texts:
I'm looking at data for an online shop with clothing items listed at different prices. I'd like to use this information to do some kind of profit maximization (i.e. I'd like to have some understanding of the impact on sales if I raise/lower price of an individual item).

Unfortunately, I don't have information of the variety "Q sales for clothing item X at price P" for a variety of prices; this would be hard to estimate due to the small number of items in each category.

However, I do have a distribution of sales vs. price and the distribution of price of items in the shop. I'm thinking if I compute
$$
\frac{\text{% of all sales at this price}}{\text{% of available items at this price}}
$$, that gives me something analogous to a "quantity demanded". For simplicity, I bucketed the prices and sales into $5 increments.

Having done this and doing your traditional log-linear fit
$
\ln(P) = a\ln(Q)+b
$ I get a pretty good fit and a reasonable number (around $-.9$).

Question 1: Does my methodology make sense? If so, what did I just calculate? I feel like it's an "aggregate" price elasticity of all items in the shop. The clothing items for sale are mostly substitutable with each other, the price elasticity of an individual item must be a lot higher (since there are substitutes available).

Question 2: Is there a way to figure the "average" price elasticity of each item from this (approximating that they all have about the same price elasticity)?

EDIT: Based on the suggestion from @optimal-control and @NickJ, it appears the issue is that I don't really have a good model of what's going on. Here's what I'm imagining:

Suppose you have $n$ unique items, each with a fixed price $p$. Each item has a limited supply available $s$. I observe $q(p, t)$ sales for each unique item, limited by $s$. Let's say $q(p, t)$ is something like a homogeneous poisson process, for simplicity.

The above is starting to look like a markdown optimization problem; I could imagine finding an optimal price for each item based on these factors and my cost structure (storage cost, time value of money, etc.), if I could, say, change prices and estimate the change in $q(p, t)$. Unfortunately, this function is so small, and $s$ is so small (maybe 1 to 5 items) that this may be impossible to estimate. What I'm trying to figure out is some way to estimate the response of $q(p, t)$ with respect to $p$ without modifying prices, off of the assumption that the $n$ items are partial substitutes for one another.

If they were perfect substitutes, I would expect ALL of my lowest price items to sell out, and then my next lowest, etc. going on upward and I could use these results to estimate $q(p, t)$. But clearly this isn't the case, because some more expensive items sell first. The problem is, $q(p, t)$ is dependent on the mix of items and prices available. Any thoughts on how to approach this?


texts: Rational expectations econometrics: a theory or an excuse?

texts:
I've been reading up on the topic of Rational expectations  econometrics, and have really been wondering if it is a theory useful for prediction or just used to "fit" a model.

Your standard rational expectations model (otherwise referred to as efficent markets model):
$$y_t=\tilde{y}+\sum_{i=1}^n\beta_i(X_{t-i}-X^e_{t-i})+\epsilon$$

$y_t=$ Economic variable of interest at time $t$ like unemployment or real output.
$\tilde{y}_t=$Natural rate or equilibrium of economic variable at time $t$
$\beta_i=$ coefficents.
$X_{t-i}=$ an aggreagte demand variable like money growth, Inflation or Nominal GDP growth.
$X^e_{t-i}=$ Anticipated aggregate demand conditional on knowing all  information at point $t-i$
$\epsilon_t=$ an error term

Where the property of "rational expectations" is defined as the true expected value of $X_t$ is equal to the markets expected value of $X_t$. Mathematically written as:
$$\mathbb{E}(X_{t}|\phi_{t-1})=\mathbb{E}_m(X_t|\phi_{t-1})$$
$$\mathbb{E}(X_{t}-\mathbb{E}_m(X_t)|\phi_{t-1})=0$$

If rational expectations hold, we should observe when expectations are taken:

$$y_t=\tilde{y}_t$$

that is $y_t$ should always be in equilibrium/ be forecasted based on its equilibrium values/growth process (providing rationale for the use of Univariate models in economics).

My Question: Are the use of expectations augmented models useful for forecasting or is it just a way to explain forecast error?


texts: Natural borrowing/debt limit and other borrowing constraints

texts:
When confronted with the simple household consumption maximization problem under uncertainty (and with Arrow security sequential trading)

$$\max_{\{c_t(s^t),a_{t+1}(s^t,s_{t+1})\}_{t=0}^{\infty}}\sum_{t=0}^{\infty}\sum_{s^t\in S^t}\beta^tprob(s^t) u(c_t(s^t))$$

$$\text{s.t.}\,\,\,c_t(s^t)+\sum_{s_{t+1}|s^t}Q_t(s^t,s_{t+1})a_{t+1}(s^t,s_{t+1})=y_t(s^t)+a_t(s^t)$$
$$-a_{t+1}(s^t,s_{t+1})\le A_{t+1}(s^t,s_{t+1}) $$

$$a_0(s^t)=0$$

we call $A_{t+1}(s^t,s_{t+1})$ the natural debt/borrowing limit and define it as the loosest possible limit. But what exactly does this mean? And what form does it take?

Moreover, in the FOCs for $a_{t+1}(s^t,s_{t+1})$ we cancel the Lagrangian multiplier of the second constraint, it doesn't bind because of the Inada conditions on the function of utility. Is the intuition here that even when you borrow an infinitesimal amount $\epsilon$, if it is repeated enough times you'd reach a point where the debt stock is so high that consumption needs to be zero (not negative because above we implicitly assume $c_t\ge0$ right?) to repay it, which would imply an infinite (?) loss of utility, and thus you shouldn't borrow at all?

Finally, what is the relation with lower asset bound, no-Ponzi scheme and no-default constraint? How do their implications differ?


texts: Savings = investment with private money creation?

texts:
I've been reading some introductory macroeconomics and I'm struggling to understand one of the basic accounting identities. In a closed economy with a fixed money supply it's clear that every dollar saved is a dollar invested. I'm happy with the standard story.

What I don't understand is how the identity works when money is created privately. I can go to a bank an ask for a million dollar business loan. The bank grants me the loan, and creates an asset (the loan) and a liability (the money in my account). I then invest the money. It seems from this example that I have created a million dollars of investment without creating any offsetting savings. Of course, I have to pay off the loan at some point, but then shouldn't the identity be something like investment = savings + debt?

What am I missing?


texts:
( The game of “ chicken”) Two cars are driving at each other at great speeds.
If nobody changes directions, in 3 seconds they will collide and die a gruesome death,
yielding payoffs of −100 for both players. At every second they have to (simultaneously)
decide wether to continue or not (i.e. there are 3 periods to this game). Payoffs are as
follows: If both players choose continue for each of the three periods, then they get −100.
If at any period one player choses “not continue” and the other chooses “continue” the
player that chose not to continue gets 0 and the other gets 100. If at some point both
simultaneously choose not to continue they both get 0.

True or False: Any equilibrium has the property that one of the players chooses
not to continue, but this only happens in the last period (as in the movies!).

I just wanted to double check my answer with someone.

My answer: I think that the answer is false. Because the strategy profile where player 1 plays continue at every stage and player 2 plays not continue at every stage is a subgame perfect Nash equilibrium I believe? Because based on the one shot deviation principle, there is not point in the history where player 2 can deviate from this strategy at one node profitably. And (continue, not continue) is a Nash equilibrium for the individual game. Thus, this strategy would result in a subgame perfect Nash equilibrium without getting to the third stage of this game.


texts: Accelerator and Multiplier effects at full employment

texts:
I have a question regarding the multiplier and accelerator effects. The way I see it, the value of the multiplier tends to be lower as the economy approaches full capacity. I would therefore expect growth to be slower as full capacity is reached. The accelerator effect works best when there is no excess capacity as an increase in aggregate demand would mean producers use their already existing idle fixed capital.

However the accelerator is based on past increases in consumption and output; for the investment to increase, growth must therefore increase at an an increasing rate. If at long run full capacity, growth is slower due to a lower multiplier value and the inability of firms to expand output, how can the accelerator effect come into existence???

I am sorry that this was long but I am unsure as to whether I have made a mistake early in my "chain of reasoning"...


texts: Conceptual explanation/prediction of utility function. Extraction of utility function from Big Data

texts:
It seems to me, that utility function usually is just a set of facts. Is there a framework or model for utility function that can explain or predict utility function. I. e. if user has value for item A and B and there is item C (which is conceptually linked to items A and B, i.e. it has the color or A and usability features of B) then this framework can predict the user's value for item C?

Maybe there ir some kind of framework that can explain utility function? I.e. there are ontologies which have ABox component which is set of concepts and TBox component which set of instances of those concepts. Maybe there is framework that can list concepts that are linked to some products and each consumer have some value on those concepts and from this it is possible to derive the utility function for the actual products?

How utility function is used for modeling single customer profiles? Maybe utility function can be extracted from the Big Data that are associated with cash register data, contact calls and so on?

Is there some trend of research and practice along these lines? Maybe these are fairly common things and I don't know relevant keywords only?


texts: What are 'Symmetric Agents' vs. 'Asymmetric Agents'?

texts:
Here is a contextual example from Landry et. al. 2006 :

  We concentrate on an economy with n symmetric agents who
  derive utility from consuming a numeraire good, yi, a public good
  at level G, and (possibly) from their own contribution bi to the
  public good. Each agent faces a budget constraint yi  bi  w and
  derives ex post utility according to

  (1) $   Ui = u(yi) + \Theta h(G)  + \gamma f(bi)$


texts: Loosely speaking, are all modern economies 'Keynesian' in their stance on spending during downturns?

texts:
Keynesian economics is defined as:

increased government expenditures and lower taxes to stimulate demand and pull the global economy out of the depression.

Do all modern economies adopt a Keynesian fiscal stance during significant economic downturns? Or have some demonstrated that they will not increase government spending at all during downturns?
Notes:

To make the question less ambiguous, please assume a country is 'Keynesian' if government spending was intentionally increased by at least 2.5% during a downturn of at least 1% at any point in the last 50 years (and 'somewhat Keynesian' if government spending increased by 1.5% during a downturn of at least 1%).

Example: According to this, Australia would be 'Keynesian', since it increased spending by 4% in response to a 1.6% downturn in 2008/9.


texts: Weighted voting: Vote of representative weighted by number of election votes

texts:
I was wondering if there is any literature on voting systems where voters elect representatives, and in the representatives' assembly the vote of each representative is weighted by the number of votes she was elected with.

E.g.: A special but easy example would be the US supreme court. The 'voters' here are the US senators, their 'representatives' are the supreme court judges. Instead of each judge having an equal vote their vote could have a weight equal to the number of votes they were confirmed with. This would make a difference, as consensus candidates seem to be confirmed by more votes - at least in the current system. Changing the supreme court's voting mechanism could of course affect confirmations, but this may be a way to incentivize consensus.

In case of general elections and parliamentary representatives such a weighted voting system would incentivize representatives to try to represent all the voters in their district, not just the majority. (Assuming representatives care about their voting power, but one could always tie their salary to the number of votes they were elected by.)

The idea is simple, so it has probably been raised before. Please refer me to some literature.


texts: How to improve the underperforming construction productivity by correcting its market failures?

texts:
Globally, labor-productivity growth in construction has averaged only 1 percent a year over the past two decades, compared with growth of 2.8 percent for the total world economy and 3.6 percent in the case of manufacturing (McKinsey, 2017).

The most common market failures / problems in the construction industry are:

asymmetric information
corruption
industry fragmentation
ismatch between the agents of risk allocations & rewards
dependence on public-sector demand.

I found many organizational answers to this question: improve communication between agents, introduce shorter contracts, improve on-site execution, etc.

However, I personally think internalization would be a great choice: bringing together the agents (like Elon Musk did at Tesla). Then the agents could optimize on a vaster decision set, and the result would be Pareto-efficient. The big question is: how?

My question is: how can a decision maker improve the construction productivity? What would be the answer from an Economist point of view?


texts: Economic theory says that interest rates fall in recessions. If they rise from risk then that defeats the theory. Why do ARM rates rise in recessions?


texts: What effect would destroying large amounts of physical currency have on government finances

texts:
India has recently recalled high denomination notes and asked people to deposit the physical currency in old notes in their bank accounts. People who have unaccounted wealth are resorting to destroying the currency rather than run the risk of declaring this to the tax-men. Some people estimate upto 20% of notes may not be returned totalling about  3 trillion rupees.

In a cash based economy what possible consequences can destruction of such large amounts of currency cause? I think that reduction in money volume may lead to negative inflation but the question is more about the impact destruction of currency will have on government finances.
Does it make the government richer or poorer?

Note that this question isn't about demonitization per se.

EDIT:

A newspaper report this morning says that the government expects a "windfall" due to cash not being returned by people. It states that any money not returned to central bank (In India that is the RBI), is a reduction in liability of RBI and therefore an equal amount can be paid by RBI to the government.

Is this how monetary policy works?

I was always under the impression that central bank buys government bonds in return for currency. Any physical reduction in currency means government cannot buy the same bonds back from central bank (as it doesn't have the hard cash) and therefore the government should become "poorer" (due to inability to decrease its debt in forms of bonds issued to central bank). The report states that government will get "richer" as central bank's liability is decreased and it can pay that amount to government as dividend.
Can someone clarify how this process is likely to work?


texts: How to estimate if goods are complementary or substitutes when one good is always offered for free?

texts:
Usually  whether two goods are complementary or substitutes can be measured by estimating cross-price elasticity of demand. If cross-price elasticity of demand is negative the two goods are complements and if the cross-elasticity of demand is positive they are substitutes. However, how would we determine if goods are complements or substitutes when one is provided for free (e.g. are free e-books on Bayesian analysis and coffee complements or substitutes?).
Now, as far as I understand, theoretically this does not pose any issue because even though price of one good is always set to 0 there will be some theoretical demand for the e-book that will depend on price (even if we can't observe any price other than 0).  But from a practical perspective would it be possible to estimate cross-price elasticity empirically in such case?
Normally, we would estimate cross-price elasticity in some sort of regression like (or more sophisticated analogues):
$$\ln q_x = \beta_0 + \beta_1 \ln p_x + \beta_2 \ln p_y +...+ \epsilon$$
but $\beta_2$ can only be identified if $VAR(p_y) \neq 0$ since $\beta_2= \frac{COV(q_x,p_y)}{VAR(p_y)}$.
Are there any models that could allow us to estimate cross-elasticity even in such cases or is it simply impossible? Are there other empirical methods of determining if goods are complementary/substitutes aside from estimating cross-price elasticity?
I tried to do due diligence search on google scholar but even though there are plenty of papers discussing estimation of cross-price elasticities (such as Deaton 1987), I was not able to find paper discussing this issue. This being said estimating such elasticities is not area of my specialty so I am not sure if I am missing some important keywords. I ask this question because I TA undergraduate microeconomics class and one of the students raised this, in my opinion very interesting, question.


texts: Capital/Income Ratio in Pikketty's Capital

texts:
In Capital by Thomas Pikketty, https://www.robertdkirkby.com/blog/2015/summary-of-piketty-i/, he states that World War I and World War II were the main reasons why the Capital Income to Labour Income ratio was lowered.

However, why is this the case if two world wars lead to capital destruction. Surely the remaining capital is more valuable? And possibly less is more labour to service this relatively than in the past.


texts:
I have given

2 firms in a market with constant marginal costs and no fixed costs
market demand has $D(p)$
The ﬁrms play a Cournot game

I'm supposed to Calculate the equilibrium quantity for each ﬁrm and the market equilibrium quantity and price. Also I have to find the implied proﬁt for each ﬁrm.

My approach:

Isolate the profit functions as $\pi_i = F(q_A, q_B)$ for $i \in \{A, B\}$
Then I compute marginal costs using that MC = the derivative of total costs w.r.t. Q
Then use that MR = MC for each firm, and solve for $q_A, q_B$
Then using this I was able to find the equilibrium quantity for each firm by substituting one into the other
Finally I subbed these quantities into $D(p)$ to get the equilibrium price

Among my results, I get that $q_A = q_B$. I'm not sure if I've solved this correctly but it seems to make sense to me that the firms have the same equilibrium quantities due to it being a Cournot game.

Was the approach correct?


texts: Government Ownership vs Private Ownership

texts:
In a debate concerning long term economic strategy, a representative of a left party was trying to support that privatisation and Small Government which minimizes its own activities is not a viable direction in a Global Economy, i.e. it will lead to a further loss of sovereignty in a sense that a country applies its policies mostly via the public sector, which if minimized will have insignificant impact. Then the opponent asked a simple, but intriguing question:

"Is there an example where a government owned company1 has a product that is competitive with a product of a private company?"

After a brief research I really couldn't find such example. Is there such an example and if not, what counter argument there could be presented against the above question?

1. Without the trivial and most frequent example of a monopoly.


texts: Comparing 2 equilibrium values (competitive vs centralized): can I compare only 1st derivative of objective function?

texts:
I have a rather complex model where analytical solutions do not seem achievable (I also tried symbolic solving in Matlab and Python and could not find any) so that I cannot get an explicit expression for my equilibrim values of two of my choice variables, $X$ and $Y$.
Let $U(c_1, c_2)$ be the objective function, where $U$ is some function, concave in $c_1$ and in $c_2$. $c_1$ and $c_2$ are functions of choice variables $X$ and $Y$. Given the complexity of my expression, I am unsure whether or not the objective function is concave with respect to X and Y (I was not able to find an explicit sign of the second derivative in Matlab).
Two agents are optimizing. Problem of agent A is of the form: $\max_{X} U(c_1(X), c_2(X))$ and problem of agent B is of the form: $\max_{Y} U(c_1(Y), c_2(Y))$. (B is optimizing the same objective as agent A, due to perfect competition: B is a bank investing deposits of consumers A).
I would like to compare equilibrium values in the competitive and in the centralized equilibrium of those two variables X and Y.
In the competitive equilibrium, agents are price takers whereas in the decentralized one, a benevolent social planner internalizes the price of assets $P$ which depends on choice variables (it is a constrained efficient equilibrium, a second best) and optimizes on behalf of agents A and B under the same constraints.
Therefore in the constrained efficient equilibrium, the problem takes the form: $\max_{X} U(c_1(X, \color{cyan}{P(X)}), c_2(X,\color{cyan}{P(X)}))$ and $\max_{Y} U(c_1(Y, \color{cyan}{P(Y)}), c_2(Y,\color{cyan}{P(Y)}))$.
As I hav no explicit solutions, I was wondering how I could compare the allocations under the competitive equilibrium ($X,Y$) to the one under the constrained efficient equilibrium ($X^*,Y^*$). As I did some numerical simulations (in Julia) for a wide range of parameters and under different form of the utility function $U$, and based on economic intuitions, I have an idea of the relative positions of $X^*,X$ and $Y^*,Y$ but I am still hoping for a formal proof.

In a partial equilibrium analysis (looking at the choice of $X$ only holding $Y$ fixed or vice versa), if i find that the derivative with respect to X in the decentralized is higher than in the constrained efficient equilibrium can I conclude that X is lower (for a given value of Y)? Do i need to prove concavity of the objective function with respect to X?

i.e. is it true and under which conditions if any that $\frac{\partial \mathcal{L} }{\partial X } \leq \frac{\partial \mathcal{L^*} }{\partial X^* } \Rightarrow X \geq X^*$ ?

How can I translate those results (if 1 can be proven) to general equilibrium? Would i need some conditions of the type $X(Y)$ and $Y(X)$ increasing, something like that?

In general if anyone could point me to the type of mathematical methods i should be looking at?
Many thanks for any help


texts: Since Changes-in-Changes model is good, why do people hardly use it

texts: I am a new master student who has just read Athey and Imbens (2006) "Identification and inference in nonlinear difference‐in‐differences models." They introduced the Changes-in-Changes (CIC) model. But why do people still rarely use it in empirical analysis? Thank you!


texts: is there a difference between E[e|x]=0 and E[e|d=1]-E[e|d=0] in continuous vs discrete case in regressions?

texts:
in the discrete case, if assignemt is random, then i can express E[y|d=1]-E[y|d=0] = B + E[e|d=1]-E[e|d=0], where the expectation of the errors are the same for both groups and become zero. Where I am confused is for a linear regression/continuous variable, we say this condition is expressed by E[e|x]=0, and I struggle to see how they are the same. its not the same as saying E[e|d]=0, right?

If I take a partial derivative of E[y|x] wrt x, I get B+ dE[e|x]/dx. cant I have this last term be zero without having E[e|x]=0? is E[e|x1,x2]=E[e|x2] the same thing as E[e|x]=0


texts:
Can anyone help me understand how to solve this type of asymmetric information Bayesian game?
So the game is a different version of the Tadelis 'trading house games'. It involves 2 players
that each own a house. Each player values his own house at $v_i$. The value of player $i$’s house to the other player, i.e. to player $j \ne i$, is $\alpha v_i − c$ where $\alpha > 1$. Each player knows the value $v_i$ of his own house to himself, but not the value of the opponent’s house. Both players know $\alpha$. The values $v_i$ are distributed uniformly on the interval [0, 1] and are independent across players.
I suppose that player $i$ will agree to exchange only if $v_i \leq \alpha v_j - c$ but I don't know how to go from there to find the Bayesian Nash equilibrium and how to assign probabilities. Are we suppose to use the expected value of $v_i$ through the uniform distribution, i.e. $E(v_i)=1/2$ ?
Would be very grateful for some help!!


texts: Endogeneity in demand estimation using demand systems estimations

texts:
Assume I have quantities and prices for J products across M markets in T periods.
I want to estimate their elasticities.
I construct J regressions of this type:
$$\log \left(q_{j m t}\right)=\alpha_{t}+\beta_{m}+\sum_{k=1}^{J} \eta_{j k} \cdot \log \left(p_{k m t}\right)+\epsilon_{j m t}$$
I want to instrument the price of $p_{jmt}$ the price in other markets at the time t (Hausman  IV).
within each regression: do I need to instruments all prices ($\sum_k{p_{k m t}}$)
or only for $p_{jmt}$.
My intuition is that IV for $p_{jmt}$ is enough, as $q_{jmt}$ and $p_{jmt}$ are being set simultanisly, but $q_{jmt}$ and other product does not.
Am I right?  Is there any reference for such a basic estimation?


texts: Envelope Theorem in Hopkins and Kornienko (2010)

texts:
This is from Hopkins and Kornienko (2010). In this model, $x$ is investments, $s$ is status, and $y=z-x$ is leisure, where $z$ is endowments. $x(r)$ is the optimal investment, and the relative investments determine the status in the model. Here they characterize the agent with the rank, $r$, and derive the reduced form utility. But, I am not quite sure about how the envelope theorem works here.

If I differentiate $U(r)$ with respect to $r$ and suppress the arguments, I have that
$$U_x x' + U_y(y'-x') + U_s s'.$$
I know that $Z'(r) = \frac{1}{g(Z(r))}$, where $g$ is the density of $z$. This implies that the first term and third term and $U_yx'$ turn out to be zero to make the above equation equal to Equation (8). My understanding is that $U_x = U_s = 0$ since $x(r)$ is the optimal investment. But, I don't know how to explain the elimination of $U_yx'$. Can anyone give me some help?


texts: Maximum price a consumer is willing to offer?

texts:
In microeconomics it is standard to maximize utility subject to a constraint. For this problem income and prices are normally and the solution is the Marshall which plugged into direct utility function gives the indirect utility function.
Similarly, taking instead the utility to be achieved and prices as given, the expenditure minimization problem finds the expenditure (income) necessary to achieve the given level of utility at given prices and the solution is the Hicksian demand and the expenditure function.
Is there in a similar fashion a problem where utility and income are taken for granted but where prices are solved for?
The idea would be to solve for the maximal price that a consumer is willing to pay for a good if the consumer is to achieve a certain level of utility given a certain income.


texts: Confused about what is meant by adjusting for inflation

texts:
In class, we have been using this calculator in order to see the effects of inflation.

https://www.rbnz.govt.nz/monetary-policy/inflation-calculator

I am slightly confused by what is meant by "adjusting for inflation". I read online that this means the effect of inflation is removed. I've also listened to a lot of speeches where people talk about adjusting for inflation.

In the case of this calculator, what does it mean to adjust for inflation? It doesn't mean we remove the effect of inflation, right? And is CPI used to measure the increase in inflation?

And with this calculator, are real or nominal values being used?

(I've been studying economics for a couple of weeks, so sorry for the basic question!)


texts: Where would the Nash equilibrium lie in the pictured scenario? Whats confusing me is that both persons best response changes depending on the choice of the other person (there is no dominant strategy). Am I correct in thinking the Nash equilibrium is at (-1,-1) as both A and B want to betray as it would be most beneficial, but as they both betray they end up at (-1,-1)


texts: Market shares of Nested Logit demand model

texts:
Consider a Nested Logit demand model with two nests, $N_1, N_2$: $N_1$ contains the outside option only (labelled "0"), $N_2$ contains all the remaining alternatives (labelled "$j=1,...,J$").
Suppose that the utility for consumer $i$ from picking alternative $j\in N_2$ is
$$
U_{ij}\equiv \delta_j+v_i+\lambda \epsilon_{ij}
$$
where $\lambda\in (0,1)$ and $(v_i, \epsilon_{ij})$ have a distribution which obeys the Nested Logit parametrisation.
Instead, the utility for consumer $i$ from picking alternative $0\in N_1$ is
$$
U_{i0}\equiv \epsilon_{i0}
$$
Question: could you help me to derive the market shares of a product $j\in N_1$ and of product $0\in N_2$?
I found the formulas for a generic nest structure (for example, this question is helpful), but when I try to apply them to my very simple case they do not seem to simplify a lot.


texts:
We know if the utility function is quasilinear (QL) w.r.t good 1, then the demand for other goods is independent of income (no income effect for goods $(2,\dots, N)$).

But is the reverse implication also true: i.e can we say if all the goods except one have demand functions independent of income then the utility function must be quasilinear?

I have been looking up all the standard micro grad level text books but haven't got an answer yet. I see books defining (rather characterizing) QL by just one side of implication (i.e QL implies No income effect) but are silent about the other.

Any reference in this regard will be highly useful.


texts: Can changes in the value of money be measured via interest rates and future contracts?

texts:
For most goods, we can compare the value of them by how people trade them. If in a free market, 10 apples can be traded for 20 oranges, then apples are twice as valuable as oranges. Likewise, if 10 apples can be traded for \$1, and 20 oranges can be traded for \$1, the same thing holds.

When I lend or borrow money, I am essentially buying or selling future money. If Alice lends Bob \$10 for 10 years with \$1 interest, then Bob is essentially selling Alice \$11 future dollars for a price of \$10 today. Additionally, if Bob buys \$10 of future corn today, and then corn is \$11 in the future, that means \$10 of todays money is worth \$10 of future money (on average since future corn today may be evaluated differently then future corn in the future, just due to unknown information. The free market is pretty smart in the long run though.)

Can this be used to track the changing value of money then, such as inflation and deflation?

(I guess its hard to use this, since both interest rates and the money supply are simultaneously manipulated by government backed institutions.)


texts: What does it mean to make an identification assumption?

texts:
Trying to understand this problem:

  Suppose you had access to a dataset that follows individuals from
  adolescence throughout adulthood. Each year, you observe earnings,
  educational attainment, health, and marital status.  Suppose you were
  interested in seeing how marriage causally affects the earnings of
  men. Using the described data, how would you examine this question?  What
  would be your identifying assumption?  How could you assess the
  plausibility of this assumption?

First I'm trying to understand, what is an identifying assumption? I think it's the assumption you test that tells you whether there was a causal relationship or not. Is that right?

And my first thoughts on answering the homework problem are these:

I would have to determine that income and marriage aren't simultaneously determined, reverse causal, or both influenced by the same variable. So creating a counterfactual group (unmarried men) and matching with married men could set up a good difference in differences.

But how to assess the plausibility of this assumption? I usually just plug numbers into the computer and don't care about plausibility. What makes an assumption more plausible in econometrics?


texts: Why can an increase in inflation rate, increase interest rates?

texts:
A Random Walk Down Wall Street (2015 11 ed). pp. 224 Bottom - 225 Top.

    Changes in the rate of inflation will similarly tend to have a systematic influence on the returns from common stocks. This is so for at least two reasons. First, an increase in the rate of inflation tends to increase interest rates and thus tends to lower the prices of some equities, as just discussed. Second, the increase in inflation may squeeze profit margins for certain groups of companies—public utilities, for example, which often find that rate increases lag behind increases in costs. On the other hand, inflation may benefit the prices of common stocks in the natural resource industries. Thus, again there are important systematic relationships between stock returns and economic variables that may not be captured adequately by a simple beta measure of risk.

Please expound the sentence bolded overhead?


texts: Why don't central banks just donate money to their poor citizens, rather than QE?

texts:
Why don't they prioritize paying their citizens directly (Americans in this case) over providing liquidity, repo, buying bonds, and lowering interest rates? I have a BA in Economics, so hope this isn't bad economics! I ask for central banks in general, not just the US Federal Reserve.

  Comment:

    SO we can afford this but not Medicare for All? Okay. Yeah, thanks.

  Pretty basic distinction here, this action was undertaken by the Federal Reserve, which is not the same thing as the federal government. The Federal Reserve does not need to raise money from taxpayers, they have the authority to create new money for these operations.

  Also, the Federal Reserve does not handle healthcare policy.

On Mar 16 2020, Federal Reserve cuts rates to zero and launches massive \$700 billion quantitative easing program. On Mar 17 2020, Fed announces move to help businesses get short-term funding in commercial paper market, and Mnuchin says Trump administration is looking to get cash to Americans 'immediately'. Why doesn't the Fed just donate that \$700B to poor private individuals?

  On Friday Mar. 20 2020 morning, the Fed announced that it would be increasing the frequency of its 7-day maturity operations with the world’s major central banks: the Bank of Canada, the Bank of England, the Bank of Japan, the European Central Bank, and the Swiss National Bank. The swap lines will now be offered daily instead of weekly.

  The announcement comes one day after the Fed announced \$60 billion of swap lines each with the central banks of Australia, Brazil, South Korea, Mexico, Singapore, and Sweden. It also unveiled lines of \$30 billion each with the central banks of Denmark, Norway, and New Zealand.

On May 4 2020, the US Treasury Department announced Monday it is borrowing about $3 trillion this quarter. The money is being used in large part to subsidize economic rescue efforts in the wake of the coronavirus pandemic.


texts: Why the prices for very popular items do not increase?

texts:
I am always surprised why there are certain services or items which are on high demand, and do not have their prices increased to generate more profit.

As an example, tickets to the very popular EDM festival are always sold out in minutes, but the price each year increases little. Every year the tickets are at around 200-300€, so why not make them 400-500€, since they would still be most likely sold out in a matter of weeks or months, wouldn't they?

Another example, I know a shoemaker who from time to time sells around 20-50 pairs of cordovan shoes, at a price of around 340€/pair. All the shoe stock is ordered (online sales) in around 1 day. Why wouldn't they increase the price by at least 10-20%, and then sell these same shoes over a week or so?

I can see one possible explanation - that getting money immediately has more value, but it seems to me that in the overall a much bigger profit could be obtained if the price was simply increased.


texts: Abolishing all tariffs without reciprocity

texts:
Is a policy of abolishing tariffs without expecting other countries do so a sustainable economic policy? What are the arguments for or against it?

Fear of imports is very common among people. Money going out and products coming in is not a loss of anything, since products and services are just as valuable as fiat money, or any medium of exchange.

In a country with trade deficit, I should expect depreciation of the domestic currency in short term. Devaluing currency is supposed to encourage exports, and exporters but things they need for cheaper too, so it should cause some growth in exports.

If abolishing tariffs is "such a good idea", why do politicians try to push for trade agreements instead of abolishing tariffs within their countries and benefit from the results?


texts: Could you recommend a book or lecture notes about time series that is easy to understand?

texts:
What are some time series texts that you would recommend to start studying? Some easy textbooks/lecture notes or step by step for undergraduate level.
I'm not so good at math/statistics.


texts: References for particular definitions of risk and uncertainty

texts:
I have some doubts about risk vs. uncertainty. I have read the thread "What is the difference between risk, uncertainty and ambiguity" and have skimmed through Knight's "Risk, Uncertainty, and Profit" Chapter VII (starting on p. 197). It seems there exist alternative definitions of these concepts, which is a bit confusing.

I have a particular example that implicitly defines risk and uncertainty. I would like to know if these implicit definitions are in line with any of the established ones.

Example: In a lottery, the probability to win is $p$ and the probability to lose is $1-p$. If I know $p$ and participate in the lottery, I am facing risk. If I do not know $p$ and participate in the lottery, I am facing uncertainty.

Does this match any existing definitions of risk vs. uncertainty?
Could I also get a reference to an academic paper or a textbook?

Edit 1: User 123 notes correctly that there seems to be risk in both cases (whether I know the probabilities or not, I am still participating in the lottery which by itself is a source of risk). Hence, the term uncertainty seems to incorporate risk + the lack of knowledge of the probabilities. This may suggest the terms risk and uncertainty are not mutually exclusive; when we call something uncertain, it might also include an element of risk; but when we identify something as risky, we must know the probabilities, thus it is not uncertain. Yeah, it is convoluted...

Edit 2: Quoting Knight via Wikipedia, a measurable uncertainty, or 'risk' proper, as we shall use the term.... Thus it is enough that the probability be measurable in the above example and is does not have to be known precisely. So I understand that the implicit definitions in the example above are not in line with the Knightian ones.


texts:
I am looking at an exchange economy where I have two types of goods and n consumers. Half of the consumers have a utility function given by $U(x)= 5\ln{x} +m $ and the other half of the consumers have a $U(x) = 3\ln{x} + m$. All of the consumers have been given an initial endowment of $20$ of good $x$ and $10$ of good $m$.

I need to find what is the maximum amount of good $x$ that the first type of consumers can get at a Pareto Optimal allocation under the constraint $m>0$ for all consumers

To solve this, I began with creating the following equation:
\begin{align*}
\frac{\frac{\partial U_1}{\partial x_1}}{\frac{\partial U_1}{\partial m_1}} &= \frac{\frac{\partial U_2}{\partial x_2}}{\frac{\partial U_2}{\partial m_2}}\\
\frac{\frac{5}{x_1}}{1} &= \frac{\frac{3}{x_2}}{1}\\
\frac{5}{x_1} &= \frac{3}{x_2}\\
\frac{5}{x_1} &= \frac{3}{20-x_1}
\end{align*}

However, this approach does not give me the correct solution, nor does it include the initial endowment of $m$. Can someone please help me understand what I am missing?


texts: Will there be any significant impact if oil was priced/traded in another currency other than USD?

texts:
There is an abundance of conspiracy theories online that the USD is propped up in part by the fact that oil is traded in USD, and that countries which think about allowing trades in a different currency like Saddam's Iraq are promptly snuffed out by the US military. In fact, I'd go on to say that this is the widely-held belief in west Asian countries.

I've been trying to find the truth for sometime but it seems that experts themselves seem to contradict each other. A reddit user explains the difference between 'traded in' and 'settled in' and a fellow at the Adam Smith Institute writes on Forbes essentially saying "no effect really". On the flip side, you have an MI-6 agent writing for HuffPo that the USD is a weapon against Russia because oil is priced in dollars, and this quora user who says that the impact on USD rates could be as high as 1-2%.

So my questions are:

Does the fact that oil is priced in USD have a tangible impact on the world, or is settlement freely in any currency as the reddit user explains?
If so, what would be the effect of countries pricing oil in another currency?
If not, what is a 'petro dollar' (as petrol can be settled in another currency), and how did this conspiracy theory come about?


texts: How does a perpetual futures contract affects the price of the underlying?

texts:
As long as I understand, a futures contract is kind of a prediction for the underlying's price at the time when it expires. But what happens if this futures contract is perpetual, and doesn't have a date where it'll expire? Like bitcoin's futures.

How does buying/selling this contract affects the price now?


texts: Why is government debt level presented as ratio to GDP, not against government budget or revenue size?

texts:
A country's public debt is often presented as ratio to GDP. For example, in Wikipedia, List of countries by public debt or National debt of the United States both use ratio or percentages of GDP.

Since government borrows the money in term of balancing budget and will have to repay using budget, shouldn't it make more sense to define the ratio against something related to the size of the budget, instead of the size of the whole economy? Someone pointed out to me that when seen this way, the debt ratio sounds more serious. For example, US public debt is ~18 trillion, which is slightly more than the annual GDP (this doesn't sound too bad), but actually roughly 6x government revenue in 2014 (~3 billion according to CIA World Factbook)


texts: What's the difference between Quantitative Easing and regular central bank operations?

texts: Most articles describe QE as purchasing government securities on the market.  I thought that was what ordinary day to day operations of the central bank were in their efforts to maintain a target interest rate.  So if they aren't buying government securities day to day, what is it they do to manage the bank lending rate?


texts: Why can't the Land-Value Tax (in some cases) be passed on to tenants?

texts:
According to https://en.wikipedia.org/wiki/Land_value_tax:

  Because the supply of land is essentially fixed, land rents depend on what tenants are prepared to pay,

That doesn't make any sense.  If more people want to live in a particular place, rents will increase.

  rather than on landlord expenses, preventing landlords from passing LVT to tenants.

Only if there's somewhere else that tenants want to be, that also has lower rents.  The real estate boom in San Francisco shows that when people with lots of money really want to live in a particular place, rents rise.

Thus, what stops the Land-Value Tax be passed on to tenants (in the situation where demand outstrips supply, and the government decides to increase the LVT)?


texts: So I have this utility function where I need to find t expenditure minimizing value of x. Normally, I would get the marginal utility of goods x and y, but doing that in this case doesn't leave any variables, so setting that equal to the prices would give me 2/5 = 3/3, which doesn't make sense. How do I solve this? I feel like I know how to do it but I'm just missing a major step or two.


texts: Linearization and the effect of a change

texts:
There is the following system of four equations and four endogenous variables $(K,L,w,q)$. Assume $F$ is a concave function.
$\partial F(K,L)/\partial K = r + (1-p)$
$\partial F(K,L)/\partial L = w$
$F(K,L)-rK-wL-q-(1-p)K = 0$
$v(w,p)=\bar{v}$
It seems to linearize the system around the equilibrium values to get $\frac{\partial K}{\partial p}$ and $\frac{\partial L}{\partial p}$ and it seems that these equations become
$\frac{\partial K}{\partial p} = \frac{-F_{LL}-F_{KL}\partial w/\partial p}{(F_{KK}F_{LL}-F^2_{KL})}$
$\frac{\partial L}{\partial p} = \frac{F_{KK}\partial w/\partial p + F_{KL}}{(F_{KK}F_{LL}-F^2_{KL})}$
I tried to Taylar expansion but I could not get these equations. How do we get these last equations? These equations are from p.85 Kousky et al. (2006)


texts: Attributing Labor Productivity Gains to Capital Deepening vs. Total Factor Productivity Growth

texts:
In a traditional Solow-Swan growth model, you can decompose growth in labor productivity (output/hour) into a component stemming from total factor productivity growth and another stemming from capital deepening (increases in the capital/worker ratio).

Let's assume that I create a new machine which doubles the output of soybean production and try to sell it to soybean farmers. Prior to adopting my machine, farmers used horses and primitive plows to grow their soybeans. From the perspective of the farmer, after buying my machine and using it, they work the same amount, but they produce 2x as much, so their labor productivity has doubled. However, to what would you attribute the growth in output? Would you attribute it to capital deepening (because the farmer is now using more capital than before), or total factor productivity?

The reason I ask is because total factor productivity growth is generally considered by economists to be a measure of "the pace of technological progress" (See: The Rise and Fall of American Growth and other books of the same nature). But the act of creating my fancy soybean picking machine was in of itself a technological act. I had to combine some other capital inputs (steel, etc.) and some labor (my own and perhaps my employees) with insight to create the machine in the first place. I'm a bit confused about the growth accounting here.

A follow up question makes the situation a bit harder. Let's say that again I have invented a new machine tool. This machine tool let's car makers make smooth surfaces that are more aerodynamic and look cooler. This improves the look and miles/gallon figure of cars made using my machine tool. Car companies realize that consumers' are going to love the new look and higher MPG of cars made with the machine, so they purchase it in droves. In this situation, would labor productivity (output/hour) or even raw output of cars increase? After all, nothing has changed about the fundamental efficiency of producing the car - if anything the cost of producing the car has gone up because the fixed costs the car manufacturer pays to buy my machine must now be amortized over every car they sell. If the former did rise, would you attribute it to capital deepening - the car OEM is using more capital than before - or total factor productivity?


texts: Question regarding demand schedule and equilibrium consumption

texts:
Please refer to the two images posted at this link: http://imgur.com/a/si3ko

Referring to Page 2, I'm not quite sure what the author is trying to say regarding the two bracketed portions. Considering the first bracketed portion, when the author says "purchased less than Q0", is the author still referring to a point on the demand schedule line? Also referring to the first bracketed portion, how do we know the consumer "value additional consumption more than its cost to her", and thus purchase more? How do I represent all these graphically?


texts:
What would be the impact on value of a country's assets and trade balance if its residents choose to increase their savings by investing in overseas assets and why?
May please help with this question family.


texts: What are the economic benefits of SLAPP in file sharing/piracy?

texts:
Spin-off from Piracy/File sharing - Why aren't songs, movies or ebooks given for free (+ads) like TV?
What are the economic benefits of SLAPP in or out of file sharing/piracy?
There's a comment in above link that says 'The relevance is that the recording industry is not obviously losing the piracy battle. The basis of the OP's question is that they are' (I'm OP, btw ^-^).
If that's the case, why did the RIAA heavily prosecute people for what some (yay, weasel words!) people may consider outrageous fines for outrageous expenses (not to mention opportunity cost)? Examples are Joel Tenenbaum (4.5m USD at one point) and Jammie Thomas-Rasset (1.92m USD at one point).

From Wiki (emphasis mine):

A strategic lawsuit against public participation (SLAPP) is a lawsuit
that is intended to censor, intimidate, and silence critics by
burdening them with the cost of a legal defense until they abandon
their criticism or opposition.
The typical SLAPP plaintiff does not normally expect to win the
lawsuit. The plaintiff's goals are accomplished if the defendant
succumbs to fear, intimidation, mounting legal costs or simple
exhaustion and abandons the criticism. In some cases, repeated
frivolous litigation against a defendant may raise the cost of
directors and officers liability insurance for that party, interfering
with an organization's ability to operate.

I'm assuming that there are some economic benefits to the government, society, the RIAA/the plaintiffs, someone or something by having pursued those individuals so persistently. But then again if it was so beneficial, then I expect we'd hear about a lot more than just these 2 SLAPP cases. (Or, what, everyone else really decided to settle? Idk. I kinda think it's more like RIAA/MPAA decreased its litigious tendencies.)
Perhaps in cases besides file sharing, this might have some benefits, but when it comes to current copyright law, file sharing, piracy, a digital world, etc, I'm drawing blanks particularly due to the 'Internet principle of the Hydra: You know, you can stomp one person, but there’s going to be seven more of us.'
Chairman and CEO of the Motion Picture Association of America (MPAA) Glickman 'concedes that piracy will never be stopped, but states that they will try to make it as difficult and tedious as possible.'
So, what exactly is the MPAA/RIAA getting out of SLAPP's? If there is no direct answer to be given, an alternative could be: What are the benefits of SLAPP's in general (then reader e.g. me infers analogous benefits)?


texts: Why does state-owned company so aggressive in making profit?

texts: Take China National Petroleum Corporation(CNPC) as an example, almost 86% of its stock is stated-owned. Its senior managers' promotion are related to the company's profit. And since there are investors who own 14% percent of its stock, maybe the company will face revenue pressure from them. But I think this is not sufficient to explain why they are so aggressive, I must overlook  something more important. Any ideas are going to be  appreciated.


texts: Non-viable Industry with demand curve above supply curve

texts:
Say we have a supply and demand relationship, in which the demand curve does not intersect with the supply curve and the demand curve is situated above the supply curve. What phenomenon describes such a relationship, does such a phenomenon exist?

I was thinking maybe country $A$ has regulations in place such that suppliers cannot sell product $a$ for more than some amount $S$. Maybe there is an ethical issue such as underpaid staff associated with the production of the item, so consumers will not buy $a$ at such a low price. However this seems quite far fetched and I don't know whether such a scenario exists.


texts: help understanding the "financing" of the current account

texts:
I often hear phrases like country XYZ "finances its current account deficit through flows in its financial account". i have a tough time understanding this idea of "financing" a current account deficit and why it happens with certainty.

i understand there is an identity that says: current account + financial account + capital account = 0. so, if the first term is negative than the sum of the second two must offset, and i suppose that is what is meant by financing - but it is not intuitively clear to me why this must be the case


texts: References where fewer rules resulted in better governance

texts:
I am trying to find references that support an idea that I think I read in a book on theory of institutions. I can't find the original reference. Basically, I'd like to find anything that talks about number of rules and the strictness of enforcement as variables in controlling outcomes.

In the reference I can't find as I remember it, there was a case study related to OSHA or Worker's Compensation where increasingly strict safety policies caused an increase in accidents. The analysis ran that the existing policies were too stringent to allow workers to get their jobs done, and that the workers were deciding which rules they could ignore to get tasks completed on schedule. In this case, they had better outcomes by restricting the set of rules to a smaller set that were realistic and strictly enforced. Basically, too many rules resulted in workers prioritizing the rules to follow, while decreasing the rules allowed management to make the decision about which rules were truly the most valuable.


texts:
This is from: https://eml.berkeley.edu//~dromer/papers/RomerandRomer.pdf

What does it mean that we are looking at a "tax increase of 1 % of GDP". What does a tax increase have to do with the GDP? If the tax is 20 %, and we raise it to 22 %, that's an increase of 2 percentage points, or 2/20 = 10 percent. What does GDP have anything to do with it?


texts: Question on a sufficient condition of contractiveness of best reply functions in Vives (1999)

texts:
I have trouble in understanding why a sufficient condition that a best reply function is a contraction. The following is a screenshot of Xavier Vives's Oligopoly Pricing: Old Ideas and New Tools from googlebooks (see here):

We have to find a constant $c \in [0,1)$ such that for all $x, y \in A$,
$$d(r(x),r(y)) \leq c d(x,y)$$

But it seems to me we don't have any parameter in this setting to calculate $c$.


texts: Currency conversion and Purchase Power Data

texts: Where can I find multipliers to convert a certain amount in a currency, say USD of 1960 to say present EUR taking account of purchase power parity ?


texts:
Please imagine that Nicole is uncertain of her future wealth. Her wealth in the bad state of the world is zero. Her wealth in the good state is $w>0$.  Each state is initially equally likely. However nikole can purchase technology (such as safety equipment) that will make the good state more likely. If she buys $x>0$ units, the probability of the good state becomes $q(x)>1/2$ where $q(x)$is strictly increasing and strictly concave in x, with $q(x)<1$ for all x. To purchase x units, Nichole commits to pay $t(x)<w$ if the good state materialized. She doesn’t pay anything in the bad state Nicole is risk natural. Andrew faces the exact same problem however Andrew is risk averse. Normalize andrew’s utility in the bad state to $u(0)=0$. Assume that $q(x) $ and $t(x)$ are such that both Nichole and Andrew would like to buy a strictly positive quantity f the technology.
So thinking of x as a choice variable formulate Nicole ‘s and Andrew ‘s maximization problem. How can I prove who buys the larger quantity of the technology? And what does this result tells to me intuitively? And secondly how can I prove how the optimal quantity for ether agents depends on $w$?
In the second case, I assume that the technology is provided by a risk national firm whose costs of supplying x units of the technology is $kx$ where $k>0$. The firm knows Nichole ‘s and Andrew ‘s preferences and is allowed to make different offers to them. If we imagine that the firm decides to offer Nichole a fixed quantity of $x_N>0$ and Andrew a fixed quantity of $x_A>0$. Let  $t_N(x_N)$  and  $t_A(x_A)$ denote the optimal price to charge Nichole and Andrew respectively (where I should remember this is allocated only in the good state).
Given a fixed $x_N$ , I need to derive  $t_N(x_N)$and the implicit expression of  $t_A(x_A)$ for a fixed $x_A$. If $x_N=x_A$, can I say that  $t_N(x_N)$  is greater than  $t_A(x_A)$? Or not?  I want to prove it and what can I say about this intuitively? And I want to derive  $t_N’(x_N)$ and  $t_A’(x_A)$. Finally how can I derive an implicit characterization of the optimal quantity to offer to Nichole $x_N$. And how can prove whether the optimal value of $x_A$ is greater than the optimal value of $x_N$ or not?

What is only done as a solution is
For Nichole
$$\max_{x} \ \ q(x) u(w-xt(x))+(1-q(x))u(0)$$
FOCs
$$q’(x) u(w-xt(x))+q(x) u’(w-xt(x))-(w-xt(x))’+(1-q’(x))’u(0)=0$$
$$q’(x) u(w-xt(x))+q(x) (-t(x)-x)u’(w-xt(x))=u(0)q’(x)$$
$$q’(x) u(w-xt(x))-q’(x) u(0)=q( x )u’(w-xt(x))(t(x)+x)$$
$$q’(x)[ u(w-xt(x))- u(0)]=q( x )u’(w-xt(x))(t(x)+x)$$
$$q’(x)[(1/q(x))[u(q(x)(w-xt(x)))- u(0)]]=q( x )u’(w-xt(x))(t(x)+x)$$
$$(q’(x)/q(x))[u(q(x)(w-xt(x)))- u(0)]=q( x )u’(w-xt(x))(t(x)+x)$$
Risk natural
$$q(x)(w-xt(x)+(1-q(x))u(0)=u(q(x)(w-xt(x))$$
$$[u(w-xt(x))-u(0)]=(1/q(x))[u(q(x)(w-xt(x))-u(0)]$$
Risk averse
$$q(x)u(w-xt(x))\le u(q(x)(w-xt(x))$$
Any help is appreciated. Thank you.

The original version of question

Edit: for adding my solution for remaining parts
Take that Nichole is risk neutral. I end up.
$${\partial u \over \partial x}[q’(x)(w-t(x))-q(x)t’(x)]=0$$
$$q’(x)(w-5(x))-q(x)t’(x )=0$$ and differentiate this w.r.t. w.
$${\partial q’(x) \over \partial x}{\partial x \over \partial w}(w-t(x))+q’(x)[{\partial w \over \partial w}-{\partial t \over \partial x}{\partial x \over \partial w}-\frac{\partial q(x)}{\partial x}{\partial x \over \partial w}t’(x)-q(x){\partial t’(x) \over \partial x}{\partial x \over \partial w}=0$$
After calculations
$${\partial x \over \partial w}=+{q’(x)\over -q”( x)(w-t(x)+2q’(x)t’(x)+q(x)t”(x)}>0$$

Another part’s solution:
$$\text{profit}=t_N(x_N)k-Nx_N$$
Subject to $q(x)u(w-t_N(x_N))\ge 0$
But again for this part I couldn’t set up the equation.
What I thought is
$$max_{(t_N(x_N), t_A(x_A))} \ \ q(x_A)[t_A(x_A)-kx_A]+q(x_N)[t_N(x_N)-kx_N]$$
First order conditions
W.r.t. $(t_N(x_N)$
$$q’(x_N)(t_N(x_N)-kx_N)+q(x_N)[t’_N(x_N)-k]=0$$
$$t_N(x_N)={q’(x_N)kx_N-q(x_N)[t’_N(x_N)-k]\over q’(x_N)}$$
Similar for Andrew
$$t_A(x_A)={q’(x_A)kx_A-q(x_A)[t’_A(x_A)-k]\over q’(x_A)}$$


texts: Cagan Model of Hyper Inflation: Zimbabwe Data Request

texts:
Cagan Model of Hyperinflation

Could anyone guide me where I could find the data for Zimbabwe that would allow me to estimate the Beta parameters. Also, what regression method would be most suitable (I was thinking of a distributed lag).


texts: Is there a financial hypertrophy ? Could you make a case for finance?

texts:
I've the impression that finance is in hypertrophy. But I'm not an expert on it, so I'd like those who are more knowledgeable than I am to do a [steelman][1] of it.
The things that make me thinking this are :

It uses many of the most talented people to lead activities that seem sometimes positive, but often neutral or negative from a global point of view (i.e either it redistributes money between ~equally rich people or it takes money from poorer people to richer ones ; the opposite seems unlikely given that financial services are more used by richer people).
The reasons for this (for picking among most talented people) is that finance, for whatever reasons, seems to have a rent (https://www.nber.org/system/files/working_papers/w14644/w14644.pdf), partly linked to past deregulation (http://www.parisschoolofeconomics.com/reshef-ariell/papers/BGR_finwage_RoF_final.pdf) and gives much higher salaries than other sectors, making it more attractive than other sectors for many people.

My non-expert view on different parts of finance is the following :

Actions and obligations are useful because they're directly linked with the real economy.
Some other tools are useful in some peculiar situations (futures, options and some derivatives to hedge, reduce some risks or whatever).
But most of it is useless (most of the flows of derivatives especially, which represents a huge amount of transaction (https://www.investopedia.com/ask/answers/052715/how-big-derivatives-market.asp#:~:text=The%20derivatives%20market%20is%2C%20in,quadrillion%20on%20the%20high%20end.) and thus a huge amount of human capital dedicated to it ; it looks like forex is more and more used for speculation aswell, given that the flows more than doubled since 2 decades).

If we were total utilitarianists (i.e we would like to improve global welfare) and if we were social planners (i.e we could do whatever we want without cost), should we delete a part of finance for the sake of humanity ?
If there is any literature on the utility of finance, I'd appreciate to read it. And I guess that for any asset, we can find a useful goal so please, talk about the representative use of a given tool. I'd especially appreciate if you were able to grossly quantify the share of useful resources / tools and useless ones (but no problem if it's just impossible). Feel free to take any coherent definition of finance.
[1]: https://en.wiktionary.org/wiki/steelman


texts: Can one calculate how much increasing the US federal debt affects the "value" of the dollar?

texts:
As I understand it, if the US government runs a deficit then it (for the most part) "pays" for that deficit by "selling" government bonds.  This tends to drive up interest rates somewhat, but also, since the US government is so "trustworthy" as a debtor (and pays fairly attractive rates), it attracts investment from non-US sources.

The net of this is that running a deficit will tend to raise the "value" of the dollar (affect exchange rates) since money coming into the country to buy bonds must ultimately be "bought" with other currencies, and supply/demand dictates that this one-way flow will drive up the dollar and drive down the currencies being exchanged.

The question is, is there some way to (very roughly) calculate HOW MUCH the value of the dollar is affected by the deficit and associated bond sales?  This would imply of course having some rough estimate as to what % of bonds are bought by non-US buyers and also some way to estimate how much the money flow implied by these purchases affects exchange rates.  (Plus probably two dozen other factors that I haven't thought of.)

A thought:

Presumably the effect on exchange rates of "exporting" a dollar's worth of government bonds is similar to the effect of exporting an extra dollar's worth of tangible goods in the balance of payments.  So if one knows the effect of balance of payments on exchange rates, and can estimate the the % of bonds "exported", one would have my answer.

So, to get me halfway there, what is the best way to estimate the effect of balance of payments on exchange rates (for the US economy)?  (I should state that, overall, I'm just looking for an order-of-magnitude answer, not anything precise.)


texts: What factors affect the temporal discount rate individuals apply in decision making?

texts:
Discount rate is rate at which actors will value something that occurs in the future at less than its value now.

A simple hypothetical test that would determine this would be:

'Would you rather have \$100 now, or \$100 in one year?'
'Would you rather have \$100 now, or \$150 in one year?'
'Would you rather have \$100 now, or \$200 in one year?'

And so forth, to determine just how much someone values money now, over money in the future.

Discount rates can explain why criminals for example, commit seemingly irrational crimes - the cost of potential imprisonment being discounted because it's an abstract outcome that occurs in the future, compared to an immediate gain now.

My question is - is there research into what factors affect and individual's discount rate?

Eg. things like age, education, income.

And in what circumstances was the discount rate being measured?


texts: What does it mean when capital is immobile as opposed to having full mobility?

texts: The economist Rudolf Hilferding refers to the immobility of capital to be able to respond to market signals. What does he mean by this and why is capital immobile?


texts: What is the game theory of retaliatory trade tariffs?

texts:
Suppose no tariffs, or negligible tariffs, exist between nations A and B, and suddenly A introduces substantive tariffs on certain products A imports from B. In theory, this could lead to B and A taking turns imposing tariffs on specific products they import from each other. Given the economic benefits of tariff-free trade, this scenario requires

(i) the optimum tariffs in one direction to depend on those in the other and

(ii) the relationship between these to bear in mind expectations of how (i) would lead to a feedback.

I'm sure economists have tried to quantify this (possibly with an eye to each nation's alternative sources for goods from third parties), but I know nothing about the relevant literature. So what do models predict?


texts: Find the utility maximizing bundle [Sundaram, P.169, Q.7 (Kuhn-Tucker Theorem) ]

texts:
A consumer with a utility function given by $u(x_1, x_2) = \sqrt{x_1} + x_1x_2$ has an income of $100$. The unit prices of $x_1$ and $x_2$ are $4$ and $5$, respectively.
(a) Compute the utility-maximizing commodity bundle, if consumption must be nonnegative.
The necessary condition for this optimization is that
$$\partial L/\partial x_1 = \frac1{2\sqrt{x_1}} + x_2 -4\lambda_1+\lambda_2 = 0$$
$$x_1 - 5\lambda_1 + \lambda_3 = 0$$
$$100 - 4x_1 - 5x_2 = 0$$
$$x_1 \ge 0, \quad x_2 \ge 0$$
There are two cases we need to consider $\{x_1 >0, x_2 >0\}$ and $\{x_1 >0, x_2 =0\}$. For the first case, if I solve the above system of equations, I have
$$100\sqrt{x_1} = 8x_1^{3/2} - 5.$$
In this case, how can we obtain the bundle $(x_1^*, x_2^*)$?


texts: What lies behind supply and demand model?

texts:
This is a very basic question. I can understand that price of goods and stocks change follows the supply and demand law. On the other hand, I find it difficult to understand what happens in the real world.

If I want to buy a particular stock I can buy it at the daily price and I can sell it at the daily price. I can't choose to sell it at a higher price as I would do if I had the only orange in the world and 1 million people wanted that orange.

Who has the ability to start selling a specific stock at a different price? Who initiate the change in price if the demand goes down? Has anyone a practical simple example for me?


texts: Gali and van Rens: The Vanishing Procyclicality of Labor Productivity

texts:
Let's see how questions like the following are taken here.

Gali and van Rens, 2014 show that empirically, the correlation between $Y, Y/L$ has been declining over time. In fact, it only was a "real thing" when the RBC theory was formed, and is now not statistically  different from zero.

Is that an end to RBC theory as we know it? And by RBC I mean anything that sets driven by a TFP shock / uses TFP shocks to explain empirical phenomena: Standard neoclassical models for sure, even Neokeynesian models rely (to a lesser extend) on these. Also the whole Diamonds-Mortensen-Pissarides literature, where the surplus of a match comes from labor productivity, seems to be affected.

Alternatively, one could argue that that the correlation has become smaller, but amplification mechanism are larger now. Or attack the measurement of Gali and van Rens (but their results seem to be pretty robust).

What are potential views on this, what arguments does the literature emphasize?


texts:
It seems that in economics, matching techniques (such as pscore, covariate matching, regression adjustment) are not as popular as selection-on-unobservables techniques (such as DiD, IV).
Indeed I recently had a paper rejected by one referee on the basis that "no-one uses matching these days".
If that's true then, why? In some case it's not possible to come up with a natural experiment or perfect instrument to tease out treatment effects, and so matching strikes me as attractive.


texts: Reference request about econometric analysis of Environmental Kuznets curve

texts: I could not find from where to learn the application of Econometrics on data analysis relating to environmental Kuznets curve. Are there any books or articles which talk about the above?


texts:
Is there any well-researched studies published about the effect of increased governmental spending and later deepening debt burden due to COVID? Appreciate that the event is quite recent, but being the #1 topic recently, there could have been some studies already out there.

Did some research but haven't found any papers focusing on this particular aspect of the topic.


texts: Why US market is falling due to greece fear?

texts: I'm kind of curious to learn why US markets are falling due to Greece - Eurozone crisis. US had almost no exposure to Greece bonds and the fear of Grexit and the future of Euro has made the investors to pull out of the European market. But their investments must go somewhere right? Ideally, they could try to invest in US markets, since the macroeconomic indicators of US has been reasonably stable this year. But instead, I see the US markets are also falling? Why is this the case and where is the money pulled out of Eurozone is getting invested?


texts: The equilibrium effects of a change in government purchases on consumption

texts:
I can't get a homework problem started due to wording. I desire to understand it, so I will only put down enough to show my line of thought.

we have a utility function to maximize, say $u(c,\ell)$, and some production function $Y=zF(K,L)$. The government purchases $g$ units of the consumption good using a lump-sum tax $\tau$.

My question: the problem states "government purchase does not enter consumer's utility."

Does this mean that we do $\max_{c,\ell}u(c,\ell)$, relating $c=\ldots - \tau$, and do not do $\max_{c,\ell} u(c,\ell) + \phi(g)$, also with some relation?

Thanks for any clarification


texts:
Many politicians argue that the minimum wage is essential for providing an sufficient standard of living to all. However, there are many issues binding price floors predicted by standard supply and demand theory. Why couldn't wage subsidies be used instead? I know that they are used. However, why do politicians always argue for increasing the minimum wage as opposed to increasing wage subsidies?

what advantages does the minimum wage have versus wage subsidies?


texts: Why did the Greek bailouts "fail" whereas the Portuguese bailouts succeeded?

texts:
While Greece has required several bail-outs and is on the brink of falling back into recession, the Portuguese economy has seemingly recovered.

Why has recovery gone so well in Portugal but failed abysmally in Greece, even though seemingly similar institutions and approaches where taken to both?

(or are we somehow deluded about Portugal's long term recovery and or Greece's problems)


texts: How are robocallers able to make international calls profitable?

texts:
I have read that robocallers are untraceable because they are usually companies in India or the Phillipines.

I don't understand how this is possible. If I call India or the Phillipines, it is very expensive, a dollar or two per call. If the robocallers are paying this kind of money for each call, I don't see how that could be profitable, considering how many hangups they get.

Are foreign companies getting some cheap way to call into the US so that the pricing of international calls is highly asymmetric?


texts: Where can I find information on relationships between different commodities?

texts:
I'm looking for information about relationships between commodities. Essentially, what things do you need to use to produce other things. The info doesn't need to reflect the current state of technology, but the newer (and bigger) the dataset, the better.

I started to look for datasets used by the Gosplan to calculate material balances for economic plans, but so far, I have found only higher level summaries and analyses, not the data itself. However, it seems that Soviet planners did have quite substantial datasets:

  Even then, industrial supply and distribution plans compiled by Gosplan have been known to (...) deal with well over 30000 commodities
  (from: Soviet Economic Structure and Perfomance)

Does any of you know where I could find these datasets? Or maybe I should be looking for something else? They don't need to be quantitative, I'm interested in qualitative relationships.


texts: How does exchange rate change with respect to interests?

texts:
If the central bank raises intereat rates, isn't the money supply now less and the exchange rate is greater? I have run into opposite statements and dont know how to approach this problem.
Thanks in advance for everyone's help


texts: Independence of price and wealth in Walras' Law

texts:
The following theorem from Mas-Collel, Whinston and Green's Microeconomic Theory (3rd Edition) assumes $\frac {\partial {w}}{\partial {p}}$ to be zero. I would to like to know the reason behind such assumption.

Notation:

$p$ = price

$w$ = wealth

$x$ = Walrasian demand function

$D$ = derivative matrix


texts: Measurement for the downstream use of a commodity

texts: I am looking to find a measurement that would tell me the size of the market of the downstream use of some particular commodity. For example, salt or wheat would be used by many companies downstream. Mangoes on the other hand will be used by less firms downstream. Therefore, there is a larger downstream market for salt and wheat. Are there existing measures that have been used to measure the size of downstream market of some particular commodity? If not, do you have any suggestions on how to build one?


texts: Why is there consumption sharing in Arrow-debreu time-zero complete markets trading model?

texts:
Specifically, I am looking at this paragraph

    The fractions of the aggregate endowment assigned to each individual are
    independent of the realization of s^t . Thus, there is extensive cross
    history and cross-time consumption sharing. The constant-fractions-of
    consumption char- acterization comes from two aspects of the theory: (1)
    complete markets and (2) a homothetic one-period utility function.

The paragraph is taken from paragraph from section 8.6 in Sargent and Ljungqvist.

I understand that the fractions are independent of $s^t$, the state/complete history of realizations. However, I don't see how this leads to the second sentence -- there is extensive cross-history and cross-time consumption sharing.

So my question is: why does the fractions of aggregate endowment assigned to each individual being independent of $s^t$ lead to cross-time and cross-history consumption sharing?

Thanks


texts: How does a national budget differ from a household budget?

texts:
We are often told by pundits that "Country X cannot spend more than they take in in revenue, because a house that makes A and spends B will always collapse if B>A". Essentially the siren calls of a balanced budget as promulgated by the talking heads.

Sadly, despite even conservative economists like Friedman citing a k-percent rule and the necessity of inflation (since the number of people demanding money seems to continue rising), many entry level students get hung up on this concept.

Essentially, what I'm asking is:

  What are the key functional differences between a household budget (or other simple toy model) and a national budget and what's the best way to communicate this to people with only a passing familiarity with economics?

I'm looking for a way to effectively communicate to group of first year students that beyond just the ability to control the supply of money (monetary policy), and control income and spending more readily than an individual or household (fiscal policy), economic policy really has nothing in common with the ability to balance a checkbook, and the dramatic oversimplification is a disservice to the dismal science.


texts: Has income inequality ever been solved in societies in the past in terms of what people make to cost of living?

texts:
One thing I've seen many on here whether life style is increasing or poor's wealth is, income inequality in terms of things like food, water, healthcare keep going up, but wages aren't keeping up.  This includes education sadly since if someone can't afford schooling, they can't escape poverty likely?

Have countries in the past ever faced these issues and solved them?  Is it possible for places like America these days?


texts: Adam Smith seems to be saying that the goal of governing is "universal opulence which extends itself to the lowest ranks of the people," which he appears to think achievable in capitalism with the minimalist government. Clearly, things did not work out the way he thought, prompting Karl Marx, 90 years later, to assert that state-protected capitalism is the legalization of thievery. What are some defenses economists make on behalf of Smith? References appreciated.


texts: Equilibria for multi-round 'Markov' games?

texts:
I'm interested in zero-sum symmetric games which have the following form. Each player has a counter which starts at 0. Each turn, a player may choose from a fixed set of actions. A player's counter is raised or lowered according to the cost of the chosen action. (If this drops the player's counter below 0, they lose.) Otherwise, look up the respective actions on a payoff matrix to determine if one or the other wins. If so, the game ends with the selected winner. If neither wins, the game is played again, but retaining the counter.

It is like a repeated game, except that the counter is not reset between rounds and the number of games is not fixed but depends on the players' actions. In that way it's more like a Markov chain with a countably-infinite state space.

Here's a toy example with three actions:

A: Add 1 to your counter.
B: Subtract 1 from your counter. You win unless your opponent chooses B or C.
C: Subtract 2 from your counter. You win unless your opponent chooses C.

I'm interested in the existence of mixed strategies for this type of game, and how to find them if they do exist. Also, if there's a name for this type of game I'd like to know (which should make finding information much easier).


texts: Heteroscedasticity and weighted least square estimator

texts:
"In presence of heteroscedasticity, OLS estimators are unbiased but inefficient"

Showing the unbiased part is relatively easy. Some authors have explained the inefficiency with the help of new variance of the least square estimator.  However, I was asked to show the same thing using the variance of weighted least square estimator ($\hat{\beta^*}$). I proceeded in the following way:-

Consider the model, $Y_t=\alpha+\beta X_t+u_t$   where $u_t$'s are  heteroscedastic.

Suppose ${\sigma _u}^2$ be the constant variance of $u_t$'s under the homoscedastic assumption.

Let $Var(u_t)={\sigma _t}^2$ be the variance of the disturbances under the heteroscedastic assumption.

In Particular, suppose ${\sigma _t}^2=k_t {\sigma _u}^2$, $k_t$'s being some non stochastic constant weights.

Now, consider the above model in deviation form

$y_t=\beta x_t +u_t$, where $y_t=Y_t-E(Y)$, $x_t=X_t-E(X)$

$\Rightarrow \frac{y_t}{k_t}=\beta \frac{x_t}{k_t}+\frac{u_t}{k_t}$

$\Rightarrow \frac{y_t}{k_t}=\beta \frac{x_t}{k_t}+v_t$
where $v_t$ has constant variance ${\sigma _u}^2$

Now, the weighted least square estimator is $\hat{\beta^*}=\frac{\sum \frac{y_t}{k_t}\frac{x_t}{k_t}}{\sum \frac{{x_t}^2}{{k_t}^2}}$

which would eventually give us $Var(\hat{\beta^*})=\frac{{\sigma _u}^2}{\sum \frac{{x_t}^2}{{k_t}^2}}$

Now, under the heteroscedastic assumption, we have $Var(\hat{\beta})=\frac{\sum {x_t}^2{\sigma_t}^2}{(\sum {x_t}^2)^2}$

Now, $$\frac{Var(\hat{\beta^*})}{Var(\hat{\beta})}=\frac{{\sigma _u}^2}{\sum \frac{{x_t}^2}{{k_t}^2}}\times \frac{(\sum {x_t}^2)^2}{\sum {x_t}^2{\sigma_t}^2}$$
$$\Rightarrow \frac{Var(\hat{\beta^*})}{Var(\hat{\beta})}=\frac{{\sigma _u}^2}{\sum \frac{{x_t}^2}{{k_t}^2}}\times \frac{(\sum {x_t}^2)^2}{\sum {x_t}^2{k_t\sigma_u}^2}$$
$$\Rightarrow \frac{Var(\hat{\beta^*})}{Var(\hat{\beta})}=\frac{(\sum {x_t}^2)^2} {\sum \frac{{x_t}^2}{{k_t}^2} \sum {x_t}^2{k_t}}$$

However, before I could proceed further, my instructor asked me to check it again. He was insisting that I should get something like  $\frac{\sum (a_t b_t)^2}{\sum {a_t}^2 {b_t}^2}$, so that I can use Cauchy-Schwartz inequality  resulting in $Var(\hat{\beta^*})<Var(\hat{\beta})$. This would eventually prove the  *inefficiency *  part.

Since I am not getting that form, I think I have made mistakes. I would be happy if somebody can point it.


texts: Is nominal/real income and nominal/real wage the same? If so, is it possible for your nominal income to rise as your real income falls?

texts:
In macroeconomics, I understand that nominal wage (W) is your wage in dollars, while real wage (W/P) is what you can get for that wage (in apples, etc...). But is this the same thing as "nominal income" and "real wage"?

If so, can the nominal income go up while the real income declines? And what would be a proper example of this?

I've researched this question online, but all searches were fruitless and failed to explain this simply. All help is greatly appreciated. Thank you.


texts: Who performs the checks for regulatory compliance at trade borders?

texts:
Customs officers check for tax compliance at trade borders.

But who performs the checks for regulatory compliance at trade borders?

Is it simply the various Government ministries (eg the one responsible for food and agriculture), or is it Customs Officers?


texts:
I have the following utility function

$$u(c_t)=g(c_t-b)^2$$ for constants $g,b>0$

Edited: in order to be bliss utility function, It must be g is negative. But in the question g is given to be positive. I don’t know so. Please help me solving this question according to true assumption of g. (I don’t know which one true. )

I want to do the following

$$ \max_{c_t} \int_0^{\infty} u(c_t)e^{-pt}$$

Subject to $$\dot{k_t} =Ak_t^a -c_t-(n+\delta)k_t$$ $$k_0>0$$ $$c_t>0$$

I set up hamiltonian function

$$H= g(c_t-b)^2 +q_t [Ak_t^a -c_t-(n+\delta)k_t]$$

where q is costate variables. $c$ is control variables and $k$ is State variables.

Focs

W.r.t $c$ : $$c_t[2g(c_t-b)-q_t]=0$$

W.r.t $k$: $$q_t[aAk_t^{a-1}-(n+\delta)]=-[\dot{q_t}-pq_t]$$

W.r.t. $q_t$ : $$\dot{k_t} =Ak_t^a -c_t-(n+\delta)k_t$$

Transversality condition $$\lim q_t e^{-pt}k_t=0$$
 When I solve them, I found

$$\frac{\dot{q_t}}{q_t} = -[aAk_t^{a-1}-(n+p+\delta)]$$

And $$\frac{\dot{q_t}}{q_t}= \frac{\dot{c_t}}{c_t-g}$$

But I could not proceed after that. Because the  denominator of the fraction is $c_t-g$ .

What should I get the results (equations) that I need to draw phase diagram? They are Euler equation and other differential equations.

Please help me at this point. If you have any material related to this, please share it with me. Thanks.


texts: consequences of an inheritance tax on family owned businesses

texts:
Whenever I see the pros and cons of an inheritance tax discusses one common argument against it is as follows:

If an inheritance tax is imposed on transferring a family owned business, then this tax will have to be taken from the cash flow of the business. This will often bankrupt the business and therefore also destroy all the jobs associated with it. Hence an inheritance tax is (on businesses) is a very bad idea.

However I think this argument is based on a simply fallacy, namely that the business has to pay the inheritance tax, whereas in fact the new owner has to pay it.

So suppose the inheritance consists of exactly the family business, previously owned to 100% by the patriarch, and there is a 30% (of the value of the business) inheritance tax. Now the successor has multiple options:

take the tax from the cash flow of the company, this is usually very destructive to the business and hence a bad idea
sell a 30% stake of the business for cash to some other investor and use the cash to pay the inheritance tax
get a credit for 30% of the company value with the business as security from some bank and use that to pay the inheritance tax

Neither of the other two options takes any cash out of the business directly, so there is no danger for the business or the jobs attached. All that changed is that the son only has about 70% of the wealth of the patriarch.

Question: Is the initially stated argument a valid argument against an inheritance tax and I overlooked something? Or is it just a plausible sounding straw man that doesn't hold upon closer inspection?

Note that I'm not interested on whether an inheritance tax would be a good or bad idea in general, that would be opinion based and not suitable as a question here.


texts: How do I plot a multiple regression graph? Shall it be a many dimensional plane(equals to number of explanatory variable)? Or will be the line for each beta, since the slope or beta is the partial derivative of y(explained) with respect to that particular x(explanatory)??


texts: Calculating expected tenure of a customer

texts:
In his How To Project Customer Retention, Fader computes the expected tenure of a customer according to $$E = \sum_{t=0}^{\infty}S(t)$$ where $S(t)$ is the Survival Function.

From a purely mathematical standpoint, expectation is calculated via $$E[X] = \sum_{x \in X} xP(X=x).$$ Hence, I would expect expected tenure formula to be $$E = \sum_{t=0}^{\infty}tS(t).$$

Can anyone shed some light on this?


texts: Interventions during the current Corona crisis: Government credits

texts:
In the light of the current public health crisis caused by COVID-19, I would like to know more about how government or central bank interventions are supposed to influence and limit the economic fallout.

How will interest-free government credits for businesses help to cover short and medium term losses and influence their financial health?
How are those credits supposed to be repaid if the current situation results in an economic downturn?
How can governments refinance those credits?
What are the short and long-term macroeconomic implications of such an intervention? (optionally: given to the current situation in the European Union)

If possible, base your answer on applicable historical examples, economic principles or (your own) expert opinion. Pointing to relevant sources and literature is also highly appreciated.

Stay healthy!


texts: The concept of expansion of an information structure

texts:
I would like your help to understand the concept of expansion of an information structure in the incomplete information game at p.6-9 this paper.

Let me summarise the game as described in the paper.

There are $N\in \mathbb{N}$ players, with $i$ denoting a generic player.

There is a finite set of states $\Theta$, with $\theta$ denoting a generic state.

A basic game $G$ consists of

for each player $i$, a finite set of actions $A_i$, where we write $A\equiv A_1\times A_2\times ... \times A_N$, and a utility function $u_i: A\times \Theta \rightarrow \mathbb{R}$.
a full support prior $\psi\in \Delta(\Theta)$.

An information structure $S$ consists of

for each player $i$, a finite set of signals $T_i$, where we write $T\equiv T_1\times T_2\times ... \times T_N$.
a signal distribution $\pi: \Theta \rightarrow \Delta(T)$.

A decision rule of the incomplete information game $(G,S)$ is a mapping
$$
\sigma: T\times \Theta\rightarrow \Delta(A)
$$

Expansion:

Consider two information structures, $S^1\equiv (T^1, \pi^1)$ and $S^2\equiv (T^2, \pi^2)$. We say that $S^*\equiv (T^*, \pi^*)$ is a combination of $S^1$ and $S^2$ if

$T_i^*=T_i^1\times T_i^2$ $\forall i$.
$\pi^*:\Theta \rightarrow \Delta(T^1\times T^2)$ has $\pi^1$ and $\pi^2$ as marginals.

An information structure $S^*$ is an expansion of an information structure $S^1$ if there exists an information structure $S^2$ such that $S^*$ is a combination of $S^1$ and $S^2$.

My question:

The game, as it is described by the authors, seems to assume that, before receiving the signal $T_i$, each player $i$ knows nothing about what will be the realisation of the state. I call this as the baseline level of information assumed.

(For example, in other contexts, one may assume that the state is a vector of size $N\times 1$ and,  before receiving the signal $T_i$, each player $i$ knows the realisation of the $i$th component of such a vector. This would correspond to another kind of baseline level of information)
Let $\underline{S}$ denote the information structure that is totally uninformative, i.e., it does not add anything to the baseline level of information assumed (also called DEGENERATE at p.26 of the linked paper). In other words, $\underline{S}$ consists of

(a) for each player $i$, a finite set of signals $T_i$, where we write
$T\equiv T_1\times T_2\times ... \times T_N$.

(b) a signal distribution $\pi: \Theta \rightarrow \Delta(T)$ such that $\pi(\cdot|\theta)=\tilde{\pi}$ $\forall \theta \in \Theta$ for some $\tilde{\pi}\in \Delta(T)$. In other words, the conditional probability is equal to the unconditional one and our belief on the probability distribution of the state is not updated.

Notice that there are many ways to characterise the uninformative information structure (just by varying $T$ and $\tilde{\pi}$).
Let $\mathcal{S}$ denote the collection of all possible information structures. More precisely,

$$
\mathcal{S}\equiv \{S| T \text{ is a separable metric space}, \text{ $\pi:\Theta \rightarrow \Delta(T)$ is a probability measure on $(T,\mathcal{B}(T))$}\}
$$
where $\mathcal{B}(\cdot)$ denotes Borel sigma algebra.

Note that $\mathcal{S}$ contains all possible ways to characterise the uninformative information structure.
Question: Can we show that, for a given $\underline{S}$, each $S\in \mathcal{S}$ is an expansion of $\underline{S}$ (including $S=\underline{S}$)?

This seems to me to hold at the light of Theorem 1 combined with reading at p.26 of the paper "Now consider the case where the original information structure is degenerate (there is only one signal
which represents the prior over the states of the world). In this case, the set of Bayes correlated equilibria
correspond to joint distributions of actions and states that could arise under rational choice by a decision
maker with any information structure"


texts: Why doesnt Law of Diminishing Marginal Utility not affect price effect?

texts:
Ok so in my textbook, it is given that the downward slope of the demand-price curve is justified by three factors:

Law of Diminishing Marginal Utility
Income Effect(Real income)
Substitution effect

Then after all this it goes on to state, that :

  price effect=income effect+substitution effect

Doesn't Law of Diminishing Marginal Utility, affect price too? By keeping a low price on a slice of pizza, the marginal utility that is gained by people with each additional slice would be more likely to be equal or more than the price per slice, and hence demand will increase. So why isnt it included?


texts: Does lowering corporate tax rates increase investment or provide some other benefit to a nation?

texts:
In Australia at the moment there is a move to lower the top corporate tax rate from 30% to 25% or thereabouts. The reasoning is that the benefits from investment will outweigh the cost to the budget.

There are claims either way e.g.

Malcom Turnbull (Current Australian Prime Minister)

  Malcolm Turnbull has recommitted to his government’s $48.7 billion tax cut for business over the coming decade, amid growing anxiety in corporate Australia over whether he might scale back the plan.

  The Prime Minister told a business audience in Sydney the enterprise
  tax plan remained “so important” because of the fall in global growth,
  emphasising the need for ways to boost investment.

http://www.theaustralian.com.au/business/turnbull-recommits-to-487bn-corporate-tax-cut/news-story/df2f1e43a756cf5654d59704c3cdb537

The Australia Institute claims:

  Dear Scott Morrison, lowering the company tax rate doesn't increase foreign investment.

  In fact, when company tax rates rose in the 1980s to 49% there was a
  rise, not a drop, in investment.

http://www.tai.org.au/content/about

So which way is it? Does the benefit of the tax reduction outweigh the cost of the revenue loss or is it the other way around? Does it depend on other factors? Are there other benefits that may not exactly be investment, like moving offices?


texts: Why do the GDP baskets of different countries have different percentages?

texts: Why might the housing part of the US GDP basket 40% of the basket, but only 17% of China's?


texts: Log-Linearizing a Dixit-Stiglitz function

texts:
In a New-Keynesian Model, the Consumption index

$C_t=\left(\int_0^1{C_t(i)^{1-\gamma} \ di}\right)^{\frac{1}{1-\gamma}}$

is log-linearized to

$\tilde{c_t}=\int_0^1{\tilde{c_t}(i)  \ di}$

where variables with tilde are log deviations from steady state and $i=[0,1]$ are varieties of the consumption good.

Even though I feel comfortable log linearizing other equations, I have no idea how to deal with the integral. How do you get to the result? And what would a second order approximation look like?


texts: How to interpret Whited Wu index (WW-index)

texts:
I want to study financial constraints on companies of different groups and for that I try to use Whited-Wu index:
WW = - 0.091CF - 0.062DIVPOS + 0.021*TLTD - 0.044*LNTA + 0.102*ISG - 0.035*SG
Where TLTD is the ratio of the long-term debt to total assets; DIVPOS is an indicator that takes the value of one if the firm pays cash dividends; SG is firm sales growth; LNTA is the natural log of total assets; ISG is the firm’s three-digit industry sales growth; CASH is the ratio of liquid assets to total assets; CF is the ratio of cash flow to total assets (see Whited and Wu. Financial Constraints Risk. 2006).

Although I managed to compute it, I have difficulties with results interpretation. My idea was to compare different companies/groups of firms using this index. As written in one of the papers, "higher index values can be associated to higher need of external capital". So if in 2010, for "Toyota" I got value -0.9 and for "Fuji Technica Inc." -0.53, may I conclude that Toyota is more financially constrained (requires more external capital)? Similarly, if I get two industries - food and car producing - then the first have higher values of WW.


texts: Bayesian Nash Equilibrium - Mixed Strategies

texts:
What's the correct way to solve BNE in mixed strategies? I've found two conflicting methods used.

Two players. Player 1 knows which game is being played, player 2 knows the game is chosen with probability $\mu$.

$
\begin{array}{c|c|c}
  \ & A & B \\
  \hline
  L & 1, 1 & 0, 0 \\
  \hline
  R & 0, 0 & 0, 0
 \end{array}
$

or

$
\begin{array}{c|c|c}
  \ & A & B \\
  \hline
  L & 0, 0 & 0, 0 \\
  \hline
  R & 0, 0 & 2, 2
 \end{array}
$

So for pure strategies I am finding a consistent method. Form a normal form game:

$
\begin{array}{c|c|c}
  \ & A & B \\
  \hline
  LL & \mu, \mu & 0, 0 \\
  \hline
  LR & \mu, \mu & 2\mu, 2\mu \\
  \hline
  RL & 0, 0 & 0, 0 \\
  \hline
  RR & 0, 0 & 2\mu,2\mu
 \end{array}
$

This allows us to find the pure strategy solution by using the normal form. How do we calculate the mixed strategies?

I've seen two different methods.

1: Look at mixing over (L, R) in game 1 with probability (a, 1-a) and (L, R) in game 2 with probability (b, 1-b).

Look at mixing over (LL, LR, RL, RR) with probability (a, b, c, 1-a-b-c).

Any advice/reading is much appreciated.


texts: Why does the Federal Reserve seem to hold so much weight on the unemployment rate, relative to labor participation?

texts:
The title is the question.

In the press conference held yesterday, the Chair referenced "unemployment" 18 times, relative to "participation" 3 times.  If the labor participation is at the lowest since the 70's, is it delusional to buy into the seemingly marketed strength of the U.S. economy?


texts: How can there be an electronic bank run?

texts:
I read that at 2008 there was an electronic bank run.

From what I undestand bank runs occur due to the fractional reserve banking system. The actual real money you can hold on your hand are a fraction of the total money in banks. So if everyone goes to ATM and gets the money in their hand, it means that the bank runs out of the "real money" and people can't withdraw these "real money".

So if the same number of people, instead of withdrawing from the ATMs, do electronic transactions that eg get their money from a bank to another bank (or any other institution) how can there be a bank run? It just doesn't make sense to me.


texts: Annual Fraud Recovery Over Time: Should I adjust for inflation?

texts:
I have a dataset of the total amount the U.S. Department of Justice obtained annually in settlements/judgments of government fraud cases from fiscal years 1988-2019.  There's a lot of variation, but more recently the total settlements/judgments range from around 1 billion to 6 billion dollars.

We're trying to decide whether it makes sense to adjust the annual totals for inflation. Is there any reason not to? If we do, should we use CPI or GDP or something else?