(1-\delta)$$
As far as I can tell, this equation isn't solvable. Does this mean I cannot say that the growth rate of consumption is equal to the growth rate of capital or have I made a mistake somewhere along the way? Also, how would one solve for the growth rates if not this way??


texts: Strategic Complementarities and Multiplicity

texts:
Consider a coordination game, in which actions taken by players are strategic complements. Moreover, assume that actions are strong strategic complements, in that the slope of the best response function is greater than unity in some range, as demonstrated in the graph below.
What is the intuition behind multiple equilibria in such a case? I understand the graphical intuition, but don't see any economic intuition.

Source for the image: https://ocw.mit.edu/courses/economics/14-462-advanced-macroeconomics-ii-spring-2004/lecture-notes/complementarties.pdf


texts: Free Disposal: the production set less the vector space of positive reals

texts:
In Microeconomic Theory (3rd Edition), Mas-Collel, Whinston and Green state that the property of free disposal implies the following:

$Y - \mathbb{R}^L_+ \subset Y $

Y: Production set

y: Production vector

L: Amount of commodities considered

Why does this formula means that the extra amount of inputs or outputs can be disposed of or eliminated at no cost?


texts:
I am undertaking some research regarding differences between manufacturing sectors across countries.

I have noted that China has taken a lot of the less skilled manufacturing work away from developed countries. It clearly has a comparative advantage with regard to unskilled labour. Generally, it will be difficult for developed countries to compete with the wages of the lesser developed countries.

This has resulted in the decline of manufacturing in some countries such as Australia (12.6% of GDP in 2000 to 6.7% of GDP in 2015) or the US (14.2% to 12.3%). Whereas other developed countries are still able to successfully manufacture. Germany for example has had ~22% of GDP from manufacturing for the last 15 years.

What factors allow manufacturing to succeed in a developed country?

I am expecting it to be related to:

Regulation
human capital
size of domestic market
trade deals

I am interested in references in particular.


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

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

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

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

EDIT. Some additional thoughts:

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

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

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

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

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


texts: Walras Law in a production economy with fixed costs

texts:
Consider a price taking firm with fixed costs $fc \geq 0$:
\begin{align*}
\Pi
&=
\max_{n^D} \left\{ P_c F(n^D) - w\times n^D - fc \right\}
\end{align*}
A representative household owns this firm:
$$\max_{c,n^S} U(c,n^S) \text{ s.t. } P_c c = wn^S + \Pi$$
Equilibrium: prices $(P_c, w)$ & allocations $(n^D, c, n^S)$ s.t. all optimize & markets clear:
1 (Labor market) $n^D = n^S$
2 (Goods market) $c = F(n)$
Rewrite the household's constraint:
\begin{align*}
c
&=\frac{w}{P_c} n^S + \frac{\Pi}{P_c}
\\
&=\frac{w}{P_c} n^S + F(n^D) - \frac{w}{P_c} n^D - \frac{fc}{P_c}
\tag{plug-in $\Pi$}
\\
&=\frac{w}{P_c} \left(n^S - n^D \right) + F(n^D) - \frac{fc}{P_c}
\tag{rearrange}
\\
&= F(n)  - \frac{fc}{P_c} \tag{Labor Market: $n^D = n^S$}
\end{align*}
Observe the household's constraint $c = F(n)  - \frac{fc}{P_c}$
is inconsistent w/ goods clearing $c = F(n)$.
Example:
$F(n)= A \log(n)$
$\Rightarrow w=\frac{P_c A}{n}
\text{ } \&\text{ } n^D(w)= A \frac{P_c}{w}
\text{ } \&\text{ } Y= A \log\left( A \frac{P_c}{w}  \right)
\text{ } \&\text{ } wn = A P_c
$
$\Pi = P_c A \log\left( A \frac{P_c}{w}  \right) - A P_c  -fc  $.
$u(c,n)=c-  \frac{n^{1+\frac{1}{\varepsilon} }}{1+\frac{1}{\varepsilon}}$  s.t.
$P_c c = wn + \Pi$
$U(n)= \frac{w}{P_c} n + \frac{\Pi}{P_c}
-  \frac{n^{1+\frac{1}{\varepsilon} }}{1+\frac{1}{\varepsilon}}
\Rightarrow
\frac{w}{P_c} = n^{\frac{1}{\varepsilon} }
$.
$\Rightarrow n^S(w) = \left(\frac{w}{P_c}\right)^\varepsilon
\text{ } \&\text{ } c=\left(\frac{w}{P_c}\right)^{1+\varepsilon} + \frac{\Pi}{P_c}
$
1 (Labor market) $n^D = n^S$
$\Rightarrow A \frac{P_c}{w} = \left(\frac{w}{P_c}\right)^\varepsilon
\Rightarrow A  = \left(\frac{w}{P_c}\right)^{1+\varepsilon}
\Rightarrow \frac{w}{P_c}  = \left(A \right)^{\frac{1}{1+\varepsilon}}
$
2 (Goods market) $c = F(n)$
$\Rightarrow
\left(\frac{w}{P_c}\right)^{1+\varepsilon} + \frac{\Pi}{P_c}
= A \log\left( A \frac{P_c}{w}  \right)
$
$\Rightarrow
\left(\frac{w}{P_c}\right)^{1+\varepsilon}
+
A \log\left( A \frac{P_c}{w}  \right) - A - \frac{fc}{P_c}
=
A \log\left( A \frac{P_c}{w}  \right)
$
$\Rightarrow
A + \frac{fc}{P_c}
=
\left(\frac{w}{P_c}\right)^{1+\varepsilon}
\Rightarrow \frac{w}{P_c}  = \left(A + \frac{fc}{P_c} \right)^{\frac{1}{1+\varepsilon}}
$
Problem:
Labor market clearing gives:
$\frac{w}{P_c}  = \left(A \right)^{\frac{1}{1+\varepsilon}}  $
Goods market clearing gives:
$\frac{w}{P_c}  = \left(A + \frac{fc}{P_c} \right)^{\frac{1}{1+\varepsilon}} $
They are only identical if $fc=0$.
Question:

is Walras law not supposed to hold here w/ $fc>0$ ?
how do you set up a GE economy w/ production and fixed costs?

Attic:
We can rewrite Goods-market clearing:
$\frac{w}{P_c} n^S + \frac{\Pi}{P_c} = F(n^D)$
$
\Leftrightarrow
\frac{w}{P_c} n^S + F(n^D) - \frac{w}{P_c} n^D - \frac{fc}{P_c} = F(n^D)
$
$
\Leftrightarrow
\frac{w}{P_c} (n^S - n^D) = \frac{fc}{P_c}
$
$
\Leftrightarrow
 \frac{fc}{P_c} = 0
$ if $n^D = n^S$


texts: Can a commercial bank lend money from transaction/checking account as it would from a deposit account?

texts:
Transaction/checking accounts are highly liquid - M1

Deposit accounts are less liquid - M2

Per fractional reserve system, banks lend deposited money as credit to clients provided they keep a reserve requirement.

Does this apply to both transaction accounts and deposit accounts? If yes, is the reserve requirement percent the same for both?


texts:
I've heard an interview with Bill Gross in which he claims that one of the problems with lower interest rate is that it leads to a lower return on investment (ROI) in the real economy.

How can that be?


texts: Investopedia has a definition about Debt ratio, I do not understand how come Debt ratio can be higher than 1. Because it means that equity is negative (because Total Assets=Debt+Equity).


texts: Are there multilevel marketing companies that aren't pyramid schemes?

texts:
I've been doing lots of research on pyramid schemes, and the rebranding and institutionalization of the industry in the 1980s with trade groups, heavy investment in politics, etc.
The term "multilevel marketing" (MLM) has been adopted as a legitimate class of business in the United States, since being created by verifiable pyramid schemes as a term used to legitimize their work and distance themselves from the earlier (and legally problematic) term of "pyramid scheme".
I'm wondering, are there are any MLM companies that are not also pyramid schemes?


texts: Open Foundational Problems in Mathematical Economics

texts:
What are some open problems in mathematical economics which are treated as if they have been solved in economics papers?

As an example, one of my teachers has previously pointed out to me that there is no existence and uniqueness proof of a specific type of Overlapping Generation problem, yet most academics with this specialty write papers that assume that their computed solution is the correct one.

Are there more examples of this sort, in which economists (implicitly) make use of a foundational result, despite no one having proven it?


texts: Why do firms bother to produce at equilibrium quantities if at equilibrium quantity, MR < MC?

texts:
For almost all demand curves, the resulting marginal revenue curve is often to the left of and steeper than the demand curve. The marginal cost curve has its distinctive U-shape, and a particular portion of the marginal cost curve is the supply curve. So the result can be shown below:

The figure above indicates that in almost any case, because MR is to the left of D, if a firm produces the quantity at market equilibrium, MR < MC, which means that the firm would be actively losing profits.  So, why do firms even bother going to market equilibrium - from a theoretical standpoint?


texts: Comparative Statics on Balanced Growth Path

texts:
It would be a silly question. In a model, I have found the BGP (balanced growth path) for all key variables.

As expected, these variables are constant variables ;

$$\mu^{BGP}=\frac{\alpha+\rho+\pi}{\epsilon\left(1+\pi\right)^{2}}$$

All paramaters on the right hand side are exogeneous constant parameters. Let's say $\mu$ is a variable for technological progress level.

For another variable, let's say capital accumulation $k$,I find a constant growth rate which is ;

$$g_{k}=\frac{\alpha\left(\rho+\pi-\delta\left(\frac{1-\alpha}{\alpha}\right)\right)}{1-\alpha}$$

The parameters on the RHS are again exogenous parameters.

My question is : Is it possible to see the effect of the variable $\mu$ on the growth rate of capital $g_k$ ?

My way of doing seems to me a little bit weird. I firstly put

$$\rho=\mu^{BGP}\epsilon\left(1+\pi\right)^{2}-\alpha-\pi$$

and replace it in $g_k$. So, I have

$$g_{k}=\frac{\alpha\left(\mu^{BGP}\epsilon\left(1+\pi\right)^{2}-\alpha-\delta\left(\frac{1-\alpha}{\alpha}\right)\right)}{1-\alpha}$$

After, I say that technological progress level at BGP affects positevly the growth rate of capital.

Do you think that it is correct to say that ? Making this kind of comparative statics analysis ?

Or any other way to do it in a more appropriate way ?


texts: R reproducible example, restrictions on cointegrating equations

texts:
The code given below estimates a VEC model with 4 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor).

nobs = 200
e = rmvnorm(n=nobs,sigma=diag(c(.5,.5,.5,.5,.5)))
e1.ar1 = arima.sim(model=list(ar=.75),nobs,innov=e[,1])
e2.ar1 = arima.sim(model=list(ar=.75),nobs,innov=e[,2])
e3.ar1 = arima.sim(model=list(ar=.75),nobs,innov=e[,3])
e4.ar1 = arima.sim(model=list(ar=.75),nobs,innov=e[,4])
y5 = cumsum(e[,5])
y1 = y5 + e1.ar1
y2 = y5 + e2.ar1
y3 = y5 + e3.ar1
y4 = y5 + e4.ar1
data = cbind(y1,y2,y3,y4,y5)

jcointt = ca.jo(data,ecdet="const",type="trace",K=2,spec="transitory")
summary(jcointt)

vecm <- cajorls(jcointt,r=4)
summary(vecm$rlm)
print(vecm)

The cointegrating vectors you will get from this estimation will look like this:

            ect1   ect2  ect3   ect4
y1.l1        1      0      0     0
y2.l1        0      1      0     0
y3.l1        0      0      1     0
y4.l1        0      0      0     1
y5.l1      b4.1    b4.2   b4.3   b4.4
constant    c1      c2     c3    c4

here, b4.1 through to b4.4 are the coefficients of the 4 cointegrating equations (ecm's) ( which are $\beta's$). Similarly, $c's$ are the intercepts of the cointegrating equation.

As you can see, there are r-1 restrictions, that's 3 restrictions, on each equation by default. I want to put restrictions on these equations matrix and
re-estimate the VECM so that I will have the following matrix of long run equations:

            ect1   ect2  ect3   ect4
y1.l1        1      0      0     0
y2.l1      b1.1     1      0     0
y3.l1      b2.1     0      1     0
y4.l1      b3.1     0      0     1
y5.l1      b4.1    b4.2   b4.3   b4.4
constant    c1      c2     c3    c4

From this output, I want to extract the first equation ect1 for inference. It should look like this:
$y_1=\beta_0-\beta_1y_2-\beta_2y_3-\beta_3y_4-\beta_4y_5$

What I do not know is how to get from the first long run equations matrix to the second one. Basically, I do not know how to construct the restrictions matrix on $\beta$.

Any suggestions and hints are welcome and appreciated!


texts: Are means-tested or universal programs more effective at reducing the poverty rate?

texts:
Advocates of means-tested programs frequently argue that they will remove inefficiences in the system by directing a larger proportion of the program's budget to people with a genuine need. By contrast, those who oppose them, and who tend to advocate for universal programs, argue that they would require the creation of bureaucracy that would eliminate any theoretical gains. Some also argue that the portion of the money that goes to wealthier people serves as an economic stimulus which increases the overall health of the economy, thus being less inefficient than it would otherwise seem.
Which of these arguments is correct? Are means-tested programs or universal programs more effective at alleviating poverty? I am aware that there are moral arguments for both perspectives as well: some say that people who make more than a certain amount (or less, for that matter) do not deserve assistance, whereas others argue that everyone deserves equal assistance. However, I am interested in the economic point of view. In addition, some people argue that any economic assistance programs have economic effects that ultimately eliminate any gains. If there is strong evidence supporting that perspective, I would be interesting in seeing it, but the question is primarily about which of the two types of programs is more effective (or less ineffective, if both are ineffective). Obviously, this is a politically heated theme, so I am ideally looking for answers based on empirical research, case studies, and to an extent modeling,


texts: Are there any states that don't have debt?

texts:
I've not been able to find any states that don't have debt to other states.  This, to me at least, seems really strange.  Are there any nation states that are not in debt to other states, if so which ones, and if not why can't everyone just settle the debts?

(Wasn't sure if I should ask this on the Politics Stack Exchange or here, please let me know if this is out of scope and I'll ask there.)


texts: Are there economic models that predict (only) a medium/long-term negative effect of protectionism?

texts:
Going by some ECB models/estimates from last year, protectionism would result in negative consequences pretty fast, e.g.

For illustration, I will use the results of simulations carried out by ECB staff using both the ECB's global model and the IMF’s multi-country model. As with all models, the uncertainties involved mean precise estimates from these scenarios should be treated with caution, but they are useful to explain the different channels at work.
To illustrate the potential effects of rising protectionism, I do not want to dwell on the specifics of the tariffs currently being discussed. This would miss the bigger picture. I rather want to consider a hypothetical scenario where the United States raises tariffs on all imports of goods by 10 percentage points, and its trading partners impose the equivalent on US exports.
According to our model simulations, such a scenario would have significant adverse effects on the global economy, including, and in particular, on the economy that raises tariffs in the first place. Specifically, real economic activity in the United States could be up to 2½% lower than in the baseline in the first year alone. [Gives some reasons for this.]
In other words, the overall scenario is clearly a net negative for the world economy as a whole. According to ECB staff simulations, world trade in goods could fall by up to 3% already in the first year after the change in tariffs and world GDP by up to 1%. Euro area GDP would also decline, but by less than in the US.

They don't make any longer term estimates for the effects of such tariffs, just mention that the EU would have been worse of by 1/5 without the economic integration since the 1950s.
Frankly it looks doubtful that US economy is showing any of that (short-term) trouble.
Are there any theoretical models of protectionism that predict short-term gain but medium or long-term loss for a country?
(Well, there's one BIS paper that advances a sort of short-term masking effect for the current US economy by advanced shipments/stockpiling:

It’s paradoxical that the United States is starting to put obstacles in the road at a time when its
economy is firing on all cylinders. Even looking through the short-term boost to GDP in the latest quarter [citing data from July 2018]
– ironically enough, partly owing to companies bringing forward cross-border shipments to skirt tariffs –
its short-term prospects are promising. But in the long term, protectionism will bring not gain, but only
pain. Not just for the United States, but for us all.

But this looks to me fairly anecdotal...)


texts:
what does this symbol mean in the discuss of locally nonsatiated preferences:
$\varepsilon > 0$ and $||y-x||<\varepsilon$.


texts: Utility Theory/Marginal Rate of Substitution: Can the marginal rate of substitution be calculated for a point of the budget line?

texts:
This a person's budget line with various points, and their consumption, C*, and their endowment e, which is worth $5000 (unimportant). Also shows is their initial indifference curve. The difference curve and budget line intersect at e and e'.

Question: Why is the marginal rate of substitution of a, on the budget line, greater than C*?

I've been told any point that lies to the left of C* (the consumption optimum) has a marginal rate of substitution higher than the one at C* which is equal to the price ratio. Similarly, any point which lies to the right of C* has a marginal rate of substitution less than the one at C* which is equal to the price ratio.

The second indifference curve that C* would form part of is not shown in the diagram.

Why can I know the marginal rate of substitutions of points on the budget line if the marginal substitution is calculated on an indifference curve? Or, in this case, the MRS of C* is calculated by equating the slope of the indifference curve to the slope of the budget line. More to the point, how can I arrive at the answer that the MRS a > MRS C* if MRS can only be calculated on for a point on the indifference curve and not for a point on the budget line? Wouldn't all points on the budget have the same MRS implied by the line's slope?

There is something simple I'm not seeing.


texts: Growth in dividends will equal growth of earnings

texts:
Let $Div_t$ be the dividend per share at date $t$.

$\displaystyle Div_t=\frac{\text{Earnings}_t}{\text{Shares Outstanding}_t}\times\text{Dividend Payout Rate}_t$ ------------------- (1)

My textbook says that if $\text{Shares Outstanding}_t$ is constant and $\text{Dividend Payout Rate}_t$ is constant, growth in dividends will equal growth of earnings.

However, differentiating (1), we get

$\displaystyle\frac{d}{dt}Div_t=\frac{\text{Dividend Payout Rate}_t}{\text{Shares Outstanding}_t}\frac{d}{dt}\text{Earnings}_t$

Clearly, $\displaystyle\frac{d}{dt}Div_t\ne\frac{d}{dt}\text{Earnings}_t$

Where have I gone wrong?


texts: How to prove convexity + quasilinear preferences imply concave utility?

texts:
Let $\succsim$ be a strictly convex and quasilinear preference relation. It's defined over, say, $\mathbb{R}^2_{+}$ and is quasilinear on good 1.

So, $U(x_{1},x_{2}) = x_{1} + f(x_{2})$. How to prove that $f$ is a strictly concave function?

I'm solving problem 15.B.8 from MWG and I can't even understand what the solutions manual did!

Thanks a lot in advance for any hints and ideas!


texts:
Consider the following quote from the book, $\textit{Men at Arms}$ by Terry Pratchett.

  “The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money.

  Take boots, for example. He earned thirty-eight dollars a month plus allowances. A really good pair of leather boots cost fifty dollars. But an affordable pair of boots, which were sort of OK for a season or two and then leaked like hell when the cardboard gave out, cost about ten dollars. Those were the kind of boots Vimes always bought, and wore until the soles were so thin that he could tell where he was in Ankh-Morpork on a foggy night by the feel of the cobbles.

  But the thing was that good boots lasted for years and years. A man who could afford fifty dollars had a pair of boots that'd still be keeping his feet dry in ten years' time, while the poor man who could only afford cheap boots would have spent a hundred dollars on boots in the same time and would still have wet feet.

  This was the Captain Samuel Vimes 'Boots' theory of socioeconomic unfairness.”

With what Pratchett wrote, I was thinking about a car-buying decision by a newly wed couple.

Consider two cars:
1. Durable Car: sturdy, long-lasting, and safe for even kids when they are born. Looking ahead for about 10-15 years usage wihtout too much maintain break downs.
2. Cheap Car: inexpensive, easy for commute, but expect maintenance cost to be high and possibly totaled withint 6-9 years.

Their financing needs are:
1. Durable Car down payment: USD 10,000
2. Cheap Car down payment: USD 2,000

Their monthly leasing fees are:
1. Durable car monthly leasing fee: USD 200
2. Cheap car monthly leasing fee: USD 300

There are two newly wed couples: a financially affluent one, and a poverty stricken one.

Control all other factors such as credit score of both couples, financing terms and horizon, etc.

According to Pratchett, the poor couple would always resort to the cheap car option while the rich couple always resorts to the durable car option. Do you agree? What are your thoughts?


texts:
I have a hypothesis that single-income families greatly increase as you get into the mid to upper middle class bracket. And that 2+ income sources are common in lower classes and also the extremely rich.

I can't verify this though because I can't find any research that looks into how many single income households there are by class. Instead, I see mostly gender connections.

Does anyone know of any research that could be helpful here?


texts: Decision over "max" production function:

texts:
I've been presented with the following problem:

$$y=3(x_3)^{\frac13}(\max\{x_1,8x_2\})^{\frac13}$$

And the objective is to both maximize profit and minimize cost. First of all, if the problems are dual, does that mean the result will be the same in variables such as demands?

STILL, MY BIGGEST ISSUE IS THIS: When you get rid of the max, this becomes a Cobb Douglas piece of cake. But I just don't understand how to do that. So far, all I've got is that this function allows corner solutions, so it's not solved just as a Leontieff function. How would you go about choosing each good? I'm also sure it has to do with input prices $w_1$ and $w_2$


texts: Empirical measurements of consumption and production elasticity of substitution?

texts:
The consumption elasticity of substitution  (ES) is the ES between different consumption goods.

The production ES is the ES between factors of production.

My question is: are there any serious empirical studies of the numerical values of these elasticities, and if so, where can I find them?


texts:
I am reading the paper "The Blockchain Folk Theorem"  by Biais et al (2019) (http://publications.ut-capitole.fr/26234/1/32/5/1662/5427771). It is a stochastic game and the authors include a sunspot random variable to "enable players to coordinate their actions using a public randomization device". I went around and tried to look more into this and I couldn't really find any intuitive explanation for what a public randomization device is (there seems to be some information on the mathematical properties of including such a device, specifically the authors reference a paper on noisy stochastic games by Duggan (2012) (https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA10125)).

I guess my question is, could anyone here provide some explanation of this concept? Or even just some reference to better understanding the concept of public randomization devices?


texts: How to add additional observations to panel data?

texts:
this is my sample dataset

How can I add for each id a new observation for 2020 month 10 which would be the average of 2020 month 8 and 2020 month 9?
I have tried the following, however, it almost works but it does not assign category name to the corresponding id value and the average is not taken correctly
egen year_m_id=group(year month) /* 127 & 128 correspond to 2020 month 8,9 */
global id=r(levels)
foreach id of global id{
generate tmp=category if id==`id'
local 2020_9=_N+1
set obs `2020_9'
local 2020_9=_N
replace id =`id' if _n==`2020_9'
sum value if year_m_id===127|year_m_id==128 & id == `id'
replace value = r(mean) if _n==`2020_9' & id == `id'
replace year = 2020 if _n==`2020_9'
replace month = 2020 if _n==`2020_9'
replace category = tmp if _n==`2020_9' & category=="" & _n==`2020_9'
drop tmp
}


texts: How can I know whether a good is inferior or normal? I can't determine elasticity with this?

texts:
I just need to make sense out of elasticities and how to determine if a good is normal or inferior.
I have determined by $X_1$ which is in the form $m/p_1 - p_1/p_2$, that I should just take the derivative with respect to $m$ to get a value, which is always negative, and by that logic a normal good. But what does it mean when the demand of a good doesn't have $m$ in its function?


texts: why doesn't every country scale up the prices to the international level?

texts:
I live in an Asian country in which the average monthly salary is maybe 300-400 dollars but things (apart from exported goods like laptops or smartphones) are reasonably cheap compared to their price in the US for instance.
One pizza is around 3 dollars, you can rent a decent hotel room with less than 20 dollars and average monthly rent for apartments in our capital city is around 150 dollars.
my question is why doesn't our government scale up everything like 5 times so the pizza would cost 15$ but at the same time salary is 2000 dollars?
That wouldn't make any difference for us but now our country seems to be a heaven for foreign tourists and I think this can make things better.
I know I'm not the first person that this idea has crossed his mind but can't figure it out what are the technical issues which prevent this idea from happening.


texts: what alternatives can possibly back a new currency

texts: A currency can be backed by a trusted issuing authority, by a scarce resource or by the scarcity of its money base (eg bitcoin). Are there any other known working alternatives.


texts: Geographic mobility of workers within Germany, as compared to within the US?

texts:
Martin Feldstein (1997, p. 36) claims that workers within the US are more geographically mobile than say within Germany. I had known that US workers were mobile. But one sentence of his seems a bit hyperbolic:

  While Americans don't hesitate to move from Ohio and Massachusetts to Arizona and California, Germans are loathe to leave one part of Germany for another.

Boston to say San Francisco (about 5,000km) is about seven times the distance from Hamburg to Munich (about 700km). It would seem surprising that Americans don't hesitate to move from one end of their country to another, while Germans are loathe to do so.

Of course there are many ways this could be measured. But here is my attempt at a question that is in principle answerable:

Each year, what percentages of US and German workers relocate to a different state (within the same country) for work? Is the figure for the US greater than that for Germany?

P.S. Feldstein was writing in 1997 but I imagine the numbers do not differ very greatly between now and then--correct me if I'm wrong.


texts: Kuhn Tucker Conditions with fewer non-negativity constraints than number of variables

texts:
I have a following type of problem:

$Maximize\,\, F(s,x,y,z)$
$s,x,y,z$

s.t. (i) $g(x,y,z) \le I$
(ii) $x \ge 0$
(iii) $y \ge 0$
(iv) $s > 0$

That is there is no non negativity constraint on variable $z$. I have read about the Kuhn-Tucker method in the books but in all those cases the problem is fourmulated such that the non-negativity constraints apply to all the choice variables. How would my K-T optimality conditions change if I have no non-negativity constraint on $z$?

My sense is that other than the regular K-T conditions for $x$ and $y$ and Lagrange multiplier, $\lambda$, we would have (a) $\frac{\partial \Large{L}}{\partial z} = 0$ (i.e. no inequality here) and NO such condition as (b) $z\,.\frac{\partial \Large{L}}{\partial z} = 0$ (which is obviously true given (a)). My entire confusion is because I have not seen such a formulation in books where K-T conditions are discussed and just want to be sure about my steps.

What would the conditions be in case of $s$, where the inequality is strict?

Here I would think that with strict inequality the problem is not well defined. The constraint set is not compact (not closed).

Thanks a lot in advance.


texts: Is there any widely accepted downsides for Cuban system?

texts:
The Cuban political, social and economic systems under communism are known for having a good medical system and high quality medical workers. Cuba also has a good educational system. The country also provides most public services (as is typical in communist or formerly communist countries).

Some fragilities of the Cuban system include patients leaving the country to obtain medical care to obtain higher-paying employment opportunities and other life conditions.

Notwithstanding, are there any disadvantages of the Cuban economic and social system that are largely accepted by:

University literature
Actual speeches of the Cuban government
Cuba-based media
Media interested in Cuba but based in foreign countries

Those downsides could be of any form, like poverty, corruption, bad quality or quantity in first-need objects....

EDIT:
To narrow down the question and make it more specific:

Is Cuban economy mainly based on what government provides, or have Cubans enough purchase power to buy "what they want"?
Did company-based economy develop? Like if I want to create a company for a specific application, it is feasible?
Is food available for middle Cuban classes at correct prices?
Are importations possible or too expensive ? If not, why are they expensive: transportation costs, government taxes?


texts: International Capital Asset Pricing Model (CAPM)

texts:
I wanted to value a High-tech start-up of which I have the cash flows of the coming 6 years. I decided to use the Discounted Cash Flow Method. To do so, I calculated the Discount rate.
For a High-tech start-up the discount rate  = Rate of equity (which can be determined by the Capital Asset Pricing Model).
So I calculated my Discount rate, used it in the DCF model And found an approximation of the Value of the High-tech Firm.

But I didn't took in consideration that the company sells their products globally. This fact has an impact on its beta Factor! and consequently on the discount rate and finally on the Value of the firm!

One option is to use the International CAPM model, but 'my' company is going to sell globally, so how do I know the impact of that to the Discount rate?


texts:
The central bank of united states is called federal reserve and central bank of india is called Reserve bank of india.
What does the term reserve in central bank mean??


texts: Literature on Recursive Preferences and Time-Additive Expected Utility

texts:
In Chapter 20 of the book Economic Dynamics in Discrete Time, named "Recursive Utility", the author asserts that the Time-Additive Expected Utility Model (TAEU) has some shortcomings when applied to dynamic economic models. He lists them as follows:

Constant marginal rate of substitution between consecutive periods.
One of the consequences of this is that a consumer that faces a given interest rate, would either save with no limit, or borrow without limit (except when the subjective discount factor equals the interest rate).
TAEU implies that the elasticity of intertemporal substitution is equal to the inverse of the relative risk aversion coefficient.
TAEU implies indifference to the timing of the resolution of uncertainty.
TAEU cannot explain experimental anomalies such as the Ellsberg Paradox, etc.

Then he introduces Recursive Utility (RU) as a class of preferences developed to overcome these issues. He then proceeds to study the properties of RU, without stopping to study these "shortcomings".

I am interested in the following: even though I could try to derive the anomalies myself, is there a article/textbook/survey article that studies formally (by formally I mean in a decision theoretic fashion, i.e studying the axioms and their effect on the representation) the structure of TAEU and show formally the shortcomings mentioned above?

The author offers references for textbook and survey treatments of RU, but not the TAEU.

Thank you very much for any comment and help!


texts: How can a currency be tied to a commodity like energy?

texts:
To make a stable (crypto)currency it basically needs to be tied to a thing of value that can not be just flooded onto the market with minimal effort. I think energy is the ideal thing to tie a currency to because basically everything in modern society is dependent on energy or creating or using energy in some form.
But energy can not be easily stored and traded for normal persons so you need some form of stand-in as a currency so i am thinking like 1 "currency coin" is worth 1 kwh. And that to make new coins for the system you have to produce/extract the same amount of energy to the grid. And when that energy is used the "currency coin" is destroyed so there will be a pretty fixed amount of money in the system at any time. And i want it to be decentralized.
But how can this be done? How do you verify that you have supplied the energy to the grid in a secure way? And how can you make sure that the currency value is always tied with the energy value?
I know that bitcoin is kind of tied to energy because you have to use X amount of energy to mine one coin, but this is wasted energy, not energy supplied to a grid to benefit the population.


texts: What is the easiest and cheapest way to store big money with option to any moment get then in cash?

texts:
Imagine I have a lot of money and my number 1 aim is to store them somewhere where I can get them fast if I need them.
I don’t want to have dividends from my money but if I will it  would be great.

For example banks are asking to wait some time before I can get big number of money in cash or even to transfer them. So banks don’t look like a good fit for my goals.

Advice me something please.


texts: Show that $W_t - \int_0^t \xi_s ds$ is forward-measure-Brownian

texts:
Definitions and stuff:
Consider a filtered probability space $(\Omega, \mathscr F, \{\mathscr F_t\}_{t \in [0,T]}, \mathbb P)$ where

$$T > 0$$

$$\mathbb P = \tilde{\mathbb P}$$

This is risk-neutral measure.

$$\mathscr F_t = \mathscr F_t^{{W}} = \mathscr F_t^{\tilde{W}}$$

where $W = \tilde{W} = \{\tilde{W_t}\}_{t \in [0,T]} = \{{W_t}\}_{t \in [0,T]}$ is standard $\mathbb P=\tilde{\mathbb P}$-Brownian motion.
Consider $M = \{M_t\}_{t \in [0,T]}$ where
$$M_t := \frac{\exp(-\int_0^t r_s ds)}{P(0,t)}$$
Define forward measure $\mathbb Q$:
$$\frac{d \mathbb Q}{d \mathbb P} := M_T = \frac{\exp(-\int_0^T r_s ds)}{P(0,T)}$$
where $\{r_t\}_{t \in [0,T]}$ is short rate process and $\{P(t,T)\}_{t \in [0,T]}$ is bond price at time t.
It can be shown that $\{\exp(-\int_0^t r_s ds)P(t,T)\}_{t \in [0,T]}$ is a $(\mathscr F_t, \mathbb P)-$martingale where bond price dynamics are given as:
$$\frac{dP(t,T)}{P(t,T)} = r_t dt + \xi_t dW_t$$
where

$r_t$ and $\xi_t$ are $\mathscr F_t$-adapted

$\xi_t$ satisfies Novikov's condition (I don't think $\xi_t$ is supposed to represent anything in particular)

Problem:

Define the stochastic process $W^{\mathbb Q} = (W_t^{\mathbb Q})_{t\in[0,T]}$ s.t.
$$W_t^{\mathbb Q} := W_t - \int_0^t \xi_s ds$$
Use Girsanov Theorem to prove:
$$W_t^{\mathbb Q} \ \text{is standard} \ \mathbb Q \ \text{-Brownian motion.}$$

What I tried:
Since $\xi_t$ satisfies Novikov's condition,
$$\int_0^T \xi_t dt < \infty \ \text{a.s.} \ \to \ \int_0^T -\xi_t dt < \infty \ \text{a.s.}$$
$$\to L_t := \exp(-\int_0^t (-\xi_s dW_s) - \frac{1}{2} \int_0^t \xi_s^2 ds)$$
is a $(\mathscr F_t, \mathbb P)-$martingale.
By Girsanov Theorem,
$$W_t^{\mathbb Q} \ \text{is standard} \ \mathbb P^{*} \ \text{-Brownian motion, where}$$
$$\frac{d \mathbb P^{*}}{d \mathbb P} := L_T$$
I guess we have that $W_t^{\mathbb Q}$ is standard $\mathbb Q$-Brownian Motion if we can show that
$$L_T = \frac{d \mathbb Q}{d \mathbb P}$$
I lost my notes, but I think I was able to show using Ito's lemma that

$$dL_t = L_t \xi_t dW_t$$

$$dM_t = M_t \xi_t dW_t$$

From those I infer that
$$d(\ln L_t) = d(\ln M_t)$$
$$\to L_t = M_t$$
$$\to L_T = M_T$$
QED
Is that right?


texts: Transformation of random variables and second order stochastic dominance

texts:
Suppose $X$ and $Y$ are two random variables where $X$ has SOSD (second order stochastic dominance) over $Y$. Let $g(\cdot)$ be a monotonic function and $X'  = g(X)$ and $Y' = g(Y)$.

Under what conditions of $g(\cdot)$ $X'$ has SOSD over $Y'$? I know that if $g$ is linear, SOSD property is reserved. Is there any sufficient and necessary conditions of $g$ that assures SOSD property?


texts: Do rising inequalities create inflation?

texts:
When the "richs"* get richers, the "poors"* get poorer... assuming:

h1) a constant volume of money,

h2) a constant volume of people,

h3) a close separation between the two groups of people,

h4) a constant influx of money from rich to poors (salaries) c1, and a constant influx of money from poors to rich (profits from stuff sold to poors) c2, such that c2 > c1

this means that the volume of money the richs have access to gets bigger over time and the volume of money the poors have access two gets smaller, therefore, also assuming:

h5) constant prices,

this means each person in this poor group has individually access to a smaller amount of money. Therefore despite a constant salary, they can afford to buy less things.

Could we therefore says that richs experiment a deflation and poors an inflation? If not, is there a more befitting name to describe this phenomenon?

Are the assumption realistics, or is the reasonment flawed?

Example:

100 persons, divided in R and P, with respectively 20 and 80 persons
1000 euros total volume of money
time t1: R has 500 euros, P has 500 euros
time t2: R has 700 euros, P has 300 euros
the prices remain constant at t1 and t2, e.g. 1 euros bread, 2 euros meat, 3 euros gas

at t1: people in P and R have on average respectively 25 and 6.25 euros

at t2: people in P and R have on average respectively 35 and 3.75 euros

therefore, despite constant salaries for people in P:

at t1 they can afford both bread, meat and gas

at t2 they can afford only bread and meat

*: I put quotation marks, because being rich or poor is subjective, but within a closed social group we can assume that such a distinction can be agreed upon.


texts:
Take some state variable $X(t)$, which follows the law of motion

$$ \dot X(t) = f(t)X(t) $$

where $f(t)$ is a policy function, and determines the growth rate of $X(t)$. As a second shock, we have $\psi$, which is iid. The agent defaults whenever

$$ g(X(t), \psi) \leq 0$$

Allow the agent to borrow some money that he will have to repay continuously. Let's compute the risk premium. The probability of default at $t+\epsilon$ is

$$Prob(g(X(t+\epsilon), \psi) \leq 0) $$

As the lending has to be repaid continuously, the interest rate, given some risk-free interest rate $r^*$ and risk-neutral lenders, is given by

$$ r^* = r \cdot \lim_{\epsilon\to 0} \left(1 - Prob(g(X(t+\epsilon), \psi) \leq 0)\right)$$

However, as the law of motion for $X(t)$ is continuous, in the limit, this becomes

$$ r^* = r \cdot \left(1-Prob(g(X(t), \psi) \leq 0) \right)$$

This would mean that the agent's risk premium is independent of what he is doing: his policy $f(t)$ does not appear anymore.

But since $f(t)$ affects the state $X(t)$ and the latter the default probability, I feel it should. What's my mistake here?

References are fine. Most of continuous time finance references I know are much too deep for this rather simple question.


texts: Is exogeneity guaranteed for a lottery-generated instrumental variable?

texts:
If using $z$ as an instrument for $x$, to study the effect $x$ has on $y$ and given that $z$ was indeed generated through a lottery, is it definite that exogeneity of $z$ will hold?
I have looked at this as two-stage OLS and I believe that the fact $z$ is lottery-generated can satisfy the exogeneity condition, i.e. $\text{corr}(z_i, \epsilon_i) = 0$. Is that true?


texts:
Economists assume that consumers have a set of preferences that they use to guide them in choosing between goods. These preferences have to satisfy three properties: completeness, transitivity and "more is better".

By completeness I mean that when consumers face a choice between any two bundles of goods, they can always rank them. This rules out the possibility that consumers cannot decide which bundle is preferable. I am wondering how to deal with the introduction new goods? Does it mean that this property only apply to available/existing goods? And should a consumer also rank today a good that is coming tomorrow? I have the intuition that if a new good replaces an existing one, the rank of preferences may change and I dont know how deal with that. Any reference would be appreciated.


texts: Microeconomics concepts greatly help us to understand the broad aggregates which are used in Macroeconomics to understand the overall functioning of an economy  but are there any ways in which Macroeconomics help us to understand the behavior of individual units?


texts:
I'm trying to get an idea of how big tech companies are based off market cap.  This is not my typical field of expertise, so please pardon me if I say something naive.

I've found this site (https://www.tradingview.com/screener/) in which I'm able to filter tickers by market cap and industry.  I tried looking through the list but didn't recognize anything in the lower areas.

I've also attempted to simply search for the market cap of tech companies I know of.  Heres' what I've got so far:

Cap   Company
----+------------
1T    Apple
950B  Alphabet
150B  Netflix
29B   Ebay
16B   Expedia
4B    TripAdvisor
2.5B  StitchFix

I couldn't find a single company under $1 Billion, thought I'm pretty certain it's possible.  Is there a minimum to this?  How can I find examples of tech companies at all ranges?  In general, how can I go about getting a grasp of size vs market cap in the tech field?


texts: Is there a journal for replications in experimental economics?

texts:
Is there a journal that publishes replications (failed and successful) of (published) experiments? And, if not, why not?
And what about failed experiments (i.e. experiments with insignificant results)?

I think replications of experiments are very important, as experiments in economics depend on many different things and most of them we don't really understand. Having replicated an experiment helps to make sure that the results obtained are not by pure chance (or worse). And, more importantly, failed attempts to replicate a study shows that there was something wrong in one of the studies.

As this was not clear: I am talking about lab experiments, not field experiments.


texts: Has there been anyone since the philosopher Thales that has held an extremely detached view of money, and also found innovative ways to profit?

texts:
According to legend anyway (ie Aristotle's account), Thales was a business man of his time! On the motive Thales had for attaining material possession, Aristotle held that Thales was only out to prove the relevance of philosophy in acquiring wealth - not wealth for its own sake. Regarding the means of his acquisitions, Thales is credited with the creation of both futures and options.

We've come a long way since Thales, for the games that both people and organizations play for financial gain today are studied in detail. Today, such a study requires rigor. The spirit of such an approach would, on paper anyway, seem to run counter to Thales' detachment towards money. After all, why go through the tedious process of innovative profit unless you're out to prove a point, like Thales supposedly was?

Along these lines has there been anyone since then that has, none the less, had such an openly negative view of wealth on a personal level, yet introduced new concepts in business and economics?


texts: Can anyone help to estimate total cost under Translog cost function. I have input output and input cost data. It would be highly appreciated if someone can provide a software demo to estimate the same is given.


texts: Why do banks keep vault cash instead of depositing all reserves at the central bank?

texts:
In what way to commercial banks benefit from keeping some of their excess reserves in the vault as opposed to depositing all of their excess reserves with the central bank (assuming the central bank pays IOER)?

What sort of proportion of a banks reserves are kept in vault VS at the central bank?

Thanks!


texts: Diff-in-Diff framework where treatment time is not fixed and multiple treatment group with sub level of treatment

texts:
The study is analyze a data for 30 yrs time period with two treatment group denoted T_1 & T_2 and a control group. Treatment T_1 has 3 levels of sub-treatment T_1.1, T_1.2, and T_1.3. Some of the T_1 members receive T_2. There is no specific time when treatment is implemented, but Participants in treatment group receive treatments on different time periods which ranges from Yr1 to Yr 30. I want to find

Treatment effect of of T_2 on T_1 members and control group members.
Treatment effect of T_1

I am using diff-in-diff method. How then I could specify the regression framework for such case? Any helpful material, any recommendation for reading will be appreciated.
Thank you for your help.


texts: Deriving FOC in OLG model with Cobb Douglas utility

texts:
I'm trying to derive the first order condition in a partial equilibrium overlapping generations model. The setup contains both consumption and housing goods.

$$
\underset{c_{t+i},h_{t+i}}{max}U_{t}^{N}=\sum_{i=0}^{N}\beta^{i}\frac{1}{1-\gamma}\left(h_{t+i}^{\alpha}c_{t+i}^{1-\alpha}\right)^{1-\gamma}
$$
S.t.
$$
a_{t+i}=y_{t+i}+\left(1+r_{t+i-1}\right)a_{t+i-1}+q_{t+i}(1-d)h_{t+i-1}-p_{t+i}c_{t+i}-q_{t+i}h_{t+i}
$$
$$
a_{t+N}\geq 0
$$
$$
a_{t}=0
$$

The paper which I'm trying to reproduce finds the following FOCs
$$
\frac{h_{t+i}}{c_{t+i}}=\frac{\alpha}{1-\alpha}\frac{p_{t+i}}{R_{t+i}}
$$
and
$$
\frac{c_{t+i+1}}{c_{t+i}}=\left(\frac{p_{t+i}/R_{t+i}}{p_{t+i+1}/R_{t+i+1}}\right)^{\frac{\alpha(1-\gamma)}{\gamma}}\left(\beta\left(1+\rho_{t+i}\right)\right)^{1/\gamma}
$$
where
$$
R_{t+i}=\frac{q_{t+i}}{\left(1+\rho_{t+i}^{q}\right)}\left(\rho_{t+i}^{q}+d\right)
$$
and
$$
1+\rho_{t+i}^{q}=\left(1+r_{t+i}\right)\frac{q_{t+i}}{q_{t+i+1}}
$$

In particular I am struggling to setup the lagrangian and dealing with the fact that utility has to be maximized across periods.
Thank you!

-----------edit----------
I've come pretty far in solving the problem. But I would still be grateful for input.

The lagrangian:
$$
\mathcal{L}=\sum_{i=0}^{N}\left(\frac{1}{1-\gamma}\beta^{i}\left(h_{t+i}^{\alpha}c_{t+i}^{1-\alpha}\right)^{1-\gamma}+\lambda_{t+i}\left(y_{t+i}+\left(1+r_{t+i-1}\right)a_{t+i-1}+q_{t+i}(1-d)h_{t+i-1}-p_{t+i}c_{t+i}-q_{t+i}h_{t+i}-a_{t+i}\right)\right)
$$

FOC
$$
\frac{\partial\mathcal{L}}{\partial c_{t+i}}=0
$$
$$
\beta^{i}\left(h_{t+i}^{\alpha}c_{t+i}^{1-\alpha}\right)^{-\gamma}h_{t+i}^{\alpha}\left(1-\alpha\right)c_{t+i}^{-\alpha} =\lambda_{t+i}p_{t+i}
$$
$$
\frac{\partial\mathcal{L}}{\partial h_{t+i}}=0
$$
$$
\Leftrightarrow\beta^{i}\left(h_{t+i}^{\alpha}c_{t+i}^{1-\alpha}\right)^{-\gamma}c_{t+i}^{1-\alpha}\alpha h_{t+i}^{\alpha-1} =\lambda_{t+i}q_{t+i}-\lambda_{t+i+1}q_{t+i+1}(1-d)
$$
$$
\frac{\partial\mathcal{L}}{\partial a_{t+i}}=0
$$
$$
\lambda_{t+i+1}\left(1+r_{t+i}\right)-\lambda_{t+i} =0
$$
$$
\Leftrightarrow\lambda_{t+i+1} =\frac{1}{\left(1+r_{t+i}\right)}\lambda_{t+i}
$$
$$
\beta^{i}\left(h_{t+i}^{\alpha}c_{t+i}^{1-\alpha}\right)^{-\gamma}c_{t+i}^{1-\alpha}\alpha h_{t+i}^{\alpha-1}-\lambda_{t+i}q_{t+i}+\frac{1}{\left(1+r_{t+i}\right)}\lambda_{t+i}q_{t+i+1}(1-d)
$$
$$
\beta^{i}\left(h_{t+i}^{\alpha}c_{t+i}^{1-\alpha}\right)^{-\gamma}c_{t+i}^{1-\alpha}\alpha h_{t+i}^{\alpha-1}=\lambda_{t+i}\left(q_{t+i}-\frac{1}{\left(1+r_{t+i}\right)}q_{t+i+1}(1-d)\right)
$$
$$
\beta^{i}\left(h_{t+i}^{\alpha}c_{t+i}^{1-\alpha}\right)^{-\gamma}h_{t+i}^{\alpha}\left(1-\alpha\right)c_{t+i}^{-\alpha}=\lambda_{t+i}p_{t+i}
$$
$$
\frac{h_{t+i}}{c_{t+i}}\frac{1-\alpha}{\alpha}=\frac{p_{t+i}}{q_{t+i}-\frac{q_{t+i+1}(1-d)}{\left(1+r_{t+i}\right)}}
$$
$$
\frac{h_{t+i}}{c_{t+i}}=\frac{\alpha}{1-\alpha}\frac{p_{t+i}}{q_{t+i}\left[1-\frac{q_{t+i+1}(1-d)}{q_{t+i}\left(1+r_{t+i}\right)}\right]}
$$
substituting definitions
$$
R_{t+i}=\frac{q_{t+i}}{\left(1+r_{t+i}\right)\frac{q_{t+i}}{q_{t+i+1}}}\left(\left(1+r_{t+i}\right)\frac{q_{t+i}}{q_{t+i+1}}-1+d\right)
$$
$$
\frac{h_{t+i}}{c_{t+i}}=\frac{\alpha}{1-\alpha}\frac{p_{t+i}}{R_{t+i}}
$$

Is this approach correct? Is a global maximum guaranteed when maximizing across two periods?

Also I am still having problems with the second FOC
$$
\frac{c_{t+i+1}}{c_{t+i}}=\left(\frac{p_{t+i}/R_{t+i}}{p_{t+i+1}/R_{t+i+1}}\right)^{\frac{\alpha(1-\gamma)}{\gamma}}\left(\beta\left(1+\rho_{t+i}\right)\right)^{1/\gamma}
$$


texts: How would a 2D model of Hotelling's law outweigh the benefits of a 1D model?

texts:
I'm not sure if this goes here, or on a math exchange. I could move it if you guys want...

Let's examine Hotelling's law on a 1D plain with two shops.

Both shops would do society a favour if placed on the 1/4 mark. But since both owners want to make money, the two shops will most likely be placed in the middle, right next to each other.

There have also been numerous mathematical formula's to analyse Hotelling's law in 1D with more than two players.

However, would this model work in a specific 2D plane with n players?

And if so, how would the information-benefits of a 2D model outweigh the ones of a 1D model concerning the real word?

Would a 2D model better help shop owners find a more suitable location?


texts: How can a company run out of cash when its stock prices is dropping?

texts:
For instance, in 2008, the Royal Bank of Scotland saw its stock price drop by ~30% in a day, and it was apparently impossible for the bank to make it till the end of the day because it would run out of cash.

Why is that so? How can its valuation affect in such a short term the cash it can disposes of?


texts:
In which situation does the demand and supply curve both shift? My professor told me for the demand curve,  the income of the consumers changes etc. will shifted the demand curve; For the supply curve, the changes technology etc will shift the supply curve.

So is this statement true: Only the types of situation with some factors causes the demand curve shift along with some other separate factors causes the supply curve shift may had both curve shift simultaneously, but in fact there is no single one factor that could shift both curve simultaneously.


texts: Building a time-series demand forecasting model

texts:
I am forecasting demand for certain types of goods and services, which I expect to be correlated to a sub-set of a basket of macroeconomic indicators (considering 15-20 indicators)

I do not know which indicators influence the demand more, whether they have a simple correlation influence or whether a derivative of change influences the demand (i.e. GDP or GDP change for example) or whether there’s a delayed effect on demand (e.g. increased government spend in last year may better predict this year’s demand?). Some macro indicators may be correlated to each other.

I have some basic hypotheses on likely indicators - that may be right or wrong.

Questions 1. What are good time-series forecasting models? What can be considered, apart from just a multivariate regression? 2. Is there a tool whereby I can input the historical demand, historical macro indicators, which will then output which set of indicators best predict the demand and which model works best?

I know how to do regressions in excel, but that’s just one set of indicators at a time. 20 indicators (plus derivatives, plus lag) throws up so many possibilities I cannot manually simulate.

Any help appreciated.


texts: Two-good economy, can we tell if the demand of good 1 rises or falls when the price of good 2 rises (price of 1 is constant)?

texts: Suppose we have a two-good economy, and we know that good 1 is a normal good. Can we then make any meaningful observation about the demand for good 1 when we change the price of good 2 and keep the price of good 1 constant?


texts: Is local non-satiation enough to talk about Walrasian Equilibrium being subset of Core

texts: In Advanced Microeconomic Theory, the author mentions that the Cobb Douglas utility function is neither strongly increasing nor strictly quasiconcave over all of R+. But the condition of strongly increasing in R+ is used to prove that set of Walrasian Equilibrium allocations is a subset of Core. So we can't apply this result to Cobb Douglas utility functions to prove that Walrasian Equilibrium obtained is part of core. Is local non satiation sufficient to say set of Walrasian Equilibrium allocations is a subset of Core as Cobb Douglas satisfies local non satiation?


texts: Income Elasticity and Convexity of Demand in Income

texts: What needs to be true about the demand function $z(y)$, where $y$ is income, for the income elasticity $\varepsilon = \frac{dz(y)}{dy}/\frac{z(y)}{y}$ to be always greater than one (so that the good is always a luxury)? In particular, does the demand function have to be convex in income? Would that be a sufficient condition?


texts: What does it mean when a bank is "fully loaned up"?

texts: Please briefly explain the situation when a bank is "fully loaned up".


texts: Is it possible for there to be a shortage of labour in an economy when there is cost-push inflation?


texts: When should a receiver randomize across actions in a signaling game?

texts:
Suppose there is a signaling game with a finite message space $M$, finite action space $A$, and finite type space $T$. Even simpler, all sender types have identical preferences (the receiver just prefers different actions in response to different types). Can the receiver ever do strictly better by randomizing across responses? When an equilibrium exists where the receiver only takes pure actions?

Ubiquitous summarized my question nicely, "Is it ever the case that the equilibrium with the highest receiver payoffs necessarily involves mixed strategies?"

Let's go with sequential equilibrium.
If you'd like some notation to start with.

$\sigma_{t}(m)$ is the probability that $t\in T$ sends $m\in M$.

$\sigma_R^m(a)$ is the probability that the receiver responds to $m$ with $a\in A.$
$\mu^m \in \Delta T$ gives the receiver's beliefs after observing $m$.

A sequential equilibrium requires $\sigma_t$ give optimal responses given $\sigma_R$, $\sigma_R$ is optimal given $\mu$ and $\mu$ is Bayesian given $\sigma$. This is really the definition of a weak sequential, but there is no distinction in a signaling game.

My intuition says no when there exists a equilibrium where the receiver only plays pure actions, but I've always been horrible with this kind of stuff. Maybe we also have to stipulate that it is not a zero-sum game, but I'm only saying that because I remember players being better off with the ability to randomize in those games. Perhaps this is a footnote in a paper somewhere?

Consider the game below where sender preferences are not identical. I apologize for the low quality. There are three sender types, each equally likely. We can create what I believe is the receiver (player 2) optimal equilibrium only if they randomize upon receiving message 1. Then types 1 and 3 will play $m_2$, creating a separating equilibrium. If the receiver uses a pure strategy in response to $m_1$, then a type 1 or 2 would deviate and make the receiver worse off.

$\sigma_R^{m_1}(a)=.5=\sigma_R^{m_1}(r)=.5$


texts: When we try to maximise utility constraint to a budget. We find the utility function or indifference curve which is having the budget line as tangent. So for solving a question we can equate the slope of budget line with the slope of a indifference curve and we will get the maximising utility coordinates.In many of the text books they equate ratio of prices with the tangent slope, but the slope of the budget line is negative where as the relative prices are positive. How does this work ? Why are they not considering the - sign of budget line ?


texts: How do you find marginal revenue if you don't have a production function?

texts:
I was given a word problem. No formulas. So I set up the following equations:

Demand Function
\begin{equation}
D(p) = a - p
\end{equation}
Cost Function:
\begin{equation}
c(q) = 9 + 10q
\end{equation}
Marginal Cost
\begin{equation}
MC = 10
\end{equation}

I am supposed to find how much the man in the problem would produce for any value of $a$. But, without a production function, I am unsure how to determine how much he will produce.

Specifically, suppose I write

\begin{equation}
R = pD(p)
\end{equation}

I can't then differentiate R by q to find marginal revenue.

So how do I know how much he would produce?


texts:
I am reading some lecture notes on asset pricing, and they use the term "ex-dividend" price of an asset.
I googled and found that ex-dividend means the time between announcement and payment of a dividend.

So, what does it mean by ex-dividend price? What does the word 'ex-" refer to?

Thank for your help in advance!


texts: Economic anthropology: Have there been cultures / societies without a market?

texts:
I was having a discussion about whether the "market" or "markets" always and inherently emerge as long as human societies exist.
Given the definition of market as the interplay of supply and demand and given that in our reality there is always a demand to sustain one's own life and at the same time there are limited resources, it is tempting to suggest that markets are an inherent feature of human societies.
Thus, the question: Have there been cultures or societes for which there is an agreement that they did not produce a market?
In this context I was reading about the terms reciprocity and redistribution. Are these mechanisms distinguished from the formal definition of a market? I.e., could one say that a group of people that exercised reciprocity observed a society without a market?


texts: Why a non-autonomous increase in aggregate demand will not trigger muliplier effect?

texts:
I understand a non-autonomous increase in AD as an increase in AD caused by an increase in income (please correct me if I am wrong). However, I do not understand why the multiplier effect must be triggered by an increase in autonomous AD.

I suppose that an increase in income will increase household's purchasing power thus consumption. This will in turn encourage the firms to increase output and hire more factors of production, thus increasing the national income, which will further increase expenditure? Is this not the multiplier effect's working?


texts: How to write budget constraint if the agent sell the goods that buy

texts:
Della’s utility is $U(G,R)$

G is the consumption of gasoline per week

R is the the consumption of other goods

Just help me to write down budget constraint.

I think that

$$R*1+(G-20)*10+20*1=1000+10*X$$

where

X is the amount of the gasoline that she sell on the black market.


texts: Is rent on a relocation — an example of unfunded liability?

texts:
I'm not too sure if the question makes much sense, but let's assume that you get a job offer in SF, and in order to accept, you basically have to sign a 6- or 12-month contract for rent in order to be close enough to the place of employment, where the rent for a 1-bedroom apartment in SF is currently at an average rate of 3.6k/month (e.g., some 2.5k/month more than the rest of the country), whereas your relocation and signup bonus may or may not cover all such rent for the whole 6-months of the minimum lease term.

Realistically, with the employment being at-will, you can be fired at any time, including even before your first day at work — companies fail, projects and requirements change, folks move on, decision makers get questioned — happens all the time.

In this sample scenario, would it be correct to refer to the rent in question as an example of an unfunded liability, or partially funded if it's not fully covered by the relocation and signup bonus allowance?  Why or why not?  If not, what is it then?  When does the liability become funded or unfunded?  Does it only become unfunded only if the job is lost, or is it always unfunded if there aren't enough money in the bank account to cover the liability?  And if it is unfunded, at what point does it become funded?


texts: I recently asked a professor if he was planning on hiring a research assistant for next semester. I thought I'd be a pretty good candidate since I have decent experience using STATA, SAS, SPSS, R Studio and Mathematica, but he started asking me about a couple programs I had never heard of before. That led me to wonder what are the most commonly used programs for Economics. A friend of mine suggested I also look into Matlab and Python.


texts: How to derive an aggregate demand function (and optimal uniform price) from two demand functions?

texts:
If I have two demand functions

$P_1=100-10X_1$
and
$P_2=50-10X_2$

and $X_1=40$ and $X_2=60$ with $MC=10$

We have two consumer groups: 1 and 2, where 1 has a higher willingness to pay, and we have one single good. $X_1=40$ refers to number of customers.

How might I derive the optimal uniform price and its aggregate demand function from this?


texts: Is Dominique Strauss-Khan really "the best economist of France"?

texts:
Dominique Strauss-Khan (often called DSK) is a French politician, from the Socialist Party. He has been Minister of Economics and managing director of the International Monetary Fund (IMF) from 2007 to 2011. He may have been the candidate for the Socialist Party during the election of the French President in 2012, and is assumed to have good chances to win. He was lecturer in economics for some years in several French universities.

French often nickname him as "the best economist of France" newspapers (e.g. here) . To be simple:

Is DSK the best economics of France?

This question is certainly opinion-based, but economics is, among other things, the science of evaluation and of utility, I hope there may exist some metrics (directing the IMF may be one of these)  that allows to estimate his importance in the current economic world so the question may be understood as

In which perspective can DSK be considered as the best economist of France? Under which criteria?

PS: I didn't know exactly how to tag this question. I used macroeconomics because of his position at IMF and his involvement in the Greek crisis.


texts: Sources of free European national income and output data?

texts:
What are good free sources of European National income and output data?

By this I mean, amongst others:
GDP and the variations of this such as; GNP, GNI, NNI and similar.

Preferable in english and with formats that are easy to work with, such as .xls, .csv, .sdv.


texts: Are corporations essential components of a free market economy?

texts:
There seems to exist a rarely-stated assumption that somehow corporations are an essential element of a free-market economy, and that they benefit a nation's economy. However, I wonder if this is really true.

Here, I am speaking of the US form of a corporation which allows a small number of people to control capital contributed by a large number and also allows those same people to disavow responsibility for the debts and liabilities of the corporation.

In the Wealth of Nations, Adam Smith deprecated any kind of joint stock companies, writing that a man would be much more careless with other people's money than his own. By this logic one might see corporate law as a way for elites to exploit society parasitically and corporate law as a damage to the economy instead of a benefit.

Is there any theoretical validity to this kind of view?


texts: Clarification on the impact of a change in the Bank Rate (UK)

texts:
I'm currently revising for my AS economics exam and I am going over Monetary Policy. In a handout, I've read the following phrases which I am a little confused about...

"A cut in the base rate, assuming it reduces market interest rates across the economy..."

This quote implies that the Bank Rate only changes the Central Bank's Interest Rate not the IR for commercial banks; so therefore, how are IRs determined in commercial banks? Do they have to be within a certain range of the Bank Rate? (Otherwise what is the point of influencing the Bank Rate if commercial banks are not forced to comply?).

"An increase in the base rate will not only reduce post-debt repayment income..."

This implies that mortgages etc. vary depending on the IR rate rather than being a fixed amount independent of changes in the IR (which is what I thought it was).


texts: Understanding agents selecting among markets

texts: Let's say an entrepreneur can choose between starting a business in a competitive market with zero economic profit, and starting a business in a market that is not perfectly competitive with positive economic profit. We would perhaps expect in an equilibrium that there would be no competitive markets unless there were no opportunities for economic profit anywhere. Where could I find more information on the structure of markets in this regard?


texts: Can there be a good which has both Hicksian and Marshallian demand curves vertical?

texts: Consider a perfectly inelastic (Marshallian) demand curve for a good X. Does this good also have a vertical Hicksian demand curve?


texts: How to get this Production Function in Growth Rates

texts:
I'm struggling to understand how Khan & Reinhart (1990) go from the next production function.
$$y=A f(K,L,Z)$$
Where $y$ is the production of the economy, $A$ is a variable which contains the technological change, $K$ is the capital stock of the economy, $L$ is the labor (work) of the economy, $Z$ is a vector of variables containing usual covariates.
Into the following result as an expression of growth-rates.
$$\frac{dy}{y} = [A \frac{\partial y}{\partial K}]\frac{dK}{y} + [A \frac{\partial y}{\partial L}  \frac{L}{y}]\frac{dL}{L} + [A \frac{\partial y}{\partial Z}\frac{Z}{y}]\frac{dZ}{Z} + \frac{dA}{A}$$
The information is that $y,K,L,Z$ are variables (redundant I know but I want to make it clear), however, in the article, they mention $A$ as assumed to grow an exogenous rate (I assume that $A$ is also taken as a variable in the first equation). They don't make clear anymore transformations, simply "growth terms".
The last expression is mentioned by the authors to be "growth terms" of $y=Af(K,L,Z)$. but I lost it that way. Usually for expressing growth rates I simply use logarithms and differentiate over time. but this approach is not clear to me.
My intuition is that $y$ was calculated with the total differential of the form of
$$dy=\frac{\partial y}{\partial K}dK + \frac{\partial y}{\partial L}dL + \frac{\partial y}{\partial A}dA$$
and then it was divided by $y$. However, I never saw the total differentials while I was studying, so I don't know if $A$ is multiplying $f$ and we may need to proceed with the product rule of the derivatives? or what is actually the process to get the result of $dy/y$ as they get.
Reference:
Khan, M. S. & Reinhart, C. M. (1990) Private investment and economic growth in developing countries World Development, Volume 18, Issue 1, January 1990, Pages 19-27, DOI: https://doi.org/10.1016/0305-750X(90)90100-C


texts: Is Quantitative Easing an asset-swapping or money-printing exercise by the Federal Reserve?

texts:
Shortly after 2008, there were prominent commentators such as Jim Rogers who called Ben Bernanke an idiot and condemn him for printing money. However, there were also articles that suggest quantitative easing is really an asset-swap and not money-printing. On the other hand, there are articles that say the opposite.

http://www.pragcap.com/bloomberg-quantitative-easing-isnt-printing-money/
http://www.bankingmyway.com/save/savings/what-does-printing-money-mean

What exactly is quantitative easing? Asset-swapping or money-printing? Does it raise the money supply? Inflationary or not?


texts:
The question that I am trying to answer is as follows:

  For a given year, South Africa's Gross Domestic Expenditure (GDE) is R 3 251 414, imports are R 987 781, and exports are R891 562. The table below lists the taxes and subsidies applicable to the South African economy:
  $$\begin{array} {|l|rr|}
\hline
\text{Taxes on production} & \text{R} & 54\ 166 \\
\hline
\text{Taxes on products} & \text{R} & 338\ 792 \\
\hline
\text{Subsidies on production} & \text{R} & 14\ 358 \\
\hline
\text{Subsidies on products} & \text{R} & 18\ 684 \\
\hline
\end{array}$$
  The gross value added at factor cost is

  A. R 2 795 279

  B. R 2 863 543

  C. R 2 835 087

  D. R 3 155 195

  E. R 3 347 633

My Answer is R 2 891 498, because I took the GDE and added subsidies and subtracted taxes. I did that because I assumed that the GDE was given at market prices. I disregarded the information about imports and subsidies because I assumed that GDE was calculated using the equation Y=C+I+G+X-M.


texts: Given an AR(2) process $y_{t}=\phi_{1}y_{t-1}+\phi_2 y_{t-2}$, I understand that the two-step ahead forecast (that is, $\mathbb{E}[y_{t+2}|y_t]$ is given by $(\phi_{1}^2+\phi_{2})y_{t}+\phi_{1}\phi_{2}y_{t-1}$. However, I am unable to derive a general expression for the k-step ahead forecast (that is, for $\mathbb{E}[y_{t+k}|y_{t}]$. How might I go about doing this? Thank you.


texts: Relationship between the Tragedy of the Commons and negative externalities?

texts:
I've read that the tragedy of the commons can be seen as a negative externality. That is, $MSC > MPC$. However, I'm having trouble understanding why the supply curve actually shifts downwards due to this.

I know, graphically, that the $MSC$ curve will be above the $MPC$ curve. But, what do the external costs mean in this context and how would it all look graphically?


texts: What are the causes of increase in productivity of labour?

texts:
This question has a specific context.
While reading Adam Smith's The Wealth of Nations, edited, with notes and marginal summary by Edwin Cannan in 1904, one comes across the following lines on the second page:

  The causes of this improvement, in productive powers of labour, and the order, according to which is produce is naturally distributed among the different ranks and conditions of men in the society, make the subject of the First Book of Inquiry.

Against "the causes" written at the outset in first line, there is a note, I presume by Edwin Cannan, which reads:

  Only one cause, the division of labour, is actually treated.

Here my aim is to know what other causes of increase in productivity of labour are known today (or were known to Edwin Cannan, back in 1904) that Adam Smith missed in his classic text.


texts:
I've been curious where the split in the wealth gap has been over time, and if it was possible to graph it.

Put another way, at what net worth is the number of those worth more shrinking in proportion to the population and the number of those worth less growing in proportion to the population?

I would love to be able to put a number on this and also see a graph of it over time. If I'm misunderstanding anything in this, feel free to inform me I'm not an economics major.


texts: Is there anything like ratio between number of manufacturing industries to number of retail shops?

texts: In my country there are very few manufacturing factories,but large numbers of small retail shops (like one shop per house or may be even more). What are the effects in the economy of a country for having large numbers of retail shops,but very few manufacturing factories ?


texts: Solution Method for Infinite-Horizon Maximization Problem

texts:
Full disclosure: this problem was part of a final exam that none of our class could really solve definitively. Below the general form is a specific utility function we worked with that I'll try to replicate my work for. Any help on the solution method would be good; specifically, it seems Euler's equations/steady states would be better for this particular form of question rather than using a Bellman, but any guidance on either method would be appreciated.

Suppose a representative agent is solving

$$
\begin{align}
& \max_{\left\{ c_t, w_t \right\}^\infty_{t=0}} \sum_{t=0}^\infty \beta^t u(c_t) \\
& \text{s.t.} \\
& w_t = Rw_{t-1} - c_t \\
& c_t \geq 0 \\
& w_t \geq 0 \\
\end{align}
$$

For all $t$, and $w_{-1}$. Additionally, $0 < \beta < 1$, $R > 1$.

$c_t$ is consumption at time $t$, and $w_t$ is wealth at the end of time $t$. $\beta$ is a discount factor.

Let
$$u(c_t) = \phi \mathrm{e}^ {\theta c_t^p}$$
where $\phi, \theta, p$ are constant parameters.

  My first question is what values of the constants $\phi, \theta$, and $p$ are needed to ensure that $u(c_t)$ are strictly increasing and strictly concave in $c_t$, for all values of $c_t$. Later on the problem asks us to assume those above conditions.

So taking the first and second derivative of $u(c_t)$ gives us:

$$
\begin{align}
u'(c_t) & = \phi \theta p c_t^{p-1}\mathrm{e}^ {\theta c_t^p} \\
u''(c_t) & = \phi \theta p(p-1) c_t^{p-2}\mathrm{e}^ {\theta c_t^p} + \phi \theta ^2 p^2 c_t^{(p-1)^2}\mathrm{e}^ {\theta c_t^p} \\
& = \phi \theta p c_t^{p-1} \mathrm{e}^{\theta c_t^p}\left[ \frac{p-1}{c_t} + \theta p c_t^{p-1} \right] \\
\end{align}$$

So $u'(c_t) > 0$ in order to satisfy the strictly increasing constraint. $u''(c_t) < 0$ must be true for strict concavity. I suggested that $\phi, \theta > 0$ and $p = 1$ for this to be true. I'm not sure how this ugly second derivative can be simplified to find the appropriate conditions.

After doing this, we had to express Bellman's equation and Euler's equation for the problem.

Bellman:

$$\boxed{V(w) = \max_\tilde{w} \left[ \phi \mathrm{e}^{\theta (Rw - \tilde{w})^p} + \beta V(\tilde{w})\right]}$$

Euler:

$$\boxed{\sum_{t=0}^\infty \beta^t (Rw_{t-1} - w_t)^p = \cdots \beta^t (Rw_{t-1} - w_t)^p + \beta^{t+1}(Rw_t - w_{t+1})^p + \cdots }$$

Finally, we got to say that $\beta \cdot R = 1$. We were then asked to find the value function and optimal decision rules for our choice variable(s). I used the Bellman to try to solve the problem, where I guessed the function form of the value function:

$$V(\tilde{w}) = F \mathrm{e}^{M\tilde{w}} + H$$

where $F, M, H$ are undetermined coefficients. After substituting this into the Bellman and putting in appropriate arguments, taking the derivative to get an optimal choice, substituting the optimal choices back into the Bellman, I got stuck trying to solve for $F, M, H$ in a way that would give me a sensible consumption choice at the end.

The little trick with $\beta R = 1$ is supposed to make consumption constant across all periods, so I assume that the point of getting the Euler's equation is so we can solve it using steady states and make life easier, but my algebra there hasn't borne any fruit either it seems.

  For the dynamic programming method, have I set the functional form of the value function correctly? If not, what should be the guess? And finally, how does all the nasty algebra work out?

  For the steady states method, what does the path of wealth look like? Does it end up constant as well? (I suppose that question applies for the Bellman approach as well.)

(If it's pedagogically interesting or useful--or if you don't trust that I'm not begging for homework help--I can show my work for both methods.)

Please let me know if anything is unclear.


texts: Detecting the presence of measurement error

texts:
When can I know that I'm in the presence of measurement errors? i.e., when can I know that I should use a measurement error model(error-in-variables model)?

Are there any statistical tests for checking that?


texts: Confusion regarding remedying negative externalities of consumption through taxation

texts:
This diagram in my textbook illustrates two solutions to a negative externality of consumption - here, the consumption of cigarettes. It states that MSC is shifted upwards by the specific tax. Since the deadweight/welfare loss is defined as the area demarcated by MSC, MSB and the quantity demanded, this would seem to imply that the deadweight loss is not reduced at all (as per the diagram). This seems rather strange.

Here's an alternate diagram I think makes more sense.

Since an increase in taxes will effect a change in the behaviour of individuals, I would argue that it is the MPC (and not MSC) curve that is affected by taxes (hand-drawn Diagram 1). Diagram 2 shows the same picture, but using an ad valorem tax. This will cause a reduction in the deadweight loss. One could argue that a tax will also cause an increase in MSC (effects on employment of tobacco farmers etc.), but, by my reasoning, for the policy to be effective ΔMPC>ΔMPC (otherwise the welfare loss will not be reduced). See Diagrams 3 and (w/ ad valorem) 4 for this scenario.

Does this make sense?


texts: Macroeconomic models with labor-replacing capital?

texts:
I am reading article http://public.gettysburg.edu/~tlin/research/robots-main.pdf "A New Keynesian Model with Robots: Implications for Business Cycles and Monetary Policy" and I wonder how actual this article is, actually, in my opinion, this article will bring Nobel prize to its authors.

My question: is there research on macroeconomic models about labour-replacing capital, i.e. about robotics and artificial intelligence as the new factor? Google search gives no relevant results and as far as I can find, the mentioned article is really pioneering in this field. Or maybe there is ongoing research on these themes but it uses different terms and keywords?

Of course, capital is usually included in all the major macroeconomic models, but the key issue is that today the certain forms of capital can almost fully replace (e.g. see https://www.hlai-conf.org/ or http://people.idsia.ch/~juergen/) labour and it brings with itself new issues, including the necessity to model new types of taxes and also the universal basic income. Maybe such labour-replacing capital has already been modeled in traditional (e.g. DSGE) models?