texts: Existence of maximum utility with two bads

texts:
I am working with a consumption set $X = R_+^2$ and preferences that are complete, transitive, continuous and strongly monotonically decreasing. The economy is characterized by the presence of two economic bads. I need to show that "there always exist a solution to the consumer's utility maximization problem".

My point is that if I had a continuous utility function over a compact budget set, using Weierstrass theorem I have the certainty of the function reaching its extrema. The problem here, if I am right, is that the budget set is no longer bounded and thus neither compact.

Are there other results I can use to show the statement?


texts: In a competitive market, is it possible to know the change (increase/decrease) in number of firms in the Long run with a positive shift in demand for increasing costs case?


texts: Subjective theory of value applied to gross domestic product

texts:
I am trying to understand the subjective theory of value and run into some considerations that make me think I got it wrong.

As far as I understand, the subjective theory of value states that the values (prices) of commodities are not related to any objective quantity but rather are a result of individual, subjective judgements. E.g. if I decide to pay 1000 \$ for a good, then for me that good has the (subjective) value of 1000 \$, and that is all there is to it.

As a result, the gross domestic product of a nation is the sum of all these subjective judgements about the values of goods that are bought and consumed by people over a period of time.

But, as far as I know, the GDP is used to evaluate the performance of an economy (growth and so on): Do economists really base their evaluation of an economy on some non-objective measure of value? Or value is subjective at the level of an individual and becomes something objective in the aggregate?

Can someone help me out?


texts: General equilibrium allocation with "altriustic" utilities

texts:
Has any work been done on market allocations where market participants have utility functions that depend on other players' allocations?

For example, suppose I have a general equilibrium model with three players 1, 2, and 3, and three goods A, B, and C. Suppose player 1's utility depends on the relative utility of players 2 and 3, say with u1 = f(a1, b1, c1) + u2(a2, b2, c2) - u3(a3, b3, c3), where ai is the number of As that player i is allocated. For particular starting allocation, player 1 may block three-cycles of trades that give him more of every good, if those trades decrease u2(a2, b2, c3) - u3(a3, b3, c3).


texts: Why did Federal Reserve buy already-issued corporate bonds, ETFs, and agency commercial mortgage-backed securities?

texts:
I screen-shot WSJ on Sep 18 2020.

I'm assuming that Fed Primary Market Corporate Credit Facility didn't buy ALL newly issued corporate bonds?

Please see question in title. Why didn't Federal Reserve just bloat or maximize its Primary Market Corporate Credit Facility? Why use its Secondary Market Corporate Credit Facility and Open Market Account?


texts: How does migration facilitate specialisation?

texts: When migrant workers arrive in a country, how do they facilitate specialisation? Is it by freeing up workers from jobs they do not want to do?


texts: Does the contract curve always have to connect the initial points on an edgeworth box? Why or why not?

texts:
What if the contract curve goes out of bounds? In that case, do I assume it superimposes itself on the axes it is closest to?

I hope this was clear. Not sure how to explain this other than visually...


texts: If someone stays at home because they can't find the type of job they want, are they included in unemployment numbers?

texts:
Say someone is looking for a job, but the ones they can find either don't give them the right compensation (businesses pay them too low) or is not the type of work they're looking for. So they stay at home until they find one.

Is such a person considered to be unemployed by official data? I understand different countries may have different policies about this -- but how is this predominantly tackled?


texts: Argentine default: "Rights upon future offers"

texts:
Argentina defaulted on its sovereign debt in 2002. It has reached an agreement with most but not all of its creditors. Wikipedia has a pretty good summary. The agreements included a 70% hair cut but also a RUFO or "Rights upon future offers" clause stating that if in the future agreement is reached with the holdouts with better terms (lower loss percentage) those better terms automatically apply to the creditors signing the current agreements. (This is similar to a most preferred customer clause.) Perhaps the Argentine government used this as a negotiation tactic as it makes it impossible to offer better terms to the holdout creditors.

Unfortunately the holdouts bought a lot of CDS insurance and now stand to win more from a default then they do from a 100% repayment. Lawsuits lasted for years. Argentina made payments to the creditors it agreed with but made no payments to the holdouts. In 2014 (maybe 2015) a court blocked payments to the non-holdout creditors because you cannot differentiate between identical bonds in case of default. This is plunging Argentina into default again which is bad for the country and the creditors with whom it already came to an agreement. (There is another court hearing scheduled for April 2016 and the US government is advocating in favor of Argentina.)

Why haven't the non-holdout creditors and Argentina signed a new agreement in 2014 without the RUFO clause but identical in all other ways? Seems like both of them would have benefited from it, just as they have by coming to an agreement in the first place. (I am not necessarily looking for the 'exact' or 'real' reasons. Any plausible reasons that make economic sense are fine.)


texts:
According to my personal observation the majority of (prominent) economists prefer use Stata for their statistical analysis and Matlab for other mathematical work. SAS and Excel are also used (especially in finance).

In my opinion R is a much better software for data cleaning, manipulation and analysis than Stata (not to mention that Stata costs) it is also seems on par with Matlab in what it does best. But I guess (as a graduate student) it will not make cooperation very smooth using a different statistical program than the rest. Use Stata like everyone else or suffer?

Thus a student who is an 'R expert' should, if having to choose between two equal departments, choose the one that uses R. But does such a department exist? A department where at least few researchers use R?


texts: Fixed effects, first differences interpretation

texts:
I am working with a fixed effects model to estimate the effect of enterprise zones on unemployment claims.

(1)  $log(uclms_{it}) = \theta_t + \beta_1 ez_{it} + c_i + \epsilon_{it} $ where $\theta_t$ are time specific effects and $c_i$ are city specific effects.

Another model is estimated that allows each city to have its own time trend:
$log(uclms_{it}) = \gamma_i t + \beta_1 ez_{it} + c_i + \epsilon_{it} $ and this model is then first-differenced to obtain

(3)  $\Delta log(uclms_{it}) = \gamma_i + \beta_1 \Delta ez_{it} + \Delta \epsilon_{it} $

I was asked to estimate (1) and (3) by fixed effects and comment on possible reasons for differences in the estimate of $\beta_1$

The estimates I got were;
from model (1) $\beta_1 = -0.1044$ with a t-ratio of -1.43 and p-value of 0.166.
from model (3) $\beta_1 = -0.252$ with a t-ratio of -2.41 and a p-value of 0.025.

So the estimate is relatively small in model (1) compared to model (3) and is insignificant in model (1), but significant in model (3) at the 5% level.

Am I right in thinking that, when (1) is estimated by FE, the city specific effects drop out, but the time specific effects remain. Whereas in (3) we only have city specific effects which drop out when estimated by FE. So the observed differences in $\beta_1$ arise because (1) includes time effects, but (3) does not. I'm also a bit confused about using first-differenced data in a fixed-effects model. Why would that be useful?


texts: Distributing inflation in a hierarchical model

texts:
I am trying to distribute inflation in a hierarchical model.  In both of the following two scenarios, the Laspeyres' Index over the entire data set is 1.8; However, in the first scenario, the inflation is caused by a rise in prices in Florida.  i.e. the inflation is 1.8, and is caused by a change in relative prices between states.  In the second scenario, the inflation is caused by a rise in the price of Juice everywhere.  i.e. the inflation is 1.8 and is caused by a change in relative prices between products.

I would like a metric that captures this intuition in a general scenario that gives a ratio (or something like it) of inflation-causality of price redistribution between states and price redistribution between products.  I have not been able to find anything in the literature, and I am having difficulty diving anything.  Any direction is appreciated.

(note that the quantity at time 1 doesn't enter into the calculation, it's just displayed for completeness)

SCENARIO 1

+---------+-------+-------------+--+-------------+
|         |       | time 0      |  | time 1      |
+---------+-------+-------------+--+-------------+
|         |       | price | qty |  | price | qty |
+---------+-------+-------+-----+--+-------+-----+
| Florida | Nuts  | 1     | 10  |  | 2.6   | 5   |
+         +-------+-------+-----+--+-------+-----+
|         | Juice | 2     | 20  |  | 5.2   | 40  |
+---------+-------+-------+-----+--+-------+-----+
|         |       |       |     |  |       |     |
+---------+-------+-------+-----+--+-------+-----+
| Alabama | Nuts  | 1     | 10  |  | 1     | 5   |
+         +-------+-------+-----+--+-------+-----+
|         | Juice | 2     | 20  |  | 2     | 40  |
+---------+-------+-------+-----+--+-------+-----+

SCENARIO 2

+---------+-------+-------------+--+-------------+
|         |       | time 0      |  | time 1      |
+---------+-------+-------------+--+-------------+
|         |       | price | qty |  | price | qty |
+---------+-------+-------+-----+--+-------+-----+
| Florida | Nuts  | 1     | 10  |  | 1     | 5   |
+         +-------+-------+-----+--+-------+-----+
|         | Juice | 2     | 20  |  | 4     | 40  |
+---------+-------+-------+-----+--+-------+-----+
|         |       |       |     |  |       |     |
+---------+-------+-------+-----+--+-------+-----+
| Alabama | Nuts  | 1     | 10  |  | 1     | 5   |
+         +-------+-------+-----+--+-------+-----+
|         | Juice | 2     | 20  |  | 4     | 40  |
+---------+-------+-------+-----+--+-------+-----+


texts: What's the difference between equity capital and market capitalization?

texts:
Is there any difference between the equity capital and the market capitalization of a company (or a bank)?

If yes then what's the difference?


texts:
Can a market be seen as a set of nodes (market actors) connected by edges with bandwidth and latency characteristics?

Are these terms used in economics?

If so would an import tariff affect bandwidth and/or latency?


texts:
The book I'm reading shows that
$$ S= I +CA$$
where $S$ is savings, $I$ is investment, and $CA$ is the current accounts surplus.

The book then states "any domestic savings not absorbed by domestic investment must be shipped outside the country in the form of goods and services." I can understand how this works from an accounting equation point of view, but intuitively it doesn't seem to make sense. It seems odd that saved money would end up in the form of exports.


texts: Can an Out the Money put option's price $>$ its Strike Price?

texts: I'd guess yes, if the put option's IV spikes. An OTM put has merely Time Value and no Intrinsic Value.


texts: In general, it is known that market volatility increases during bear markets while it decreases during bull markets. Why is this the case? It seems strange that volatility is linked to the the general direction of price movements. Volatility is a measure of how much fluctuation there is in stock prices. During the bear market, prices go down and during a bull market, prices go up. There seems to me no relationship between the general direction of price movements and market volatility.


texts: Do central banks pay their staff and other costs with money that they create?

texts:
Central banks like the Bank of England and the Fed must cover their costs. I was wondering how they do this? I can think of two possible mechanisms:

Government allocates money from its tax revenue to the central bank, which then uses this money to cover costs.
The central bank creates an amount of money necessary to cover its costs.

This question is specifically about central banks as they alone have the authority to create new money.


texts:
A recent op-ed (paywall) in the Financial Times about inflation stated that (emphasis mine):

Across the developed economies, the Phillips curve has gone ignominiously flat. The world's leading central bankers are scratching their heads.
[...]
Rather than a response to tightness in the markets for products and labour, [in earlier theories] inflation was understood as a barometer of the political system’s ability (or lack of it) to resolve struggles over the distribution of income and wealth. Workers and bosses, creditors and debtors, fought one another for a larger slice of the pie. When negotiations failed, the path of least resistance was the excessive expansion of credit.
[...]
Stop dreaming of mythical beasts like the global output gap and the natural rate of interest, they would say. Wake up to the political realities.
Globalisation and the march of technology have strengthened the hand of employers and weakened that of workers. So it is no surprise that though unemployment has relentlessly fallen, wage growth remains in the doldrums.
[...]
What these unfashionable theories of inflation see — that the central bankers’ current models do not — is simply put. It is the dirty secret of economics: the central importance of power.

The author is referring to "old" political theories of inflation. I have struggled to find references about them. I wonder if someone has come across some of these political theories of inflation?


texts: Show the growth rate of technology and capital are eventually continuously increasing

texts:
(Romer 3.6.b) Consider an Endogenous Growth rate model including capital and knowledge with the following equations of motion and $\beta + \theta > 1$ and $n > 0$

  \begin{cases}
Y(t) = [(1-a_k) K(t)]^{\alpha} [A(t)(1-a_L) L(t)]^{1-\alpha}, & 0 < \alpha < 1 \\
\dot{K}(t) = s Y(t) & 0 < \alpha < 1 \\
\dot{A}(t) = B[a_k K(t)]^{\beta} [a_L L(t)]^{\gamma} A(t)^{\theta}, & B > 0, \; \beta \geq 0, \; \gamma \geq 0
\end{cases}

  Show that regardless of the economy's initial conditions, eventually the growth rate of $A(t)$ and $K(t)$ (and hence the growth rate of $Y(t)$) are continuously increasing

We have computed

$$ \frac{\dot{g}_A}{g_A} = \beta g_K + \gamma n - (1 - \theta)g_A $$

$$ \frac{\dot{g}_K}{g_K} = (1-\alpha)[g_A + n - g_K] $$

and drawn in $(g_A, g_K)$ space the paths of each when $\dot{g}_A = 0$ and $\dot{g}_K = 0$.

Is the question asking to show either:

$\exists t_0, s.t. \; \frac{d}{dt} g_A (t) = \dot{g}_A (t) > 0 $ and $\frac{d}{dt} g_K (t) = \dot{g}_K (t) > 0$ $\;  \forall t \geq t_0$
$\dot{g}_A (t) > 0$ and $\dot{g}_K (t) > 0$ occur infinately often

That is, I am not sure if we need $\dot{g}_X (t) > 0$ to hold for all $t \geq t_0$ or if it may fluctuate between positive and negative and hits positive infinite times, I feel the latter is more reasonable to see in the real world so it would suffice to show (but most certainly not the method they intend to solve this problem)

$$ \displaystyle P( \dot{g}_X > 0 \; i.o.) = 1 $$

Where $i.o = infinately \; often$.  But here have the problem of defining a probability measure on $\dot{g}_X (t)$

Can we give this the following probability?

| growth rate | positive | negative | zero
| probability |   1/3    |    1/3   |  1/3

Then summing over all possible initial values (countably infinite)

$$ \sum_{n=0}^{\infty} P(\dot{g}_X > 0) = \sum_{n=0}^{\infty} \frac{1}{3} = \infty $$

And by Borel-Cantelli Lemma 2, since the events $A_n := \dot{g}_X > 0$ are independent and the sum of the probabilities is infinity then:

$$ P( \dot{g}_X > 0 \; i.o.) = 1 $$

Which tells us that the event the growth rate is positive occurs infinately often.  Would this answer the question?


texts: The effect of future increase in production on current market equilibrium

texts:
I am going through the microeconomics course of the MRUniversity and in the end of the chapter on supply and demand there is a question that I don't get. Here is the question:

  If oil executives read in the newspaper that massive new oil supplies
  have been discovered under the Pacific Ocean but will likely only be
  useful in 10 years, what is likely to happen to the supply of oil
  today?

  a. The supply of oil will rise today
  b. The supply of oil will fall today
  c. There will be no change in the supply of oil

Now my analysis is that this means there would be more competition between the oil suppliers in the future and as a result some oil suppliers may decide to leave the market sooner and as a result the supply of oil will decrease. But according to the site the correct answer is that the supply of oil will rise. What is wrong with my analysis?


texts:
Suppose that $z(\cdot)$ is the demand function of an individual (consumer/investor) and $p$ is the price of the commodity/asset demanded. Does anybody know what is the intuition behind the following expression?
\begin{align}pz^{'}(p)+z(p)\end{align}
It seems to me like the derivative of $(pz(p))^{'}$ with respect to $p$. What is the intuition behind this? Has anybody seen anything this expression before?


texts: How do government purchases crowd out the private sector?

texts:
I am curious about how government purchases crowd out the private sector (if it does). If we look at a graph of the composition of US GDP, it seems that government purchases and investment are somewhat negatively correlated. It's obvious during WWII that government purchases skyrocketed while investment shrank significantly.

I am wondering about the intuition behind why this happens. If I had to guess, it's because at a given snapshot in time, the capital and labor in the economy is limited, and if the government is spending more money to use capital goods and labor, then there are less capital goods to go around for the investment. Is that line of thinking correct?


texts: Modelling involving sum of random variables: Simple CDF?

texts:
This question emerges from a project in microeconomic modeling.

I have $n$ agents receiving noisy i.i.d signals $s$.

In my model, a situation of interest occurs when the average signal across $n$ agents, say $\bar{s} := (1/n) \sum_{i=1}^n s$, passes a certain threshold $t$.

I would like to be able to express the probability that this happens, i.e. $P(\bar{s} > t)$, in an algebraically simple way.

Of course, $P(\bar{s} \geq t) = 1 - P(\bar{s} \leq t)$ so the probability I am interested in is a simple function of the CDF of $\bar{s}$.

My problem is I am unable to think of a distribution for $s$ that would make the CDF of $\bar{s}$ easy to play with and obtain analytical results from.

For example, letting $s \sim N(0,1)$ leaves me with a $P(\bar{s} \leq t)$ depending on the very unhandy error function (I know it's easy to obtain computation results based on $erf(\cdot)$ but I am aiming at analytical results here). Letting $s$ be a Bernoulli or a Uniform leaves me with the CDF of a Binomial or an Irwin-Hall, which aren't much nicer to play with...

Any suggestions as to what I could use for the distribution of $s$?

Bonus requirements:

in another part of my model, I am also interested in $P({s} \geq t)$ itself, so it would help a ton if both $s$ and $\bar{s}$ had simple CDFs.
for reasons I cannot yet lay down myself, I feel like I will be happier further down the line if $s$ has a continuous and somewhat symmetric distribution, but I am happy to hear about discrete and asymmetric solutions as well.


texts: Suggested model for dependent variable of different groups

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


texts:
The production function is $F(K_t,N_t)=AK_t^\alpha N_t^{1-\alpha}$ and depreciation $(\delta)$ is equal to 1. The given preferences are as follows: $$U(c_1,l_1,c_2,l_2)=\gamma log(c_1)+(1-\gamma)log(l_1)+\beta[\gamma log(c_2)+(1-\gamma)log(l_2)]$$
From which $\gamma\in(0,1)$,$\beta\in(0,1)$. We assume $\forall t:l_t + n_t ≤ 1$ and all non-negativities on all variables. How would we solve the Social Planner?
Since $\delta=1$ we would have the constraint for period 1: $$c_1+k_2=AK_1^\alpha N_1^{1-\alpha}$$, from which $$c_1=AK_1^\alpha N_1^{1-\alpha} -k_{2}$$.
For period 2, $$c_2=AK_2^\alpha N_2^{1-\alpha}$$ since we don't have anymore capital for next period.
Now we need to find the allocation $\{c_1,c_2,l_1,l_2\}$ by doing the Lagrangian.
$$U(c_1,l_1,c_2,l_2)=\gamma log(c_1)+(1-\gamma)log(l_1)+\beta[\gamma log(c_2)+(1-\gamma)log(l_2)]-\lambda_1[c_1-AK_1^\alpha N_1^{1-\alpha} -k_{2}]-\lambda_2[c_2-AK_2^\alpha N_2^{1-\alpha}]$$
Finding F.O.Cs wrt $c_1,c_2,k_2:$
{$c_1$}: $\frac{\gamma}{c_1}=\lambda_1$
{$c_2$}: $\frac{\beta\gamma}{c_2}=\lambda_2$
{$k_2$}: $\lambda_2A\alpha k_2^{\alpha-1}N_2^{1-\alpha}=\lambda_1$
Generating $\frac{\lambda_1}{\lambda_2}$ we would get $$c_2=A\alpha k_2^{\alpha-1}N_2^{1-\alpha}c_1\beta$$
That we substitute in the original constraint to get $$k_2=c_1\alpha\beta$$ to which we substitute in $$k_2+c_1=Ak_1(1-l_1)^{1-\alpha}$$
Some algebra and we get $$c_1=\frac{Ak_1^\alpha(1-l_1)^{1-\alpha}}{\alpha\beta+1}$$
$$c_2=k_2^{\alpha}N_2^{1-\alpha}$$
For $l_t$ we substitute $c_1,c_2$ in the FOCs that equal each $\lambda$ respectively along with the FOCs of $l_1,l_2$ and get the following, again after the algebra:
$$l_1=\frac{1-\gamma}{\gamma(\alpha\beta+1)(1-\alpha)+1-\gamma}$$
$$l_2=\frac{1-\gamma}{\gamma(1-\alpha)(1-\alpha)+1-\gamma}$$
Phew! This was hella lot of algebra and I don't know if I made a mistake or not. I hope this is correct but feel free to point my errors.

Define the Arrow-Debreu equilibrium for this economy. Find the equilibrium prices and quantities.

Besides the market clearing and prices and allocations conditions how do we continue from here :)


texts: Can an appreciating currency lead to inflation?

texts: If a currency, e.g. the rupee (INR), is appreciating against, say, the USD, it possibly means that there is a high demand for the former. India could have net exports, high remittances, increasing FIIs all leading to the appreciation of the INR. Does that not mean a lot of rupees flowing into circulation in the country? Should that not decrease the value of the currency and lead to inflation? Where exactly am I wrong?


texts: Proving a result In Jones (1999) "Growth: With or Without Scale Effects"

texts:
Jones (1999) builds his semi-endogenous growth model where output is produced with only one input, labour, in the following "research" function:

$$ Y = A^\alpha L_Y $$

Labour is augmented with technology $A$ which is also researched by
workers, $L_A$, in the following production function:

$$ \dot{A} = \delta L_A A^\phi. $$

We have that $L_A + L_Y = L$ and $0 < \phi < 1$.

He then writes:

  Assuming that the labour force L grows at some constant exogenous rate
  $n$, it is easy to show that there exists a stable balanced growth
  path for the model where

  $$ g_A = \frac{n}{1-\phi}$$

  and

  $$ g_Y = \sigma g_A = \frac{\sigma n}{1-\phi} $$

He says it's "easy to show", but I can't for the life of me show it! We know that $g_A = \dot{A}/A$, and on the balanced growth path $g_A = g_Y = g_L = n$. So I try to plug $g_A = \delta L_A A^{\phi-1} = n$ but that gets me nowhere.


texts: Value added by sector of economic activity

texts: I am trying to make a pie chart of value added by economic activity (as a % of gdp). I am trying to use data from world bank for each of the four sectors: manufacturing, agriculture, industry, services http://data.worldbank.org/indicator/NV.IND.TOTL.ZS?display=default , but surprisingly the percentage share for each of those sectors, for one country do not add up to 100 but to 120. Why is that?


texts: Can minimum or subsidies or tax cuts really work? Or will resultant inflation always counterbalance such initiatives?

texts:
I was born at the tail end of Eisenhower era and what is clear is that the dollar does not buy what it used to and this inflation has been more or less the trend for many decades.

I have yet to hear of a program that sounds to me like it will work. Recently min wage was increased where I live and sure enough prices and rent went up and businesses also laid off people, reduced hours and continued to automate.

A pilot subsidy program will appear to work: if you take a small number (say 100 in a city of 100k) of poor people and give them 1000 bucks each month, it seems obvious that they will benefit because this money will not significant affect prices. Do that for 10k out of the 100k and prices will go up.

Maybe I am not understanding the situation which is why I ask but is it possible that any program that puts "artificially" more money into the hands of the poor will eventually be counterbalanced by inflation?

If inflation is always the result, what is the solution?


texts: Bond pricing, compute YTM ... why t not = 2?

texts:
Consider a two-period corporate bond with the following characteristics. The bond was issued at $t = 0$ with face value $FV = 100$ at $t = 2$. In period $t = 1$ and $t = 2$ coupons of $5$ are paid out ($c = 5$). We are in $t = 1$ and the bond issuer has just paid the first coupon. The price of the bond is 101.942.

Suppose that the bond is callable at $101$. The bond issuer is informed by an investment bank that it can issue a new one period zero coupon bond worth $101$ today for a face value of $104.030$ in $t = 2$.What is the yield to maturity on this hypothetical bond?

The eqaution is given by:
$$P_0 : \frac{c}{(1+r)} + \frac{C}{(1+r)^t} + \frac{FV}{(1+r)^t}$$

Where

$c=0$

$FV= 104.03$

$P_0 = 101$

$t=2$

And solve for $r$.
But the right answer is all of this above, but $t=1$ .. Why? When they say that $t=2$?


texts: Considering existence of firms with sticky prices of goods, why are we sure that SRAS will be upward slopping?

texts:
One of theories that explains why the SRAS is upward slopping is the theory of sticky prices.

For an example, suppose there is inflation. In the short run it will take different time for firms to adjust their prices. And the ones that will adjust their prices quickly will be able to rip additional short-term profit. If my inputs (raw materials, labor, etc) are slow to increase their prices, then I will be able to rip additional profit by using said inputs and then selling the outputs under prices that correspond to new price level. Theoretically people like me are responsible for upward slopping nature of the SRAS.

BUT, the coin has two sides. There are firms that have sticky prices. For an example, maybe they need to honor some kind of contract that made prices immutable for some time period. Or maybe they need approval of government officials to rise their prices and it can take time. They can't rise prices for given time period, but they will face increased demand from firms that have less stickier prices for their outputs. The only other way to reach equilibrium in their local markets in face of increased demand would be to DECREASE QUANTITY SUPPLIED. And this will happen all over the country, making the real GDP smaller.

In other words, there would be two kinds of reactions to increased price level in the short run by firms. "Flexible" firms (i.e. firms who quickly adjust prices of their goods) would increase quantity supplied (and consequently, increase real GDP), while "rigid" firms would DECREASE quantity supplied (and consequently, decrease real GDP).

Now it's not obvious why it would lead to the SRAS having uppward slope. How can we know for sure? Maybe profits received by "flexible" firms will be compensated by decreased output by "rigid" firms. Or maybe a decrease in real GDP caused by underproduction by "rigid" firms will outweight gains by "flexible" firms, leading to decreased real GDP in the short run.


texts:
I am working with a Realized GARCH model. I have am having some trouble understanding a concept:

Paper: Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility, Hansen & Haung

  "A key feature of the Realized GARCH framework is a measurement
  equation that relates the observed realized measure to latent
  volatility".

Or from the rugarch-vignette (R), page 14:

  "Unlike the naive augmentation of GARCH processes by a realized
  measures, the realGARCH model relates the observed realized
  measure to the latent volatility..."

I am confused to exactly does "observed realized measure" mean?


texts: which is an example of demand curve that is always inelastic/elastic?

texts: Which class of functions have the property of being always elastic?and instead always inelastic?


texts:
Lately, rising longer-maturity bond yields have been in the news. Many people write as though the rising yields show that "the market" believes that the Federal Reserve will raise interest rates within the next few years (presumably due to rising inflation rates).
But isn't a rising expected rate of inflation reason enough for yields to rise? After all, higher inflation means lower real yields. What does this have to do with the Federal Reserve?


texts: What does Smith mean by "price of work" in this context?

texts:
I've read these excerpts from The Wealth of Nations multiple times:

In reality high profits tend much more to raise the price of work than high wages
In raising the price of commodities the rise of wages operates in the same manner as simple interest does in the accumulation of debt. The rise of profit operates like compound interest.

But I struggle to grok what he means.
What is "price of work" and how is it different to "wage", and why does profit have an exponential relative growth, not a linear one?


texts: Are White's Robust standard errors robust to clustered errors?

texts:
I want to ask about OLS White's 1980 "robust" standard errors.
The key assumption, is that regression errors $u_i$ have distinct variances $σ_i^2$. Then the variance matrix is: $$\Sigma = \operatorname{diag}(\sigma_1^2, \ldots, \sigma_n^2)$$ with its White's estimator: $$\hat\sigma_i^2 = \hat u_i^2$$ This is the HCE (heteroscedasticity-consistent estimator).
 Is the White's robust variance of $\hat{\beta}$ estimated by OLS assuming  independence? For example, assume that there is some $i,j$ such that $$Cov(u_i,u_j)\neq0$$ Because $i,j$ are part of a cluster. In that case $\Sigma$ is not diagonal but has the same diagonal as before. Will the White estimator converge to the diagonal of the true $\Sigma$?


texts: Can repeated game sustain a discounted average payoff that is not individually rational?

texts: Look at the following payoff matrix, there are two stage Nash equlibria, and we consider a infinitely repeated game with discount factor $\delta\in(0,1)$, can players sustain an average payoff of (2,2) under any strategy? (I am confused because the individually rational(i.e. minmax) payoff is (3,3)) If not, why?


texts: Fixed cost, sunk costs and variable costs

texts:
i need to answer to this question but i'm wonder if i need to use the short-run cost function (C = wL * rK) of not. Can you help me ?
This is the statement :
A small business owner employs 5 workers. The annual wage bill is $75000. The book value of the assets is $540 000. If workers are fired, they are entitled to a legal compensation of $30 000 each. The current market value of the assets is $430 000. In the short run the business owner may increase production hiring additional workers or may decrease production firing workers but is not able to change their fixed assets.
If it is not necessary to use the function, the answers are :
 -What is the value of the fixed costs?
Value of the fixed cost = $75000
-What is the value of the variable costs if one worker is fired?
value of the variable costs if one worker is fired = $30 000
-What is the value of the sunk costs?
Value of the sunk costs = $75000 + ($540 000 - $430 000 (depreciation)) = $185 000
Many thanks,


texts: In microeconomics : is this the contradiction in the atomicity of firms ?

texts:
Let $p$ be the market demand. It is a function of the market production $Q$. Let $q_i$ be the production of firm $i$.

Reading Steve Keen (in Debunking Economics, chapter II) quoting George Stigler, I think the first wants to deduce the following contradiction in the atomicity of firms.

Using the chain rule, we get : $\frac{dp}{dq_i}= \frac{dp}{dQ} \frac{dQ}{dq_i}$.

The firm $i$ is price-taker, so the market price is the same whatever its production and so $\frac{dp}{dq_i}=0$.

The demand $p$ is a (strictly) decreasing function of $Q$ (supposing the law of demand is true). Thus $\frac{dp}{dQ} < 0$

The other firms than firm $i$ are not supposed to react to a change in production of firm $i$, so that $\frac{dQ}{dq_i}=1$.

We get : $0 < 0$. Is that the contradiction that Steve Keen means (or another way of expressing it) ?

Thank you so very much !


texts: confusion regarding elasticity of a demand curve

texts:
The following question is on a quiz at Marginal Revolution University:
https://mru.org/practice-questions/calculating-elasticity-demand-practice-questions

The elasticity of demand is 2.0. Is the demand curve relatively steep
or flat? Will a fall in price raise total revenue or lower it? Note:
we present the elasticity in terms of its absolute value.

The official answer is "relatively flat; raise total revenue".
I can't understand this; isn't it true that elasticity > 1 means higher responsiveness of demand to changes in price?  And isn't 1.0 defined as neither steep nor flat, and anything above 1.0 being steeper?
I can understand that a fall in price will lead to a huge surge in demand, because of the high elasticity, and therefore more profits.
I missed another question on the quiz that, for me, should be explicable in terms of the same reasoning as above.

The elasticity of demand is 1.1. Is the demand curve relatively steep
or flat? Will a fall in price raise total revenue or lower it? Note:
we present the elasticity in terms of its absolute value.

Again, the official answer is "relatively flat; raise total revenue".


texts: Is there a universal type space involving infinite players?

texts: Having just dabbled in 7.1of rationality in extensive games by Andres Perea, I got an impression all constructions of universal type space are restricted to finite players. What's the obstacle to extend it to countably infinite players? For example, is it trivial to extend them to cover OLG games in which each stage game is only played by finite players?


texts: Does decreasing marginal utility imply risk aversion?

texts:
Unless I misunderstood something, seems like risk
aversion and decreasing marginal utility is the same thing in the utility model, but intuitively, it seems entirely possible that an individual with no decreasing marginal utility is still risk averse.

For example, I can be exactly twice happier with 1000 dollars than only with 500 dollars. This implies constant marginal utility. With that, I can still be unwilling to enter a bet that pays me +1 or -1 with equal probability and generates an expected return of 0. It is the uncertainty that i do not like, irregardless of marginal utility.

Am i misunderstanding something? Can anyone please explain?


texts: Reconciling low wages with high technology and high education

texts:
This is one example of many recent doom storied prognosticating that the "millennial" generation will be the first in (recent) history to experience lower incomes than their predecessors—at least in western societies like the UK.

How can we reconcile the idea that millennials will earn lower wages with the observations that

millennials work with better production technology than their parents did
millennials have enjoyed higher levels of education/training than their predecessors, and are therefore presumably more productive?


texts: What is the most important factor in sample selection for time series models?

texts:
Is there some convention in sample selection for time series analysis? And what is the most important factor in this regard?
I mean, I have seen Kónya, I. (2018) use annual data from 1995–2016 to estimate a DSGE model.
I have seen Uribe, M., & Schmitt-Grohé, S. (2017) use annual data from 1980-2011 to estimate a VAR model.
I have seen Drechsel, T., & Tenreyro, S. (2018) use annual data from 1900-2015 to estimate a VAR and DSGE model.
Shousha (2016) uses a quarterly sample from 1994–2013.
What appears to be the pattern in these papers for me is the following;

First, choose a sample period you want to analyze, maybe, based on a structural break in the data or maybe before or after some event.
Then choose which frequency you want to analyze...annually, monthly, quarterly.
Then use all available data you can get based on 1 and 2.
Then check the parameters of the model if they are stable after estimation.

With all that said, there is a ton of information on the internet saying, for example, that sample size should be at least 50 or 80 or some threshold. Meanwhile, I do not see these thresholds in the literature. Instead, what I see is that researchers focus on some period they want to analyze at some desired frequency, not caring so much about the number of observations (which as I have shown above can be even 20).
By the way, let's say the parameters of the model are stationary for the sample 1980-2018. Then quantitative results would change if say the sample 1985-2018 is used, although both models are valid. I guess one should place more weight on qualitative results (like signs) than on quantitative results which are relatively more sensitive to sample size.


texts: Finding equilibrium of perfect competition in the short run with a cost function

texts:
I am having a lot of problems trying to find the equilibrium price when we are given a cost function and demand function, but no supply function.

  All firms have the following production function: $Q = \sqrt{K \cdot L}$

  Wages are w = 9, and the rental rate of capital is r = 36.

  In the short run, capital is fixed at ̅ = 3 units. Market Demand is given by P = 360 – 2Q

  There are 9 firms in the market, find P*, Q*, and Total Surplus

In solving the production function with a fixed K:

$MPL$ = K$^{1/2}$ \cdot L$^{1/2}$

$MPL$ = ${1/2} \cdot $K$^{1/2}$ $\cdot$ $L^{-1/2}$

= 1/2 \cdot (K$^{1/2}$ $\cdot$ L$^{1/2}$)

Substituting 3 for K:

= 1/2 \cdot ($\sqrt{3}$ \cdot $\sqrt{L}$)

$\sqrt{3}$/2 =  $\sqrt{L}$

$\sqrt{L}$ = .8660254

$L^*$ = .75

Where C = wL + rK

C(Q) = w($L^*$) + r($K^*$)

C(Q) = (9*.75) + (36*3)

C(Q) = 114.75

C(Q) @ 9 Firms =  (114.75 * 9) = 1032.75 (I think???)

But this doesn't have a slope, so how does this make sense? Obviously you would normally find the equilibrium through Qd = Qs, but what do I equal Qd to now?


texts: External economies of scale: who will produce when going from autarky to free trade?

texts:
Hi

"Assume that two countries can potentially trade goods in an industry that is characterized by external economies of scale. Country B produces at Q(B) in autarky and country A produces at Q(A) in autarky. What will the allocation of production look like if the two countries start to trade?"

My intuition would be that country A would produce a greater output since they have a lower AC than country B at the autarky outputs, but will this continue so that country A actually produces everything?

Thanks!


texts: study methods for first year phd courses in econ

texts:
I'd really like some tips on how to master the material for first year phd econometrics (texts: hayashi chap 1 -3, - econometrics, casella and berger 5 - 8th chapter - statistical inference) apart from doing problem sets set by professor on my own and struggling through them :) I have a month and 10 days and get stuck easily while solving problems.

I am a self-taught mathematician (multivariable calc, linear algebra, single variable) and so I don't quite know how to utilise the tools in my toolbox although I know them in theory, if that makes sense. With practice questions, I start seeing a pattern and I am not seeing one in metrics yet. constructive advice much appreciated


texts: Unclear reasoning for the specific inclusion of categories of complexity in the GSIB buffer setting

texts:
Based on [Basel Comittees Methodology] paper for GSIB buffer setting (https://www.bis.org/publ/bcbs255.pdf), they compute the complexity of a bank based on:
(i) notional amount of over-the-counter (OTC) derivatives; (ii) Level 3 assets; and (iii) trading
and available-for-sale securities.
The idea is that those categories would increase the costs and time to resolve the bank. However, it is not clear how do these relate to the resolution process despite having checked the methodology (https://www.bis.org/publ/bcbs255.pdf).  Would anyone care to explain?


texts: Multivariate implicit differentiation (Samuelson, 1948)

texts:
I am studying "The Simple Mathematics of Income Determination", by Paul Samuelson (from book is called "Macroeconomia (artigos selecionados)", by APEC-CAEN. It is the 1st chapter of the book, the 13th page), and I am having some troubles in understanding a calculus passage.
First, Samuelson states the income equation:
$(1)$ $ Y =  C (Y - \bar{W}) + \bar{I} + \bar{G} $
Where $Y$ corresponds to income, $C$ corresponds to consumption, $\bar{W}$ corresponds to taxes (actually, I don't exactly know the odd reason why the letter W was picked as taxes instead of a more common letter as T), $\bar{I}$ corresponds to investment and $\bar{G}$ corresponds to government spending). For purpose of simplification, these three last variables are treated as constants.
Then, $Y$ is differentiatied in $\bar{G}$ (which I suppose it is an implicit differentiation, in the form of $\frac{dy}{dx} = - \frac{F_x}{F_y}$):
$(2)$ $\frac{dY}{d\bar{G}} = \frac{1}{1 - C'(Y - \bar{W})}$
But my doubt emerges in the following passage:
$(3)$ $\frac{dY}{d\bar{(-W)}} = \frac{C'(Y - \bar{W})}{1 - C'(Y - \bar{W})} = \frac{dY}{d\bar{G}} - 1  $
I realize that Samuelson did the same implicit differentiation as in step 2 and I can visualize that
$\frac{C'(Y - \bar{W})}{1 - C'(Y - \bar{W})} = \frac{1}{1 - C'(Y - \bar{W})} * C'(Y - \bar{W}) = \frac{dY}{d\bar{G}} *  C'(Y - \bar{W})$
but, how does $\frac{dY}{d\bar{G}} *  C'(Y - \bar{W})$ turns to $\frac{dY}{d\bar{G}} - 1  $?
I mean, how did this $-1$ replace the multiplying term $C'(Y - \bar{W})$
I tried to get it, but unsuccessfully. I hope you could shed some light on it.


texts: Why are countries in the Gulf rich but lagging in technological innovation?

texts:
Countries in the gulf are oil rich. But they are lagging in R&D sector. Governments do not spend much on R&D. Most countries employ foreign contractors or import technologies.

What is the reason?


texts: Introduction of an asset tax in the AK model

texts:
Let's start by analyzing the family's problem with the imposition of a tax. Assuming a CRRA utility function:
\begin{equation}
    U = \int_0^\infty e^{-(\rho-n)t} \cdot \left[ \frac{c^{1-\theta}-1}{1-\theta} \right] \operatorname{dt} \hspace{5mm} (1)
 \end{equation}
Agents maximize $(1)$ subject to the assets' restriction:
\begin{equation}
        \dot{a} = w - c + (1-\tau)r \cdot a - n \cdot a
\end{equation}
The Hamiltonian is given by
\begin{equation}
    \mathcal{H} = e^{-(\rho-n)t} \cdot \left[ \frac{c^{1-\theta}-1}{1-\theta} \right] + \lambda \cdot [ w - c + (1-\tau)r \cdot a - n \cdot a ]
\end{equation}
The maximum principle conditions are:
$$\begin{cases}
    \frac{\partial \mathcal{H}}{\partial c} = 0 \implies e^{-(\rho-n)t} \cdot c^{-\theta} = \lambda \\ \dot{a} = \frac{\partial \mathcal{H}}{\partial \lambda} \implies \dot{a} = w - c + (1-\tau)r \cdot a - n \cdot a  \\ \dot{\lambda} = -\frac{\partial \mathcal{H}}{\partial a} \implies \dot{\lambda} = -\lambda \cdot [(1-\tau)r - n] \\ \lim_{t \to \infty}  [\lambda \cdot a] = 0
\end{cases}
$$
Is my reasoning correct so far? Or should I have included a transfer from the government to the agents somewhere? Furthermore, whether the government spending is productive or not would also change how we deal with the tax in our AK model, right?
UPDATE: Thinking a little bit more, I've reached the conclusion that the problem should be reestated as:
Maximize $(1)$ subject to assets' restriction
$$
\dot{a} = w - c + (1-\tau)r \cdot a - n \cdot a + v
$$
where $v = \frac{V}{L} = \frac{\tau \cdot r \cdot a}{L}$ is a per capita lump-sum transfer from the government to the families. Therefore, the Hamiltonian is now given by:
\begin{equation}
    \mathcal{H} = e^{-(\rho-n)t} \cdot \left[ \frac{c^{1-\theta}-1}{1-\theta} \right] + \lambda \cdot [ w - c + (1-\tau)r \cdot a - n \cdot a + v]
\end{equation}
The maximum principle conditions are:
$$\begin{cases}
    \frac{\partial \mathcal{H}}{\partial c} = 0 \implies e^{-(\rho-n)t} \cdot c^{-\theta} = \lambda \\ \dot{a} = \frac{\partial \mathcal{H}}{\partial \lambda} \implies \dot{a} = w - c + (1-\tau)r \cdot a - n \cdot a + v \\ \dot{\lambda} = -\frac{\partial \mathcal{H}}{\partial a} \implies \dot{\lambda} = -\lambda \cdot [(1-\tau)r - n] \\ \lim_{t \to \infty}  [\lambda \cdot a] = 0
\end{cases}
$$
Using the equations above, we can find that:
$$
\frac{\dot{c}}{c} = \frac{1}{\theta} \cdot [(1-\tau)r - \rho]
$$
Considering now a production function in per capita form given by
$$
y = Ak, A > 0
$$
we have that the firms profits are (note that I didn't include the tax in $r$ here, per the reasoning that since $r$ enters profits as an expense, in this case it's not taxable, because it's not an asset income as in the representative family's problem)
$$
\pi = Ak - \underbrace{w}_{=\frac{\partial y}{\partial L} = 0} - \delta \cdot k - r \cdot k
$$
which means the first-order condition of profit maximization will be given by
$$
\frac{\partial \pi}{\partial k} = 0 \implies A = f'(k) = \delta - r
$$
or
$$
r = A - \delta
$$
Therefore,
$$
\boxed{ \frac{\dot{c}}{c} = \frac{1}{\theta} \cdot [(1-\tau) \cdot (A-\delta) - \rho]}
$$
Now, in equilibrium, $a = k$. If we substitute this and $v = \tau \cdot r \cdot k$ in the assets's restriction, we have:
\begin{align*}
\dot{k} &= -c + (1-\tau) \cdot r \cdot k - n \cdot k + \tau \cdot r \cdot k \\ &= -c - (r+n) \cdot k
\end{align*}
and, therefore,
$$
\boxed{ \dot{k} = -c + (A-\delta-n) \cdot k}
$$
Is what I did correct?


texts: Decreasing interest rate effect on economy

texts:
Central banks decrease sometimes the interest rate by saying this has positive effect on the economy and the development of countries.

One of the reasons is that it can be easier to do investments (business, government, etc.). Are there other reasons? And does somebody have deeper insights about doing this and the benefit of it?

(Of course there are also disadvantages and risk of doing this (but I am not interested in that for now))


texts: Solow model golden rule with my exact answer

texts: In a perfectly competitive Solow economy with physical capital accumulation, population growth and a Cobb-Douglas production function, show that the “golden rule” steady-state would be reached if at every period aggregate consumption coincides with the aggregate labour income.


texts: Would it be appropriate to include state level variable with MSA model?

texts: Greetings I am running a time series which will use vector error correction model. My dependent variable is economic base which is comprised of manufacturing, mining and construction sectors. I have a different economic base for each MSA in PA. One of the regressors is noneconomic base which are the remaining industries for each MSA. THe objective is apply the dynamic time series methods of the cointegration and error correction model that enables sectoral interactions. These model fully estimate the long-run equilibrium relationships among the economic sectors in these MSAs. Would it be feasible to add state GDP as a regressor for each MSA equation?


texts: Substitution effect when price of both goods change by the same percentage

texts:
I am trying to grasp the concept of income- and substitution effects.

The way, I've understood it, the decomposition bundle is found, at the original indifference curve, where the slope equals that of the new budget line.

Does this mean that if the price of both goods (assuming a simple model of 2 goods) change by the same percentage, the substitution effect is zero? As the slope of the budget line will remain unchanged.

This seems to intuitively make sense to me, but I would greatly appreciate a 100% confirmation, that this is correct.

Thank you!


texts: Algebraic demand curve in a perfectly competitive market for a firm

texts:
I've had a few years of economics courses already but still there are some basic things in the field that I just can not wrap my head around... (let's say economics is not my favorite field of study)

The problem that I'm having is about an algebraic representation of a demand curve in a perfectly competitive market.

Say that there is a set of N suppliers (with |N| possible tending towards infinity, hence a perfectly competitive market; let's just assume free entrance to the market too), consider a supplier i. The market demand function in terms of the output of supplier i can now be written as:

Here what is in the curly brackets is just the total market output. Now here's my problem, if you take the derivative of this function wrt. q_i, then you find that this derivative equals beta. However, I've also heard that the derivative of market demand with respect to a firm's output, in a perfectly competitive environment, is 0; as in perfect competition, a firm cannot control the price through its output this effect is very very small because of the many other suppliers.

Where in my reasoning did I go wrong?


texts: What does economics say about “starting from” pricing?

texts:
I was wondering what economics says about what I would call the “starting from” pricing pattern in advertising. My first question would be whether there’s a more properly defined term for it.

It’s a common enough pattern: for example, an advertisement on a website that promises “Spend a weekend in Paris!” highlighting a price of “€150”, preceded by, in small type, the words “starting from”. When you click through, this price turns out to only apply to the weekend of Saturday December 25th, which most people would prefer to spend with their family and when many sights in the city are closed. Not to mention that it’s in winter time. Every other weekend the website offers and which is closer to what you had in mind when viewing the advertisement (Paris in summer!) is really priced at €300. (I just made up those numbers).

More generally stated, the pattern consists of advertising a highly desirable price for a seemingly desirable product, which really only applies to an undesirable version of the product, while offering a more desirable product at a less desirable price.

On one hand, I assume this pattern is effective in enticing people to check out the advertiser’s offerings. On the other hand, there’s an ineffectiveness in making people feel disappointed or outright deceived by the advertisement, possibly making them turn away.

I was wondering what economics says about this pattern. Some more specific subquestions:

Is there a more properly defined term for it?
Is there some more formal or experimental study on the relation between the “starting from” price point and the more realistic one and the effectiveness of such advertisements?
Is there some comparison on this advertising pattern and others, such as one in which both price points are stated? (like “Spend a weekend in Paris! Summer weekends at €300 or in winter as low as €150”)


texts: Effect of changing MC on monopolists' maximised profits

texts:
Let a monopolist have constant MC = c, with no fixed costs. If $p(c)$ and $q(c)$ are the profit maximising price and output as a function of MC and the market demand schedule is given by $q = D(p)$, how does the monopolists' profit vary with a small change in MC? This is what I have so far:

Maximised profits is given by:

$$
π = p(c)q(c) - cq(c)
$$

Differentiating w.r.t c:

$$
\frac{dπ(c)}{dc} = q(c)[p'(c) - 1] + q'(c)[p(c) - c]
$$

The first term $q(c)[p'(c) - 1]$ is clearly positive because $q(c) > 0$ and for a monopolist $[p'(c) - 1]$ is also positive because:

$$
p(c) = \frac{c}{1+\frac{1}{Ɛ}}
$$

$$
p'(c) = \frac{1}{1+\frac{1}{Ɛ}}
$$

and for there to be a profit maximising level of output, $Ɛ < -1$

$$
p'(c) =  \frac{1}{1+\frac{1}{Ɛ}}> 1
$$

For the second term, $q'(c)$ is clearly negative since higher MC leads to higher price and therefore lower quantity. $[p(c) - c] > 0$ since for a monopolist $p > MC = c$.

At this stage, the effect on profits of a rise in MC is ambiguous since both terms have opposing effects (one is positive, other is negative) and how profits change depends on the magnitude of the two terms. How can we quantify the effects or at least know the relative magnitudes of both terms to find how profits will change to an increase in MC?


texts: How to derive the standard euler equation from the Expanding Variety Model

texts:
In the standard expanding variety model where the representative household faces the following CRRA utility function
$$
\int_{0}^{\infty} \exp(-\rho t) \frac{C(t)^{1-\theta}-1}{1-\theta}dt
$$
and final goods that is produced competitively with the following production
$$
Y(t) = \frac{1}{1-\beta} \left( \int_{0}^{N(t)}x(v,t)^{1-\beta}dv\right)L^{\beta}
$$
with the following resource constraint
$$
C(t) + X(t) + Z(t) \leq Y(t)
$$
where $X(t)$ is the total spending on machines, and $Z(t)$ is the total expenditure on research and development.
The innovation possibilities frontier takes the form
$$
\dot{N}(t) = \eta Z(t)
$$
The intermediary goods firm faces the following problem where
$$
r(t) V(v,t) - \dot{V}(v,t) = \pi(v,t)
$$
The thing I don't understand about the model is how the Euler Equation is derived. In almost everywhere I look the Euler Equation is the standard
$$
\frac{\dot{C}(t)}{C(t)} = \frac{1}{\theta}(r(t)-\rho)
$$
I don't understand how you would derive this equation.


texts:
Let $M^d (Y,r)=a+bY-cr$ where $M^d = M/P$ is the money demand in the economy.  $a,b,c>0$. Derive $LM$.
My try
$M/P=a + b Y - c r$
$b Y = -a + \frac{M}{P} + c r$
$Y = -\frac{a}{b} + \frac{M}{b P} + \frac{c r}{b}$
Is this all there is to it? Equal the equations and solve for $Y$?


texts: General Equilibrium with Perfect Substitutes

texts:
I came across the following problem:
The quantities of an economy’s only two goods are denoted by $X$ and $Y$; no production is possible. Ann’s and Ben’s preferences are described by the utility functions
$u_A(x,y) = X+Y$ and $u_B(x,y) = XY$.
Ann owns the bundle $(0,5)$ and Ben owns the bundle $(30,5)$. Determine the Walrasian equilibrium
price(s) and allocation(s).
It is quite easy to determine B's offer curve (with the price of $Y$ ($p_2$) normalised to 1): $$OC_B = \left(\frac{30p_1 + 5}{2p_1}; \frac{30p_1 + 5}{2}\right)$$
However, I don't know how to proceed now, since consumer A is indifferent between good X and good Y. The general Marshallian demands for a function of the form $u_A(x,y) = \alpha X+ \beta Y$ are (if we assume that the consumer consumes the same quantities in case we have $p_1 = \frac{\alpha}{\beta}p_2$) are the following:
$$
X^{M} = \left\{
    \begin{array}{ll}
        m/p_1 & \mbox{if } p_1 < \frac{\alpha}{\beta}p_2 \\
        m/2p_1 & \mbox{if } p_1 = \frac{\alpha}{\beta}p_2  \\
\ 0 & \mbox{else}
    \end{array}
\right.
$$
and
$$
Y^{M} = \left\{
    \begin{array}{ll}
        m/p_2 & \mbox{if } p_1 > \frac{\alpha}{\beta}p_2 \\
        m/2p_2 & \mbox{if } p_1 = \frac{\alpha}{\beta}p_2  \\
\ 0 & \mbox{else}
    \end{array}
\right.
$$
So if we replace exogenous income with the endowments $\omega = e_1p_1 + e_2p_2$, and normalize the price of Y to 1 again, our offer curve would look exactly the same as the one of consumer B (since $\alpha = \beta = 1$), because we are in the case where consumer A splits his consumption equally (by assumption), since we have that $MRS_A =  \frac{1}{1} = 1$. And since $MRS = \frac{p_1}{p_2}$ in equilibrium, we must have that $p_1 = p_2 = 1$ if I'm not mistaken.
$$OC_A = \left(\frac{30p_1 + 5}{2p_1}; \frac{30p_1 + 5}{2}\right)$$
Solving for the Walrasian Equilibrium, we would get that $p_1 = 1/6$, which corresponds to our price ratio, since $p_2 = 1$.
This somehow doesn't seem right to me, because the fact that consumer A wants to consumer both goods equally if $p_1 = \frac{\alpha}{\beta}p_2$ is just an assumption that we have made to be able to define that case. In reality, however, consumer A is totally indifferent between goods X and Y, so he can freely switch between the two and does not have to consume them $50:50$. Also, what makes this approach very confusing to me as well is the fact that the prices are endogenous within this framework. So the prices should be able to adjust freely according to demand, which makes the above definition of the Marshallian demands redundant.
My second question is that given this logic, would it even make sense to look at what happens if $p_1 \neq \frac{\alpha}{\beta}p_2$? As I said, the prices are endogenous, so we cannot impose certain prices in the beginning already. How do you approach such a problem with perfect substitutes in general then? Say we have for example $u_A(x,y) = 2X+3Y$ and $u_B(x,y) = XY$. Does the result change?


texts: Is a resource allocation problem in mechanism design a direct or indirect mechanism?

texts:
From L. Hurwicz's work and book "Designing Economic Mechanisms," I cannot figure out whether a resource allocation problem in mechanism design is a direct or indirect mechanism.

I think the answer is yes since a resource allocation mechanism can be described as a tuple of two components, i.e., $\langle M, g \rangle$, where $M = (M_1, \ldots, M_n)$ and $M_i$ defines the set of possible messages of agent $i$. By writing the agents' complete message space as

$$\mathcal{M} = M_1 \times M_2 \times \cdots \times M_n$$

we can define the outcome function $g$ as

$$g : \mathcal{M} \to \mathcal{O},$$

where $\mathcal{O}$ is the output space defined by

$$\mathcal{O} = \{(\theta_1, \ldots, \theta_n), (t_1, \ldots, t_n) \; | \; \theta_i \in \mathbb{R}_{ > 0}, \; t_i \in \mathbb{R} \}.$$

Then, the outcome function $g$ determines the outcome, namely $g(\mu)$ for any given message profile $\mu = (m_1, \ldots, m_n) \in \mathcal{M}$ and the payment function is defined as

$$t_i : \mathcal{M} \to \mathbb{R}$$

which determines the monetary payment made or received by agent $i \in \mathcal{I}$.


texts: I am wondering if there is any work in search models that discusses firm behaviors. Most common search models that I am familiar with talk about the job seeker's threshold rule. Is there any model that discusses similar firm threshold rule, in investment in capital, effort etc.


texts: What are some common causes of jobless growth?

texts:
While "jobless recovery" is often discussed in the aftermath of recessions in Western countries, it seems it's always a short-lived phenomenon. On the other hand, it looks like in other parts of the world, e.g. South Africa, Nigeria, or even India have experienced much longer periods of "jobless growth"; e.g. for the latter country:

  Jobless growth has surfaced over the past few years as an unsettling element in India's economic picture. The 2011 census showed that the Indian economy grew at an average rate of 7.7% annually over the prior decade, while employment grew by only 1.8%.

So what are the (common) causes of jobless growth in developing countries? And if I'm not wrong about their occurrence in the West, why is it that we don't see such long periods of jobless growth in the West?


texts: Application of Laffer Curve on the price of Goods and Services

texts:
The Laffer Curve shows the relationship between Tax-Rates and the Amount of Tax Revenue Collected. Can't a similar principle be used on the price of goods?
To elaborate: The total revenue of a firm will only go up to a certain extent when they increase the price before it starts falling, just like the Laffer curve shows for tax revenue.
I couldn't find much on this on the internet; So wanted to see if there is anything wrong with this assertion.


texts:
In closed loop toy models with a fixed money supply, what are the downsides of calculating probable outcomes with a binomial coefficient?

For example, given a toy economy where trades yield a profit or loss of $t$, and all participants start with wealth $W$ as expressed by:

$f(x_{n+1})=x_n \pm t$

and

$f(x_0)=W$

I would predict the probability of one participant reaching a wealth of $0$ by iteration $q$ to be :

$$
P = 1- \prod\limits_{n=1}^{q} {\left(1-\dbinom{n}{\frac{W+tn}{2t}}\frac{(n+1)\bmod 2}{2^n}\right)}
$$

Are there better methods?


texts:
I am having trouble completely understanding the mathematical definition of non-satiation. I have stated the definition from Wikipedia below. It would be great if someone can graphically explain.

  Formally, if $X$ is the consumption set, then for any $x \in X$ and every $\varepsilon > 0$, there exists $y \in X$ such that $||y-x|| \leq \varepsilon$ and $y$ is preferred to $x$.


texts: Does savings always equal investment? Are there any cases where savings could be removed from the economic system altogether and break the balance?

texts:
Assuming a closed economy, does savings always have to equal investment?
If an individual produces a certain amount of a resource and saves it, that becomes part of the savings of the economy. However, if the resource is subsequently destroyed, it is then removed from the economy. In that case, the savings have increased but the investment hasn’t?
Does destroying a resource count towards investment? Is that an edge case we don’t consider at all? Is this any different from the way investment takes resources away from an individual and puts it into an economy?


texts: Is inequality increasing? Does it correspond to increasing social harm?

texts:
I have a series of related questions.

My understanding is.

Economic wealth (ie. GDP) per capita is increasing around the world. We can refer to this as 'the pie is getting bigger'.
At the same time, inequality (the distribution of the pie) is also increasing.
Economic inequality is correlated with social harm, such as crime.

The questions I have is:

Is it correct to say that inequality is correalated with social harm? What do we mean by this?
Is inequality increasing consistantly around the world? Or is it decreasing in some places?
If it is increasing, are we also seeing a corresponding increase in social harm?


texts: If a retailer consumes a good he bought from the producer, does that get accounted into the GDP of a nation?

texts:
Let's say we have a soft-drinks store. Say the store sells Pepsi and Coke. If the retailer drinks a bottle of coke from his own store, does that get counted into the GDP of a nation?

Or is it only counted if someone else apart from the store owner consumes it by paying for it?

How does this work?


texts: Can there be a sample such that SRF and PRF do not intersect?

texts: I am confused if it is possible for to randomly select a sample such that SRF and PRF do not intersect. I have thought of the concept of parallel lines, which allows for such a case but I am unsure if concepts of probability and statistics allow for it.


texts: How do I obtain a correlation between two variables?

texts:
Can I differentiate a quadratic regression model formula with the form
$$Y_i=\beta_0+\beta_1 X_{1i} +\beta_2 X_{1i}^2+\epsilon_i$$
(added to this formula would be other control variables e.g dummy variables) to obtain the correlation between X and Y holding everything else constant? Also, if I were to add a female dummy variable, how would the correlation of X and Y differ between men and women? Or would the correlation be the same?


texts: Is the utility of money *actually* logarithmic?

texts:
Apologies for asking what is probably a basic question from someone that is not in the economics field.

But I was playing around with the idea of determining how a group of people could split a bill "fairly", meaning they each spend an equal amount of utility, calculated from their yearly income. And I did it using logarithms since that is the common recommendation.

I have seen many mentions that the utility of money is roughly logarithmic as it increases. And it is usually phrased as a rule of thumb, but I don't see actual justification. And the assumption seems embedded everywhere. For instance, a (real) flat income tax that taxes all income (not just consumption or earned income) is seen as neither regressive nor progressive - but the flat tax assumption (that everyone would pay the same percentage) again points to the idea of money having logarithmic utility.

My question is, has this actually been measured? I have seen indications that economists actually do studies where they analyze purchasing decisions across a wide range of income levels. It seems that with enough data points, a utility function could actually be calculated.

Has this been done? And is it actually logarithmic? What is it? Is there an up to date utility function for the value of money?


texts: Risk with unknown probability distribution of the outcomes

texts:
From Wikipedia:
"Risk aversion comes from a situation where a probability can be assigned to each possible outcome of a situation and it is defined by the preference between a risky alternative and its expected value."
"Ambiguity aversion ... is defined through the preference between risky and ambiguous alternatives, after controlling for preferences over risk."
What is the preference between an ambiguous alternative and a certain outcome referred to? For example, the choice between a certain reward and an unknown probability to win a larger reward.
I think it is not risk aversion, because an alternative's probability distribution of the outcomes is unknown, and not risk ambiguity because one alternative does not entail a risk.


texts: Are short-let platforms really contributing to rising rent prices?

texts:
Short-term rent services such as AirBnB are often criticized for eroding the communities by increasing rent prices for locals:

  ... as short-term letting transfers much-needed housing from the residential sector into the tourist economy, it [...] contributes to rising rent levels ...

While it makes sense that with less houses available for long-term rent, the rent price goes up, I would expect the effect of short-term rents to be insignificant, as most properties proposed on AirBnB are not available for long-term rents anyway.

Are there any studies which managed to quantify how big this effect really is?


texts: How could the Roman sestertii/sesterces be converted into modern terms (say 2017 US$)?

texts:
Of course, the value of the sesterti must itself have fluctuated over the centuries it was in use. And so if I must narrow it down, I am particularly interested in its value during

the time of Lollia Paulina who was once covered with 40M sesterces' worth of jewels; and
the time of Cleopatra, who once drank a dissolved pearl worth 10M sesterces,

both of these stories being from Pliny, Book 9, Ch. 58.

Adam Smith writes in The Wealth of Nations:

  When we read in Pliny, therefore, that Seius bought a white nightingale, as a present for the Empress Agrippina, at a price of six thousand sestertii, equal to about fifty pounds of our present money; and that Asinius Celer purchased a surmullet at the price of eight thousand sestertii, equal to about sixty-six pounds thirteen shillings and fourpence of our present money

Smith also writes:

  Three sestertii, equal to about sixpence sterling,

which would be consistent with the previous quote, since £1 = 240p.

So according to Smith, 6,000 sestertii ≈ £50 "of our present money". The Wealth of Nations was first published in 1776. Using the Bank of England's inflation calculator, £50 in 1776 = £7,519.57 in 2016, or about US\$10,000 at current conversion rates (according to Google).

So 6,000 sestertii ≈ US\$10,000 in 2017 or 1 sesterti ≈ US\$1.67? Thus

Lollia Paulina's jewels (40M sesterces according to Pliny) would be worth US\$66.7M today? And
Cleopatra's swallowed pearl (10M sesterces according to Pliny) would be worth US\$16.7M today?

Of course, I have no idea how Adam Smith did his conversion, but presumably some modern day historians/economic historians have since done better.

(This question was originally posted over at History.SE, but unfortunately the folks there don't seem to know anything about economics. So I'm trying here instead.)


texts: Does education have any value for most people's work?

texts:
Let me first say that I am not an economist. However, I was having a discussion with one of my friends who claimed that he had absolutely no gain from his education other than it actually being the ticket for him to get a job. He argued that he hardly ever used any of the stuff he had learned during his education. So while it was a formel requirement for him to have some kind of education to gain entry at the firm where he is currently working, he sincerely believed that his education did not make him a better worker in any way.
I must admit I was a bit offended. I love my own job and I maybe also have some idealistic notions on behalf of education that it can both make us better as humans as well as help us work in better ways. However, I think that what most annoyed me was that I could see he had point and still felt that economists must have some kind of counter argument against this notion that education is basically valueless. So my question is:
Do there exist in economics a serious discussion along these lines?
and furthermore, if that is the case,
What are the main arguments on behalf of those arguing that education certainly has its economic merits?


texts: Can one forecast $\Delta Unemployment$ and $\Delta Inflation$ using a VAR model based on Okun's law?


texts: Help in interpreting this graph? Assets/Liability ratio

texts:
I'm having some doubts on how to interpret the following ratio.
I tend to think of leverage as a measure of how much debt the firm takes on.
By equity=Assets-Liabilities. When Equity is negative, I would say a firm is insolvent or very close to not meet its financial obligations.

What's the rationale for the ratio below? When asset/liability is smaller than one, doesn't it mean that assets < liabilities, and so the firm is insolvent? Do they mean these Chinese industries are insolvent?

Wouldn't it be better to use equity instead of assets for a measure of leverage?


texts: proof verification in George J. Mailath and Andrew Postlewaite (2001b)

texts:
I am reading George J. Mailath and Andrew Postlewaite (2001), and this is the lemma 1 in this paper. I don't understand the induction process in this proof. I think that we should use the fact that $x_{i+1} + p_{k+1}< v(b_{i+1}, s_{i+k})$ to show $x_{i+k-1}+p_{i+k} < v(b_{i+k-1}, s_{i+k})$.
At first, I did induction with respect to $k$. Since $k>1$, the first step of induction is $k=2$.  Then, we should show that $x_{i+1} + p_{i+2} < v(b_{i+1}, s_{i+2})$. But, I have no idea of how to show this.
Is my approach of induction correct? I appreciate if you give any help.  Please tell me if more context is needed.


texts: Would trade openness reduce market-seeking FDI?

texts:
My question is motivated by thinking about the prospect of attracting FDI into developing countries. Since developing countries do not have high skilled labor or better financial / governance institutions, the motivations for FDI are either 1) cheap labor force, or 2) local market.

The first advantage (cheap labor) will gradually wither away as developing countries develop. But it seems that the second advantage will go away too if developing countries engage in trade liberalization and open up their local market.

Is it true that trade openness would reduce market seeking FDI? If so, is there any reason for FDI investors to bring to developing countries anymore?


texts: How to derive cubic cost function from a problem of constrained optimization?

texts:
The cubic total cost function usually take the form

$TC(q)=a+bq+cq^{2}+dq^{3} \qquad a,b,d>0, c<0$ and $c^{2}<4bd$

I know that from a constraint maximization problem

$min\quad wL+vK$

subject to

$q_{0}=f(k,l)$

i can express it with the lagrangean function

$\mathcal{L}=wl+vk+\lambda(q_{0}-f(k,l))$

with some algebra for the case of a Cobb-Douglas production function $q_{0}=k^{\alpha}l^{\beta}$ i can reach

$TC=q^{\frac{1}{\alpha+\beta}}w^{\frac{\beta}{\alpha+\beta}}v^{\frac{\alpha}{\alpha+\beta}}\left(\frac{\alpha+\beta}{\alpha^{\frac{\alpha}{\alpha+\beta}}\beta^{\frac{\beta}{\alpha+\beta}}}\right)$

I could give values to $\alpha$ and $\beta$ to obtain a cubic function, but not the one I described in the preamble. It could also fix some other factor such as the size of the factory, but would not work.

Any idea?

Thanks in advance


texts: Yield curve flattening- abstract question

texts:
I just stopped and thought about the current economic state, and yield curve in particular.

As you can see here, the yield curve is starting to flatten, means longer bonds demand is high, while short term bonds demand are low.

This is happening due to the "fear" from the upcoming short term economics, so the investors are selling short bonds and buying long bonds.

In US, the chance for government default are very low, as they can print more money and never declare a default, which will cause inflation (something that affect both short term and long term).

So why does the investors are buying longer bonds, with the same yield as short term yield, while the risk is so low? What is the rational behind getting longer bonds?

Thanks.


texts: Incentive compatibilty conditions for multi-item auctions

texts:
In this paper by Myerson on optimal single item auctions, the incentive compatibility condition is shown to be equivalent to the following simpler conditions on the auction - (i) the allocation probability being monotonic in bid (ii) the form of the payment rule.

Is there a similar characterization for multi-item auctions? Any reference regarding this would be helpful.


texts: Per capita income growth rate is difference between income growth rate and population growth rate?

texts:
We know: $PCI = \frac{Y(Income)}{P(population)}$ and that
$PCI$ growth rate is $\frac{\Delta PCI}{PCI}$.

How is this equal to the difference between income growth rate and population growth rate?

In other words how is $\left(\frac{∆\frac{Y}{P}}{\frac{Y}P}\right) = (∆Y/Y) - (∆P/P)$ ?


texts: How did the Exchange Rate Mechanism work?

texts:
The Exchange Rate Mechanism was introduced by the European Economic Community in 1979.

It fixes the Exchange rates between currencies to a specific margin.

But how does it do this?


texts: Large consumer goods companies not using advertising, and what their reasons are

texts:
Recently I've learned that Inditex (owner of Zara brand) is the biggest fashion group in the world and it's using almost no advertising at all.

I would like to know more examples of such big companies that use no advertising and why might a large company not invest directly in advertising?


texts: How to average CDFs of one variable across years

texts:
I have wealth-to-income data for 10 years. I computed the cdf of this variable in each year.
Now I'm trying to average the cdfs across years. In each each, the number of observations is different.
Does anyone know how to do it?
Thank you in advance.
Susan


texts: Differentiate a positive externality and the absence of a negative externality. Tax or subsidize?

texts:
I hope this isn't overly semantic, but I'd like to gain some clarification on the use positive (or negative) externality.

I usually shoot down suggestions for examples of positive externalities like organic agriculture. We can grant that organic agriculture is better than conventional, but that doesn't mean it is producing additional external benefits. Instead, organic agriculture might feature fewer negative externalities compared to the status quo.

I've even seen examples like smoking being a positive externality because smokers die sooner and save governments money on Social Security (perhaps that accounting might be questionable, but let's grant it for the sake of argument). Again, my semantic preference would be to label this as the absence of status quo negative externality.

If the semantics aren't interesting, might there still be something interesting on the tax vs. subsidize side? Returning to the agriculture example, taxing the negative externalities associated with conventional agriculture seems smarter than subsidizing organic. This seems like a case where it's more efficient to regulate the end and not the means. But what market characteristics might make subsidizing specific not-negative-externality-producing things more efficient?


texts: Which measures are there to evaluate a country economical development?

texts:
I'm familiar with the measures of Gross domestic product (GDP PPP) total, per capita and GDP nominal total and per capita. But I'm not sure if these measures evaluate the economical development of a country since they don't take into account what a country owes, and external debts sometimes get countries into economical crisis when they become unable to pay them.
Then I found about net international investment position (NIIP) that is defined as a country's external financial assets and liabilities.

My question is, can this measure be used to evaluate the economical development of a country and if not, are there specific measures which are used to evaluate economical development?


texts: Welfare function in General Capital model (Search and Matching)?

texts:
i'm working on a model from the Mortensen textbook: "Wage dispersion why are similar workers paid differently?". To be precise, i'm working on the model about general capital. In this case, capital is viewed as embodied in the job rather than the match. In other words, when the job is created, investments are made in the equipment any worker needs to be productive in the job.

I have resolved the model and make some simulation on Matlab, but I'm stuck when it comes to find the optimal "b" which represent the optimal reservation wage/unemployment benefit. I assume that it could be found with the Welfare function (maximizing output minus costs).

Here are some the equation from the model:

$ rJ=f(k)-w-\delta J + \lambda(1-F(w))(V-J) $
$ rV=\dfrac{\lambda}{v}\dfrac{\delta}{\delta + \lambda(1-F(w))}(J-V)-c-\delta V $

where $rJ$ is the expected value of a filled post, $rV$ the expected value of a vacancy, $\delta$ the exogenous destruction rate and $c$ the recruiting cost.


texts: Why is the derivative of a monotonic transformation of a utility function assumed to always be greater than 0?

texts:
I'm looking into utility functions and their relation to indifference curves.
Now, I understand a positive monotonic transformation does not change the order (it's a rank-preserving transformation).
I thought the same is true for a negative monotonic transformation (I'm reading H. Varian, he distinguishes between negative and positive monotonic transformations) except it reverses the order.
However in a paper I've read just recently: https://ocw.mit.edu/courses/economics/14-03-microeconomic-theory-and-public-policy-fall-2016/lecture-notes/MIT14_03F16_lec3.pdf
It says:

Definition: Monotonic Transformation
Let I be an interval on the real line ($R1$) then: $g : I → R1$ is a monotonic transformation if
g is a strictly increasing function on I.
If $g(x)$ is differentiable then $g'(x) \gt 0\ \forall x$
Informally: A monotone transformation of a variable is a rank-preserving transformation. [Note: not all rank-preserving transformations are differentiable.]

But how is that true for a negative monotonic transformation such as $g(x) = -x$ where $g'(x)=-1$?
I don't understand. Does the paper not take into account that there are negative monotonic transformations?


texts:
If $u(x)=\frac{x^{1-\mu}}{1-\mu}$, then the elasticity defined as $\frac{\partial u}{\partial x}\frac{x}{u}=1-\mu$.

However, when we define $u(x)=\frac{x^{1-\mu}-1}{1-\mu}$ (usual def. for isoelastic utility), we have $\frac{\partial u}{\partial x}\frac{x}{u}=(1-\mu)\frac{x^{1-\mu}}{x^{1-\mu}-1}$. And this doesn't seem to give a constant elasticity. So, why do we call this utility isoelastic?

Any help would be appreciated.


texts: What are the arguments against a zero corporate tax?

texts:
I've read a title in the news proposing a zero corporate tax. Thinking about it I couldn't figure a good reason against.

Why couldn't a country just set the corporate tax rate for firms to zero and then tax any gain obtained via negotiating shares or receiving dividends? Tracking the latters seems way easier (via a digital national registry of ownership and trades and mandating disclosure of dividends ) than burdening firms with complicated tax codes and the state with the burden of chasing them.

I am sure I am missing some theoretical and real world complications, so please, enlighten me.


texts: Differential form of the quantity theory of money

texts:
The quantity theory of money is $MV = PY$.
Why is the differential form $\delta M + \delta V = \delta P + \delta Y$?
Shouldn't it be $V\delta M + M\delta V = Y\delta P + P\delta Y$?


texts: Gresham's Law applied to wampum and gold/silver coins in the 1600s

texts:
So I was reading an article by Nick Szabo called "Shelling Out"

And in his introduction paragraph he explains how American Indians use bones and shells as a currency called "wampum".

This currency was accepted as legal tender in New England between 1637 and 1661. While the Colonies still accepted coin from the British.

He points out that :

  The beginning of the end of wampum came when the British started
  shipping more coin to the Americas, and Europeans started applying
  their mass-manufacturing techniques.

  By 1661, British authorities had thrown in the towel, and decided it would pay in coin of the realm – which being real gold and silver, and its minting audited and branded by the Crown, had even better monetary qualities than shells. In that year wampum ceased to be legal tender in New England.

Now I'm pretty new to economics but I thought Gresham's Law meant that people will not spend valuable assets such as gold or silver instead they will spend less valuable currency for fear of it depreciating.

So did wampum cease to be legal tender because the government "said so" and if so, why would they make this decision?


texts: How is after market tradings inserted in stock market graphs?

texts:
When I open a stock market graph tool such as Metastock and enter in the intra-day periodicities, I can never found the data related to the after market operations. I know (by observation) that when the market is in the initial moments just before being closed, all the operations are put inside the last candles (so e.g. if the market closes at 5 pm, the after-market operations between 5pm and 5:15 pm are all inserted in the candle related to 4:50-5:00 pm in the 10 minute graph).

But what about all the moves done after that? Are all after market operations inserted as part of the last candle?


texts: How will the economic effects of Brexit impact a middle-class American family?

texts:
On the news it was stated that the UK leaving the EU has already caused trillions of dollars of loss to the world economy. While the newscaster made it sound very serious, I don't have any international finances at all, and my employer only operates in North America. It seems to me that the ripples will be so small by the time they reach me that I wouldn't even notice, but I don't know much about the global economy.

Is the buying power of the USD likely to fall? Will certain categories of goods become more expensive than others? Will employment rates change significantly? Interest rates on savings and/or debt?

Will my pocketbook really notice over here in the USA?


texts: Proof that EV = CV when there is no income effect

texts:
In every textbook it says that it is easy to see that with no income effect, the integral

$\int_{p^0_1}^{p^1_1} \! h(p,u_0) \mathrm{d}p_1. = \int_{p^0_1}^{p^1_1} \! h(p,u_1) \, \mathrm{d}p_1$

Could someone explain to me why?


texts: What are the defining features of Capitalism?

texts:
What are the necessary and sufficient conditions for an economic system (or mode of production) to be classified as "Capitalism"?

Is it markets? Is it for-profit corporations? Is it limited liability companies? Is it workers selling their labour to capitalists/employees? Is it freedom to set up companies? Is it a low degree of government productive activity? Is it a subset of these or other elements?

I imagine the answer would depend on a particular schools of thought, so in principle I would expect different answers.

Disclaimer 1: this question is not requesting opinions about what capitalism is, it is not, it should be, it should be not, but authoritative answers, with proper references.

Disclaimer 2: for those voting to close this as too-broad, I asked on meta whether this question was on-topic, and (albeit not a popular post) it seems people agreed it was.


texts: What econometrics book or textbook should I use?

texts:
I'm doing my Master thesis in economics. I have only a very basic understanding of econometrics, and honestly, I hate it, the same things go for stats and probability etc.

Now, at my school my supervisor allowed me to get help to analyze the data using VAR or GARCH so the analysis itself will be done by an assistant at the school. However, my supervisor told me I should be able to answer questions regarding the model once I defend.

I have been watching tons of YouTube videos about econometrics, but I think I should get a book to understand econometrics better. I don't want to master it, I just want to pass the defense. Once I'm done I'm not interested to learn anything about econometrics ever again. So, any Econometrics book you suggest? I found many online and not sure which one is the easiest to use.


texts: What at all justifies income taxes (as opposed to sales taxes only)?

texts:
For those who do not know, in America, the higher your income, the higher the percent of it is spent on taxes. This means that, whatever tax money is used for, those who are more hardworking (or, at least, those who are more skilled) are essentially punished. And, because we tax low-income citizens less, we are making their life quality nearly the same as everyone else, which encourages unemployment.

If, on the other hand, income taxes were to be eliminated and sales taxes raised significantly, we would be punishing those who spend a lot - essentially, those who abuse their wealth more. (Obviously this is not necessarily always so, but it is more so than if we apply taxes to anything else like income). This, therefore, would encourage philanthropy (and otherwise spending money on things other than buying.)

Note that this can be engineered in such a way that the total tax money the government gains stays the same.

The Question: Why does much of the world still have income taxes? Is there anything (and if so, what?) that makes them better, fairer, or more productive than sales taxes?

*This question is not a copy of the question Are sales taxes regressive? because the linked question is asking specifically whether sales taxes decrease in burden as income increases. My question is explaining that that doesn't matter.


texts: Decentralization of business due to internet/mass communication, or mere bosses-at-a-distance?

texts:
Excuse my question if it sounds brutish and uneducated but I'm curious about the recent trend of businesses like Uber, Google Play Store, Apple Store, possibly even Craigslist (et al) which are more of a platform to offer your services/wares versus the "traditional" large-corporate employers (e.g. Macy's) which employ you multiple days and provide benefits and whatnot.
My question is multi-faceted so I will ask first:

Is there a paper or are there papers that talk about this trend and its implications? Or am I seeing something that is irrelevant to a change in markets/employment/the way we typically do business?

And, if indeed it is merely (as in the title) "bosses-at-a-distance" (that is, not face-to-face with you), does this bode well for people as even unskilled laborers can find menial employment, albeit without benefits and whatnot?
Moreoever, is this "decentralization" in any sense of the word? And, if it is, how does it bode for the future? Will odd-jobs be the daily endeavors of the 22nd century human?
Thank you for putting up with my ignorance!


texts: What impact does deficit spending have on economic inequality?

texts:
Taxation schemes can be classified as progressive (the tax rate is higher for higher income brackets), regressive (the tax rate is lower for higher income brackets), or neutral (the tax rate is the same for all income brackets).

Conceptually, as compared to a neutral taxation scheme, a progressive one shifts the tax burden more towards the higher segments of the income distribution, and a regressive one shifts the tax burden more towards the lower segments.

Is there a way to reason about deficit spending in these terms? That is, which segments of the income distribution does the debt incurred by deficit spending burden more?


texts: Two-player first-price auction with resale

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Exercise 2.5 in Vijay Krishna's Auction Theory (slightly modified):

  Consider a two-bidder ﬁrst-price auction in which bidders’ values
  are distributed according to $F$. Let $\beta$ be the symmetric equilibrium, i.e., $$\beta(x)=E[Y\mid Y<x],$$ where $Y$ is drawn from $F$.

  Now suppose that after the auction is over, both the losing and winning bids are publicly announced. In addition, there is the possibility of postauction resale: The winner of the auction may, if he so wishes, offer the object to the other bidder at a ﬁxed “take-it-or-leave-it” price of $p$. If the other bidder agrees, then the object changes hands, and the losing bidder pays the winning bidder $p$. Otherwise, the object stays with the winning bidder, and no money changes hands. The
  possibility of postauction resale in this manner is commonly known to
  both bidders prior to participating in the auction. Show that $\beta$ remains an
  equilibrium even if resale is allowed. In particular, show that a bidder with
  value $x$ cannot gain by bidding an amount $b>\beta(x)$ even when he has the
  option of reselling the object to the other bidder.

Call the two bidders Jane and Mike. Given Mike's bid, and assuming that Mike follows the equilibrium strategy $\beta$, Jane can determine Mike's exact value. This implies that if Jane wins the item but realizes that she has lower value than Mike, she will resell it to Mike at exactly Mike's value.

We should calculate Jane's expected payoff when bidding $\beta(z)$ with $z\geq x$ when her value is $x$, and show that the expected payoff is maximized when $z=x$.

Jane wins with probability $F(z)$. If she loses, her payoff is $0$. If she wins and her value is higher than Mike's value, her payoff is $x-\beta(z)$. If she wins and her value is lower than Mike's value, $Y$, her payoff is $y-\beta(z)$. As a result, her expected payoff is $$-F(z)\beta(z)+F(x)x+(F(z)-F(x))E[Y\mid x<Y<z].$$

The term $F(x)x$ does not depend on $z$, so we are left to maximize $$-F(z)\beta(z)+(F(z)-F(x))E[Y\mid x<Y<z].$$

How do we maximize this?


texts: Why did fed increase interest rates in 2018?


texts: Why absolute value in elasticities and marginal rate of substitution?

texts:
This is a point I find very confusing and very hard to justify to students. Depending on the books, one finds many different conventions regarding the sign of elasticities and marginal rate of substitution (MRS). Some define them with absolute value, some don't, and  one sometimes finds inconsistencies inside a single book or set of notes.

My questions are :

To your knowledge, what is the most conventional position regarding the use of absolute value in the definition of

Own-price elasticity
Cross-price elasticity
MRS

Is it mere convention or is there somewhat of a rationale for taking absolute value in some/all/none of the cases?


texts: Transforming a matrix of explanatory variable in regression

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Given the partitioned regression equation (into $X_1$ and $X_2$), I want to transform $X_1$, say $X^*_1$, such that $X_2$ and $X^*_1$ becomes orthogonal ie. $X_2^T$. $X_1^*$= 0.
A matrix can be transformed as $X_1^*$ = $X_1$.p where P is transformation matrix.

If we premultiply $X_1^*$ = $X_1$.p with $X_2^T$ we will get $X_2^T$.$X_1$.p = $X_2^T$.$X_1^*$= 0. How can I find P?

Part (ii) is easy to solve. Parameters of $X_2^T$ and $X_1^*$ will depend on their separate regression with Y.


texts: How to calculate bond price and the relationship between bond price and repo rate?

texts: Suppose that there is a gilt Tr 7.5pc '06 in 2006 with interest yield 7,32% and redemption yield 4.31%. How can I compute the price of this gilt per 100 face value. The problem is that the numbers I get from using interest yield and redemption yield are different. Suppose that the central bank reduces its repo rate from 4.5% to 4.25%, how is that going to affect the gilt price>


texts: GNP, GDP, GNI, GNDI and their relationships?

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GDP - Gross Domestic Product

GNP - Gross National Product

GNI - Gross National Income

GNDI - Gross National Disposable Income

We know that GNI=GNP, and that GNP=GDP+Net income from factor ownership abroad.

What I don't understant is how according to IMF Balance of Payments terminology, we have that GNDI=GDP+net primary and secondary income from abroad, when we know that GNDI = GNI+net current transfer from abroad?
Wouldn't this be tantamount to say that GNP=GDP?


texts: Weakly Dependent Time Series | Common Error

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I am watching a video, that mentions for the following time series:

$x_t=\epsilon_t+\theta\epsilon_{t-1}$

$\textrm{Corr}(x_t,x_{t-1})≠0$

Then it mentions if we have anything greater then 1 such as $x_{t-2}$ then $\textrm{Corr}(x_t,x_{t-2})=0$ because $x_{t-2}$ doesnt share any common erros with $x_t$ now my question is : if the error is gaussian or a white noise then isnt any $x_{t-\tau}$ correlated with $x_t$?


texts:
Fonseca (HET Website) writes:

Only much later did Piero Sraffa (1960) finally solve the "invariable measure of value" problem and re-ignited interest in Ricardo's theory.

What was the "invariable measure of value" problem and how did Sraffa solve it?


texts: Government bonds - the most simple example

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I would like to have an example of a common case of buying government bonds. (Wikipedia: it is issued generally with a promise to pay periodic interest payments and to repay the face value on the maturity date).

What is the maturity date (years I guess), how much is that period of "periodic interest payments", how much is that interest, and what is the "face value"?

A simple example of the most common case. Or at least a known case of such a transaction. Say for example one of the latest government bonds issuing of Germany or Spain.

Say for example I buy German government bonds at a maturity date of N years, with a periodic interest of M months, and with the interest at P percent each month. Replace N, M, and P with a known case. In case I spend 100,000 Euros for such bonds, how much do I get back? (periodically, in the end and in total)

I think such example would make it easier for the common people like me to understand how government bonds work.


texts: advanced mathematical treatement of revealed preference and utility theory?

texts:
I am looking for a textbook that treats revealed preference and utility theory much more thoroughly than does Mas-Collel.

What would be suggestions for this? Specifically I'm interested in conditions under which utility functions are characterized uniquely up to monotonic or linear transformations.


texts: Suppose I have a preference satisfy all basic assumptions, how to show consumer problem solution is unique

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The preferences are complete, transitive, continuous, strictly monotone and strictly convex

The textbook says it is because
 (1) Budget Set is compact so that a solution exists;
 (2) B is convex and the utility function representing this preference is strictly quasi-concave

What if I have no information on budget set, that is, I don't know what properties B might have. Can all arguements above still hold?

Can I use the strict increasing utility function to prove the solution is unique? Since a preference with all these assumptions ensures a continuous, strictly increasing and strictly quasi-concave utility function. Then by contradiction, there can not be two or more maximization point of utility function.


texts: How can people save in a equilibrium economy?

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Two people on a desert island:

John produces 100kg potatoes and sells them to Paul for \$100. Paul catches 100kg fish and sells it to John for \$100. GDP is \$200\$, right?
Next year, they improve their techniques and produce 150kg of potatoes and fish, respectively.
Now, John would love to sell 150kg potatoes to Paul for \$150 and buy only 100kg of fish for \$100, so he can save apart \$50. Unfortunately, Paul has the same wish!
It seems there is no way they can both save. If both transact \$100, the GDP will be like last year. If both transact \$150 the GDP will be \$300.
In both cases, the economy is at equilibrium. It can grow or stay the same. But no saving is possible!
It seems that, in order for John to save \$50, Paul must consume more than his income (or the other way around).

How then is saving in the real economy possible?

Is it a zero sum game, that is, for every John saving, there must be a Paul that consumes more than he can afford?