texts: Explaining negative "cyclic" unemployment with a production function

texts:
First of all, here is a related post. Unfortunately, it does not answer my question.
I have heard that there is an understanding of negative unemployment in economic theory. Obviously, absolute unemployment cannot be negative as it is just a number of unemployed divided by a number of potential workers at the end of the day. Yet, according to Friedman and Phelps, there is some natural rate of unemployment ($ u^* $). Therefore, it would be handy to break absolute unemployment into two:
$$ u = u^* + u_{cycle} $$
So:

When $ u_{cycle} = 0 $, the economy is working at its best.
$ u_{cycle} > 0 $ is pretty much the standard situation.
$ u_{cycle} < 0 $ is what we are interested in.

I tried to explain the existence of negative $ u_{cycle} $ to myself the following way (and I mean from the economic perspective, not mathematical):
Say, $ f(L) $ is our production function (having all input factors but labour constant to make things easier). We know the law of diminishing marginal productivity. Formally, we can have a situation when $ \displaystyle\lim_{L \to \inf} MP \ge 0 $. And that is the main blank point in my argument. If we agree that $ MP $ might turn negative, it would mean that we passed through $ f $'s optimum to the right, having the economy "overheat", not being able to perform at its best due to too many workers (which need to be paid wages).
Is my understanding right? If so, how can we be sure $ MP $ turns negative?


texts: If a substantial (though admittedly I have no idea how large) part of the natural rate of unemployment is caused by the job search, do more efficient means of communication create more efficient labor markets, and if so, can anyone quantify their impact with data?


texts: Recommended reading to understand American economic history

texts:
In India Unbound, the author goes over India's economic history, right from independence to present day. I am interested in a similar reading for the United States, specifically conditions in the 20th century.

Any decent suggestions which comes close? I found 10 books but any one in particular which stands out and is a must read?

Currently this one stands out to me, other suggestions welcome. The Rise and Fall of American Growth: The U.S. Standard of Living since the Civil War


texts: What was economics like as a field before Adam Smith, the father of *modern* economics?

texts:
Adam Smith is called the "father of modern economics" and his book The Weath of Nations, a fundamental work in the field of economics, is considered the first modern book on economics.  In addition, economics first became a study in 1776 when The Wealth of Nations was published.

Why is the word "modern" used in both descriptions?  I know that individuals throughout the centuries and even Aristotle have dabbled with some economic theories, but I do not recall anyone making any significant contributions to economics before Adam Smith.

Were there important contributions to economics made before 1776?
If not, then why do we use the term "modern" even if there was no one in the study previously?


texts:
Why unemployment quantity can be larger than the market employment based on this price ceiling supply/demand chart?

Also, Isn't that (quantity demanded at minimum wage + unemployment = market employment)?


texts: Joint Dynamic Programming: Group Activity

texts:
Here we have two agents who can spend their time doing some group activity ($h$) or staying at home ($l$). Each agent $i$ is trying to maximize their respective dynamic programming problem:

\begin{align}
& \max \sum^\infty_{t=0} \beta^t h^{\alpha_i}l_i^{1-\alpha_i} \\
& \text{s.t.} \quad h_i + l_i = \bar{T} \\
& h = \min\left\{h_i, h_{-i}\right\}
\end{align}

Is this problem well defined? That is, is there a solution/does the question make sense economically?
Is there an equilibrium where $h_i = h_{-i}$, and if so, when? Only when $\alpha_i = \alpha_{-i}$?

(Note that typical Inada conditions and non-negativity constraints apply.)

Edit: Okay, to make this an actual dynamic programming question (derp), I offer a modified version of this question as well for your perusal:

\begin{align}
& \max \sum^\infty_{t=0} \beta^t h_t^{\alpha_i}l_i^{1-\alpha_i}k_t\\
& \text{s.t.} \quad h_{i,t} + l_i = \bar{T} \\
& h_t = \min\left\{h_{i,t}, h_{-i, t}\right\} \\
& k_t = (1-\lambda + \frac{h_t}{\bar{T}})k_{t-1} \cdot
\end{align}

Where $k$ is some "capital" stock in the group activity that makes people enjoy the activity more, the more it is done. Obviously $\lambda \in (0,1)$


texts: Elasticity with perfectly inelastic / elastic demand

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


texts:
I have to maximize following expected utility function using Kuhn tucker conditions -

Since expected utility function are increasing $C_{1,t}$ and $C_{2,t}$ so constraints (i) and (ii) will hold with equality. Thus, I substituted these constraints into the objective function.

Note: Here, only $q_t^e$ is the only variable and expected utility function is maximized subject to $q_t^e$

For simplification, I denoted M= (1-$q_t^e$)$w_t$ + $q_t^e$$w_t$$z_t$

This made $C_{1,t}$ = nM and $C_{2,t}$= (ARθ/$z_t$)M

I also broke down constraint iii into two constraints $q_t^e$≤1 and -$q_t^e$≤0

I set up the legrange:

L = (1-π)[${(nM)}^{-γ}$]/(-γ) + π[${((ARθ/z_t)M)}^{-γ}$]/(-γ) + $λ_1$(1-$q_t^e$) + $λ_2$(0+$q_t^e$)

Differentiating with respect to $q_t^e$

(1-π)[${(nM)}^{-γ-1}$][n($z_t$-1)] + π[${((ARθ/z_t)M)}^{-γ-1}$][(ARθ/$z_t$)($z_t$-1)] = $λ_1$ - $λ_2$

$λ_1$(1-$q_t^e$) =0;   $λ_1$≥0

$λ_2$(0+$q_t^e$) = 0;  $λ_2$≥0

Case 1: $λ_1$=0 and $λ_2$

I got (1-π)[${(nM)}^{-γ-1}$][n($z_t$-1)] + π[${((ARθ/z_t)M)}^{-γ-1}$][(ARθ/$z_t$)($z_t$-1)] =0

Which boils down to M=0

which gave me - - > $q_t^e$ = 1/(1-$z_t$)

But solution provided is of the following form -

My answer doesn't match the solution provided. Can someone please look at my solution and tell me what did I do wrong?


texts: How does the notion of utility differ from that of value?

texts: Is utility merely the notion of value in the subjectivist/marginalist (aka neoclassical) school?


texts: Can stimulus packages lead to hyperinflation?

texts:
I have a limited understanding of economy, however, I've been trying to catch up from various resources. Recently, the news are all about the enormous stimuli bills debated/implemented by governments all around the world to counterbalance the negative effects of the coronavirus. My question has two parts:

First, where do those numbers come from? In the US they are talking about $2 trillion rescue plans, a number which I have no sense whatsoever for. In simple terms, which are the most important factors lawmakers consider when coming to this number (or, at least to the order of magnitude)?
Is it possible these stimuli will lead to hyperinflation? On the short run, the stimuli won't increase the productivity since businesses will still be closed. "Dumping" money on them will indeed help them from default, but with no underlying productivity I can't see how this extra liquidity won't boost inflation. In other words, the supplies are limited due to the reduced productivity, but now the demand will increase because everyone will have free cash in their hands.


texts: Pure exchange economy with free and non-free disposal

texts:
Question is as follows:

My answers are

(I)

Let k is constant utility level

Then

$$k=\sqrt{x_A^1x_A^2}$$

$$k^2/x_A^1=x_A^2$$

The first derivative is negative. So the indifference curve is decreasing.
The second derivative is positive.

Since utility function is quasiconcave, then preferences are convex because his prefers averages to extremes.

For B

Similarly

For constant utility level k

$$k=x_B^1/(1+x_B^2)$$

Then $$x_B^2=x_B^1/k-1$$

This is straight line.

Due to the linear indifference curve he is indifferent between averages and extremes. Thus not strictly convex preference.

(II)

In order to analyze whether preferences are nonstaiated and strictly monotonic, we need to look at its MU’s.

For A,

since good 1 and 2 may decrease the marginal utility, preferences are not monotonic.  But preferences are non-satiated.

For B,

Since marginal utility is increasing, the preferences are monotonic. But preferences not strictly monotonic because getting more x2 decreases utility. However preferences are locally nonsatiated because by giving the consumer a bit more $x_B^1$ holding $x_B^2$ constant, he strictly better off.

(III)

I did first three parts in this way. However, I couldn’t proceed the last three parts that I marked with red pen. Please help me to do this. Thank you.


texts: Effect of today's decision in the US to no longer mandate contraception coverage

texts: Today the Trump administration in the USA announced they are removing the mandate that company provided health insurance include free contraception coverage. My understanding is that providing contraception for free actually reduces the overall healthcare cost in the US, since the price of pregnancy and births is extremely high compared to inexpensive pills. Therefore, from a strictly economics standpoint, I would expect that companies that elect to not cover contraception might pay higher premiums than if they were to choose policies that included coverage. Is this the case? Prior to today did religious organizations and private companies that chose not to cover contraception actually pay higher premiums, or did insurance companies just raise everyone's premiums to compensate? (Or is my original premise flawed that premiums should be higher when contraception is not covered?)


texts: Software to simulate the effects of interest rates on an economy?

texts: Is there open source software that simulates the effects of interest rates on an economy?


texts:
I encountered a question where it was given that the consumers had asymmetric preferences. I couldn't find the definition of the term in any of the microeconomics book available to me.

Can anybody explain the terms and the difference between symmetric and asymmetric preferences? Please!


texts: How to show that the estimator is consistent?

texts:
$Y_i=\beta_0+\beta_1X_i+U_i$ is my regression model for an I.I.D. sample with N=1000 observations. Suppose $U_i\sim I.I.D.(0,\sigma^2)$ and Xi are also I.I.D for i=1,2,3......1000. Xi is independent of Ui. How to show that the estimator $\beta_1={{Y_3-Y_2}\over {X_3-X_2}}$ is a consistent estimator of the OLS estimator?
Simplication gives
$\tilde {\beta}={{\beta_0+\beta_1X_3+U_3-\beta_0-\beta_1X_2-U_2}\over {X_3-X_2}}={{\beta_1(X_3-X_2)+U_3-U_2}\over {X_3-X_2}}=\beta_1+{{U_3-U_2}\over {X_3-X_2}}$
What is the next step?


texts: What caused "excess liquidity" in equity market, when CPI was deflationary at the same time period, which caused 'market crash in 1929' in USA?

texts:
To begin with, my question is NOT about the reasons of "the great depression" or "market crash" which led to the great depression.

Rather, my question is about the reasons for the 'excessive cash liquidity' which resulted in 'market crash in 1929'.
Traditional patterns tends to reflect cash liquidity distribution somewhat even across different sectors. How liquidity during 1920's in USA stands different was that, the sectors like Consumer Price Index is constantly DEFLATIONARY in the same decade when share market(and only share market) was extremely inflationary.

1970's : CPI inflationary : Other sectors inflationary(caused bubble burst)

1990's : CPI inflationary : Tech market inflationary(caused bubble burst)

2000's : CPI inflationary : Housing market inflationary(caused bubble burst)

1920's : CPI DEFLATIONARY : Equity market inflationary(caused bubble burst)

To simplify, my question is, what caused 1920's stock market inflation(presumably due to excessive liquidity) at the same time period when CPI was DEFLATIONARY(enough money was not present/spend in sector).

I am not educated in economics. I follow the subject only because it interests me. I work in a totally different field of study and thereby please excuse my ignorance about the subject for where ever I went wrong :).

thanks in advance.


texts: What impact did major fiscal policy actions taken during the Great Recession (2007-09) have on U.S. economic performance?

texts:
What impact did fiscal policy actions taken during the Great Recession (2007-09) have on U.S. economic performance?

Bush passed the Economic Stimulus Act of 2008 and also the Emergency Economic Stabilization Act of 2008 which established the Troubled Assets Relief Program. Obama passed the American Recovery and Reinvestment Act in early 2009.
Let me know if I missed something.


texts: The correlation between depreciation rate and variance of output in RBC model

texts:
I would like know the correlation between depreciation rate and variance of output in RBC model.

As you know, the basic motion of capital is as follows.

$$K_{t+1} = (1-\delta) K_t + I_t$$

If $\delta$ increases, what could happen in the variance of output?

My intuition is this; if $\delta = 1$, explanatory variable is only $I_t$.

Thus, the variance of output might increase.

However, I do not know how exactly this is going.

Anyone has specifically economic explanation of this?


texts: Calculating the optimal portfolio for an investor with quadratic utility

texts:
The problem is from Asset Pricing and Portfolio Theory by Back and can be found here.

The relevant info from section 2.5 can be found here. Given that we have the Expected value and the variance of end of period wealth, I tried substituting them into the equation, differentiating and setting to 0.

I'm not sure this is the right method, or if I'm even taking the derivative correctly. Any help would be appreciated.


texts:
I'm pretty sound with the concept behind comparative advantage, but still don't get how to calculate the exchange rate in terms of quantities of each products being exchanged, e.g. 1 apple for 2 cars etc.

Specifically: when two counties, each having two separate comparative advantages in producing two separate goods, wish to exchange these goods, how will the exchange quantity/rate be calculated?


texts: Osborne, Nash equilibria and the correctness of beliefs

texts:
In Osborne's An Introduction to Game Theory Nash equilibrium is described as follows (p. 21–22):

  First, each player chooses her action according to the model of
  rational choice, given her beliefs about the other players' actions.
  Second, every player's belief about the other players' actions is
  correct.

It seems to me that this definition is not completely equivalent to the usual definition of the Nash equilibrium as a strategy profile where each player's strategy is a best response to the strategies of the others.

The usual definition says nothing about beliefs and therefore allows for the possibility that beliefs might be incorrect.

To take a trivial possibility, consider the Prisoner's Dilemma. Suppose each player believes that the other player will not confess. Since confessing is a dominant strategy each player would still confess. So the actions constitute a Nash equilibrium even though the players' beliefs are completely the opposite of the actual equilibrium actions.

Am I right in this understanding that Osborne's definition characterizes something other than Nash's equilibrium?


texts: How much better off would the average person be if we took away enough money from the top 1% to make them no richer than the average person?

texts: In my hypothetical situation, the USA population takes enough money away from the top 1% so that they are no richer than the average person. That money is then redistributed to the lower and middle class in the country. How much better off would the lower and middle class be if this happened?


texts: I've read that increased trade tends to decrease relative wages of labor. What is the intuition behind this? Lower wages in labor imply lower demand for workers, but doesn't trade just encourage specialization, meaning that workers can just be hired by whatever industry they decide to specialize in?


texts: Germany's current account surpluses: Negative effect? How to solve them?

texts:
The case for a pernicious persistent current account deficit is easy to build: the home country is borrowing abroad for a long period and that debt may reach a point of becoming unsustainable. There are several ways to put pressure of the debtor to ensure repayment. The home private and government agents may self-regulate their spending, by incorporating their future expectations of what happens when their debt is no longer repayable (not likely). Another way is by market forces, if creditors think the home country is no longer able to service its debt, then funds for home will disappear, or there could be political pressure for repayment.

However, for Balance of trade surpluses, there doesn't seem to exist any 'economic' force at work for a downward pressure... or is it?

For example Germany has been amassing enormous surpluses since the 70's, and recently, their surpluses have reach 8.5% of GDP in 2015. How does one explain this 'economically'?

Any help would be appreciated.


texts: Can i check monotonicity with the marginal utility?

texts:
For example I have a Cobb-Douglas utility function $U(x,y)$ and I want to check the monotonicity property.
Can I use the marginal utility functions to see that they are always positive to conclude that $U(x,y)$ has the monotonicity property?


texts: Why don't profitable firms use previous profits to offset current loss

texts:
It is being reported that EasyJet expects a heavy loss in the current year due to Covid-19 pandemic. The report states that

The airline said it expected to sink into a pre-tax loss of between
£815m and £845m in the current financial year, which is worse than
analysts' forecasts of a £794m loss. It would be the first time in
EasyJet's 25-year history it has not made an annual profit.

The report also says that EasyJet has laid off more than 4000 people and has taken a government loan.
I looked at their profit profile and it looks like they have made more than 300 Million pounds profit for last many years.
Why can't they offset the loss (caused by special case) from their earlier profits rather than resort to drastic job cuts and government bailout?


texts: Does the term 'marginal' refer to the last consumer?

texts:
I was reading this answer on this website which talked about how MB = P at allocative efficiency. "Why does allocative efficiency occur when P=MC rather than MB=MC"

In this answer, it is stated that the last (i.e. marginal) consumer who buys will be the one for whom the benefit is just equal to the cost.

I'm a bit confused about the use of the world marginal. I read online that it means "one more", but isn't that different from the use of the word marginal above? And how is MB = P, isn't marginal benefit referring to many points along the curve?


texts: What does it mean when R&D is "3% of GDP"?

texts: When we talk about R&D, does it mean that the final goods of R&D amount to 3% of GDP? Or does it mean that a specific nation is spending an amount of money on R&D that is equivalent to 3% of GDP?


texts: What happens to interest rates when they are already at (near) zero and the stock market crashes?

texts:
Let's say the global stock market crashes in the coming months (it's currently at an all time high in the western world). What happens to interest rates?

"Usually", as I understand from my absolute layperson perspective, interest rates would be lowered as a counter measure. But what happens if interest rates are already (nearly) zero, as is the case in some countries?


texts: Why does the US have such low price flexibility?

texts:
I am speaking only from an observational point of view and don't have any experimental data to back-up my observations so feel free to correct me.

Why does the US appear to have a market that does not follow basic rules of Price and Demand? Higher priced products are automatically considered of better quality. And this excludes products that provide a status quo, like iPhones and designers clothing. Things that we do not even have to advertise about their brand to our friends such a basic goods, like furniture, beds, tooth brush etc.

I have observed that products above medium priced are doing better financially than lower priced products that offer the same quality of product. Hence it is difficult for a competitor to just launch a cheaper same product and do well in the market.

My personal hypothesis:

Lack of knowledge from the public, lack of skepticism, and deceiving marketing strategies from the manufacturers

Also the public in the US is highly less likely to research a purchase, and opt for a medium priced product. In addition to that, the economy does well and people feel like their time is worth more than their money


texts: If the consumer is not a price taker, does she still set marginal rate of substitution equal to the price ratio?

texts:
Consider some consumer who consumes good $x$ and $y$. The price of $x$ is fixed to be $k$. The price of $y$ is $c(y)$. The consumer's marginal rate of substitution is given by $\frac{-x}{y}$. If the consumer optimises and is a price taker, I know she should set the absolute value of this equal to the price ratio. However, her quantity demanded affects the price ratio, as her demand influences the price of $y$. So, does it still hold that she would set

$$\frac{x}{y}=\frac{k}{c(y)}$$

Or does this result fail since her quantity demanded has an affect on the price of $y$?


texts:
Assume that the instantaneous utility function $u(C)$ in equation $(2.1)$ is $\ln(C(t))$.  Consider the problem of a household maximizing $(2.1)$ subject to $(2.6)$. Find an expression for $C$ at each time as a function of initial wealth plus the present value of labor income, the path of $r(t)$, and the parameters of the utility function

\begin{equation}
U = \int_{t=0}^{\infty} e^{-\rho t} u(C(t)) \frac{L(t)}{H} dt
\tag{2.1}
\end{equation}

\begin{equation}
\int_{t=0}^{\infty} e^{- R(t)} C(t) \frac{L(t)}{H} dt \leq \frac{K(0)}{H} + \int_{t=0}^{\infty} e^{- R(t)} W(t) \frac{L(t)}{H} dt
\tag{2.6}
\end{equation}

Firstly I want to check solving for the right right values: initial wealth is $K(0)$, labor income is $W(t)$, $r(t)$ is the real interest rate defined as $R(t) = \int_{\tau=0}^{t} r(\tau) d \tau$, and parameters of the utility function are: $\rho, L(t), H$.  I have tried to solve this using the Lagrangian and using an informal approach of calculus of variations so we can ignore the integrals in these terms so that:

$$ \mathcal{L} = e^{-\rho t} ln(C(t)) \frac{L(t)}{H} + \lambda \left[ \frac{K(0)}{H} +  e^{- r(t)} W(t) \frac{L(t)}{H} - e^{- r(t)} C(t) \frac{L(t)}{H} \right] $$

$$ \frac{\partial \mathcal{L}}{\partial C} = \frac{e^{- \rho t} L(t)}{C(t) H}  - \frac{\lambda e^{- r(t)} L(t)}{H}  $$

$$\Rightarrow C(t) = e^{-\rho t}e^{r(t)} \lambda^{-1} $$

$$ \frac{\partial \mathcal{L}}{\partial \lambda} =  \frac{K(0)}{H} +  e^{- r(t)} W(t) \frac{L(t)}{H} - e^{- r(t)} C(t) \frac{L(t)}{H} $$

Plug the $C(t)$ obtained in the first partial to get

$$ \frac{K(0)}{H} + e^{-r(t)}W(t)\frac{L(t)}{H} = e^{-r(t)} \left( e^{-\rho t}e^{r(t)} \lambda^{-1} \right) \frac{L(t)}{H} $$

$$ \Rightarrow K(0) + e^{-r(t)}W(t) L(t) = e^{-\rho t} \lambda^{-1} L(t) $$

$$ \Rightarrow \lambda = \frac{e^{-\rho t} L(t)}{K(0) + e^{-r(t)} W(t) L(t)} $$

Now plugging this into the $C(t)$ equation to this obtain

$$ C(t) = e^{-\rho t}e^{r(t)}* \frac{K(0) + e^{-r(t)} W(t) L(t)}{e^{-\rho t} L(t)} $$

$$ = \frac{K(0)e^{r(t)}}{L(t)} + W(t) $$

However the solution manual has the following:

$$ C(t) = e^{R(t) - \rho t} \left[ \frac{W(t)}{L(0)/H} (\rho - n) \right]$$

It would be great if these were equivalent! .. but it does not look so to me.  And my solution does not include the $\rho$, nor $H$, so somewhere I must have messed up.


texts:
Public Good Contribution: Three players live in a town, and each can choose
to contribute to fund a streetlamp. The value of having the streetlamp is 3 for
each player, and the value of not having it is 0. The mayor asks each player to
contribute either 1 or nothing. If at least two players contribute then the lamp
will be erected. If one player or no players contribute then the lamp will not
be erected, in which case any person who contributed will not get his money
back.

a. Write out or graph each player’s best-response correspondence.

b. What outcomes can be supported as pure-strategy Nash equilibria?

Consider player $i$ with beliefs about the choices of players $j$ and $k$. If neither $j$ nor $k$ contribute then player $i$ does not want to contribute because the lamp would not be erected and he would lose his contribution. Similarly, if both $j$ and $k$ contribute then player $i$ does not want to contribute because the lamp would be erected without his contribution so he can free ride on their contributions. The remaining cases is where only one of the players $j$ and $k$ contribute, in which case by contributing $1$ player $i$ receives $2$, while by not contributing he receives $0$, and hence contributing is a best response. In summary,

$BR_i(s_j,s_k)=\begin{cases} 0 , \text{ if $s_i=s_j$}\\1 ,\text{ if $s_k=1$ or $s_j=1$}\end{cases}$

Would this be correct for (a)?

for (b) :

The best response correspondence described in (a) above implies that there are two kinds of Nash equilibria: one kind (which is unique) is where no player contributes, and the other kind has two of the three players contributing and the third free riding. Hence, either the lamp being erected with two players contributing or the lamp not being erected with no player contributing can be supported as Nash equilibria.


texts:
Here it says

In mathematics, deconvolution is an algorithm-based process used to
enhance signals from recorded data. Where the recorded data can be
modeled as a pure signal that is distorted by a filter (a process
known as convolution), deconvolution can be used to restore the
original signal.1 The concept of deconvolution is widely used in the
techniques of signal processing and image processing.
The foundations for deconvolution and time-series analysis were
largely laid by Norbert Wiener of the Massachusetts Institute of
Technology in his book Extrapolation, Interpolation, and Smoothing of
Stationary Time Series (1949).[2] The book was based on work Wiener
had done during World War II but that had been classified at the time.
Some of the early attempts to apply these theories were in the fields
of weather forecasting and economics.

How exactly is deconvolution applied on econometric time series? what are good present-day examples, or from those "early attempts", that really demonstrate the value that deconvolution brings to economics, as said above?


texts:
I am trying to test if $a_t$ granger causes $b_t$:

$$a_t=\rho_1+\phi_{11}a_{t-1}+\alpha_{11}b_{t-1}+\beta_{11}c_{t-1}+u_{1t}$$

$$b_t=\rho_2+\phi_{21}a_{t-1}+\alpha_{21}b_{t-1}+\beta_{21}c_{t-1}+u_{2t}$$

$$c_t=\rho_3+\phi_{31}a_{t-1}+\alpha_{31}b_{t-1}+\phi_{31}c_{t-1}+u_{3t}$$

I am trying to use an F test.

However, should be null be: $\phi_{21}$ = 0.

Or do I also need to set: $\beta_{21}$ = 0 because a impacts b through c.


texts:
In MWG, the authors introduce the consequentialist view of risk by assuming for any risky alternative, only the reduced lottery over final outcome matters to decision maker.

From philosophical view, how reasonable and unreasonable is this assumption? Can you provide examples where this assumption is in fact reasonable while it isn't?


texts:
Let $u(x,y)=f(x)+y$ be a quasilinear utility. Now we rotate it by 45 degrees, (such that the $x-$axis becomes the direction of $(1,1)$)

$v(x,y)=f(x-y)+x+y$. Is $v$ also a quasilinear utility? What is its name? It share many similarity with quasilinear utility such as parallel indifference curves. Being a rotation of quasilinear utility seems like the iff condition of parallel indifference curve.


texts: Why would creditors accept a comfort letter that can't be legally enforced, from borrowers that refuses to guarantee?

texts:
Prof Richard Taylor, Damian Taylor. Contract Law Directions (6 edn, 2019). p 65. Para 1.

  You might be wondering why businessmen bother to make an agreement
  if it has no legal effect—is it worth the paper it is written on? [mine] In banking practice ‘comfort
  letters’ are used literally; they provide comfort to a lender that he will get his money back. A
  borrower’s parent company (i.e. its main shareholder) will usually be saying something along
  the lines of ‘we will try to be a really good parent company and make sure that our subsidiary
  pays all your money back’. The bank does not expect to be able to sue on this agreement, and
  should insist on receiving a guarantee if it wants to have legally enforceable rights against the
  parent company.

  In Kleinwort Benson Ltd v Malaysia Mining Corp. (1989) the following wording in a comfort
  letter was held not to contain an intention to create legal relations: ‘It is our policy to ensure
  that the business of [our subsidiary] is at all times in a position to meet its liabilities to you under
  the above arrangements.’ Companies must be careful not to promise to ‘guarantee’ or ‘undertake’
  to do anything as this is more likely to be interpreted as a binding agreement.

I'm not swayed by Shawn Goldmintz's (BBA York, JD Windsor) article.

  It may seem as though comfort letters have the potential to be absolutely useless in certain circumstances. The question begs as to why a creditor would accept a comfort letter from a guarantor that refuses to give a guarantee when the letter cannot be enforced at law. The commercial reality is that when a business fails to meet its obligations, whether as a matter of law or honour, it reflects poorly on that business. A bad reputation can be much worse for a company than having to repay a loan. While this may not seem like an appropriately harsh punishment for one who fails to honour a non-contractual version of a guarantee, it should be remembered that, unfailingly, the author of a comfort letter will have been asked for a guarantee first, and the author refused.

  In addition to this weak punishment, it is entirely possible, and in fact probable, that some comfort letters will be interpreted as binding legal obligations in the future. All it would take is for the wording of a letter to indicate promissory intent (perhaps by using the future tense), and the letter would be held to create legally binding obligations.

I'm asking just about comfort letters that aren't legally enforceable. Viz. disregard last para above.

If I were the lending officer at a rich bank, I'd distrust any borrower or its parent company that can't guarantee! I wouldn't lend it. After all, I can just lend to someone else who does guarantee, though I may have to sweeten my offer.

The emboldened quote doesn't feel true to me. Any examples? To the lender, "a bad reputation" won't get her his money back, and feels useless.
Are there other reasons?


texts:
Any company may "feel" obligated towards several parties at once:

its shareholders
its employees
its customers
its partner companies (sub-contractors and suppliers)
its country and social environment (if it is based in one country)
(wo)mankind in general (present and/or future)
environment in general (locally and/or globally)

I wonder if this list is kind of complete - or if I've overseen important parties (what about the company itself as an economic subject?) - and more important: If there are schemes to display such obligations (traffic light rating system or pie charts - depending on obligation being an extensive or intensive property) - and where I can find them realized.


texts: How does reducing government spending increase the money supply?

texts:
According to the following question, it seems as though cutting back on government spending increases the money supply (the answer is C).

The only possible explanation I can think of is that in the second fiscal year, the government continues to spend, but this time it spends less while not changing tax revenue ("In the absence of offsetting factors"), hence the MS still grows but the following fiscal year's deficit has reduced.


texts: Why do currencies cover orders of magnitude?

texts:
Using 1 USD as a reference, most currencies are within an order of 5 away from the USD: that is, one unit of most currencies is worth between 0.2 USD and 5 USD. (Source.) In fact, most European currencies (Pound, Euro, Franc) are almost exactly 1 USD (0.75, 0.90, 0.98, respectively).

However, there are some currencies that are orders of magnitude away from the USD: 100 Yen constitutes a USD, and 1000 Won constitutes a USD.

Why are these currencies so far from the value of 1 USD? What happened during the development of these countries (in this case, Japan and South Korea) that caused their currency unit to be astronomically different from the USD?


texts:
In order for a DSGE model to have a unique solution, it is required to satisfy the Blanchard Kahn conditions. However, these conditions seem very abstract to me.

Is there an intuition behind the blanchard kahn conditions? Why does a DSGE model have a unique solution iff the number of unstable eigenvalues at the linearized steady state is equal to the number of control variables?


texts:
I have a mock-up exam that my teacher gave me and one of the questions was the following:

  Given these four graphs, which one represents regressive tax?

I'm quite sure it's graph A, but I don't seem to be able to find a proper reason why. Any help and/or tips are welcome!

Thanks in advance

EDIT: As per request. How I interpret this: regressive means the higher the income, the lower the tax. Thus: tax drops with higher incomes. But I can't really determine to which graph this applies.

(T is tax, Y is income)


texts:
I wanted to use STATA for a kalman filter simulation and wanted to go about it the following way

1. Generate iid error terms

$$
{e_t}, {n_t}, {u_t}
$$

2. Generate three AR1 process like so

$$
             \beta_t  = a*b_{t-1} + u_t
$$
$$
             x_t = c_0 + c_1*x_{t-1} + n_t
$$
$$
             y_t = b_t*x_t + e_t
$$

 3. use Kalman filter to predict b_hat

I have been able to use rnorm() to generate the iid error terms, but I am stuck at the second step. I know how to run a state space model to get the kalman filter estimates but AR1 has really tripped me up.


texts: Is it reasonable to consider government bonds as money

texts:
Some measures of the money supply include governments bonds... but I wonder to what degree governments bonds can be considered money.

IMHO the degree to which X can be thought of as money equals the degree to which you can easily buy things with X. What can you buy with bonds? If your answer is that "you can sell your bonds for money and then buy things" - that simply underlines that the bonds themselves were not money.

Perhaps some mega purchases like buying companies could involve the transfer of bonds directly?? I have no idea how common this is.

Are there any other reasons that bonds can be considered money?


texts: How can economies grow if every account is perfectly balanced against others?

texts:
In an economy with finite actors, if every account is perfectly balanced against another account, how can the economy grow when new money enters?  I am thinking of the following chain of events:

The Fed prints money
   + Fed: $+$ debit (imbalanced book)
A Bank recieves cash from one of the 12 regional Fed banks

Fed: $-$ credit (balanced book)
Bank: $+$ debit (imbalanced book)

Lady takes loan out from the Bank

Bank: $-$ credit (balanced book)
Lady: $+$ debit (imbalanced book)

Lady is payed by her company

Lady: $-$ credit (balanced book)
Company: $+$ debit (imbalanced book)

People buy good or service from company

Company: $-$ credit (balanced book)
People: $-$ debit (imbalanced book)

And from here I am too confused to continue $\dots$ I am not sure we can say credit and debit in this sense, I just mean to show there is someplace that is always unbalanced.  The conclusion I always end up with is that this chain is complete (all parties are balanced) when a new loan is taken out, .. but this makes another chain, which I feel just cannot be the answer!


texts: I was wondering if certain government coupons like food stamps can be considered a form of near cash. I recall my professor saying something like near transfer, but I am unsure if the terms "near transfer" and "near cash" are interchangeable.


texts: How does paying off debt to the bank work?

texts:
So, I understand that banks create money by making loans which end up as deposits. But what I don't get, is how paying off debt works in the big picture. Let me explain.
Let's say Jim got a loan of \$100 from the bank. He now owes the bank \$100 + \$10 interest. Where is he getting the money to pay off the loan? All of the money in the economy is created by the bank. So in this simplified example does he get it from someone else who took out a loan? Multiple people? Let's say he sold apples to Sarah and Bob for \$60 each. He would be able to pay the \$110 he owes to the bank. But Sarah and Bob would have had to take out loans, so they would also be in debt to the bank. Where would they get the money to pay off their debt?
Does the economy depend on a majority of people being unable to pay their debt? But if that was the case, how would the bank make money? I must be missing something here.


texts: Given a rational $\succsim$ over a finite set $X$, show that there exists $x \in X$ such that $x \succsim y, \forall y \in X$

texts:
I have been able to show this constructively, but would like to prove it by induction. However, I am stuck with the induction step:

Consider $\succsim$ defined over $X=\{x_1,...,x_n\}$ and where without loss of generality $x_1$ is the element such that $x_1 \succsim x, \forall x \in X$. Now, consider adding element $x_{n+1}$ to the set. My reasoning is that since $\succsim$ is defined over the original $X$, there is nothing telling us that $x_{n+1}$ should be in a complete relation with the elements in $X$ (i.e. $\succsim$ is not defined over a bigger set).

Is this reasoning correct? In that case, I don't see how you could prove this by induction.


texts: Optimal population allocation layout over the Earth

texts:
Does exist some model of optimal people occupancy over whole our planet?

Something accounting for climate, resources (with and without existing settlements) availability, progress and grows perspectives and so on.
I would like to find it in form of heat map.
All I can find is just studies about cities layout or population size and density.

I came to the question thinking about advisability of my little hometown existence and ways to improve it - may be the game is not worth the candle.


texts: extensive vs intensive labor in US in recent decades

texts:
Total Hours worked is a mix of extensive (to work or not, the usual standard working week) and intensive (how many hours to work).

I'm interested in how this balance of extensive and intensive margins worked in the US over time, particularly from the 1980s onwards, and over the financial crisis.

Can anyone suggest a source carrying out such an analysis?


texts:
I'm trying to understand valuation of the Euro BUND Future.

As to my understanding, the price of the future should be:

The price of a government bond issued by the Federal Republic of Germany
That bond must have a maturity date between 8.5 and 10.5 years from expiration of the futures contract
The bond must have an issue volume of at least 5 billion EUR
The price is converted by a conversion factor. That factor depends on the coupon. The conversion factor crosses 1 at a coupon of 6%.

Now, the current price of the September contract of the Euro BUND future (FGBLU19) is (at the time of writing) 172.35 EUR.

Now I looked up bonds that meet the criteria, and found: ISIN DE0001135143 (in German, it's tricky getting quotes for German bonds in English).

Now to my checklist:
 - Maturity date is January 4th, 2030. From September 6th, 2019 (Futures contract expires) that's less than 10.5 years and clearly more than 8.5 years.
 - Issued by Federal Republic of Germany, checks out
 - Issue volume more than 9 billion, fine
 - Coupon is 6.25%, that's even more than 6%. Conversion factor should be even better than the 1 I'm assuming (it should be 1 at 6%)

Now the current price (as of writing) of this bond is 170.59%.

Even without the conversion factor (which should make things even better), that looks to me like an arbitrage of 1.75% (when selling a futures contract and buying the bond, holding till September).

Finding that big of an arbitrage so easily makes me skeptical, so I'm assuming I'm overlooking something. What is it?


texts: Would a society of cannibals be self-sustaining?

texts: Bit of a weird one, but here goes. Say there is a human society whose diet is 100% the human flesh of their own members. Would this society be able to maintain replacement population, or even shudder grow? I suppose figuring this out would require daily caloric requirements, caloric value of human flesh, length of gestation, average age and a host of other variables, but is there some economic principle to short-cut to a solution here? Apologies if you've been sick.


texts: What do banks do with "Repaid Principal"?

texts:
When a bank receives payments towards repayment of the principal of a loan, it is called "Repaid Principal". What does a bank do with this amount?

Does "Repaid Principal" add up to their pool of funds or reserves which they lend again in form of new loans, or do they utilize it in some other ways?

Where exactly does the "Repaid Principal" end up?


texts:
I am a little confused about how the parameter $\tau$ is usually estimated in a cognitive hierarchy model (recall that $\tau$ is the mean number of 'thinking steps'). For example, suppose that subjects play Arad and Rubinstein's 11/20 game and that their choices are:
Subject 1: 20 (corresponding to 'level 0')
Subject 2: 19 (corresponding to 'level 1')
Subject 3: 18 (corresponding to 'level 2')
How could we then estimate $\tau$ (e.g. using maximum likelihood methods)?
My thoughts on this (added): Of course, it is easy to find a $\tau$ that maximises the likelihood of the data. In this example, the likelihood is
$$
\text{P(first player is level 0)}\times \text{P(second player is level 1})\times \text{P(third player is level 2})
$$
or (using the assumption that the levels are Poisson distributed with mean $\tau$)
$$
e^{-\tau}\tau^0/0! \times e^{-\tau}\tau^1/1! \times e^{-\tau}\tau^2/2!
$$
Maximising the likelihood is then equivalent to maximising
$$
e^{-3\tau}\tau^3
$$
which then yields a maximiser $\tau = 1$ (note that we have perfectly matched the average level of the participants, even though the estimator was not chosen to match this moment). However, this procedure totally ignores the constraint that every type (level) optimises given their beliefs about the distribution of levels below them. Is this is problem -- or is it somehow OK to totally ignore this constraint?


texts: Different terminology for discrete vs. continuous "marginal" concepts?

texts:
e.g. Marginal Utility.

If the good you're consuming is discrete, like "slices of pizza eaten", then authors (or at least the author of my textbook) talk about Marginal Utility at each quantity eaten as "the amount of extra utility you get from eating 'one more' slice".

If the good you're consuming is continuous, like "amount of juice drunk", then if you did that you'd just always get "an infinitesimal amount of extra utility, from 'the next' infinitesimally small sip". That's useless, so instead you use derivatives and ask what the instantaneous rate of change in utility is, with respect to juice.

Though related, these are different quantities, and they have different units ("difference in height" vs. "slope" of the total utility curve).

Do they also have different names?


texts: What does it mean by saying someone is "effectively risk averse/loving"?

texts:
Recently I am reading a paper by Ortner & Chassang (2018) on corruption control. It is a nice paper to read, and the idea is kinda cool.

The game is as follows. There are 3 players, a principle, a monitor, and an agent. The agent can choose to engage crime, and the principle offers a wage structure to the monitor in order to deter crime (for details, please refer to the paper if you are interested). One of the results says that, when the monitor's private cost of misreporting is strictly concave (convex) over the support, the agent is effectively risk-loving (risk-averse).

However, I do not quite understand the concept of being "effectively risk averse/loving" that they mentioned. I never saw this before. What does it mean? Does it simply mean that it is beneficial for the agent to be risk-loving?

Thanks for your clarification in advance. Please kindly provide some reference if there is any.


texts: Theories relevant to institutional quality and economic development

texts: I want to write a term paper on institutional quality and economic development. What will be its possible theoretical framework?


texts: Unemployment and its relationship with Inflation

texts: Can anybody please explain me "Inflation-Unemployment Trade-off under Adaptive Expectation and under Rational Expectation"?


texts:
This is somewhat related, but distinct from Cyclicality of Markups

Basically, I'm looking for papers on whether firms profits are (on average) procyclical or not, and I appreciate theoretical, but look mainly for empirical papers.


texts: Ln differenced price level times 400, why 400?

texts:
I am replicating a 2001 Journal of Economic Perspectives methodology paper on Vector Autoregression by James H. Stock and Adam Watson. The paper can be found here: http://faculty.washington.edu/ezivot/econ584/stck_watson_var.pdf

I'm having a slight problem with the log differencing. In the paper the researchers state that they multiply the ln differenced price levels by 400.

I have no clue why this is done. The price level data is quarterly chain-weighted and seasonally adjusted implicit GDP deflator of the US. I would understand if they would multiply by four to get the annual inflation figures, but this is unclear. Any suggestions?


texts:
In my text book, many theories are explained using ad unitary demand curve: a consumer can buy 1 quantity of the product, or none.
The example of the demand function is $ p(q) = 1- q $

but that means if I want to sell one quantity the price should be 0?
I did simply p(q=1) = 1- 1 = 0

What does it mean?


texts: Euler equation through tangency conditions

texts:
I am rather new to economics in general and to the Neoclassical Growth Model in particular and I was wondering if there was a way to get the Euler equation for consumption without using the Lagrangian multiplier? Assuming no corner solutions, let's say the agent solves  $$\max_{c_t, k_t} \sum_{t=0}^{\infty} \beta^t U(c_t)$$  subject to $$c_t + k_{t+1} \leq f(k_t) \\ c_t \geq 0 \quad \forall t \\ k_{t+1} \geq 0 \quad \forall t$$

The Lagrangian is given by $$L = \beta^t [U(c_t) + \lambda_t ( f(k_t)- c_t - k_{t+1})]$$ which can then be solved for the Euler equation $U'(c_t) = \beta U'(c_{t+1})f'(k_{t+1})$.

Why is that if I try to use the tangency condition of the gradient of $U$ and the resource constraint I don't get the same EE? Taking partials with respect to consumption and investment ($\delta =0$ so $k_{t+1}=i_t$)

$\nabla U = \langle \beta^tU'(c_t), 0\rangle$ and

$\nabla RC = \langle -\beta^t,  -\beta^t+\beta^{t+1}f'(k_{t+1})\rangle$.

Using tangency I should get $\frac{U'(c_t)}{-1} = \frac{0}{\beta f'(k_{t+1})-1} \Rightarrow U'(c_t) = \beta U'(c_{t})f'(k_{t+1})$. Clearly my time subscript is off. Can someone tell me if my approach is wrong? or if I made a mistake in the algebra? I think the optimizing condition should hold with tangency so its not obvious to me why this approach gives a result different from the Lagrangian.


texts: Uniform price vs discriminatory price double auction

texts: Uniform price and discriminatory price double auctions are the most commonly used auction mechanisms in the trading markets especially in peer-to-peer energy trading markets. However, I could not find which one is the better option in this particular domain. Can someone provide a comparative analysis of both auctions mechanisms?


texts: Why shouldn't the relative prices change in the Heckscher-Ohlin model?

texts:
I'm having trouble with the Rybczynski theorem. Let's say there's a migration to the domestic economy, increasing the Labor endowment. It states that the production of the good that uses labor more intensely will increase and the other one will decrease (which makes a lot of sense). However, it also states that the relative prices (both for goods and factor remuneration) will keep constant.

This doesn't make sense for me because when I solve for the equilibrium, the relative prices do depends on the relative scarceness of production factor. If I change this, it should go to a whole new equilibrium, shouldn't it?


texts: How is equilibrium reached in CAPM such that the tangency portfolio = market portfolio?

texts:
From my research online, when learning CAPM with $n$ risky assets and a risk free asset with return $r_f$, I always see the conclusion that in equilibrium, the market portfolio = tangency portfolio from mean-variance (Markowitz) theory.
However I don't really understand how the price mechanism will work to reach equilibrium.
This is the story in my head so far:
We have $n$ assets with pre-defined expected returns $\mu_i$ and standard deviations $\sigma_i$. We also have a risk-free asset with return $r_f$. We assume we have an economy of rational investors, who all seek to maximise their expected utility, which we assume only depends on standard deviation and expected return.
Question 1.  Are these $n$ assets already distributed within the economy? They are randomly allocated among investors (who will become potential buyers/sellers)?
Now from this information $(\mu_i, \sigma_i)$, which we assume all investors agree upon, all investors will conclude that the optimal weights for risky assets is $T = (w_1^*, w_2^*, ..., w_n^*)$, i.e. the weights for the tangency portfolio, as this has the highest sharpe ratio, which investors are looking to maximise. Then, they will decide based on their own risky preferences an $\alpha$ to make an efficient portfolio $\alpha \text{Tangency} + (1-\alpha)\text{Risk free}$.
Now. All investors in the economy demand the portfolio T. This will drive up the price of assets in $T$ with high weight and cause the price of assets in $T$ with low weights to fall. This will cause the expected return of the high-weight assets, which is inversely proportional to the price, to fall.
Question 2. Won't this change in expected returns cause a change in the tangency portfolio from $T$ to some new $T^*\ne T$? And will this cause a change in the standard deviation of asset returns?
Again, all investors are now chasing $T^*$. Driving the prices of those high-weight assets up, and the prices of low-weight assets down.
Question 3. How do we know this cycle will ever come to an end? And more surprisingly, how is it that the market portfolio will converge to the original $T$ when the prices will keep changing as investors chase this optimal portfolio?
To me, it seems like equilibrium will be more like a situation where there is no longer an optimal portfolio, and investors are indifferent between all portfolios (i.e. they all have a return correlation of 1).


texts: Regarding different areas of specialisation in development economics in relation to their application for the betterment of real world

texts:
Developing economies need to put in lot of hard work in order to reach the level of developed economies of the world.Or to put it in other words,in order to improve the lives of the millions residing in these countries,where unemployment,increasing population and poverty is creating vicious circles,bringing them out of it is really a big challenge.

My question is: For a person who wishes to bring about a little change in the lives of those underprivileged people for their betterment,which area of specialisation in development economics would suffice?

Update: don't know where to put up this question here or somewhere else?

I searched stack exchange sites where I could put up this question.I did put up this question on academia SE,but they told me to post it on Economics SE.But here on this site none has answered my question.Can anyone help me out here?


texts:
We define the change in demand due to income effect as (assume there are 2 goods and the price of only one of them, say $p_1$, changes)

$dx_1^N = x_1(p_1 + dp_1, p_2, m) - x_1(p_1 + dp_1, p_2, m + dm)$.

The total change in quantity demanded is supposed to be

$dx_1 = dx_1^S + dx_1^N$

However, for the Slutsky equation, we adopt the convention

$dx_1 = dx_1^S + dx_1^M$, where $dx_1^M = -dx_1^N$.

My first question - why exactly do we adopt this convention?

Now assuming that we start off with an endowment $(\omega_1, \omega_2)$, the Slutsky equation has to be modified to accommodate the endowment income effect, because a change in price will necessarily lead to a change in income. In the Intermediate Microeconomics book by Varian, the rate of change in demand due to endowment income effect is defined as

$\frac{\partial x_1^M}{\partial m} \frac{\partial m}{\partial p_1}$,
and so the Slutsky equation becomes (in terms of rate of change w.r.t price)

$\frac{\partial x_1}{\partial p_1} = \frac{\partial x_1^S}{\partial p_1} - \frac{\partial x_1^M}{\partial p_1} + \frac{\partial x_1^M}{\partial m} \frac{\partial m}{\partial p_1}$

Why can't we define the endowment income effect as $\frac{\partial x_1^N}{\partial m} \frac{\partial m}{\partial p_1} = - \frac{\partial x_1^M}{\partial m} \frac{\partial m}{\partial p_1}$?

A mathematically rigorous answer would be appreciated.


texts: What does DOD stand for in this indicator?

texts: I was looking at the indicator External debt stocks, total (DOD, current US$) on the worldbank website and I don't understand what DOD stands for.


texts: Percentage of workforce change, with two PPFs

texts:
A hypothetical economy produces two goods, X and Y. The performance (yield) for every worker is steady, and every worker for Y can produce 10 units of product. If $L_x+L_Y=200 $ (meaning that the total workforce is 200):

(My problem is in (d), everything else is just assisting so you get a better view of the problem)

-a) How many units can every X worker produce?

-b) Find the equation of the first production possibilities frontier (PPF)

-c) Find the equation of the second production possibilities frontier (PPF)

-d) If the technology of the production and the performance of workers for X and Y did not change, what was the change of the workforce between the first and second PPF?

My tries:

-a) If $L_Y=0 \to Y=0$ then $L_X=200$ and for $Y = 0 \to X=400$, so every worker for X can produce $\frac{400}{200}=2$ units

-b) For $y = λx+β \Rightarrow ... \Rightarrow y = -5x+2000$

-c) As the two equations are parallel, $y' = -5x + β' \Rightarrow ... \Rightarrow y' = -5x+2500$

-d) Now for d, where my problem is situated, my try is that the percentage change must equal = $\frac{2500-2000}{2000}100= 25$% but even if that's the correct answer I can't fully understand why this would be the case. What does the $β$ and $β'$ have to do with the workforce? I can't seem to be able to wrap my head around it. Can anyone help me?


texts: How does buying/selling houses affect the GDP?

texts: Suppose I buy a house and sell it off in the same year for the same price, would the GDP for that year increase by twice the value of the house, or only once, or not at all?


texts: Why are the YTMs of TIPS of longer maturities more sensitive to current interest rates and inflation rates?

texts: According to this website, the yields of TIPS of longer maturities are greater than that of TIPS of shorter maturities. It seems counterintuitive since yields of longer-maturity bonds, which are based on expectations of the average of future inflation and interest rates over the holding period of the bond, should be less affected by current economic conditions. On the other hand, the site writes that the shorter-maturity TIPS are less sensitive to current interest and inflation rates. Why is this so?


texts: (Modified comparative advantage model)Can trade with a country that only has one industry be mutually beneficial?

texts:
Suppose there are two countries, China and Japan. Suppose there are also only two goods, namely food and bronze mirrors. China produces both food and bronze mirrors, while Japan produces only food. In order to produce 1 unit of food China has to give up 0.3 units of bronze mirrors, while Japan needs to give up 0 units of bronze mirrors due to absence of bronze mirrors production.
In order to produce 1 bronze mirror China has to give up 3.33 units of food, while Japan can't sacrifice anything for 1 bronze mirror because it doesn't produce bronze mirrors in the first place.

Given this situation, can it make sense for China to start specializing in producing and trading bronze mirrors with Japan?

Normally we would compare opportunity costs for both industries in both countries in order to conclude who has comparative advantage in what industry and then make countries specialize and trade accordingly, but in this example this will work only with one country. In this example Japan has comparative advantage in food production because it's opportunity cost of producing food is zero. So Japan should specialize in producing food. BUT, it's unclear how can we justify trade where China specializes in producing bronze mirrors. After all, it's incorrect to say that China has COMPARATIVE advantage in producing bronze mirrors (how can there be any comparison if there is nothing to compare with? Besides, from more mathy point of view, attempt of such comparison will fail due to division by zero).


texts:
For an report (professional not academic) I was asked for the Labor Rate Index of my region, which is a data point I've never been asked for before.

After some googling I've found the term referred to in a small number of papers (listed below) and oddly they seem to be from military organizations. Often times when I'm asked for a datapoint that uses the word "index", it comes from a proprietary report that costs money. I apologize if that's the case. Anyways, here are some references I've found to a Labor Rate Index with no explanation of what it is:

INFLATION AND ESCALATION BEST PRACTICES FOR COST ANALYSIS: ANALYST HANDBOOK

  The term Constant Price (CP$) may be used to refer to costs normalized
  with an escalation index. Constant Price indicates what a narrowly
  defined basket of goods or services would cost had it been fully
  produced and purchased in the base year. Examples of Constant Prices
  include contractor labor rates normalized with a labor rate index;
  aircraft unit costs normalized with an aircraft index; and fuel costs
  normalized with a fuel price index. Constant Prices remove both
  inflation and real price change from observed dollars, returning the
  base period’s price.

Inflation & Escalation

  “Constant Price” (CP) may be used to refer to costs normalized with an escalation index

  – Constant Price indicates what a narrowly defined basket of goods
  would have cost in a base year

  – Examples of Constant Price include contractor labor rates divided by
  an labor rate index, aircraft unit costs divided by an aircraft
  index, etc.

  – CP addresses market forces (supply and demand) with respect to goods
  and services

  – CP is the normalization used for estimating purposes

A STUDY OF SHIP ACQUISITION COST ESTIMATING IN THE NAVAL SEA SYSTEMS COMMAND

  (2) A Labor Rate Index Provides Similar Allowance For Inflation In The
  Labor Portion Of The Estimate Since 1970, the Branch has produced an
  annual guidance table for use by estimators in selecting labor bid
  rotes. Data sources for this task are some 80 union-management
  agreements. Bureau of Labor
  Statisticsstudies,historicalbids,U.S.DepartmentofCommercesta- tistics,
  naval shipyard employment figures and other sources. This guidance
  promotes consistency in all estimates and is intended to narrow ihe
  margin of error over previous personalized methods.

Anyways, as you can see the term is never defined or sourced. I've tried reaching out to the company to find out why they asked for this, but I'm working through a consultant and so many degrees of separation make it hard to get nit-picky questions answered.


texts:
I was wondering if there is a classic instrument for minimum wage as there is for schooling or other variables. If so, how does it fares with respect to most established designs like spatial differences http://davidcard.berkeley.edu/papers/njmin-aer.pdf or recent spatial regression discontinuity designs.
Assume even that one has panel data is it enough to control for its deep lags.
This is a reference question but if you have your own ideas feel free to post.


texts: Help understanding definition of expected utility function

texts:
This is the definition of an expected utility function that I'm working with:

The utility function $U:\mathcal{L}\to\mathbb{R}$ has an expected utility form if there is an assignment of numbers $(u_{1},...,u_{N})$ to the $N$ outcomes $\{\omega_{1},...,\omega_{N}\}$, such that the following is satisfied for any simple lottery $L=(\omega_{1},...,\omega_{N};p_{1},...,p_{N})\in\mathcal{L}$:
\begin{equation}\label{eq:vnm}
    U(L)=\sum_{i=1}^{N}p_{i}u_{i}.
\end{equation}
My question: Is it true that the assignment of numbers $(u_{1},...,u_{N})$ are given by the Bernoulli function $u:\Omega\to\mathbb{R}$, where $\Omega$ denotes the sample space. And is it true that $U(L):\mathcal{L}\to\mathbb{R}$ is called the Von Neumann-Morgenstern expected utility function, where $\mathcal{L}$ denotes the set of simple lotteries?


texts: How to calculate and interpret a marginal treatment effect (local instrumental variable)? (Intuition through simple example.)

texts:
I am working on the intuition behind local instrumental variables (LIV), also known as the marginal treatment effect (MTE). I have worked some time on this and would benefit from solving a simple. I hope I may get input on where my example goes awry.
As a starting point the standard local average treatment effect (LATE) is the treatment among individuals induced to take treatment by the instrument ("compliers"), while MTE is the limit form of LATE.
A helpful distinction between LATE and MTE is found between the questions:

LATE: What is the difference in the treatment effect between those who are more likely to receive treatment compared to others?
MTE: What is the difference in the treatment effect between those who are marginally more likely to receive treatment compare to others?

The term "marginally" is key and what it specifically implies in this context eludes me (in economics I am used to understanding it as the change in one variable given a one unit change in another). From what I gather, under MTE it is the change in outcome with a marginal change in the probability of receiving treatment, although I am not sure if this is correct. If it is correct I am not sure how to argue for policy or clinical relevance.
To understand the mechanics and interpretation of MTE I have set up a simple example that starts with the MTE estimator (from Cornelissen et al. 2016):
$MTE(X=x, U_{D}=p) = \frac{\partial E(Y | X=x, P(Z)=p)}{\partial p}$
Where $X$ is covariates of interest, $U_{D}$ is the "unobserved distaste for treatment" (not intuitively explained what implies), $Y$ is the outcome, and $P(Z)$ is the probability of treatment (propensity score).
Specifically, Shafrin (2007) state,

The LIV [MTE] estimates the derivative of the expected outcome
conditional on observed characteristics and the probability of
electing to be in the treatment group, $E(Y|X=x, P(z,x))$, with
respect to the probability of treatment.

Example
We want to estimate the MTE of college ($D=(0,1)$) on earnings ($Y>0$), using the continous variable distance to college ($Z$) as the instrument. We start by obtaining the propensity score $P(Z)$, which I read as equal to the predicted value of treatment from the standard first stage in 2SLS:
$ D= \alpha + \beta Z + \epsilon$
$=\hat{D}=P(Z)$
Now, to understand how to specifically estimate MTE, it would be helpful to think of the MTE for a specific set of observations defined by specific values of $X$ and $P(Z)$. Suppose there is only one covariate ($X$) necessary to condition on and that for the specific subset at hand we have $X=5$ and $P(Z)=.6$. Consequently, we have
$MTE(5, .6) = \frac{\partial E(Y | X=5, P(Z)=.6)}{\partial .6}$
Suppose further that $Y$ for the subset of observations defined by $(X=5,P(Z)=.6)$ is 15000,
$MTE(5, .6) = \frac{\partial 15000}{\partial .6}$
My understanding of this partial derivate is that the current set up is invalid, while substituting $\partial .6$ with $\partial p$ would simply result in 0 as it would be the derivate of a constant. I therefore wonder whether anyone has input on where I went wrong, and how I might arrive at MTE for this simple example.
Note that this post is moved from Cross Validated as this community may be more familiar with MTE.


texts: Interest rate - Price of Credit vs Price of Money

texts: I read somewhere that interest rate as the price of money is wrong but rather it is the price of credit. Can someone elaborate and explain what this means?


texts: Mathematical framework for modelling the relationship between price and sales of a product

texts:
In my job as a data scientist, I am required to model the relationship between the price of a product and the sales or number of unit sold. I am trying to build a simplistic model, the assumptions of which are given below. I am not sure if all the assumptions will hold true simultaneously, or if there is a missing assumption or if some assumptions are wrong. Can any expert have a look and comment/give suggestions?

Assumptions:

Different customers have different income so the product priced at $P$ may be affordable to some and not affordable to others. But from a practical business point of view, we cannot build a model of each individual. So we assume that average income of the customers remains fairly constant in the short term and so we assume that we are trying to model the behavior of a single customer whose income is constant and equal the average income of all the customers.

All other conditions external conditions such as macro economics, competitive products, government policies and business rules remain constant
The product has demand, it is mature and stable and so at present the no. of units of the product sold depends only on its price.
As the price changes, the probability that th customer will purchase the product changes. Let $a_1$ be the probability that the customer purchases the product at price $P_1$ and $a_2$ be the probability that the customer curchases the product at price $a_2$. Then $a_2$ depends only on the initial price, initial probability and the new price i.e. $a_2 = f(a_1,P_1,P_2)$ where $f$ is some probability function whose behavior we are trying to find out assuming that such a function exists in the first place.
If price remains constant, then the purchase probability remains unchanged i.e. $f(a_1,P_1,P_1) = a_1.$
Hypothetically, if the product is critical for survival (e.g. purchasing your daily oxygen in a Mars colony) the customer will buy it no matter what the price is i.e. $f(1,P_1,x) = 1$ for all $x$.
If the product is not critical for survival then it will be out of demand at infinite price i.e. $ Lim_{x \to \infty} f(a_1,P_1,x) = 0.$
If the product is important and very cheap then everybody will but it i.e. $ Lim_{x \to 0} f(a_1,P_1x) = 1$.
As price increases, sales decreases i.e. if $P_1 < P_2 < P_ 3$ then $0 \le f(a_1,P_1,P_3) < f(a_1,P_1,P_2) \le  1.$
Since $f$ is a probability density function, its value must be between 0 and 1 i.e. $0 \le f(a,x,y) \le 1$ for all $x$ and $y$.
Mathematically, since $f$ is a probability density function, and price cannot be negative the total area under the probability density curve must be 1 i.e.
$$\int_{-\infty}^{\infty} f(a_1,P_1, x) dx = \int_{0}^{\infty} f(a_1,P_1,x) dx = 1.$$

Now there will be infinitely many functions $f$ satisfying all the above conditions. For example

$$
a_1^{P_2/P_1}, \frac{a_1\log(1+P_2/P_1)}{\log 2}
$$

We eleminate the ones that do not fit the observed data. But even then we can still be left with multiple functions that satisfies all the assumptions of the framework as well as fits the data within an acceptable error range as defined by the business.

Question 1: What other criteria/conditions/assumptions can we use to choose one mathematical model over another?

One way is to use Occam's Razor and go with the simplest model defined as the one which uses the least number of parameters in which case
$$
f(a_1,P_1,P_2) = a_1^{P_2/P_1}
$$

Question 2: Lets ignore my entire framework. What are the other models in economics that can be used to estimate the purchase probability given $a_1, P_1$ and $P_2$.

Question 3: Which assumption is simple impossible and should be removed? What additional assumptions are required if any?


texts: Is MRS supposed to have a minus sign or not? What's there to say about convexity of preferences?

texts:
If we have a utility function $U(x_1, x_2) = x_1(x_2+1)^2$ of some consumer, then

$$MRS_{x_1, x_2} = \frac{\color{red}{-}(x_2+1)}{2x_1}$$

Some books have a $\color{red}{-}$. Others and Wiki don't have a minus. What exactly does this mean?

Bundle/basket/portfolio(is that only for finance?)/whatever $(3,5)$ and has a utility of $108$.

Bundle/basket/portfolio(is that only for finance?)/whatever $(27,d)$ has the same utility of $108$ for $d=1$

The MRS's are as follows:

$$MRS_{x_1, x_2}(3,5) = -1$$

$$MRS_{x_1, x_2}(27,1) = -1/27$$

  Question: What can you say about the convexity of the preferences of said consumer?

I don't quite know what to say here. The two bundles lie on the same indifference curve ($U = 108$). As we move to the right of the curve, the slope becomes less steep, as expected...I think?

This says MRS supposed to decrease if we move down a standard convex-shaped curve. So this curve is not convex? Or not standard?


texts: Robust predictions in single-agent decision problem with uncertainty

texts:
I would like your help to better understand the possibility of using the notion of Bayes Correlated Equilibrium (BCE) in a single-agent decision problem with uncertainty to make predictions on optimal strategies that are robust to the belief environment. The notion of BCE is provided in this paper for a generic $N$-player game.

Consider the following single-agent choice problem under uncertainty.

Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{v})$. First, let nature draw a realisation $v$ of $V$ from $P_V$.
Then, let the decision maker choose an action $y\in \mathcal{Y}$, with $\mathcal{Y}$ finite, without observing $v$. Upon the decision has been made, the decision maker gets a payoff $u(y,v)$.

For example, suppose that $\mathcal{Y}\equiv \{1,2,3\}$. $V$ is a $3\times 1$ random vector, $V\equiv (V_1,V_2,V_3)$. $P_V$ is the 3-variate standard normal distribution. $u(y,v)\equiv v_y$.

Before choosing an action, the decision maker can receive at least one  signal to refine her prior (minimal amount of information). I assume that this minimal signal is completely uninformative (degenerate information structure).

Now, I want to use Theorem 1 in Bergemann and Morris (2016) to characterise the set of optimal strategies under minimal assumptions on the amount of information that is processed by the decision maker (degenerate in this case). To do that, I introduce the notion of one-player Bayesian Correlated Equilibrium (BCE).

A one-player BCE of the game described is a probability distribution $P_{Y,V}\in \Delta(\mathcal{Y}\times \mathcal{V})$ such that:

1) $\forall v \in \mathcal{V}$
$$\sum_{y\in \mathcal{Y}}P_{Y,V}(y,v)=P_V(v)$$

2) $\forall y\in \mathcal{Y}$ and $\forall \tilde{y}\neq y$
$$
\sum_{v\in \mathcal{V}} (v_y-v_{\tilde{y}}) \times P_{Y,V}(y,v)\geq 0
$$

Question:

1) Is it obvious that a BCE exists and is unique in my example?

2) Suppose now that I know for sure that the decision maker does not have any information in addition to the degenerate information structure. How would I characterise an optimal strategy in such a case (without the necessity of being robust to possibly richer belief environments)? How would that definition differ from the BCE definition given above?


texts: Macroeconomic effects of Profit Maximizing Federal Reserve

texts:
The Fed makes money through its open market operations. I am considering a scenario in which the Fed, instead of trying to achieve goals like controlling inflation, tries to maximize its profits in real terms.

What exactly would such a policy mean- would it be equivalent to the Fed targeting a certain variable like inflation or output? In the event of a supply or demand shock, what would the Fed do?


texts: How to keep a constant reserve deposit ratio

texts:
First note that the question comes out from Mankiw's intermediate macroeconomics textbook.

Question: The Fed increases the interest rate it pays banks for holding reserves.  Explain how each of the following events affects the monetary base, the money multiplier, and the money supply.

Textbook Solution: It will cause the bank to have more money in reserve, which increase its reserve-deposit ratio, and cause a decrease in the money multiplier. And thus the money supply decreases. But the monetary base will increase because of the increase in reserve.

My wonderings: A decrease in money supply means a decrease in demand deposit. And hence the reserve-deposit ratio will drop as it is equal to $\frac{\text{Reserve}}{\text{Demand Deposit}}$.To keep the reserve ratio same, it will then have to decrease its reserve, which might offsets the increase in reserve before, maybe partially. So it is not at all certain whether the actual reserve has increased or not and thus not sure whether monetary base has increased or not.

Any answers or comments is appreciated.


texts: How to account income from the informal sector?

texts:
Some context here.

I'm from India and over here around 80% of the public work in the informal unaccounted sector.

Yesterday, the main opposition party said that if they're elected, they'd compensate each individual who's earning less than 12K per month.

For example, if someone earns 5K, govt will add 7K or if someone earns 10K, govt will add 2K

But as almost 80% of the people belong to the unaccounted informal sector, how would govt come to know the exact figures?

Okay 1 easy way to guess would be how much money an individual spends, how much money in the bank etc but don't you think people will have an incentive to show lower incomes?

How would the govt know the exact figures then.

PS- I'm not concerned from where the govt gets the money to balance, I'm only concerned regarding the validity of the income figures.

Thanks!


texts: Constraints on a symmetric pareto allocation under uncertainty

texts:
I've been trying to figure out how the author came up with the constraints for this liquidity model in a textbook I'm reading.

details: http://imgur.com/TpVjg4w

$U = \pi_1u(C_1) + \pi_2u(C_2)$ where $\pi_i$ denotes the probability of an agent being of type $i$ and $C_t$ denotes consumption at time $t$.  Agents of type $1$ consume at time $1$ and agents of type $2$ consume at time $2$.

In autarky, $C_1=1-I+lI$ and $C_2 = 1-I+RI$ where $0\leq I \leq 1$, $l < 1$, $R > 1$.

The setup for the unique ex ante symmetric Pareto-optimal allocation (not autarky) is

$\max \pi_1u(C_1) + \pi_2u(C_2)$

subject to the following constraints, which is what I don't understand:

$\pi_1C_1=1 - I$ and $\pi_2C_2 = RI$

There's a footnote on the word symmetric which says:

  Since agents are ex ante identical, we only consider symmetric allocations $(C_1, C_2)$, where an agent's consumption profile does not depend on the agent's identity.

I think the symmetry definition might be part of what's tripping me up.  It seems to me that since an agent of type $1$ can only consume at time $1$ his bundle should be $(C_1, 0)$, and the bundle for a type $2$ agent should be $(0, C_2)$, which would mean that the only symmetric bundle is $(0,0)$, but clearly this is not the author's intention.


texts: Question about skill-biased technical change, Acemoglu

texts:
I am writing about skill-biased technical change, and in particular the 2001 Acemoglu (http://economics.mit.edu/files/283) paper on the topic, in which there is a part I am very stuck on.

In the paper he suggests there is a market size effect and a price effect which directs technological change. The price effect directs technological change to areas which are relatively more expensive, and the market size effect to areas which are relatively bigger. The elasticity of substitution between two factors plays an important part, so that a low elasticity between two inputs will result in the price effect dominating, since in this situation scarce factors are relatively more expensive and innovation will intend to economise on this. With a high elasticity, the market size effect dominates, since scarce factors do not have a different relative price, so innovation will make widely used factors more efficient.

He applies this to skill biased technical change, in which he says one of the reasons the skill premium has increased so much over the past 60 years is because of the influx of skilled workers (i.e. the market size effect is dominating), so that with more skilled workers, innovation is directed at making them more efficient and they enjoy a higher wage. On page 18 under section 4.2 he states that this will happen with no reference to the degree of substituability between skilled and unskilled workers.

This is where I am stuck. I am trying to explain the theory, in words like I have above, so that it would read something like this: with a high degree of substitutability, technical change favours the more abundant factor (the market size effect). Skilled and unskilled labour have a high degree of substitutability, so an increase in the supply of skilled workers will direct innovation towards complementing that factor. But surely skilled and unskilled workers have a low degree of substitution? In which case surely the price effect would dominate?

I would greatly appreciate any help on this, I am sure I am making a big error somewhere, since it makes sense for the market effect to dominate here due to the empirical evidence of the increasing wage premium over the years... I also hope what I am asking makes sense. I wouldn't have written such a long question, but I feel it wouldn't have made sense without the context of the theory.


texts: Marginal productivity of aggregate labor relation to wage

texts:
I know that $f'(l)=w$. But if i have that the aggregate production is $Y=AL^{1-α}$  with $L=N*l$ (The number of workers, $N$, multiplied by the labor force). So basically I want to find an expression for $w$ (the wage.).

Full problem:

Consider a one period economy, with aggregate technology given by: $Y=AL^{1-α}$ ,$0<α<1$. $L$ denotes the aggregate labor. The economy is integrated by $N$ identical agents, that offers labor force for a remuneration $w$. Also each person receives an Nth part of the earnings $π$ that generates the aggregate production. The objective of each agent is:

$\max \qquad γ\ln(1-l) + \ln(c)$.

$\text{subject to} \qquad c = wl + \frac{1}{Nπ(w)}$


texts: Reason behind the decomposition of price effect into substitution and income effects

texts:
I was studying the decomposition of price effect into substitution and income effects. I am finding it a bit complicated.

This is what I have understood:

(0) Let us assume that there are two commodities. We have a budget line and an indifference map. The budget line is tangent to one of the indifference curves. This point of tangency is the initial equilibrium point.

(1) Due to the change in price of a commodity, the budget line rotates to a new position and we obtain a new equilibrium point. This change in position of the equilibrium point is known as the price effect.

(2) Due to price change, the relative price of the commodity as well as the real income of the consumer changes. Due to change in relative price of the commodity, the consumer will substitute the relatively less expensive commodity for the relatively more expensive commodity and we get a new equilibrium point. This change in equilibrium point is the substitution effect. Due to change in real income, the consumer will change his consumption of the two commodities depending on whether they are normal or inferior commodities and we get a new equilibrium point. This change in equilibrium point is the income effect. Hence we can say that the price effect is the resultant of the substitution effect and the income effect.

(3) To segregate the two effects we draw a hypothetical budget line by shifting the rotated budget line to compensate for the change in real income and the magnitude of the shift varies according to the approach of compensation followed (Hick's approach or Slutsky's approach).

(4) The budget line thus obtained as a result of rotation and shift starting from the original budget line shows the substitution effect.

(5) The remaining part shows the income effect.

(6) Thus we get the substitution effect by rotating and shifting the budget line and then the price effect can be viewed as the combination of substitution and income effects.

Have it grasped it correctly? I am finding all this a little twisted and kind of a reversed logic. First we rotate the budget line to get the price effect and then shift the budget line to obtain the substitution effect or segregate the substitution and income effects. Finally to get to the price effect, we first get to the substitution effect and then the income effect.

I do not understand the rationale behind the decomposition of price effect. Why are we decomposing the effect of a change in price of one commodity into all these effects which are (as I have understood), all hypothetical. Is there any particular advantage of this decomposition? Also I don't exactly understand the meaning of real income. Does it mean the quantity that we can buy given the income and price? If someone could explain it with an example I would be very grateful. Also in substitution effect, why do we substitute the relatively less expensive commodity for the relatively more expensive commodity? Why not the reverse? Also what is the significance of the compensated demand curve? Why do we need two demand curves.


texts: What determines the exchange rate of two fiat currencies if the supply of each is known?

texts:
In this blog post, economist Steve Landsburg posed a question about the value of Bitcoin which he didn't know the answer to.

Imagine a future in which Bitcoins (or some other non-governmental
currency) are widely accepted and easily substitutable for dollars, at
an exchange rate of (say) $X$ dollars per Bitcoin.
Then if there are $M$ dollars and $B$ bitcoins in circulation, the money
supply (measured in dollars) is effectively $M + X B$ .
Money demand is presumably $P D$, where $P$ is the general price level and
$D$ depends on things like the volume of transactions and the payment
habits of the community. (If it helps, we can write $D = T/V$ where $T$ is
the volume of transactions and $V$ is the velocity of money.)
Equilibrium in the money market requires that supply equals demand, so
$M + X B = P D$
Now $M$ is determined by the monetary authorities; $B$ is
determined by the Bitcoin algorithm, and $D$, as noted above, is
determined outside the money market.
That leaves me with two variables ($X$ and $P$) but only one equation.
What pins down the values of these variables?

As he suggests in parenthesis, this isn't a problem specific to Bitcoin, it's a general problem for non-governmental currencies that are perfect substitutes for dollars.
So does anyone know the answer to Landsburg's question?  Are there any models that shed light on what determines the exchange rate $X$ and the price level $P$ in a situation like this?


texts: Name of example of irrationality of proportional and absolute cost

texts:
I am trying to give a puzzle from behavioral economics illustrating on the irrationality of thinking of costs in proportional rather than absolute terms. I remembered vaguely an example like this but could not find the exact term or if another more salient example exists:

  You can buy a computer nearby for \$1k or 1 hour away for \$950. Most people think that \$50 is only 5% of the cost and so would not drive 1 hour  away.

  You can buy a stereo system nearby for \$100 or 1 hour away for \$50. Most people think that \$50 is 50% of the price and so would drive 1 hour to get the cheaper item.

  The problem is that it's the same 1 hour away and the same \$50.

What is the name of this puzzle or irrationality?


texts: Universal Basic Income: Indexation and Inflation

texts:
Let’s assume a monthly Universal Basic Income (UBI) payment of \$1,000 and an annual inflation rate of 2%. I would like to understand what would happen to the real value of this UBI (its purchasing power) in terms of year-zero prices each year for say 20 years. Namely, how much the original \$1,000 worth after 5,10, and 20 years?
This is the link to a google spreadsheet - I hope that I did the calculations right.

My questions are:
How to calculate the real value of the UBI in each year in terms of year-zero prices if there is NO INDEXATION? Obviously, the real value must decrease due to inflation, but I would like to see what is left from the original purchasing power of $1,000 in years-zero every year for 20 years.

This is what I have done in the Excel file attached:

The Column “Real Value” represents the purchasing power of the nominal (NOT indexed) UBI of 1,000 dollars. Is it correct?

The Column “Inflated Value” represents the INDEXED UBI, namely the UBI than would maintain the real purchasing power of the original $1,000 despite inflation. It is correct?

If the calculations are correct, why then the loss to inflation is lower (and decreasing) than the amount of yearly compensation by indexation which is also increasing? What is the logic and intuition behind this?

Thanks a lot!


texts: The rationale for using a lagged variable to address endogeneity arising from simultaneous causation?

texts:
when there is simultaneous causation  between  dependent and  independent variables often in papers we see a  lagged  variable being  used in place of contemporaneous variable. For  example,  Clemens,   Radelet,  Bhavnani  and  Bazzi  (2012)  say - “We  avoid  poor-quality  instrumental variables and instead address  potential  biases from   reverse  and  simultaneous  causation  by  the   more   transparent   method  of  lagging".   Hayo,  Kutan,  and   Neuenkirch  (2010)  - “The  vector  of  controls  contains  lagged    returns...Contemporaneous  U.S.  returns  are  excluded  to  avoid    simultaneity  problems”  However what is the rationale for lagging? This  short article   looks at estimators of lagged variables used in such  cases. It  deduces  that either there is no serial correlation in the  variable and  the  value of the lagged estimator is 0. Or that there is  serial   correlation and the value of the lagged estimator is quite a meaningless value of  ((c+bf)/(1-be)), where b is the coefficient of x(t)  on y(t), f is the serial correlation, e is the effect of y(t) on x(t) and c is the true effect of x(t-1) on y(t). Further the article finds that these estimators are consistent but converge to true value  only for n>100 approximately, further leading to wrong significance interpretations. Given this,   what is the rationale of  using a lag to deal with simultaneity? If the lagged  variable is not serially  correlated its  coefficient on y(t) is 0,   it does not capture the  effect of x(t) on y(t) and one only risks to make false significance inferences in small samples. If on the   other hand the variable is  serially correlated than it does capture the   effect of x(t) on y(t), but  only by the fraction of serial correlation and further that result  is distorted in non linear way because  the  estimator also captures the  effect of 1 - (y(t) on x(t) times x(t) on y(t)) in the denominator. So it is just a   meaningless result. Henceforth,  why do people use the lagged  variables  to address simultaneity  endogeneity? It seems to make no  sense.

The aforementioned article is this one: https://www.otago.ac.nz/economics/news/otago075947111111111.pdf

Your thoughts are much appreciated!


texts: Why has Apple increased app store prices in the UK?

texts:
Apple have recently announced an increase in app store prices, ostensibly due to the weakening of the pound following the Brexit vote and its fallout.

Why has apple done this when the marginal cost of production of an (already developed) app is zero? Will this not reduce income for these apps?


texts: Why does Fed buying mortgage backed security help lower the interest rate for mortgages?

texts: If Fed buys more mortgage-backed securities, does it necessary mean that the interest rate will go down? Consider the supply and demand market for mortgages  and let us assume the supply side is the commercial banks and the demand side is households. It follows that supply increases as Fed buys mortgage-backed securities, which causes the interest rate to fall. However, suppose that although the Fed starts buying mortgage-backed securities from the banks, the banks think it is too risky to hold mortgages after the increase in the delinquency rate during the financial crisis. So the supply does not actually increase and thus the interest rate does not increase. Is this scenario possible?


texts: How to find the present value of a perpetuity with a non-constant growth rate?

texts:
I've got a perpetuity problem where an organization pays out 50 equal valued grants each year in perpetuity, adding an additional 5 grants each year (i.e. 55 in year 2, 60 in year 3, etc.).

We've only been shown how to do perpetuity problems with a constant growth rate (e.g. the payout increases by 5% each year), so I'm not sure how to deal with this one.

Anyone have any insight?


texts: When demand increases why does the price decrease but equilibrium price increase?

texts:
On a demand curve when the demand increases the price will decrease. However on a demand and supply graph, when the demand shifts to the right, the price will increase. I understand why, but then what is the point of analyzing a demand curve, if it contradicts the market equilibrium graph?

I am sorry if this is a stupid question. It has only been a month since I have started economics in high school.


texts: Does a rate hike by the Central Bank increase or decrease inflation?

texts:
Mainstream economic theory tells us that, in order to decrease inflation, the CB increases its rates so as to decrease loan creation which should decrease Aggregate Demand and thus lower inflation.

However I've read from other economists (especially Post-Keynesians and MMT'ers), that it would have an opposite effect and that an increase in those rates would increase inflation instead of decrease it since the government is a net payer of interest.

Which one of these two views is correct? And which is more supported empirically?


texts: Limit of this sequence // broadness of inputs

texts:
Let there be a unit measure of inputs. Define by $C_i = \left[\int_0^i c(i)^{1-\alpha}\right]^\frac{1}{1-\alpha}$ a cost index of using up to $i$ as input.

I discretize $c(i)$ by $c_0, \dots c_i, \dots c_I$. Let for example $c_i = 1 \,\forall i$, and $\alpha = 0.5$. Let $I = 5$. To approximate the integral, I simply sum up terms and divide by $I$.

Then we have $C_1 = (\frac{2}{5}\sqrt 1)^2$, $C_2 = (\frac{3}{5}\sqrt 1)^2$ etc. So this is an increasing sequence, and $C_1 = 4/25=0.16$.

Now I need the corner case, $C_0$. $C_0$ only uses $c(0)$ as input, so I'd think that

$$ C_0 = (c(0)^{1-\alpha})^\frac{1}{1-\alpha} = 1$$

But that clearly can't be the limit of the discretized sequence, since $\lim\limits_{i\to 0} C_i \to 0$.

So, as the variety of inputs decreases, the cost index decreases - until you only have one variety, and then it explodes? Could someone please shed some light on this?


texts: Can corporate tax loss carryforward function like a sort of insurance policy?

texts:
I'm a graduate student in mathematics, with a casual knowledge of economics, so please let me know if this question is a non-sequitur or off base.

Here's the intuition I'm trying to capture: Suppose corporation A has a good year and makes a lot of profit, and corporation B, their competitor, has a bad year wherein they have a net loss. It seems that the following year, corporation B has a relative competitive advantage, in that they have a lower tax burden.

In a system with no corporate tax—and thus no tax loss carryforward—it seems that corporation B wouldn't have this advantage which might give them some time to recover. In a system with a very high corporate tax, this benefit would be even greater.

Value judgments about the utility of a high corporate tax aside, is there anything to the idea that corporate taxes can serve as a sort of "insurance policy" wherein companies with a bad year are more likely to survive?


texts: Why car rental companies have different models in the same group?

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When booking a car, car rental companies do not guarantee that a specific model will be available. Normally they can only guarantee you'll get a model in the same category (or above). For example, you book category B and get a Golf, Corsa, Megane, or something like that.
How does that make business sense? Couldn't they just buy all Golfs for their category B? It would be easier to maintain the vehicles, they could get a bulk discount when buying every car from the same manufacturer, and they would not annoy the clients, showing a picture of car X but delivering car Y.


texts: Monopoly equilibrium with a completely inelastic demand

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What is the impact of an inelastic demand function on a monopoly production and pricing strategy ?

Theory states, that a monopoly will strive to maximize its profits, by arriving to a point where the difference between the revenues and costs is at a maximum

The potential revenues derive from quantity of sales at a certain price, whixh by turn, are affected by demand

If the demand is inelastic, that means that quantity will remain fixed, no matter the price

Does that narrow or broaden the monopoly's options ?
What's the impact of that type of demand on the equilibrium price ?


texts: Intuition: Why does perfectly elastic supply imply no producer surplus?

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Foreword: I ask NOT about the whole question; so I quote only the following part of the answer.
Source: p 153, Question 7c, Principles of Microeconomics, 7 Ed, 2014, by NG Mankiw
= Chapter 7, Question 6c, Principles of Microeconomics, 4 Ed, 2008, by NG Mankiw

... To take the most dramatic case, suppose the supply curve were
horizontal, as shown in Figure 12. Then there is no producer surplus at all. ...

From the graph, I see that perfectly elastic supply $\iff$ a flat supply curve
$\iff$ producer surplus := Amount received by sellers $-$ Cost to sellers $\qquad = 0$.
But please help me dig deeper than the graph, which I already understand and so ask NOT about. Intuitively, why is the above true? I seek only intuition; no maths arguments or formal proofs please.


texts: Convergence in probability and convergence in distribution

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Im a little confused about the difference of these two concepts, especially the convergence of probability. I understand that $X_{n} \overset{p}{\to} Z $  if    $Pr(|X_{n} - Z|>\epsilon)=0$ for any $\epsilon >0$ when $n \rightarrow \infty$.

I just need some clarification on what the subscript $n$ means and what $Z$ means. Is $n$ the sample size? is $Z$ a specific value, or another random variable? If it is another random variable, then wouldn't that mean that convergence in probability implies convergence in distribution? Also, Could you please give me some examples of things that are convergent in distribution but not in probability?


texts: Why is the graph of unitary elastic demand a hyperbola?

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My teacher said that the graph of unitary elastic demand is a parabola:

But i fail to understand how in a hyperbola the percentage change of price and quantity demanded remains same. Can someone explain the same to me? First i thought that it remains the same rather in a straight line but a quick study proved that it is not the case in a line with a negative slope. But the question remains the same, how is it in a hyperbola the percentage change remains the same.


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I've been looking for a dataset with a single education indicator by country so I can rank/compare them but I haven't found anything.

Already seen Unesco and Worldbank data but info is too much for what I really need at this point. Also had a look at the  Human Development Index (HDI)  but this is a composite statistic of life expectancy, education, and income per capita indicators so my analysi will be obscured by other elements.

I just need (for now) to be able to say for example Japan > Spain or Canada ranks 10th worldwide.

Does anyone have any idea as where I can download (if exists) this data set? API can work too. Ideally info comes with country iso code.

Thanks in advance.


texts: Why does decrease in fixed taxes accompanied by a decrease in Government Spending of the same amount will decrease GDP?

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I personally don't agree because change in GDP caused by decreased in fixed taxes should be

$\triangle$ fixed taxes $ \times \frac{-b}{1-MPE}$(fix tax multiplier), which turns out to be a positive number while change caused by decrease of Government Spending is

$\triangle$ Government Spending $ \times \frac{1}{1-MPE}$(autonomous multiplier) which is a negative number. Therefore I don't think we can make conclusion. Does anyone know what did I do wrong?