texts: A maximization program expressed by per capita variales - Ramsey model

texts:
I have a problem to be maximized with the following program

$$max\int_{0}^{\infty}\left\{ u\left(C\right)+\beta S^{\chi}\right\} e^{-\rho t}dt$$
s.t

$$\dot{K}=AK-C$$
$$\dot{S}=\left(1-S\right)S-\gamma AK$$

where $K$ is physical capital $S$ is the natural capital. All capital letters represent aggregate variables. The economy enjoys the natural capital as a positive amenity and the natural capital is negatively affected by the physical capital accumulation by a rate of $\gamma$.

I am trying to express this program by variables per capita since I would like to have constant steady state values. Note that the population grows at rate $n$. ($L(t)=L(0)e^{nt}$ with $L(0)=1$) It is easy for physical capital.

I will have something as

$$\dot{k}=Ak-nk-c$$

However, for the natural capital, the logistic growth of the natural capital and the amenity $S^{\chi}$ complicate the issue.

Is there a way to express all the maximization program by variables per capita? I would really appreciate if you have some hints to give or some solutions. Or if it is not possible to express by per capita variables, I would be happy to know the reason. Thanks!


texts: What is the logic the Fed used for paying interest on reserves?

texts: During the last few years, the Fed has been paying banks interest on reserves. Its a strange policy if you want banks to invest their money in the real economy. Why did they do this? Is it a way to recapitalize the banks? Is it a way to guarantee their solvency irrespective of the availability of investment opportunities? Is it a way to limit the potential inflation of QE?


texts:
I have a question regarding GE modelling.
The firm's problem is to:
$$
\max\pi=pf(k,l)-wl-rk
$$

If this is true, we choose $l$ and $k$ to maximize the difference
between costs and revenues. This yields the familiar FONCs for $l$
and $k.$ However, in equilibrim, we set the profits equal to 0.

My intuition tells me that after we solve the above problem, the equilibrium
condition implies our selecting a price $p$ such that $\pi$ equal
$0$ in equilibrium. Is this correct?


texts: Independence axiom of lottery when $\alpha \ge 1$

texts:
When studying preference over lotteries we learned the independence axiom which goes like this:

The preference relation $\succsim$ on the space of simple lotteries $\mathscr{L}$ satisfies the independence axiom if for all $L$，$L^\prime$，$L^{\prime \prime} \in \mathscr{L}$ and $\alpha \in (0,1)$ we have
$$L \succsim L^\prime \iff \alpha L + (1 - \alpha) L^{\prime \prime} \succsim \alpha L^{\prime} + (1 - \alpha) L^{\prime \prime} $$

What if $\alpha \ge 1$?  I guess that will be a quick extension for the case of $\alpha \in (0,1)$ but I don't know how to show it.


texts:
I am trying to understand to what degree tariffs (or other restrictions like quotas) were the cause of the trade imbalances between the US and China. One might imagine that it was simply a matter of the Chinese making goods more efficiently... So what exactly were (pre-Trump) the level of tariffs (or other restrictions) in US-China trade? Were they actually asymmetric?

EDIT: I found a page about quotas by country on Wikipedia here. It suggests that typical Chinese import tariffs are 7.5% and those in the US are 1.66% - that doesn't feel like enough of an asymmetry to explain the massive trade imbalance... maybe there are some legal or quota issues I have yet to discover...


texts: Correct scientific term to describe this system property

texts:
I am from a non-economic background so please bare with me.

I have a crowdsourcing system that enables businesses to request individuals to perform certain tasks in exchange for a monetary payment. For any task t, the business pays an amount of p units as long as the participant is taking on only one task. If a user wishes to multi-task, the system pays an amount p-x where * x < p* and both are nonnegative. This motivates users to take on multiple tasks as it will achieve higher profitability to each user. At the same time, the incurred costs for businesses will be reduced. Is there a scientific term that describes this mechanism? Is the term "cost-efficiency" correctly describes what the business is trying to do?


texts: Any databases with CEO letters and shareholder letters?

texts:
I am doing a research with content analysis, verifying certain disclosures on CEO letters and Shareholder letters present in annual reports of listed companies in the London Stock Exchange.

Can someone recommend a database where these letters would be available in plain text? Or at least where all the PDFs could be downloaded as a whole package? All I've found until now was the website AnnualReports but I believe someone must have done already this work :)


texts: Generalization of Tauchen 1986 approach to a case of time-varying volatility

texts:
My question is about generalization of Tauchen'86 approach to a case of time-varying volatility.

Say, I have a process $$z_{t+1}=\rho z_t+\sigma_t \varepsilon_{t+1}$$ where $\varepsilon\sim \mathcal{N}(0,1)$ and $\sigma_t\in\{\sigma_L,\sigma_H\}$ with $\sigma_L<\sigma_H$.

I want to get the nodes and a corresponding transition matrix. Does anyone know how to implement that in Matlab?


texts: Did the robbers from Money Heist real steal noone's money?

texts:
Money Heist (original Spanish title: La Casa de papel) is a Spanish TV show about a bank heist.

From Wikipedia (bolding mine),

  In Money Heist, a mysterious man, known as "The Professor", is planning the biggest bank heist in history. (...) The goal is to enter the Royal Mint of Spain in Madrid (...) and print €2.4 billion.

The idea of the Professor is that, since they don't rob a classic bank, the money they steal is no one's property. I would argue that it is actually everyone's money. Precisely, since we are speaking about euros, it is every European's money. Even if this money belongs to no one, there is still a large sum of money suddenly appearing "out of nowhere".

In real life, what would be the effect on the economy if the group of robbers carried its plan to its success and ended up with 2.4 billion euros?


texts: How to calculate change in GDP using valued added?

texts:
Suppose that Roots buys 5 million dollars in leather produced this year in Alberta and 1 million dollars in zippers produced last year in Toronto to make 9 million dollars worth of leather jackets in Montreal this year. They sell 7 million dollars worth of jackets this year.  What is the total contribution to Canadian GDP this year contained in these jackets? (million means million dollars)

A) 5 million   B) 6 million C) 7 million    D) 8 million    E) 9 million

Here the answer is D), which I don't quite understand. We calculate contribution to GDP through value added. In my opinion, the final sale, which is 7 million dollars, should be the sum. Could someone explain?


texts: Can anyone recommend a resource for very long term trade data? (1500-2014). I have looked and found bits and pieces here and there but haven't come across any single data-set covering all of it. I am thinking of mashing my own together but I really do expect it to have been done already.


texts:
Both Mastercard and Visa are charging merchants a fee, that is called interchange fee. The customer's bank, the payment receiving bank and Visa/Mastercard gets a cut of this fee.
How does this process work in real life, who gets how much % of the fees? Is there anything I'm missing?


texts: Difference between LMSR and Liquidity-Sensitive LMSR

texts: What is the difference between the LMSR (logarithmic market scoring rule) and the Liquidity-Sensitive LMSR (LS-LMSR) and what would cause prediction markets like Augur to focus on the later model?


texts: Distribution of US after-tax money income by household size

texts: I'm looking for the US household distribution of after-tax after-transfers income by household size, at a finer grain than quintiles. CPS has total money income (after-transfer) in ~$2,500 increments, but  I can't find an after-tax version. Do the full census, BLS, or think tanks estimate this?


texts: Is there a study of world poverty rates over time pre 1800?

texts: There seems to be research showing that world poverty rates have declined since 1800, see eg this. Is there any research on world poverty rates before this period? I am guessing that during this period poverty in much of the world would have gone up as a result of European colonisation.


texts: Total differentiation in a IS curve context

texts:
everyone. I'm having a hard time trying to figure out how the total differentiation occurs in this exercise.
In this excerpt, from Inflação e Crises", by Affonso Celso Pastore, the author develops an alternative form of the IS curve. First, he states some equations for its development.
The aggregate demand as the sum of household consumption (C), investment (I) and government spending (G):
$(1)$     $y = C + I + G$
Consumption as a function of disposable income ($y_d$) and non-human wealth (A):
$(2)$ $C = C(y_d, A)$      with $0 < C_y < 1$; $C_a > 0$
Investment as a function of the real interest rate:
$(3)$ $I = I(r)$ with $I_r < 0$
Non-human wealth (A) being equal to the sum of the money stock and the income originated by the stock of government bonds (B) divided by the real interest rate:
$(4)$ $A = M + \frac{B}{r}$
Disposable income (y_d ) being equal to the sum of the labor income (y) and the income originated by the stock of government bonds (B) minus the taxation, that applies both to the labor income and the income originated by the stock of government bonds:
$(5)$ $y_d = y + B - T (y + B)$
On (5), the author also states that
$T = T (y + B)$ with $T'> 0$
With this definitions, we finally arrive at this form of the IS curve:
$(6)$ $y = C\{[y + B - T(y + B)]; [M + \frac{B}{r}]\} + I(r) + G$
And we finally get where I'm having troubles in understanding it, when he uses the total differentiation:
$(7)$ $[1 - C_y(1 - T')]dy - (I_r - C_A \frac{B}{r^2})dr - [C_y (1 - T') + \frac{C_A}{r}]dB - C_AdM + dG = 0$
I've already tried so hard to understand it, but it always seems that I am missing some parts of the process. I explicitly have three doubts:
(i) I would like to know if there is a particular reason that, in this total differentiation, we use the derivatives dy, dr, dB, dM and dG, but we do not use dT, since T is a variable that appears in the original equation too.
(ii) Second doubt: although I can see how the "inner" derivation processes occur, I am not sure I can correctly interpret the signs (the "plusses" and the "minuses"). I mean, why C_a dM is a negative term while dG is a positive term? This doubt extend to the other terms as well.
(iii) The third one: I have a doubt in the derivation of the T variable in dy and dB. I don't know exactly how it got derived in dy and dB.
By the way, if necessary, I can provide some more informations of my book for contextualization purposes. Sorry if I'm sounding confused, I study economics by self-taught and this is my first time using Economics Stack Exchange.
Thanks for your attention!


texts:
A multi-plant firm will never produce at a plant with an increasing marginal cost when they own another plant with a decreasing marginal cost. Is this true?

My reasoning behind this is that firms would want to minimize their cost so they would prefer to produce at a plant with a decreasing marginal cost.


texts: What behaviour do different values of Relative Risk Aversion imply?

texts:
What behaviour does it imply that Relative Risk Aversion of consumption, say R(c) is less than 1, equal to 1 or greater than 1?

I am reading an article of Diamond & Dybvig (1983), about Bank Runs, Deposit Insurance and liquidity and they assume a relative risk aversion greater than 1. Unfortunately, some of my microeconomics are a couple of years ago. I know the formulas and so on, but am unsure of the intuitive implications on behaviour for different values of Relative Risk Aversion.


texts:
My high-school Macroeconomics textbook states that 'There is an inverse relationship between the price of foreign currency, or exchange rate, and demand for foreign exchange. When the exchange rate rises, demand for foreign exchange falls and vice versa'
Is there any particular reason for making the exchange rate the dependent variable in this scenario? I believe if I take demand to be the independent variable; that is- when demand rises, the foreign exchange rate rises. This case exhibits a direct and not an inverse relation and, hence, creates a contradiction.
All in all, I want to know if there is any procedure to decide what becomes the dependant variable. Or both of the cases are distinct and valid in their own.


texts:
Consider a welfare system u dear which a single cash transfer(guaranteed income ) is given to every citizen. Then for each dollar the person earns the payment is reduced to by a where 00 you get a transfer. If t<0, you pay taxes. If t=0, you don’t pay taxes or receive transfers.

Suppose that te wage rate is $w>0$. And so a person who works H hours gets $y_e=wH$. A typical individuals utility function is $$u(y_d, H)=y_d/(1+H)^2$$

The question has multiple part. I tried to do most of them. But I’m not sure please check my solutions also I cannot do some parts.

First of all I write an expression for individual’s disposable income $y_d$ as a function of $y_g$ and $y_e$ and other parameters.

$$y_d=(1-a)y_e+y_g$$

secondly I try to draw indifference curves for that utility function and his disposable income line as follows

I only put this image to show the graph.

Thirdly, I try to drive utility maximizing labor supply function $H^*$ by assuming that $(1-a)w-2y_g>0$

$$u(y_d, H)=y_d/(1+H)^2$$

$$u(y_d, H)=((1-a)y_e+y_g)/(1+H)^2$$

Derivative with respect to $H$

$${(1-a)w(1+H)^2-((1-a)wH+y_g)2(1+H)\over (1+H)^4}=0$$

$$\iff$$

$$(1+H)[(1-a)w(1+H)-2(1-a)wH-2y_g]=0$$

Since H>0, $(1+H)≠0$

So,
$$[(1-a)w(1+H)-2(1-a)wH-2y_g]=0$$

$$H*={[(1-a)w-2y_g\over (1-a)w}>0$$

Additionally,

$$\partial H^*/\partial y_g=-w/((1-a)w)<0$$

By intuition, as the guaranteed income $yg$ increases labor supply will decrease.

$$\partial H^*/\partial a=-2y_g/. ((-a)^2w)<0$$

So for each dollar the person earns the reduction amount of a in the single cash transfer increases iff the labor supply decreases.

these intuitions are enough? What do you say about these results ?

Then,

Fourthly What is the utility maximizing labor supply when  $(1-a)w-2y_g\le 0$

In this case I said that

$$H*={[(1-a)w-2y_g\over (1-a)w}\le 0$$

Thus, the labor supply will be optimally zero.

I am stuck at this point. Is what I said true?

And then,

Assume that the government wants to choose its policy $(y_g, a)$ in such a way that a citizen utility is maximized subject to the constraint that the net transfer is zero   How can I derive the optimal policy? I tried to derive it. But I guess my solution is not true. How do you derive it? Is it correct? This point is really important.

$$u(y_d, H)=Y_d/(1+H)^2=((1-a)wH+y_G)/(1+H)^2$$

Subject to $ T=Y_G-aY_E=0$

So $y_g=aY_E=awH$

So
$$u(y_d, H)=Y_d/(1+H)^2=((1-a)wH+awH)/(1+H)^2=wH/(1+H)^2$$

Derivative w.r.t. H;

$$(w(1+H)^2-wH2(1+H))/(1+H)^4=0$$

$$(w(1+H)^2-wH2(1+H))=0$$

Iff

$$w+wH-2wH=0$$

So $H^*=1/2$

So, $y_g^*=aw/2$ and $a^*=2y_g^*/w$

I am really stuck at this part.

And my last question is based on above assumption. But different citizens earn different wages. What do you think about the merit of this policy?

Thank you in advance.


texts: How should I interpret (BTC/CNY) / (BTC/USD)?

texts:
So, I've been following bitcoin for a number of years now and I decided to look at how it plays with the dollar and the Chinese yuan. I'm wondering if someone can help me interpret the graph below. I have some background in physics but not much in economics.

So I understand that the green line ("USD/CNY") is the value of the dollar compared to the yuan in the global foreign exchange market. When it goes up, that means the value of the dollar has gone up for those buying with yuan.

The purple line is "BTC/CNY" divided by "BTC/USD", and here's where I'm interested in your help. I have a couple thoughts:

The lines both have the same units
The purple line represents the same thing as the green line EXCEPT that it's mediated by the bitcoin market instead of the global forex market
The purple line compares the value of bitcoin for buyers with yuan to the value of bitcoin for buyers with dollars; When the purple line is above the green line, bitcoin has a higher value to buyers with yuan than buyers with dollars.

Are those reasonable interpretations? Thanks in advance!


texts: Can measures of "efficiency" be objective?

texts:
So I've noticed the reliance on the term "efficiency" on some cases of economic practice. But I've also recognized problems, e.g. problems of abstraction or problems of pseudo-objectivity, related to making claims about "economic efficiency".

I wonder whether "efficiency" can ever be an objective quality? Or whether it's in practice a very complicated concept.

E.g. while slaves could be efficient in terms of output, using slaves would negate many other aspects of humans and thus is not necessarily a "complete" view on "efficiency". Also, while "exploiting" laborers for gains might offer efficiency, it again might neglect that laborers have more aspects than "mere cold production". And that those other aspects (e.g. life quality) might have correlation between how they perform in work.

Also, since communities or societies cannot necessarily be shown to have "objective goals", then concepts such as "economic growth" may seem absurd. Because objectively, there's nothing to fundamentally motivate it.


texts:
It seems an obvious fact (not explained by authors but stated) that when a Central Bank purchases foreign currency (to stabilise its own), the domestic money supply goes up.

It seems to me that the CB in question would use its domestic currency to buy foreign exchange but I don't see how this increases domestic money supply (I assume domestic money supply to be the amount of domestic currency in circulation in the domestic market).


texts: What measure of unemployment is used by central banks to find out whether the rate of unemployment is below the natural rate of unemployment?

texts:
Having an unemployment rate below the natural rate of unemployment (NRU) leads to wage inflation and a reduction in productivity. Seeing the consequences of that, and knowing that one of the roles of a central bank is to control unemployment and inflation, central banks must accurately determine what the unemployment is currently at and see whether it is above or below the NRU.
I ask this because after looking at the Bureau of Labor Statistics' data on U-3 and U-6 (seasonally-adjusted) between the years 2010 and 2020, the lowest U-3 got was 3.5% in 2019Q4, whereas U-6 was 6.5%. However, the NRU in 2019Q4 4.45%
So, what measurement is used by central banks and what would be the best way to measure unemployment so that it can best be compared to the NRU?


texts: What causes the "imperialism of economics" and how did it start?

texts:
Wikipedia defines "economics imperialism" as follows:

  Economics imperialism (often economic imperialism) in contemporary economics refers to economic analysis of seemingly non-economic aspects of life, such as crime, law, the family, prejudice, tastes, irrational behavior, politics, sociology, culture, religion, war, science, and research. Related usage of the term predates recent decades.

My question is this. What is it about economics as a discipline that has allowed the it to extend to these "seemingly non-economics aspects of life?" Also, when did economic analysis in these so-called unrelated fields become accepted as part of mainstream economics?


texts:
The Federal Reserve Coin and Currency Service Website
describes their currency order process thus:

The 7.2 billion notes included in the FY 2015 order reflect the Board’s estimate of net demand for currency from domestic and international customers.
The print order is determined, by denomination, based on historical
payments to and receipts from circulation, destruction rates, and also
to build inventories of new-design notes before issuance.
Historically, most of the notes that the Board orders each year
replace unfit currency that Reserve Banks receive from circulation.
The estimated number of notes that Reserve Banks will destroy accounts
for nearly 85 percent of the proposed FY 2015 print order and includes
both unfit currency, as well as all old-design $100 notes received
from circulation.  The expected growth of Reserve Bank net payments
(payments less receipts) to circulation primarily accounts for the
remainder of the notes in the FY 2015 print order.

From this description, it is unclear to me how and when M0 Money is created. It seems this is tied to 'Reserve Bank net payments'.
How and when is M0 money created?


texts: An approximate measure of the real interest rate applying rule of thumb for growth rates

texts:
I don't understand how one can get from:

$1+r_{t+1}$=$\frac{1+i_{t}}{1+\pi_{t+1}}$

to

$1+r_{t+1}$$\approx1+i_{t}-\pi_{t+1}$

by applying the following rule of thumb:

$Z$=$\frac{X\cdot{Y}}{Q}$

implies

$\frac{\Delta{Z}}{Z}$=$\frac{\Delta{X}}{X}$+$\frac{\Delta{Y}}{Y}$-$\frac{\Delta{Q}}{Q}$

Note:

$r_{t+1}$: real interest rate

$i_{t}$: nominal interest rate

$\pi_{t+1}$: inflation rate

I hope someone will help :)


texts:
It seems like the vast majority of all goods and services don't change price so often.

I guess I should be careful the way I say this, because as far as I understand, they're actually very information sensitive.

So what I really mean is, why do they have 2 second ticks where the price might change, rather than changing daily to adjust for information? It seems like a 2 second tick is a little over the top.

If it is really necessary to have such a frequent possible update of prices, why do other goods and services not need that? Or which ones also do?


texts: what is exactly total bid quantity and total ask quantity?

texts:
this is the definition formulated by me:

Quantity total bid: It’s the sum of currently open (remaining untraded and active) orders on the bid side.

Quantity total ask: It’s the sum of currently open (remaining untraded and active) orders on the ask side.

I'm a programmer so I'm not an expert in this kind of stuff.

So, could you please explain it more?
And I will appreciate if you give me the formulas and an example to calculate them.


texts:
I'm having trouble understanding how to find the offer curves in general equilibrium. Is there a general way that we can use to find it?
I can understand the Pareto set and contract curve but when it comes to equilibrium I'm stuck.
For ex. if we have two consumers: Consumer 1 has as his initial bundle all of good $2:(0; 10)$ ;
while consumer 2 has all of good $1 : (10; 0)$.
Let their utilities be
$$u_1= min (x; y)$$
$$u_2= min (4x; 5y)$$
What would be the steps for finding the offer curves? Appreciate any help given.


texts: Do the three ways of measuring producer’s surplus give the same result?

texts:
In the Firm supply chapter of the microeconomics Varian's book, they show "three equivalent ways to measure producer’s surplus" using marginal cost, average cost and the average variable cost curves.

But my teacher says, "those three ways give different results. You have to keep the same method during a given analysis".

So are they or not giving the same result?

Intuitively I think they do give the same result and do not understand why my teacher says they do not.


texts: Is there any work on equality in a market versus friction?

texts:
This is a question about educational economics.

There is a phenomenon when studying countries like the USA and Chile (that have implemented voucher systems) that reducing the friction in a "marketplace" in education (e.g. choosing a school) results in a reduction in equality. It results in stratification of students into schools that match with social class.

It seems fairly obvious to me that this is a phenomenon that I'm sure has been studied or talked about in economics in a general way - I just don't even know where to look.

I'm looking for research into the idea that where there is some kind of inelastic good (e.g. health, housing, education) then reducing friction in a market will always have an effect of reducing equality.

Has anybody studied this? Any pointers to literature? Or if I'm just wrong in my observation of this being "fairly obvious" then I'd love to hear it.


texts:
Oil prices have a significant impact on the world economy, positive for exporters and negative for importers to oversimplify a bit.
They are also known to be highly volatile, and depend on hard to predict parameters, such as the changing policy of the OPEC which resembles a cartel.

Most international organizations (European Commission and IMF for instance), seems to use future prices.

Do you have any studies mentionning or better menchmarking oil prices forecast methods ?


texts: Are real wages a good measure of economic progress?

texts: Why do we tend to use Real GDP Per Capita instead of the real wage? What is the issue of using the real wage instead?


texts: New-Keynesian Model: Log-linearizing the firm's FOC

texts:
In Gali's book (chapter 3), the FOC of a firm is given by:

$$(\sum_{k=0}^\infty \theta^k E_k(Q_{t,t+k} Y_{t+k|t} (P_t^*/P_{t-1} - \alpha MC_{t,t+k} \beta_{t-1,t+k}))) = 0 $$

Basically, the first order condition for maximizing a firm's profit. $0< \theta <=1$, $\alpha$ is markup over competitive price. MC is marginal cost. And $beta = P_{t+k}/P_t$.

At the zero inflation steady state (the point we're supposed to linearize this around),

$P_t^*/P_{t-1} = 1$
$beta = P_{t+k}/P_t = 1$
$P^*=P_{t+k}$
Thus Y is constant. $Y_{t+k|t} = Y$ and so is MC.
Q is stocastic discount factor and equals $B^k$ around steady.
Similarly, Marginal cost (MC) is the reciprocal of the markup. i.e. $MC = 1/\alpha$

I need to expand this lovely expression. The problem I'm having is that if I do an expansion around the steady state, everything seems to be cancelling out, leaving me without anything that looks like the intended solution to the problem.


texts: Any research done on relationship between fertility rate and wealth?

texts:
I am discussing about evolution theory with a philosophy student and she observes that wealthier families tend to have fewer children, which kind of goes against natural selection, i.e. the genes of smarter/healthier people do not necessarily pass along the generations.

Now I am thinking:

Is there really such a pattern? If yes,
Does it vary across different environments (e.g. developed vs developing countries)?
What is the economics explanation?

References to papers are very welcome.

I am not sure how to tag this question, feel free to edit.


texts:
I am currently writing a news commentary on music streaming services. My commentary is focused on demand and supply, consumer and producer surplus, externalities, and public goods. And there are a few things that I am kind of confused in some parts:

Are music streaming services considered public goods?  My teacher said they are public goods as it is non-rivalry in consumption. But don't users need to pay for the service and therefore excludable in consumption?
Does music streaming create a negative externality to the producers? The producers are supposed to earn money through creating music but with music streaming they earn less than they should.
Finally, why do artists still decide to put their music on the music streaming services even they earn less than they should?

Thank you all very much for helping me. I just started learning about externalities so the questions may seem dumb. Thanks a lot!


texts:
I am attempting to solve the following problem
The demand functions for two substitute goods, the production cost of which equals $c_1$ and $c_2$,
are $q_1 = a_1 + b_{11}p_1 + b_{12}p_2$ and $q_2 = a_2 + b_{21}p_1 + b_{22}p_2$.
How can I find equilibrium under simultaneous and sequential interaction in a price oligopoly
(the values of the coefficients $a_1,a_2,b_{11} ...$ can be selected by yourself.
Although, if I'm not mistaken, the sign matter)
I need help in understanding the difference between simultanious and sequential interaction solution


texts: Conditional distributions in model with continuum of agents

texts:
Many economic models consider a continuum of agents, $i \in [0,1]$. Suppose these agents have characteristics $(x_i, y_i)$, which are independently distributed. Are all possible values of $(x_i,y_i) \in \mathbb{R} \times \mathbb{R}$ held by some agent $i$? If I pin down a specific value $\bar{x}$, is there still a continuum of individuals with $x_i = \bar{x}$ and holding all possible values of $y_i$? Some models appear to rely on this being the case (see e.g. the 'island-economy' proof in Appendix B.1 of http://www.jonathanheathcote.com/hsv_taxation_final.pdf - it seems like on each 'island' there is a continuum of agents with different values for $\epsilon_i$).
Is there a more mathematically formal way of setting this up which could clarify it? Does my confusion have something to do with the agent space being one-dimensional, whereas the characteristic space is two-dimensional?
Is the case different if each agent has characteristics $(x_i, y_i(j))$, where $y_i(j)$ are a set of values for each $j \in [0,1]$? In this sense, the characteristic vector exists in an infinite-dimensional space. In the previous example, the characteristic vectors have values in $\mathbb{R}^2$, which has the same cardinality as the agent space $[0,1]$. But in this example, the characteristic space $\mathbb{R} \times \mathbb{R}^{[0,1]}$ has greater cardinality than the agent space. I'm not sure if this is relevant though.
Thanks!


texts:
I'm trying to determine which strategy is stochastically stable.

In my lecture notes, we assign probabilities $a$, $b$ $1-a-b$ to player 2 strategies $T,M,B$ resp.
Hence we have the payoffs
$$u(t)=2a+1-a-b$$ $$u(m)=b+2-2a$$ $$u(b)=4-2b-3a$$
And it is inferred from this that $b,b$ is stochastically stable. I tried using the utilities to derive a system of three equations, and showing that $B$ yields the highest payoff for the largest range of $a$ and $b$, but this did not seem to succeed.


texts: What is a substitute/complement in terms of mixed partial derivatives?

texts: I am trying to understand how substitutability relates to mixed partial derivatives. I thought the change in marginal utility with respect to a change in the amount of $x$ would correspond to $$\frac{\partial U}{\partial x}$$ so I got confused when I take the partial of that with respect to $y$. Does this measure the rate MU changes wrt $x$ as we change $y$? How is that related to being a substitute?


texts: Why does the bond market induce efficient allocation of capital?

texts:
Going from this quote by Bryan Collins of Fidelity on China's economy:

  One of the nice things we see from the development of a domestic bond
  market is that it starts the process of pricing capital better. And
  when you price capital better, you get a much better chance of that
  capital being allocated more efficiently.

I can certainly follow Collins' logic, but I don't understand the economic theory that underpins this logic.

Question

Why is it exactly that a developed bond market leads to more efficient allocation of capital?


texts: Contest game: second order condition satisfied, but negative profits?

texts:
The following is taken from Nti (1999)

Consider a 2 player game in which each exerts effort in attempt to win a prize. Let $V_1$ be player $1$'s valuation of the prize and let $V_2$ be player $2$'s valuation, where $0<V_1< V_2$. Player $1$ and $2$ expend efforts $x_1$ and $x_2$ respectively to win prize $p=1$. The cost of effort is $1$ per unit. Given a profile of effort levels ($x_1$, $x_2$),the probability that player i wins the prize takes the symmetric form

$$p_i(x_1,x_2)=\frac{x_i^r}{x_1^r+x_2^r}$$

$r$ is the returns to scale parameter associated with effort $r>0$. Profit is

$$\pi_i(x_1,x_2)=v_i\frac{x_i^r}{x_1^r+x_2^r}-x_1$$

In equilibrium (Nash-Cournot) player $i$ exerts effort $x_i^*$: $$x_i^*=\frac{rv_i^{r+1}v_{-i}^r}{(v_1^r+v_2^r)^2}$$

If both follow the equilibrium strategy, $i$'s probability of winning is
$P_i=\frac{v_i^r}{v_1+v_2^r}$. Inserting these two into the second equation for player 1 (with simplification) yields

$$\pi_1(x_1^*,x_2^*)=\frac{v_1^{r+1}}{(v_1^r+v_2^r)^2}\big[v_1^r+v_2^r-rv_2^r\big]$$

The second order (sufficiency) condition $\frac{\partial^2\pi_1}{\partial{x_1^2}}=\frac{rv_1^{1-r}x_2^rx_1^{2r-2}}{(x_1^r+x_2^r)^3}\big[rv_2^r-v_2^r-v_1^r-rv_1^r\big]$ is satisfied iff $$rv_2^r-v_2^r-v_1^r-rv_1^r<0$$

However, it is clear that for $x_1^*$ to be a Nash Equilibrium, $\pi_1(x_1^*,x_2^*)\geq0$ and hence that $$v_1^r+v_2^r>rv_2^r$$

which is a stronger requirement than the second order condition. Hence, it is possible that the second order condition is met but not that $v_1^r+v_2^r>rv_2^r$. My question is what happens when this occurs? Is there no Nash equilibrium here? Does the player who makes negative profit drop out, if so what does the remaining player do?


texts: If I have a £25,000 loan, in a balance sheet do I include it in the Cash as well as a liability?

texts:
I'm new to all this and balance sheets are extremely confusing.

In this example I've received a £25,000 loan from the bank, it has a fixed interest rate of 6% to be paid over 1-5 years.

This is the only cash I have to finance my business at the moment and I don't have any other assets (2000 cash from personal finance)

So what I'm wondering is, in a balance sheet do I include the 25,000 as a Cash asset as well as putting it in the liabilities as I have to pay that back?

If someone could explain this to me or maybe show me what it would look like in a mini balance sheet I would be super grateful!


texts: Interpeting equivalent annual cash flows

texts:
So i have this question:

RainMan Inc. is in the business of producing rain upon request. They must decide between two investment projects; a new airplane for seeding rain clouds or a new weather control machine built by Dr. Nutzbaum. The discount rate for the new airplane is 9%, while the discount rate for the weather machine is 39% (it happens to be higher risk). Which investment should the company select and why?

Cash flow of airplane= -900,500,600 (life span of 2 years)
Cash flow of weather machine=-900,550,600,685 (life span of 3 years)

I proceed calculating the NPV of the airplane=63.72 and the NPV of the weather machine=61.29.

I calculate the annuity factor of the airplane which is 1.759 and the annuity factor of the weather machine which is 1.60935.

Then the annuity payment of the airplane is 36.38 and the annuity payment of the weather machine is 38.08.

It would appear to me that since the annuity payment (or the equivalent annual annuity) of the payment is lower, then it should be chosen

HOWEVER! Thesere are the possible answers to the question :

A) Airplane, because it has a higher equivalent annual cash flow

B) Airplane, because it has a higher NPV

C) Weather machine, because it has a higher NPV

D) Weather machine, because it has a higher equivalent annual cash flow

The answer on the sheet states to choose D. It says that since they have different life spans the weather machine has a higher EAA and should be accepted.

My current knowledge has taught me to choose the project with the lowest equivalent annual annuity . Other questions on my text book had answers that preffered projects with lower equivalent annual annuities.

Then what am i doing wrong ? Am i confusing the equivalent annual cost principle with the equivalent annual annuity approach which states to choose the project with the highest equivalent annuity ?

I am quite confused since the methods used to calculate the EAA and the EAC appear to be the same on my answer sheet ( different questions obviously ) but yet this question tells me to choose the highest annuity payment and some the lowest?

The other question in which the answer was to choose the project with the lowest EAC is this:

Two machines, A and B, which perform the same functions, have the following costs and lives. Machine A has a PV of costs of 6000 and its life is equal to 5 years. Machine B has a PV of costs of 8000 and its life is 7 years. Which machine would you choose? The two machines are mutually exclusive and the cost of
capital is 15 percent.

Yet again i would still do the same process (other than calculating the NPV which is already states) and i would come to the conclusion that the EAC(A) is 1789.89 and the EAC(B) is 1922.88.

The possible answers to this question are:

A) Machine B, because it has longer life

B) Machine A, because it has lower PV costs

C) Machine B, because the EAC is $1,922.88

D) Machine A, because the EAC is $1,789.89

Then obviously I would choose D (which is correct since the EAC of machine A is 1789.89 which is indeed lower than B)

Please explain in the simplest way possible what i am not understanding. Thank you !


texts: Are Investments positively or negatively correlated with interest rate

texts:
Having just begun self-studying economics, I apologise if this question is too simple.

Do investments increase or decrease with increased interest rate?

According to the small, closed economy model (as far as I understand it) increased interest rates make borrowing harder and hence crowed out investment.
However, in the large, open economy model it is mentioned that higher interest rates encourage both domestic and foreign investors to lend in the country, so investment can increase?

I appreciate that this boils down to a difference in foreign vs. domestic, and ultimately into the question wether investment is lending or borrowing. Anybody who could put me on the right track please?


texts: Log-linearization of the market clearing condition

texts:
I am dealing with a paper of Walsh & Ravenna.

www.banque-france.fr/fondation/gb/telechar/bourses_recherche/Welfare-based_Ravenna.pdf

I am kind of confused by the euqation (19) on page 33.

The market clearing condition goes as follows:

$$Y_{t} = C_{t} - w^{u}(1 - N_{t}) + \kappa\upsilon_{t}$$

Log linearization around the steady state yields

$$\hat{y}_{t} = \frac{\bar{C}}{\bar{Y}}\hat{c}_{t} - w^{u}\hat{n}_{t} + \left( \frac{\kappa\bar{\upsilon}}{\bar{Y}}\right)(\hat{\Theta}_{t} + \hat{u}_{t} )    \;\;\; \mathbf{(19)} $$

I don't know how this formula (19) is derived?
Isn't there something missing? From my basic understanding of log linearization it ought to look like this:

$$\hat{y}_{t} = \frac{\bar{C}}{\bar{Y}}\hat{c}_{t} - \left( \mathbf{\frac{\bar{N}}{\bar{Y}}} \right) w^{u}\hat{n}_{t} + \left( \frac{\kappa\bar{\upsilon}}{\bar{Y}}\right)(\hat{\Theta}_{t} + \hat{u}_{t} )$$

with
$$ Y_{t}\;\;...\;\; output $$
$$ C_{t}\;\;...\;\;  consumption $$
$$ w^{u}\;\;...\;\;  wage\;of\;unmatched\;workers $$
$$ 1-N_{t}\;\;...\;\;  unmatched\;workers $$
$$ w^{u}(1-N_{t})\;\;...\;\;home\;production$$
$$ \kappa\;\;...\;\;  cost\;of\;posting\;vacancy $$
$$ v_{t}\;\;...\;\;  vacancies $$
$$ \hat{v}_{t} = (\hat{\Theta}_{t} + \hat{u}_{t} ) $$
$$ \omega = \frac{v_{t}}{u_{t}}\;\;...\;\;measure\;of\;labour\;market\;tightness$$
$$ \hat{\cdot}\;\;...\;\;log\;deviation\;from\;steady\;state\;value$$
$$ \bar{\cdot}\;\;...\;\;steady\;state\;value$$

Small letter with a hat: log deviation of a variable arount its steady state.
Big letter with a bar: steady state value.
K: cost of posting a job vancancy.
w^u: "wage" of unemployed workers.

I've read the paper and the appendix aswell, read both the papers in the bibliography of this one aswell as later ones basing on this publication, but I could not find a helpful hint.

Is there any special relationship between N and Y in the steady state that explains why this whole term vanishs? Or do I have a wrong understanding of log-linearization?

I have to apologyze for my rusty English. I am already taking care of this problem. But for the above mentioned I would like to have your help. Does anyone has a decisive hint?


texts: Sunk costs - Book value and Market value

texts:
i try to understand the concept of sunk cost and how we compute sunk costs when there is a difference between book and market value.
For example, if the book value of assets is $300 000 and the market value of the assets is $150 000.
Sunk costs = ($300 000 - $150 000 (depreciation)) = $150 000 ?
Or the sunk costs = 300 000 because the assets have been already paid ?
Many thanks,


texts: How to solve leader's problem in stackelberg game when follower's optimal decision is implicit function of model parameters?

texts:
Suppose there is a leader with net profit function $EC(P_{1},Y,X)$ where $P_{1},Y$ are decision variables of leader. The follower's problem is given as follows:
$$\max_{X}ENP(P_{1},Y,X)=\max_{X}P_{1}X-c_{1}(X^2+\sigma^2)-p_{1}\int_{LB}^{Y-X}(Y-X-\epsilon)f(\epsilon)d\epsilon$$ where $c_{1},p_{1}$ are parameters of the model and $X$ is follower's decision variable. Here $\epsilon$ is random variable with support in $[LB,UB]$ ,probability density function $f(.)$ and cumulative distribution function $F(.)$. The follower's problem is solved. $ENP$ is concave function of follower's decision variable $X$ with optimal $X$ coming from first order condition given by:$P_{1}-2c_{1}X^{*}+p_{1}F(Y-X^{*})=0$. From this expression it can be seen that $X^{*}$ is an implicit function of model parameters and customer's decision variables. Then how do we substitute $X^{*}$ in leader's problem and solve the leader's problem.


texts:
We have two firms with identical cost structure compete in a market

Demand function = $p=a-bq$

And $q=q_1+q_2$

They are identical in every way. However, firm 1 maximizes profit and firm 2 maximizes revenue as long as shareholders are satisfied, which he achieves by keeping profits nonnegative.

Both firms have constant and equal marginal cost c. So I want to find the quantities that they will choose.

———

What I did is...

For firm 1,

$$\pi_1=max[(a-b(q_1+q_2))q_1-cq_1]$$

FOCs for $q_1$

$$a-2bq_1-bq_2-c=0$$

So $$q_1={a-bq_2-c\over 2b}$$

For firm 2,

$$max [(a-b(q_1+q_2))q_2]$$

FOCs $$a-bq_1-2bq_2=0$$

$$q_2={a-bq_1\over 2b}$$

So,
$$q_1={a-b({a-bq_1\over 2b})-c\over 2b}$$

$$q_1^*={a-2c\over 3b}$$

And $$q^*_2={5a+2b\over 6b}$$

—-

The question says that “* firm 1 maximizes profit and firm 2 maximizes revenue as long as shareholders are satisfied, which he achieves by keeping profits nonnegative.*”

Because of this sentence, I am exactly not sure about my solution. Especially for firm 2.

I’m confused at this point. Please tell my mistakes. Thank you.


texts:
Thought I'd post interesting questions that come my way to try and boost activity!

A seller and a buyer negotiate over trade of a single indivisible
good. The good is either of low quality (in which case its value is 0
to the seller and $0.5$ to the buyer) or high quality (in which case its value is $1$ to the seller and $1.5$ to the buyer). The seller knows the quality but 2
the buyer knows only that the probability that the quality is high is $θ$ (0 < $θ$ < 1).

Consider a two-period bargaining game. If the buyer’s first-
period offer is rejected, the buyer makes a second price offer in
period 2. If the second offer is rejected, there is no trade. Both
players discount the future slightly.

Assume that in each period
the only offers permitted are $0.5$, $1$ and $1.5$ (the buyer could also decide not to make any offer).

a) Define Perfect Bayesian Equilibrium
in this context.

b) Does there exist a pure strategy perfect Bayesian
equilibrium in which the first price offer is $0.5$?

c) Under what conditions does a pure strategy equilibrium exist?


texts: Can the demand curve be a rectangular hyperbola, but $E_D \neq 1$?

texts:
So, I am given the next table:

I am asked to find $Q_D$.
So the prerequisites to find $Q_D$ is that the price must change, and all other factors of demand must be steady. So, I can find the $Q_D$ between A and C. Our professor stated that, as $P_A Q_A= P_C Q_C =20000$ , the demand curve is a rectangular hyperbola and $Q_D = \frac{20.000}{P}$. However, in the rectangular hyperbola, $E_D=-1$ in every point of the demand curve, but here we have that $E_{D}=-0,8$. Is there something I am missing? Does $E_D=-0.8  \neq -1$ imply that the curve is a line or not? Thanks!


texts:
First picture: we always do the roll back scenario, (B,M,F) so Francisco start and 2 > 0 in the last node so therefore he will be in.

And if Franscisco is in, McDonalds at the last node, have to choose to fight or coop, and since 4 > 2, they will coop.

And at McDonalds first node, he will coop since fight will have a payoff of 0.

And first node, Bobs burger, he choose in because if he is out he will get 0.

Is this correct?

And when it comes to this:

We look at player 3's payoff, shown with the highlighted lines.

And then player 2, will choose F since it is his best payoff at that node

And then we look at player 2 again at the second node, he will choose  D since it is his best payoff,

And then last, at the first node, player 1, he will choose  A since it is his best payoff?

And therefore the correct answer is (A).

Is it right?


texts: Fixes of quadratic utility when probability of decreasing utility is large

texts:
In finance and specifically portfolio theory, a popular utility function is quadratic utility
$$
u(x)=x-\frac{\lambda}{2}(x-\mu_x)^2
$$
where $x$ is wealth and $\lambda$ is the parameter of risk aversion. For $x>\mu_x+\frac{1}{\lambda}$ the utility is decreasing in $x$. This is undesirable as we do not think investors derive disutility from a high-enough return on investment. Is this a common problem? Let us consider an example.

An investor holds shares of a company worth around \$$100$ with $\mu_x\approx\$100$. Daily fluctuations of share prices of around 0.25% (corresponding to $\pm$\$0.25) and larger are not uncommon. Given a reasonable value of $\lambda=4$ (see "Typical risk aversion parameter value for mean-variance optimization"), this means $x>\mu_x+\frac{1}{\lambda}$ will not be uncommon, i.e. a sufficiently large gain in wealth will lead to a reduction in utility quite frequently. If the investor holds shares worth \$$10,000$ instead, close to half of the days will show $x>10,000+\frac{1}{4}$. Hence, the problem seems to be very common.

Are there any common approaches in the literature to fixing this flaw while sticking to quadratic utility? What are they?

(I could come up with some simple modifications of the utility function myself, but I would like to follow the relevant literature instead, if there is any.)


texts: Interpreting the Reference Outcome in Thaler (1985)

texts:
On page 18 of  Thaler 1985 on Value-functions $V(\cdot)$, he makes an example about an individual expecting some outcome $X$, who instead obtains $(X + \Delta X)$ which he then defines as the reference outcome $(X + \Delta X:X)$.
How is the ':' interpreted in this case?
In this post the ':' implies $(X + \frac{\Delta X}{X})$. However, I don't how that fits into the overall problem stated in the paper.


texts: Subgame Perfect Nash equilibrium: two stage game

texts:
Charitable organizations are ranked according to the proportion of their total budget that is spend on programs(what directly goes to the recipients of their services) relative to money spent on administration(e.g salaries paid to its staff). Suppose there is a charitable organization which spends P on its programs and S on administration (salaries). So its total budget is B = S + P and a proportion P/B goes to programs. The manager of the charity cares about the charity's reputation (ranking) but also cares about his salary. So suppose he maximizes $Q =(P/B)^a$ $S^{1-a}$ ,$ 0 <a< 1 $.

The only donors to the charity are players 1 and 2, who care about the total amount of money that goes to the recipients of the charity's services. Donor k has a budget W and a utility function
$U_k$ = $c_k$P, where $c_k$ is the dollar amount spent on a private good. Let player k's donation to the charity be $D_k$, k = 1 ,2 .
The timing of actions is as follows: In stage 1 the donors choose $D_1$ and $D_2$ simultaneously, and in stage 2 , the charity then chooses S and P.

a) Find the sub-game perfect equilibrium of this game.

b) Someone clams that the donors give less in total to the charity as the efficiency level of the charity (from their standpoint) increases. Verify the validity of this claim in this simple model and give the intuition for your answer.

c)Now suppose that in addition to the charitable organization above, there is another charity which is identical to first charity except that its manager's objective function is $Q =(P/B)^b$ $S^{1-b}$ ,$ 0 <b< 1$. Call these charities a-type and b-type. Assume that a >b . Denote player k's donation to charity j as $D_k^j$, k=1 ,2 and j=a ,b. What is the  sub-game perfect Nash equilibrium of the game? (Hint: write down the donors' Kuhn-Tucker conditions).

What I did is that

For a) I start from the 2nd stage game and maximize the charity's utility function

max $(P/B)^a$ $S^{1-a}$

s.t B = S+ P

The unconstrained problem becomes:
max $(P/B)^a$ $(B-P)^{1-a}$

Taking FOC wrt P  we obtain P*= aB

Then going in state 1, I determine the Best response function.Donor 1 wants to maximize

max (W -D1)(D1 +D2)

The best response function for donor 1 is D1 = (W- D2)/2 .
Doing the same for donor 2, the besr response function is   D2 = (W- D1)/2
Solving the optimal choices are D1*=D2*= W/3 .
Going back to stage 1 and substituting , P*=2W/3 , B*=2W/3a and S*=2W(1-a)/3a
This is the Nash equilibrium.

For part b)

The d Q/ d(P/Q) = a $( P/ B)^{a-1}$ $S^{1-a}$ > 0

and $d ^2$Q/d $(P/Q)^2$ = a(a-1)$(P/B)^{a-2}$ $S^{1-a}$ < 0

But I stuck and I do not know how to interpret it.

For part c) the donors' Kuhn-Tucher conditions  are :

$D_1^a$ + $D_2^a$ $\geq$ $D_1^b$ + $D_2^b$

$D_1^a$ + $D_2^a$ $\geq 0 $

$D_1^b$ + $D_2^b$ $\geq 0 $

But if I plug them into the donor's maximization problem I do not end up to a result.

Any help will be appreciated.
Thank you


texts: Are any of these tax dodging schemes actually realistic or exclusive to billionaires?

texts:
So there's been quite a bit of fuss over how the rich supposedly pay lower taxes (proportionally of course) than regular, hard-working Americans because of various tax schemes that "let the rich get richer"

This website - http://www.salon.com/2013/04/12/10_tax_dodges_that_help_the_rich_get_richer_partner/

probably makes the boldest claims - according to it, a billionaire could

avoid even capital gains taxes by borrowing money because the tax isn't due until the shares are sold (and they don't ever need to be sold) - but wouldn't the interest rate over 30 years wipe out the savings? Also, couldn't a regular person do that too?
It then (on #3.) it describes bartering - but I thought bartering was still taxable?
(on #4) it then describes fake charity scams - but wouldn't the IRS (not to mention some other federal agencies) audit multi-billion dollar charities for that?
(on #5) Couldn't a regular employee convince their boss to pay for their car "on paper" and split the tax savings?
(on #6) I always thought you'd go to jail for that stuff?
(on #7) Again, seems like just some more regular business expenses that incentivize R&D
(on #10) I don't understand how an IRA would benefit a billionaire more than a millionaire. Actually, 401(k) plans seem to be better than dividend stocks since they aren't taxed until it's converted to cash.


texts: Can futures buying/selling distort price discovery?

texts:
How credible is the suggestion that specific parties distort price discovery (rig the market) of a given asset by buying/selling corresponding futures contracts or any other derivatives.

Should these position not unwind at some point causing a reversal effect?


texts: How to work out average income based on square meter of property rented

texts:
Is it possible work out the average income of a household if one knows the rental cost per square meter of property?

Example: Edinburgh, Scotland = £2,125.00 per square meter.

I hope I have posted this in the right SO platform.

Thanks


texts: What are the main differences in the methods of game theory and experimental economics? Which method is better suited to analyze strategic behavior?


texts:
Consider a macroeconomy defined by following equations:
$$M = kPy + L(r)$$
$$S(r) = I(r)$$
$$y = m $$
 Where $M$ is money supply, $P$ is price level, $y$ is output, $r$ is interest rate, while $k,m$ are constants. $S(r)$ is saving function with $S'(r) >0$, $I(r)$ is investment function with $I'(r) <0$,  and $L(r)$ is speculative money demand function with $L'(r) <0$.

Now how an increase in M affects P? Does P decrease or increase more than proportionately or less than proportionately or proportionately?

I am more interested in approach than in solution. I am not able to understand how to approach this problem.


texts: Is $\lim_{t \rightarrow \infty} B_t = 0$ at equilibrium in classical monetary model, where $B_t$ represents bond holding?

texts: At equilibrium of classical monetary model, does $\lim_{t \rightarrow \infty} B_t = 0$, where $B_t$ represents bond holding has to hold? I was wondering about this question because there is no ponzi solvency condition in classical monetary model, and usually when inequality exists as part of constraints in economics model, they often can be represented as equality at equilibrium.


texts: Non random matrix as instrument: consistency and bias

texts: Where can I find references to see what happens theoretically if I want to use a non random matrix as instrument in terms of consistency and bias?


texts: Is anti-competitive behavior a threat in a society with free trade and no regulation?

texts:
A question that I have is whether a truly economically free society needs to (or should) have laws against anti-competitive behavior.

Take liquor distribution as an example. In the United States liquor distributors widely employ anti-competitive tactics. For example, they will threaten liquor stores that sell product from competing distributors with being cutoff. Since liquor stores rely on key brands, this is a lethal threat so the distributor can essentially prevent them from selling product from someone else. The six or seven liquor distributors in the US have essentially divided up the country geographically among themselves using this mechanism.

Some economists might argue, however, that this is only possible because of government regulations on alcohol. So, for example, for years regulations prevented small brewers from being possible, so there were only a few large brands, Budweiser, Schlitz, Michelob, etc. Because of the artificially restricted number of brands that opens the door for anti-competitive distribution monopolies, they argue. If there were no restrictions on distilleries, then the distribution monopolies would vanish, is the contention.

What is the basis for that kind of theory? Does it have a name? What is the argument against it?


texts:
Where to find the latest statistics of brain drain in the world?

I would appreciate your suggestions.


texts: Seigniorage, or monetary financing of fiscal policy

texts:
In reading a textbook on seigniorage, the authors define seigniorage as $\frac{\Delta H}{P}$, where $\Delta H$ is the change of high-powered money, and $P$ is the price level. In the IS-LM model, and assuming that H is proportional to money demanded, and assuming that factor/multiplier constant, we have that in the medium-run, the growth-rate of high-powered money is equal to the growth-rate of money supplied, which in turn is equal to inflation: $\gamma_H=\gamma_M=\pi$.

What would happen if instead of the IS-LM model, the Central Bank(CB) was active/forward looking, and guided the economy by setting the interest rates, i.e. use an interest-rate rule, instead of passively adjusting the money supply? In this setting, except for abnormal times like today's, the medium-run equilibrium would be $\pi=\pi_T$, where $\pi_T$ is the inflation target of the CB. Can the CB use an interest-rate rule while monetary financing the government's fiscal stance?


texts: Net Neutrality and Recent Telecom Projects

texts:
It has come to my attention that the big telecom providers are launching some big infrastructural projects recently (at the time of post, Jan. 2018). I presume by that they mean talking laying cables and related activities. Supposedly this is being at least partially attributed to the repeal of net neutrality.

Question: What is it about net neutrality that would impact the profitability of these projects? Would it be fair to compare this to the price of gold and mining? If the costs to mine gold (per unit) outweigh the trading price of gold (per unit), the miners close up shop; and likewise if net-neutrality hurts the big telecom companies' margins enough for them to forego big projects?

Or what is really behind the incentives here?


texts: Complexity economics and computational economics books recommendation

texts:
I'm looking for books in complexity economics and/or agent-based computational economics.
What are some good introductory and advanced books in these fields?
Thanks in advance


texts: Where does the current debate stand on passive vs active monetary policy?

texts: The debate between active and passive monetary policy is mentioned in most macroeconomics textbooks. Where does the current debate stand? Has a consensus been reached among economists? Do economists today broadly agree that one is better than the other, or, at least that one is better than the other in certain situations etc.?


texts: What is the right amount of money supply?

texts:
As Bitcoin limits the money supply and the total amount of coins in circulation, whereas central banks have a degree of freedom to influence the money supply, I came to wonder what perspectives and constraints exist to determine the right amount of money supply.
Could one definition be "The right amount of money supply incentivizes economic activity without causing excessive inflation"?


texts: How are price and quantity demanded going to be affected?

texts: The consequences of decriminalizing illegal drugs have long been debated. Some claim that legalization will lower the price of these drugs and reduce related crime and that more people will use these drugs. Suppose that some of these drugs are legalized so that anyone may sell them and use them. Based of positive economic analysis, how are the price and quantity demanded going to be affected? How will the legalization affect related crime?


texts: Do leverage pools force net negative outcomes? How are leveraged futures profits payed?

texts:
Pre-note: Although I am trying to make this question general, in the case that there are any ambiguities, I would like to direct this question toward cryptocurrency futures trading platforms that offer leverage

In general, when it comes to trading, one can make the statement "for every person that gains money, someone else loses money".
What this means is that the net outcome of an entire system is zero, i.e the profits and losses sum to zero.
This is indeed the case between two time periods if the opening and closing price of a stock happens to be the same. However, if the closing price is greater than the opening price, then the net outcome in that time window is positive/profit, and vice versa.
So in simple terms, if the general trajectory of a price is upwards then there are more people making profit than making losses.
In general, when the economy is going well, you do expect more people to be making profits than making losses.
However, this begs the question, how is this net positive outcome achieved when trading with leverage pools?
Those that put money into these pools are expected to be able to eventually take that money out (let's forget for a moment that they also intend to make interest).
However, if more people are making profit than making losses, doesn't money have to be taken from the pools to be paid out to gainers, which results in the available money in the pools shrinking? Is this the case, and if so how does this not pose problematic? What solutions are used to prevent this in these pools?
The only solution I can think of is to force the system to be a net zero outcome (where there are equal gainers and losers) or a net negative outcome (where there are more losers than gainers). This solution could be achieved through transaction fees, funding fees, lending fees, etc. Is this the case in these pools, is the net outcome forced to not be positive? If so, wouldn't people be less likely to use these leverage pools?
One of the things that makes me confident when investing money is that long-term (assuming the economy is going well), there are more gainers than losers. Is it possible to still have this confidence in leverage pools? Or are there more losers than gainers? Because it seems to be that you can't have this confidence, because it seems to me that leverage pools have to force a net zero or net negative outcome.
It would be great to get clarity on this, please let me know if my question is too complicated and needs improvement.

Edit: This question seems to apply more to future/perpetual markets, where you are in a closed system. When working with the actual underlying asset, profits are also gained from selling to people outside the leverage exchange you are using, so this problem doesn't seem to exist here.


texts:
What's the difference between "industrial capitalism" and "agrarian capitalism" and "mercantilism" and the "industrial revolution" and the 20th century ideas of "Keynesianism"?

Is agrarian capitalism- plantations, industrial capitalism- the exploitation of women working in clothing factories?


texts: MLE using multivariate normal distribution

texts:
I am reading econometrics lecture notes of a Japanese professor. To explain MLE estimation he uses multivariate normal distribution.

As you can see, the first line is the loglikelihood function and the second line is proportional to the first line equation. I cannot get my head around this. How and why the first equation can be written as the second one using trace of a matrix. I heard about "trace trick" and this must be the application of this trick, but I need help to understand it and possibly use it.
Thanks


texts: What does the GNI/GDP ratio of a country signify about?

texts: What does it mean, if the GNI of a country is lower than the GDP


texts: Was the 2008 financial crisis caused more by the US subprime mortgage lending or more by an international energy and oil pricing crisis?

texts: I recently read The Big Short by Michael Lewis in which the depiction of the role of subprime mortgage lending in the US and then run away speculation on CDOs are shown to be the central and primary cause of the 2008 financial crisis.  Then today I watched a lecture called The Third Industrial Revolution (https://www.youtube.com/watch?v=QX3M8Ka9vUA) by Jeremy Rifkin in which he portrays the 2008 subprime mortgage crash as being an "aftershock" of the real financial "earthquake" which was international oil prices hitting $147/barrel 6 months prior to the 2008 crisis.  He continues this analogy by insisting global policy makers are, when they bail out the banks who invested in subprime mortgages or change investing laws, "trying to address the aftershock rather than the earthquake."  I have never heard this view of the situation and am ignorant as to how international oil pricing functions and affects the world economy.  How do people in the know square the relative significance of the US subprime mortgage investment bubble with this international oil price situation when trying to label the root causes of the 2008 global financial crisis?


texts:
In 1966 Kevin Lancaster proposed a new Economic Theory based on product characteristics instead of product utility. I would like to know the status of this theory nowadays among economists specifically those dedicated to Economic Theory.
Thank You


texts: Why does a rise in the savings rate result in an increase in the capital stock intuitively?

texts:
I understand mathematically how it works. But what is the actual process intuitively.
Thanks


texts: Equations of "rational mechanics" and general equilibrium

texts:
Vilfredo Pareto, referring to the equations that determine equilibrium, wrote:

  These equations do not seem new to me, they are old friends. They are
  the equations of rational mechanics.

This quotation appears in the paper On the Economic Phenomenon: A Reply to Benedetto Croce he doesn't make clear what specific equations he's referring to. As someone with a physics background I am curious if anyone knows/could guess what he is referring to.


texts: Why is the rising price of a commodity inflationary, while the rising price of money is disinflationary?

texts: Everybody buys oil and everybody borrows money. If the price of oil goes up, we call that inflation and the central bank uses monetary policy (rising interest rates) to reduce inflation. Why is the price of money (i.e. interest rates) different from the price of any other commodity in regards to its impact on inflation? Does not a rising price of oil in itself cool the economy in the same way as a rising price of money?  If we need to spend more to drive our cars, then we can spend less on televisions?


texts: Why can't countries immediately stop the deficit?

texts:
Governments often say things like "we will reduce the deficit by 2025".

Why can't they simply eliminate the deficit immediately by spending less than the taxes they receive?

Surely if a country is in debt, it should try and run a surplus so it can start paying off it's debts and reduce its interest payments.

Is there some reason why they can't do this?


texts:
I recently joined an econ class. I am so lost on how to prove their equality. As a math standpoint, these are completely different equations. Please help!

u1 (x1, x2) = x1^(2/3) x2^(1/3)
u2 (x1, x2) = 4ln (x1) + 2 ln(x2) +3


texts: Indirect Impacts Of The Netherlands Cutting Greenhouse Emissions?

texts:
On 24 June 2015, the Dutch District Court in The Hague ruled that the government must put policies in place to deliver, by 2020, cuts in the country's greenhouse gas emissions of at least 25%, relative to 1990 levels.

The government, for months leading up to the tribunal appearances, had been saying that it was hard for them to cut it down by any more than 17%.

What are the likely economic consequences of this ruling?


texts: Short run Aggregate supply curve is horizontal or positively sloped?

texts:
I want to understand the adjustment process from Very short run production decision to Short run production decision to Long run production decision. As far as I've understood: consider an increase in demand due increase in money supply. This shifts AD curve to the right.
 Now in the very short run firms are willing to supply whatever demanded at the same price (I want to know why. They'll ask workers to work overtime so they'll have to pay extra wages so why would they not charge higher price instantly?)
After the very short run, prices rise(why?) and demand falls so output goes down after the initial increment.
In the long run, prices keep rising (why?) and output finally comes back to initial full employment level.
I couldn't find proper coherent explanation of this process in mankiw or in dornbusch or in Able and Bernanke.


texts: Model for simple production chain economy

texts: Given a simplistic economical model with a finite number of possible resources, and a set of machines that can be produced (with a cost) that that take some or none input, and give some output per time-division, I wish to find the time-optimal production chain for a goal. What sources of information and fields of production management and economics could I use to find a solution? Can the solution be found with any other method rather than a deep search of a Markov-decision chain?


texts:
I'm reading a paper and at some point the author writes :

"We do this by decomposing monthly real crude oil prices and analyzing the
effect of the smooth part on the degree of the stock market instability."

What does he mean by "smooth part"? Is it the same meaning we have when dealing with integers?(factoring to prime numbers) Or is it something else? I don't understand what "the smooth part" means and how it is of any importance.

Sorry in advance if the question is too beginner.


texts:
Many firms in the United States file for bankruptcy every year, yet they still continue operating. Why would they do this instead of completely shutting down?
Well, obviously there's a reason behind this like it's less costly somehow. But I can't understand it completely, though.
Can anyone explain this, please?


texts: Why 1000 Rs and 500 Rs not accepted in Bhutan and Nepal?

texts: In Nepal and Bhutan, Indian rupee is accepted but 500 Rs. And 1000 Rs note is not accepted. Cam there be any specific reason behind this?


texts:
I have the following optimisation problem:

max $E_{0}\sum_{t=0}^{\infty}[log(c_{t}) + log(m_{t})]$ subject to $y + \frac{M_{t-1}}{p_{t}} + R_{t-1}\frac{B_{t-1}}{p_{t}} = c_{t} + m_{t}+b_{t}+\tau_{t}$

Where lower case letters indicate real variables and $R$ is the gross nominal interest rate.

I am trying to solve this using the value function approach but I am having a difficult time understanding what the state variable should be in this case. I tried using wealth as the state and formulated the following value function:

$V(a_{t}) = \max_{c_{t}, m_{t},b_{t}} [u(c_{t},m_{t}) + \beta V(a_{t+1})]$

where $a_{t} = y+ \frac{M_{t-1}}{p_{t}} + R_{t-1}\frac{B_{t-1}}{p_{t}} $ and initial values are assumed to be given. My problem now is that I don't know what to substitute for $a_{t+1}$. I have tried forwarding the left-hand side of the budget constraint (i.e $a_{t+1} =  y + \frac{m_{t}}{\pi_{t+1}} + R_{t} \frac{b_{t}}{\pi_{t+1}})$ and then differentiating w.r.t c,m and b but my results are very strange. Furthermore, if I have understood correctly, I also have to find $V_{a}(a_{t})$ which I cannot do with this substitution.

I am trying to learn this using Walsh's book and in his example, the budget constraint has capital which appears on both sides of the budget constraint, this allows him to re-write capital as a function of $a_{t}$. I tried to do the same but with real balances;

From the budget constraint I can write $m_{t} = a_{t}-c_t-b_t-\tau_t$

So, $V(a_{t}) = [u(c_{t},m_{t}) + \beta V(y + \frac{a_{t}-c_t-b_t-\tau_t}{\pi_{t+1}}) + R_{t} \frac{b_{t}}{\pi_{t+1}} ]$

Again I differentiate w.r.t c,m and b and this time my results are looking less crazy but still not correct. I get:

(c) $u_{c} - \beta V_{a}(a_{t+1})[\frac{1}{\pi_{t+1}}] = 0$

(m) $u_m + \beta V_{a}(a_{t+1})[\frac{1}{\pi_{t+1}}] = 0$

(b) $\beta V_{a}(a_{t+1})[\frac{R_{t}}{\pi_{t+1}} - \frac{1}{\pi_{t+1}}] = 0$

And lastly, $V_{a}(a_{t}) = \beta V_{a}(a_{t+1})[\frac{1}{\pi_{t+1}}] $

The final condition implies that $u_{c} = V_{a}(a_{t})$ which is similar to Walsh's answer but I can't seem to obtain a form of the Fisher equation and money demand function from my workings.

There is also the equilibrium condition $c_{t} = y-g$ but I have no idea when to impose it.

Any thoughts on what I have done incorrectly?


texts: Data Request: Raw housing stock of particular city

texts:
I want to get the raw number of units of housing stock that there is in a particular city in month $X$ of year $Y$ (even yearly data would be fine). This place shows yearly stock from 2010 onwards. Here shows data for every 10 years. This link makes me think there should be more yearly data since this has 2013 data.

Is there anywhere I can find a more comprehensive data set?


texts:
It's been awhile since I've taken introductory microeconomics. I read budget lines can be discontinuous awhile ago but am suspicious as to such a concept being discussed in intro micro classes particularly calling them budget 'lines'.

The problem:

  Say Jill likes food and clothing. Jill has 200 to spend on food and clothing. One unit of food costs \$1 while one unit of clothing costs $2.

Budget line is 200=F+2C

  Say Jill receives an 80% discount on food but it applies up to 100 units.

New budget line is 200=0.2F+2C for 0-100 then same as old for 100 onward?

So it's discontinuous? So it's not really a budget 'line' right (though piecewise, it's a line, I guess).


texts: Walrasian Equilibrium intuition given prices and some initial allocation

texts:
Suppose we have two agents who are each assigned some initial allocation of two different goods, where the prices of each good are given. Also, suppose the utility functions for each agent are weakly concave and strictly increasing.

If, after receiving their allocations, no trades occur between the two agents, can we infer that this initial allocation represents a competitive equilibrium (CE)?

My intuition says that it may not be a CE, because perhaps agent 1 has an optimal allocation, but maybe agent 2 wishes that he could trade with agent 1 to change his (agent 2's) allocation. Although this would not be a competitive equilibrium, this scenario would still be Pareto efficient. Is my analysis correct?


texts: Why goods prices are normalized in each period in growth models?

texts:
As it is known, in simple economic growth models such as the Solow or the Ramsey model, all goods prices are set equal to 1 in each period.

Also, as we known from general equilibrium theory, homogeneity of degree zero of demand implies that only relative prices matter. Therefore, we can always set one price equal to 1 (or do other types of "normalization").

However, in economic growth models (which are general equilibrium models) we have an infinite number of good prices and all are set equal to 1. Why do we always do that? Doesn't it affect the analysis of the model?

I have search for an explanation, but I've been unable to find one. I have a hypothesis, though. Maybe we can normalize goods prices in each period because we assume the economy is in equilibrium at each instant. Then, by the same argument we use in static models, we can normalize goods price in each period. Is this explanation true? Or there is some other reason? And, if it is true, how do models that feature inflation are made?


texts: Is whatever they calculated a valid "demand elasticity"?

texts:
https://medium.com/@kwrdarisipudi/demand-elasticity-of-iphones-1e3a7bbb9eac
They are saying iPhone demand is less responsive to price over time, but I disagree.
Income shifts the demand curve. Higher income exposes preference to more expensive phones, which makes it appear the consumer doenst care about price when in reality they have the same preference just scaled by income.
And it doesnt look sustainable, either, because the latest apple phones are price cut. There's additional factors like financing availability and competing products that make this not useful as a demand elasticity.
Am I right or they?


texts: German economic growth in the 20th century

texts:
Regarding this great animation:

Animation: The World’s 10 Largest Economies by GDP (1960-Today)

I have the following questions:

Why did Germany's GDP shrink so much from 1995 to 2000, while the GDP of the US grew very healthily?
What was the factor of US growth in that period and why did other economies did so poorly, especially Germany's?
Is it because the GDP is counted in US dollars which makes other countries' GDP under-counted?


texts: Microeconomics book for a mathematician?

texts:
Background

I have studied matematics for 4 years at the university, both pure and applied, e.g. topology, functional analysis and valuation of Derivative Assets. Currently I'm taking a course called advanced microeconomics, using Hal Varian Microeconomics Analysis. I feel that this book has a lot of explaining text that I would better understand with "pure math definition". E.g. Just defining risk-averse as a concave utility function.

So I wonder if there is book more related to the format of a math textbook that I can use as a secondary book, to get another perspective? I'm asking this question because during my studies I often find myself reading through a lot of text and when I arrive at a mathematical definition in the book or e.g. wikipedia, then I can understand what the author is trying to tell me.

I have looked at this and this questions but both are >2 years old, thus maybe there is something new on the market?


texts: Changes to lookup code/symbols on the NASDAQ?

texts:
I'm not entirely sure if I've asked the right question, but does anyone know why certain symbols (I assume they are the symbols) change on NASDAQ?

In particular I'm wanting to keep a track of the Natural Gas price. It's current code is NGH16.NYM and I've been following it here http://finance.yahoo.com/q?s=NGH16.NYM&ql=0

However last month the code was NGG16.NYM and had this URL http://finance.yahoo.com/q?s=NGG16.NYM&ql=0

I've been struggling with this for a while now, and at first thought it was an incremental code. That pattern didn't seem to stick.

Any ideas? And any idea if I can predict the next ones?

Thanks :)


texts:
I am supposed to calculate term structure of interest rate. I got the table including several bonds with price of the bond, face value and number of years till maturity.

I calculated yield of each bond, picture attached below.

My question is.. how am I supposed to calculate the term structure of interest rate from this data? In other words I need the spot rates.
Comma is meant as decimal seperator.
Thanks for any help.


texts: Is this an an endogeneity/simultaneity problem?

texts:
I would like to know if the logic in these two situations is correct.
Situation 1: Let's say we have a continuous dependent variable, $y_1$, that then has a causal impact on an unobserved variable, $\rho$. This unobserved variable then has a causal impact on a variable, $y_2$, which has a causal impact on $y_1$. We want to estimate $ \frac{\partial y_1}{\partial y_2}$. So, we have a set of structural equations as follows:
$$y_1 = f(y_2, \mathbf{x_1})+ e_1$$
$$\rho = f(y_1, \mathbf{x_2})+ e_2$$
$$y_2 = f(\rho, \mathbf{x_3})+ e_3$$
where the $\mathbf{x_i}$ terms are exogenous and the $e_i$ terms are errors. By substituting the second equation into the third, we can see that we would have simultaneity and our estimates of the impact of $y_2$ on $y_1$ would be biased if we could not control for $\rho$ or some proxy for it in our estimate of the structural equation for $y_1$.
I am particularly unsure about this last part in italics. Could we use the proxy for $\rho$ in the estimate of the structural equation for $y_1$, or would we have to do 2SLS, with the proxy for $\rho$ being included in the first stage but excluded in the second?
Situation 2: Let's say we have a percentage dependent variable, $s_1$. Let's say the complement of $s_1$ is made up of two other percentages, $s_2$ and $s_3$. Furthermore, let's say that $s_3$ has a causal impact on an unobserved factor, $\rho$, and that $\rho$ has a causal impact on $y_2$, which has a causal impact on $s_1$. We want to estimate $\frac{\partial s_1}{\partial y_2}$. Thus, we have the following structural equations:
$$s_1 = f(y_2, \mathbf{x_1})+ e_1$$
$$\rho = f(s_3, \mathbf{x_2})+ e_2$$
$$y_2 = f(\rho, \mathbf{x_3})+ e_3$$
Let's now say that $s_2$ is more or less constant across observations. Thus, there is generally an inverse relation between $s_1$ and $s_3$. This implies that we can rewrite $s_3$ in the second structural equations in terms of $s_1$:
$$\rho = f(1 - (s_1 + \bar{s}_2), \mathbf{x_2})+ e_2$$
Then, just as in situation 1, by substituting this equation into the structural equation for $y_2$, we can see there would be simultaneity and our estimates of the impact of $y_2$ on $y_1$ would be biased (once again, I am unsure about whether controlling for $\rho$ or a proxy for it in our estimate of the structural equation for $y_1$ would solve this).


texts: Willingness to accept is different from willingness to pay - is there a name for this

texts:
Given the situation below, can someone help me identify/name the logical phenomenon?
So I own a laptop that I don’t use…. Someone has offered me £1000 dollars  for it but I decided not to sell it. I myself would NOT pay £1000 dollars for it… I feel like there’s some kind of illogical behaviour going on here because me not selling it for £1000 is financially equivalent to me buying it for $1000. I think in both cases I’m giving up £1000 for a laptop. Do you guys know  if there a word/name for this?


texts: Unable to determine price ratio for a pure exchange economy

texts:
The problem is simple. However, I'm having trouble deriving the price vector for the system. What exactly am I doing wrong/missing out?

Two consumers.

$$
U_A = \min(x,y), \hskip 20pt U_B = x+y.
$$

Initial endowments
$$
(x_A,y_A)=(100,100), \hskip 20pt (x_B,y_B)=(50,0).
$$

Putting A on the bottom left, the contract curve will be a line with slope 1 from A, from point (0,0) to (100,100), A's endowment point. [Seen from A's perspective.] All points on this contract curve are points of 'tangency' between A's kinked indifference curves, and B's linear indifference map.

$x_A= 100(p_x+p_y)/p_x $

$x_B = 0$  (if  $p_x>p_y$)

$x_B = 50$  (if  $p_x<p_y$)

A cannot benefit from more than (100,100), while B will benefit from as much of either good as she can get: i.e. endowment point lies on contract. Thus, the endowment point can be the competitive equilibrium allocation.

The question is, what will be the equilibrium price vector.

If we keep the price vector as (1,1), X can sell and buy back endowment, and so can B. So, (1,1) makes the endowment point affordable. However, so does any price vector where $p_x<p_y$ (ensuring 0 demand for Y from B.)

Does a unique price vector (ratio) exist for this system? How do we derive it? And what am I doing wrong?

Any help (resources on CE problems of this kind) will be wonderful. Thanks.


texts: Question on Fama-French Three Factor model

texts:
I am currently taking an econometrics course, and the final assignment in that course is to write a research paper using econometric ideas. I have read Fama and French paper on the three-factor model and was impressed by the model. I would like to write my research paper using the same methodology for the Hong Kong stocks and see if I get the same results.

I am wondering if it's possible for me to run regression using the same data sets that Fama and French used in the model on the U.S. stocks. It will help me to see if I am on the right track. If I get the same numerical values and results as theirs, it shows that I am doing it correctly. Then I can use the methodology to the Hong Kong stocks.


texts: Interpretation of coefficients in ECM for consumption

texts:
Say that we are regressing consumption $C_t$ on time $Y_t$. Furthermore, suppose that both series are $I(1)$ and are co-integrated.

Given this, we set up the error correction model (ECM) as follows: $$\Delta C_t = \beta_0 + \beta_1 \Delta Y_t + \theta(C_{t-1} - \gamma_0 - \gamma_1 Y_t) + u_t$$ which is estimated using the 2-step Engle-Granger approach.

My question is: What is the economic interpretation of $\gamma_1$? Surely we cannot interpret this as the marginal propensity to consume (MPC)? I interpret it as describing the long-run equilibrium of the system.

However, I'm struggling to explain why this is the case, since mathematically: $$\gamma_1 = \frac{\partial C_t}{\partial Y_t}$$ which is exactly the definition of the MPC.

On the Wikipedia page on ECMs, they describe $\gamma_1$ as the average propensity to consume (APC), which makes a lot more sense to, but which doesn't sit well with me since mathematically: $$\text{APC} = \frac{C}{Y}$$ and clearly that is not the definition of $\gamma_1$ since: $$\frac{C}{Y} = \frac{\gamma_0}{Y} + \gamma1$$

Could someone help me sort out my confusion?


texts:
Suppose I have two markets, Home and Foreign. Suppose that

$$\frac{p_1}{p_2} = \frac{c_2^F}{c_1^F}$$

$$\frac{p_1}{p_2} = \frac{c_2^H}{c_1^H}$$

Supposedly I am supposed to be able to show

$$\frac{p_1}{p_2} = \frac{c_2^F + c_2^H}{c_1^F+ c_1^H}$$

But by rules of simple algebra, it would seem

$$\frac{p_1}{p_2} = \frac{c_2^Fc_1^H+c_1^Fc_2^H}{2c_1^Fc_1^H}$$

MY QUESTION:
What step am I missing to get
$$\frac{p_1}{p_2} = \frac{c_2^F + c_2^H}{c_1^F+ c_1^H}$$ ?


texts: What exactly are Giffen goods and are they of purely theoretical interest or has there been empirical evidence of their existence?


texts: What was the Summers memo of 1991 sarcastic about?

texts:
I have read a twitter thread about Summers memo (wikipedia article) today, and trying to understand the last part (bolded).

  The problem with the arguments against all of these proposals for more pollution in LDCs [Least Developed Countries] (intrinsic rights to certain goods, moral reasons, social concerns, lack of adequate markets, etc.) could be turned around and used more or less effectively against every Bank proposal for liberalization.

So, if I understand, moving toxic production to LDC to decrease world-wide cost of healthcare is a bad thing due to some argument. But there are policies that are deemed to be good and accepted by World Bank, that can be struck down using the same argument?

Question: Which policies are those? Which "Bank proposal for liberalization" does the memo refer to?

The wiki article says also that

  Summers had only signed it, and that it was intended to be "sarcastic"

But I am not sure toward what policies or arguments this sarcasm was pointed.


texts: How do U.S. treasury yields impact yields of other sovereign debt markets?

texts: I read somewhere that when the U.S. Treasury yields rise, it will also have a "gravitational pull" on yields of other sovereign debt markets. For example, when the U.S. Treasury yields rise, the German bund yield will also rise. Is it because when US yields rise, sovereign bond investors will move out of lower yielding Eurozone sovereigns into US Treasuries? Can someone please explain the relationship or transmission mechanism?


texts: What happens to the stock market if no one wants to buy?

texts:
When the stock market crashes, if everyone wants to sell, who will buy? Is it possible that  no one could sell his shares because no one wants to buy them?  If so, what would happen? Would share price decrease? Would it drop to zero?
I was told that the company will buy if everyone wants to sell. I don't think that is true.


texts: Do large public companies ever "quit while they're ahead"?

texts:
Large public companies (e.g. S&P 500) seem to end their lives in one of two ways: either they're acquired (or taken private), or they go bankrupt.

Theoretically it seems like there should be a third option: to wind up the company and return assets to shareholders (as Michael Dell famously suggested Apple should do). A company that realises its industry is in decline and it's about to become unprofitable as a business surely ought to do this; it would give the shareholders at least some cash, rather than the nothing they'll get in bankruptcy. But I can't remember this ever happening, at least in my lifetime (alternately, maybe it's common enough to simply not be news?). A struggling company like HP or Nokia or Blackberry seems to always keep going to a buyout or the bitter end, even when "everyone" can see they're doomed.

Are large public companies ever simply wound up? If not, why?


texts: Models for online markets with reputation system

texts: The only relevant model I'm aware of is Liu Qingmin(2011 R.E.S). Is there any other decent models dealing with the mechanism of online markets under reputation system, and perhaps linking to regulation?


texts: Why can't goverments print money to fund their economies?

texts: In previous questions I understood that printing money and injecting it in the economy generates inflation because there is a bigger demand for the same offer (please correct me if I'm wrong) so it's not a good idea. After thinking this, a new question arose. Why can't goverments print money to fund the productive sector? In that way, it can get money in circulation while generating more offer so there is no inflation. I can't understand what prevents goverments to do that.


texts: utility maximization with nested Cobb–Douglas–CES preferences

texts:
I'm trying to understand the following paper: Hsieh & Ossa: A global view of productivity growth in China (2016). The pdf can be found here: https://faculty.chicagobooth.edu/chang-tai.hsieh/research/hsieh_ossa_jie.pdf

I struggle to understand the utility maximization problem right at the beginning of the paper. Can someone show me how to maximize the following utility with respect to $x_{ijs}$:

$U_j=\prod_s^S\left(\sum_i^N \int_0^{M_is^e}x_{ijs}(\nu_{is})^{\frac{\sigma_s-1}{\sigma_s}}d\nu_{is} \right)^{\frac{\sigma_s}{\sigma_s-1}\mu_{js}}$

The end result is:

$x_{ijs}=\frac{p_{ijs}^{-\sigma_s}}{P_{js}^{1-\sigma_s}}\mu_{js}E_j$

where $P_{js}=\left(\sum_i^N M_{is}^ep_{ijs}^{1-\sigma_s}\right)^\frac{1}{1-\sigma_s}$

$N$: number of countries

$S$: number of industries

$M_{is}^e$: number of entrants in industry s of country i

$x_{ijs}$: quantity of an industry s variety from country i consumed in country j

$\mu_{js}$: fraction of country j income spent on industry s varieties

$\sigma_s>1$: elasticity of substitution between industry s varieties

$p_{ijs}$: price of an industry s variety from country i in country j

$P_{js}$: ideal price index in industry s of country j

$E_j$: total expenditure in country j


texts: Are there two deadweight welfare losses associated with a Pigovian tax?

texts:
I am constructing a diagram for an indirect tax (specific) imposed to correct a negative externality of consumption.

There is a deadweight welfare loss from the externality (represented in blue) because, although it is reduced,the tax does not achieve to shift the supply curve to a point where MSB=MSC (Qm).

However, the tax itself also should produce a deadweight welfare loss (represented in green). Is it correct that there are two deadweight welfare losses in this situation or is there no deadweight welfare loss associated with a Pivogian tax?


texts: Why consumption is defined as $ C_t:= \left(\int^1_0C_t(i)^{\frac{\epsilon-1}{\epsilon}}di\right)^{\frac{\epsilon}{\epsilon-1}} $

texts:
I am reading Monetary policy, inflation, and the business cycle: an introduction to the new Keynesian framework and its applications by Gali.

In section 3.1 he presents/defines the consumption as
$$
C_t:= \left(\int^1_0C_t(i)^{\frac{\epsilon-1}{\epsilon}}di\right)^{\frac{\epsilon}{\epsilon-1}}
$$

$\epsilon$ is the elasticity of substitution and $i$ indexes the goods available for consumption. It is related to the New Keynesian Model.

Can someone give me verbal explanation of why it make sense to define the consumption this way?

$C_t(i):$ How should interpret the $i$-line?


texts: All-Pay Auction Mixed Strategy Equilibrium

texts:
I am currently struggling with this exercise.
Professor Nash announces that he will auction off a 20 dollars bill in a competition between two students chosen at random. Each student is to privately submit a bid on a piece of paper; whoever places the highest bid wins the 20 dollars bill. In the event of a tie, each student gets 10 dollars. The auction is all-pay: each student must pay his/her bid regardless of who wins the auction.

HERE is the question

Suppose each student could borrow money from the other students in the class, so that each of them had a total of $11 to bid. Find a Nash equilibrium in this case?
I know I have to find a mixed-strategy  nash equilibrium but I don't understand how I can't compute it.

Thanks


texts: If two utility functions represent homothetic preferences, will their sum also be homothetic?


texts: Wouldn't an unconditional basic income lead to an inflation that negates its effect?

texts:
There are several version and denomination for a basic income. In this question, I will call unconditional basic income the situation were all citizens of a country receive regularly a lump-sum of money, independently of their age, their employment status and job,etc. I will assume that, at the moment the basic income is  instituted, it is larger than the poverty threshold. I am also assuming that the basic income is not a substitute of other welfare subsidies.

The concept is gaining popularity these days, and for many reasons, economical or philosophical.

My understanding of offer and demand is that, if people can pay more for a product and are willing to do so, then prices will increase. So, it seems that, after the introduction of the basic income, there will be mechanically a large inflation.  In a short time, people with no job and that relied mostly on the welfare system will be poor again. Worse, people with low income will be closer to the new poverty threshold.

My questions:
1) What natural mechanical effects prevent an over-inflation after the introduction of a substantial basic income? By natural, I mean any direct or indirect effects of the sole introduction of the basic income.

2) If an inflation cannot naturally be avoided, what measures are usually suggested together with the introduction of the basic income?

Edit: my question is close but not an exact duplicate of this question. In the example of the other question, $A$ would receive $30$ and $B$ would receive $90$ for an unconditional basic income of $30$. If the two questions are equivalent, please explain.


texts: How Does GDP Differ From NNW as an economic measure?

texts:
When people talk about the size of an economy, they often refer to the GDP or changes to it, but seldom refer to the Net National Wealth. Obviously there are some superficial differences:

GDP is Gross not Net
GDP is Domestic not National (Within borders vs. owned by citizens)
GDP is $\Delta$Capital whereas NNW is theoretically all the capital stock owned by a country's citizens.

It appears the US switched from publishing GNP to GDP relatively recently (~1970), which seems like a less direct measure of its citizens economic welfare, but even that seems like an already abstracted measure from NNW.

So again, what are the differences between the two measures as economic indices that makes one more desirable (or at least discussed) than the other.


texts: "risk free interest rate" in Black Scholes

texts: In Black Scholes model r is defined as risk free interest rate. Could you please explain what is risk free? Is it same as interest rate on checking account?


texts: What physically happens when foreign currency reserves change?

texts: Assume that the United States decided to hold more yuan in the federal reserve. Which processes does that involve? I assume there is some sort of electronic exchange between the two central banks where dollars are exchanged for yuan. What happens physically? I assume that the Fed will only need to hold a portion (say, 10%) of the reserves as currency, and the other 90% will be just based on the credibility of the bank. Does that mean that the currency worth 10% of the exchange needs to be loaded in a special plane and flown from China to the US and vice versa? How often do those sorts of plane trips happen?


texts:
Can someone give an example and an exponation of how a currency may be undervalued when considering its REER (real exchange rate) in PPP terms, but overvalued when looking at the REER based on ULC (unit labor costs) in manufacturing.

So far, I have gone back to definitions:

$$REER_{ULC} \ overvalued = S \times \dfrac{w^*}{w} \\ REER_{CPI} \ undervalued = S \times \dfrac{P^*}{P}$$

Where $S$ is the exchange rate, $w^*$ wages in manufacturing sector abroad, $w$ wages in manufacturing sector at home, $P^*$ the level of prices abroad, $P$ level of prices at home.

To be overvalued we need that $REER_{ULC} < 1$. To make things simple lets say that $S = 1$. Then it should imply that $w>w^*$. For the undervaluation of the REER in PPP terms we need that $REER_{CPI}>1$. Which implies that $P < P^*$.

That being said I thought we could take a developed country as an example, where wages in the manufacturing sector would be higher. But however I don't see how we could get $P<P^*$ even if we take into account a tradable and non-tradable sector. Would it be because the prices in the non-tradable sector at home are lower than the one abroad so that they somehow compensate the overall level of prices? This would really go against my intuition.


texts: Empirically checking efficiency and equity

texts:
I am aware that because of externalities or public goods (or for other reasons) there can be no allocative efficiency on the market. I am also aware that policy makers' subjective judgement of the situation on the market (if market outcomes are distributed "fair") can be considered as equity in economics.

I wanted to empirically check if government spending can potentially increase efficiency or equity (as I think it should). I took labor productivity (a percentage of GDP) as a measure for efficiency and Gini index in disposable income as a measure for equity. While I am quite convinced with my measure of equity, as Gini tells me about the inequality of income distribution - I am not entirely sure about labor productivity. I am curious if I could choose better statistics to measure either efficiency or equity?

In my results I got that government spending on environment is positively correlated with increase in efficiency in only about 30% cases and in equity in about 50% cases. This seems a little bit counter-intuitive as environment seemed like a textbook example where there is a negative externality, so the firms maximizing their profits based on private costs tend to overproduce - and that the government intervention in that case is justified. So that I thought after the intervention, there should be increase in allocative efficiency, right? But it is a case in only around 30% of cases. What could be a reason for that?

Similarly, government spending on health. To my contention, it should increase both, equity and efficiency - but from what I've got it seems to be true in about 20% of cases. Why would that be a case?

Is it because of the measures I chose? Or my logic was simply wrong and government spending on environment causes efficiency to decrease and on health cases both, efficiency and equity, to decrease?


texts: Why are real median household incomes stagnant?

texts:
This image shows US real median household income.

It seems remarkable for its lack of growth over the last 20 years. This has been the subject of much political debate (around the "1%" and "occupy Wall Street" movements, etc.) but I am interested in more objective economic analysis of this phenomenon.

Given that people are better educated and are working with better technology (which should make them more productive), and that the real economy has grown more generally, what economic theories can explain the lack of growth in real median household income?