texts: Are all points on the Long Run Average Cost (LRAC) curve productively efficient?

texts:
The definition of productive efficiency is that any given output is produced for the lowest possible cost.

In the short run, only the minimum point on the SRAC curve is productively efficient - this makes sense because at any other output, the firm could move to a different SRAC curve that would give a lower cost for that output.

However, the LRAC is, by definition, the envelope of all SRAC curve - it shows the cheapest way to produce any given output.

Agree / disagree?

If true, why is it that so many economics sources claim that "productive efficiency is achieved when the firm produces at the lowest point of its AC curve"? Is it simply that firm decisions are perpetually taken in the short run?


texts: Relationship between tax rate and the yield curve

texts:
Suppose that financial market participants now expect a future tax increase in one year. Also assume that the yield curve is initially upward sloping. Given this information, we would expect which of the following to occur?
(a) the yield curve will become steeper
(b) i2t will increase
(c) i2t will decrease
(d) the yield curve will become downward sloping
(e) the yield curve will be the same
For our macroeconomics class, we learn LM curve as the flat line, where the interest rate it totally up to the central bank, so I thought (e) might be the answer. However, I cannot really tell the relationship between the tax and yield curve. I can tell that increase in tax will shift IS curve to left, but how does it will affect the yield curve?
Also, I cannot tell the difference between the choice (a) and (b). Isn't the yield curve being steeper the same as the increase in a 2-year interest rate? Thanks a lot!


texts: How to write the dual problem of this maximization problem?

texts:
On this note for  Shapley-Shubik model, there's a maximization problem:

$$\max_{x_{ij} \in \mathbb{R}^{M \times N}}\sum_{j \in N}\sum_{i \in M}v_{ij}x_{ij}$$
$$\text{s.t.}  \ \sum_{j \in N}x_{ij} \leq 1 \ \forall i \in M$$
$$\\ \sum_{i \in M}x_{ij} \leq 1 \ \forall j \in N$$
$$x_{ij} \geq 0 \ \forall i \in M\forall j \in N$$

The dual problem of it is

$$\min_{s_j \in \mathbb{R}^N, p_i \in \mathbb{R}^M }\sum_{j \in N}s_j+\sum_{i \in M}p_i$$
$$\text{s.t.} s_j + p_i \geq v_ij \ \forall i \in M\forall j \in N$$
$$\\ s_j, p_i \geq 0 \forall i \in M\forall j \in N$$

What's the rule of writing this dual problem?


texts: Why Chinese exports increased even though Yuan appreciated after the Chinese removed the peg against USD?

texts: After the Chinese central bank removed the peg against USD, yuan appreciated but Chinese exports didn't seem to be affected. They are steadily increasing. How can this be explained ?


texts: In difference-in-difference approach, would it be possible to add a dummy variable indicating whether a data point belong to treatment group?

texts:
Since there is the possibility that there are some factors result in whether a data point belong to treatment group, I think we should add a dummy variable indicating  whether a data point belong to treatment group when using difference-in-difference approach.

However, this was not done in research generally, e.g. this paper:
Chhaochharia, Vidhi, and Yaniv Grinstein. "CEO compensation and board
structure." The Journal of Finance 64.1 (2009): 231-261.

Are there reason for not adding the dummy variable? Would colinearity be an issue? (I don't think it is an issue in the above example.)


texts: What may have caused these blips in the value of Euro vs. US dollar

texts:
I was looking at the USD/EUR exchange rates a few minutes ago (Saturday evening, Eastern Time Zone here in USA) at xe.com and noticed some sharp blips on it from earlier today.

The graph looked as shown below.

The times (on the X-axis) are in the GDT/UTC timezone but these fluctuations are from activity caused during Saturday. Notwithstanding that I assumed that the exchanges are closed on Saturday, the blips are interesting because the value after the blip is the same as before it.

Are these blips caused by

some algorithmic trading happening during the weekends, or
perhaps something in how xe.com calculates the currency rates, or
something else?


texts: Are there any examples where fractal geometry is applied in economics or finance?

texts: Can fractal geometry give better insights into the working of the financial markets or give rise to better financial models? If so, are there any existing models?


texts: Question on Central bank loss function interpretation

texts:
How do you interpret this central bank’s loss function:

$$L(\hat x, \pi)=\alpha \hat{x}^2+(\pi-\pi^T)^2$$

where $\alpha >0$ and $\hat x$ is output gap.

Phillips curve is $\pi = \theta \hat{x}+\pi^T $

Sorry I am not economist, I am studying math, and I need its interpretation.

I guess I need to interpret the value of $a$, and I need to look at the geometry of the loss function in the Phillips curve diagram.

What is its interpretation in economic view?

Thank you so much!


texts: Is a country in economic downturn if its growth rate is negative, but improving?

texts:
As I understand it, economic downturn means that economic growth is significantly slowing down or entering into recession. (If anyone wants to correct me, please do so). i.e. Growth rate is decreasing.

But what if the country is already in recession, but its growth rate is increasing? i.e. -5% one year, -3% the next, -2.5% the next, etc. Is this still classed as downturn (since the economy is still shrinking) or is it not since the growth rate is actually increasing despite being negative?


texts: Repeated games with decreasing marginal returns

texts:
The standard analysis of repeated games assumes that the payoff of a player from a repeated game is a sum (or arithmetic mean, or discounted sum) of the payoffs in the basic games.

But what if the players have decreasing marginal returns?

For example, suppose the basic game is Matching Pennies. In each basic game, a player can either win 1 or lose 1. However, the average utility of a player from winning e.g. 10 times, is not 1 - it may be less than 1 if the player has decreasing marginal returns.

Are there references that deal with such repeated games?


texts: Relationship between strictly convex preference and convex preference

texts:
Let X be a convex subset of linear topological space and let binary relation  >=
be a complete preordering.

prove: If preference relation is strictly convex and continuous, then it is convex.

Since the definition of weakly convex preference is equivalent to weak upper contour sets and strict upper contour set being convex. The relationship between convex and weakly convex preference can be easily established.
But there is no such relationships exist with convex preference.
I have no idea how to prove the above mentioned proposition.
thanks!


texts: Is it possible and logical to have an upwards sloping budget line?

texts: The question I have is, for example, say Garry has two goods, cookies he pays 1 to consume a cookie and a maximum of 10 can be consumed, whilst he gets PAID 2 to consume vegetables. Garry is also given an initial budget of $5. Placing cookies on the vertical axes and vegetables on the horizontal axis. Would the budget line not start from 5 cookies (0 vegetables) and increase up to 10 cookies, 2.5 vegetables (or 3) before forming a horizontal line as the maximum cookies consumed is 10. I've looked online and it mostly states that budget lines are always downwards sloping. Thanks for your help


texts:
My question is about the following notation:

I have noticed in several places (for example here (page 15)  and here (page 1)) that different authors use different notations for choice correspondences. Given a set $X$ of objects that might be chosen and a collection of non-empty subsets $\mathcal{A}$ of the power set of $X$, some use

$c:\mathcal{A} \rightarrow 2^{X}\backslash \emptyset$ (as in the second link)
$c:\mathcal{A} \rightarrow 2^{X}\backslash \{ \emptyset\}$ (as in the first link)

They both want to express that the co-domain of the choice correspondence must include all the non-empty subsets of the power set of X, i.e from any menu of options, you must choose something.

My question is, which one is the correct way to define it? Clearly, since $\emptyset \neq \{\emptyset\}$, both definitions cannot be equivalent.

My intuition would tell me that from the list above, (1) is the correct one. For example, if $X=\{\text{pasta (p)},  \text{chicken (c)}, \text{sushi (s)}\}$, then the power set of $X$ is:

$$
2^{X}=\Bigg\{\emptyset, \{p \},  \ \{c \}, \{s \},     \{p,c \}, \{p,s \} , \{c,s \}, \{ p,c, s\} \Bigg\}
$$

Since I want to “take out” the empty set from $2^{X}$ so that the choice from any non-empty subset of $X$ is itself non-empty, and since $\{\emptyset\} \notin 2^{X}$, it should be

$$
c:\mathcal{A} \rightarrow 2^{X}\backslash \emptyset
$$

Thank you for any answers!


texts:
A rough estimate of the oil and gas reserves in some country at the beginning of 2010 was 15 billion tons. production that year was approximately 250 million tons.

when will the reserves be exhausted if production is kept at same level?

I have no clue on how to solve and tackle this problem, it seems kind of odd to me that there is nothing to indicate at which level the reserves are being consumed.

Really appreciate any hints on how to solve it.


texts: Why would a CBDC (Central Bank Digital Currency) be good for the economy?

texts:
I've read about CBDC, how it could be a cryptocurrency like digital payment system, that could replace fiat currencies. But what I don't get is what value would it give to the economy?
Someone who works at a Central Bank explained to me, that by holding the a currency in your own crypto wallet, and not not as a deposit in a commercial bank, the commercial bank's balance sheet would shrink significantly. By shrinking, it could lend out less money with higher interest rates, and could disrupt the complex commercial banking system in a bad way.


texts:
In an ols model demand ~ price , is it reasonable to use log-log for price and demand, but in a 2sls model does the logic remain the same?
I found articles simply using 2sls without using a log to find the equilibrium, does that make sense?


texts:
I know one form of a derivative, which is

$$ f'(x) = \lim_{\Delta\to 0} \frac{f(x+\Delta) - f(x)}{\Delta}$$

Let $x_{t+\Delta} = x_t + \Delta \dot x_t$. Achdou and coauthors (end of appendix A1) claim that

$$ \lim_{\Delta\to 0} \frac{f(x_{t+\Delta}) - f(x_t)}{\Delta} = \lim_{\Delta\to 0} \frac{f(x_t + \Delta \dot x_t) - f(x_t)}{\Delta} = f'(x_t)\dot x_t$$

I understand the first equality, that's merely the substitution. I can't wrap my head around the second one. How exactly does one show it?


texts: What does a central bank guarantee against its currency?

texts: During the Bretton Woods system, currencies were issued against gold. In contemporary times, what is the real thing against which currency is issued? What does the fiat currency actually guarantee?


texts: Show that $x(p,w)=w\cdot x(p,1)$ with homothetic preferences

texts:
Someone gave me a proof of this, but I am not sure if it is correct.

Let $B(p,w) = \{x: p\cdot x \leq w\}$ (the budget set). Then:

\begin{align}
x(p,w) &= \arg \max_{x\in B(p,w)} u(x)\\
&=\arg \max_{\alpha x\in \alpha B(p,w)}  u(\alpha x) \\
&=\arg \max_{y\in B(p,\alpha w)} u(y) \\
&=\frac{1}{\alpha} \arg \max_{y\in B(p,\alpha w)} u(y) \\
&=\frac{1}{\alpha} x(p, \alpha w)
\end{align}
Where the result follows from taking $\alpha=\frac{1}{w}$.

Is this proof correct (I am not sure of the middle three equalities)? Where is homotheticity used?

EDIT: A monotone preference relation $\succsim$ on $X= \mathbb{R}^{L}_{+}$ is homothetic if all indifference sets are related by proportional expansion along rays; that is, if $x \sim y$, then $\alpha x \sim \alpha y$ for any $\alpha \geq 0$.

Also, recall a continuous $\succsim$ on $X = \mathbb{R}_{+}^{L}$ is homothetic iff it admits a utility function that is homogenous of degree one; $u(\alpha x) = \alpha u(x)$.


texts:
While reading economics papers, especially those related to economy with land, I often encounter the terms $L^\infty$ and the "weak* topology". They seem like very basic terms, but I couldn't find a basic explanation of them. Here is a typical paragraph which I am trying to decipher (it is from page 4 at the introduction of A foundation of location theory):

Let:

$$[0,\frac{1}{n}]\cup[\frac{2}{n},\frac{3}{n}]\cup[\frac{4}{n},\frac{5}{n}]\cup...\cup[\frac{n-2}{n},\frac{n-1}{n}]$$

$(n=1,2,...)$ represent a sequence of commodities of increasing utility. If the indicator functions of these sets are embedded in $L^\infty$ with the weak* topology, then the limit is $\frac{1}{2}1_{[0,1]}$, half the indicator function on the interval $[0,1]$. This, indeed, is a natural limit that is not in the commodity space.

So my questions are:

What is $L^\infty$?
What is the "weak* topology"?
What is the meaning of "embedded in $L^\infty$"?

NOTE: I have some basic (undergraduate) knowledge of topology. I have heard about "weak topology" but never heard of "weak* topology". I will be very thankful for a simple, intuitive explanation that will help me continue reading!


texts: What happens when government bonds purchased as part of central bank quantitative easing (QE) reach maturity?

texts: Does the central bank ask the government to pay or are they rolled over?


texts: Hi the textbook i am studding from simply states that 'the rule for rational consumer behaviour is know as the equi-marginal principle. This states that a consumer will get the highest utility from a given level of in come when the ratio of the marginal utilities is equal to the ratio of prices'. I was hoping someone could maybe give me a bit more intuition behind this. Maybe it is self-explanatory... maybe not.


texts: Economic Theories for the creation of a new or separate Industry?

texts:
Hey i'm doing a paper on the creation of an industry that has spawned from the another industry. I was wondering if there was particularly any interesting economic theory i should look at.

Some of my ideas For example because of the inherent social values of society demand is formed for newer services not traditionally offered by the industry creating a niche market segment. To which i guess i can talk about utility maximisation. And that's about how much i have so far.


texts: Robust Standard Errors for Control Function Approach?

texts:
I need to know how to find robust S.E. for the CF approach to endogeneity.

Consider the model:
$$y_i=X_i\beta_1 + W_i\beta_2+\epsilon_i$$

Assume:
$$E[X_i\epsilon_i]=0$$
$$E[W_i\epsilon_i] \neq 0$$

Thus, $W_i$ is endogenous.

Now, let:
$$E[Z_iW_i] \neq 0$$
$$E[Z_i\epsilon_i]=0$$

The control function approach:

$W_i = \gamma_1 X_i + \gamma_2 Z_i + \phi_i  $
$\epsilon_i = \alpha \phi_i + \chi$

now we replace $\epsilon_i$ in our original equation:

$$y_i=X_i\beta_1 + W_i\beta_2+ \phi_i \alpha + \chi$$

where now we have $E[W_i \chi]=0$

Intuition: I think I used the series of linear projections to 'control' for the endogenous portion of $W_i$.

EDIT: I originally typed this incorrectly. I have changed the relevant orthogonality condition. Here is the intuition behind the (correct) orthogonality condition $E[W_i \chi]=0$:

Since $W_i$ is a linear function of $X_i , Z_i$, and both are themselves orthogonal  to $\chi$, we obtain the given orthogonality condition.

Okay - the question. I think that $\hat \beta_{2.CF} \equiv \hat \beta_{2.OLS} \equiv \frac{cov(W_i,Y_i)}{Var(W_i)}$

If this is correct, do I just use the R.S.E. form that I use in OLS if I want heteroskedasticity robust S.E. when using the C.F. approach?


texts: Slutsky Decomposition of Given Labor Supply Model

texts:
Let utility curve an individual given as $U(C,R) = C^aR^{1-a}$ where $(0\lt a  \lt 1)$ and $C$ denotes consumption commodity and $R$ denotes its leisure, and price of $C$ is given as $P$, and the nominal wage for a unit of labor given as $W$. Total amount time available for the individual is $T$.

Now I would like to derive the change of labor supply when nominal wage get increased with two different effect decomposed - income effect/substitution effect.

What I have got is $L^s$ only, which is equal to $T-R$, following below process:

first, $P\cdot C = L^s\cdot W $

second, $T-R = L^s$

by, first and second, $P\cdot C= (T-R)\cdot W$ (*)

and the from the utility function we can derive the condition of maxmizing its utility, $MU_C = MU_R$, which is eqaul to $\frac{a}{1-a}=\frac{C}{R}$(**)

Now, since the (*), (**) must hold at the same time, we can derive equation between $W$ and $R$ without $C$ as below:

$P\cdot \frac{a}{1-a}\cdot R = (T-R)\cdot W$

Then we get $R = \frac{TW}{P(\frac{a}{1-a})+W}$ and $L^s =T\frac{P(\frac{a}{1-a})}{P(\frac{a}{1-a})+W}$

but my derivation of $L^s$ looks only decreasing while W is increasing.

Any points did I do wrong? I want to did some decomposition of Slutsky, but lack of skills to deal with partial derivatives, it makes me hard to do also.


texts: Second derivative of Capital stock per unit of effective labour

texts:
Let $K=$capital, $L=$ labour, $A=$ knowledge or effectiveness of labour.  And put $\mathcal{K} = K/AL$ the capital stock per unit of effective labour.  If the following is negative

$$ \displaystyle \frac{\partial \dot{\mathcal{K}}(\mathcal{K})}{\partial \mathcal{K}} \bigg|_{k=k^*} $$

is this then concave down, and if so what does this mean?  More simply I am asking when we have two different partial derivatives of a variable, does it still have the same properties of the usual second derivative?


texts: Why are indifference curves (often) of infinite length?

texts:
Indifference curves are often of infinite length.

Is this implied by monotonicity or non-satiation?

If not, what is/are some condition(s) that are sufficient for indifference curves to have infinite length?

More generally, indifference curves are almost always manifolds without boundary. Which means that the curves don't have endpoints. What property of the utility function guarentees this?


texts: Interchangeability between knowing an event obtains with probability 1 and knowing an event obtains with absolute certainty?

texts: In the literature of interactive epistemology, for a player, knowing an event obtains with probability one and knowing an event obtains with absolute certainty are different. Is there a nontrivial (say, it could be the case, an event is a proper subset of the event that player $i$ knows this event obtains with probability one, but never the case for knowledge operator with absolute certainty) proposition that could serve as an example to show they're not interchangeable in the language which consists of two corresponding knowledge operators, a set of states of world, set relations, set operations, and all logical connectives.


texts: Is there some consenus in the literature as to what features characterize a bubble investment as distinct from a productive investment?


texts: Maximization under two different states of the world

texts:
What I did is the following one but I am not sure at all:

Any help will be appreciated. Thank you.


texts:
I have the following True/False question:

  A single price-taking firm on the market is called a monopoly.

As far as I know, a monopoly is a price maker not a price taker. That being said if it is a single firm how in the world can it not be a monopoly?

In my opinion, the answer to this question is False.

Could anyone possibly explain to me if my way of thinking is correct? and if a monopolistic firm can be a price taker?

Thank you very much


texts: What would make a restaurant offer all-day breakfast?

texts:
Some restaurants particularly fast food ones offer breakfast food only during, well, breakfast hours. Other restaurants however offer breakfast food throughout their opening hours. Some restaurants are specifically breakfast only so of course they do.

What's up with that? What would make a restaurant offer some food only sometime while others (besides breakfast restaurants) offer said food throughout opening hours?

I was thinking that this might have something to do with low demand or something, but then why do all-day breakfast restaurants, like, not go out of business?


texts: IV：Quasi-random variance V.S. 'Placebo' check

texts:
I read some papers about transportation infrastructure. I am confuse with the following two case.

Some routes are unlikely to have been randomly assigned across cities over time. Thus, In some papers(i.e. Baum-Snow, 2007), they attain consistent estimates of the effect of transportation network on interest by the planned route IV.
But some papers (i.e. Donaldson 2012) use the planned route IV to test 'Placebo' effect.

These two case seems contradictory. I'm quite new to this and hope someone can help me.


texts:
Suppose a bank makes a loan of $1M to someone taking out a mortgage to buy a house by crediting that person's bank account with a deposit equal to the size of the mortgage. Suppose the required reserve ratio is 10%.

a)How much has the money supply increased by?

b)Does reserve or high powered money change? Why or why not?

What I did: $\frac{$1M}{0.10}$ = $10M (this will be the increase in money supply)

Because the reserve ratio is 10%, the reserve money changes by 10% of 10,00,000 = 1,00,000

Is this correct?


texts: Helicopter Money in the time of Covid-19

texts:
In this voxEU article by Jordi Galí, he says the following:

  In the current context, the central bank could credit the government's account (or governments, in the case of the ECB) for the amount of the additional transfers and for the duration of the programme. That credit would not be repayable, i.e. it would amount to a transfer from the central bank to the government. From an accounting viewpoint, it would be captured by a reduction in the central bank's capital or by a permanent annotation on the asset side of its balance sheet. Thus, it should not have an impact by itself on the central bank’s profits which are periodically transferred to the government, especially if the interest rate on reserves were to remain at zero.

I don't understand the last two sentences here. Why should this not count as a loss that is being absorbed by capital (which, admittedly, is owned by governments in most cases)?

He also says the following in a footnote:

  An alternative approach, proposed by Paris and Wyplosz (2014) in the aftermath of the European debt crisis (and referred to as PADRE), would involve the conversion of ECB government debt holdings into zero interest perpetuities to be held permanently on the balance sheet, in exchange for a permanent reduction in the transfer of ECB profits to governments in proportion to the effective debt cancellation. Such a debt restructuring would generate sufficient fiscal space to allow governments to run large fiscal deficits if needed without the risk of triggering a debt crisis.

Prima facie, it seems to me that the reduction in profit transfers would have a neutralising effect on the debt conversion. Unless perhaps the reduction were to take place over time.


texts: Group-level random effect correlated with within-group independent variable

texts:
Dear StackExchange community,

Question:

According to, e.g., Wikipedia, random effects models assume "that the individual specific effects are uncorrelated with the independent variables."

I understand that to mean that, in the context of a shared frailty model (see below), a control variable that varies on the group level must not be correlated with the group level frailty. But:

Question: are variables that vary within groups allowed to be correlated with the group-level frailty?

Example: imagine that

one is modeling the time for siblings to reach their terminal educational degree,
the control variables include dummy variables for each kind of terminal degree (BSc, MSc, etc.),
the shared frailty at the sibling level represents the sibling-level speed, i.e., tendency to finish degrees faster

Imagine also, that people who run through their education at a faster pace also tend to continue into higher levels of education. Faster families will be overrepresented among higher degrees. Therefore, the researcher wants to correct for the sibling-level speed. But at the same time, the degree dummies will be correlated with the frailty.

Would the shared frailty model be valid in such a case? Would the model correctly estimate the associations between types of terminal degrees and the the time to completion?

Background:

I would like to estimate a shared frailty model (see these lecture notes; the following draws on this document). It is a a random effects survival analysis model where unobserved heterogeneity between groups are modelled as a so-called shared random effect common to each group. It takes the form:

$h(t_{ij})=h_0(t)\exp(\beta' \mathbf x_{ij} + \varphi'w_i)$,

where $h(t_{ij})$ is the hazard of individual $i$ in group $j$ at time $t$ given the baseline hazard, $h_0$, the control variables for each individual, $\mathbf x_{ij}$, and the shared frailty for group $i$, $w_i$.

The $w_i$ are assumed to be drawn from an independent sample from a distribution with mean 0 and variance 1.

I hope my question makes sense and I look forward to hear your answers.


texts: Why did coronavirus cause a food shortage?

texts: The argument I have seen is that since restaurants closed, demand for food is down.  I understand how demand being suddenly lower could disrupt supply.  What I don't understand is why demand is down.  I mean, people still need to eat just as much as they did before the coronavirus.  What is going on here?


texts: Convert DSGE paper to structural econometrics, anything to be noted？

texts:
I'm intent to bring some insights of a DSGE paper to a structural econometric model. The paper is Liu, Wang and Zha's 2013 Econometrica paper on land collateral channel. Now I have some good datasets containing firm's land holding information, so I want to "estimate" than "assume and simulate". However, my coauthors and I are largely macro guy and know only a little about structural estimation.

(1). We are focusing on firm's investment decision (purchasing land or real estate asset) and borrow behavior. In Liu et al, they also modeled the household sector. So for our purpose , we can safely ignore the household sector, and treat (land) price exogenous ,right?

(2). The macro paper normally contains dozen of shocks, some of which we are interested (like the "collateral shocks"), some we are not (habit persistence). Then we just treat those we are interested in as parameters to be estimated , and others as unobservable impact?

Personally, I don't quite believe the DSGE model which specifies dozens of shocks .  I want to "bring some insights" and replicate from the LWZ paper. Most DSGE studies struggle to meet the general equilibrium condition, which , in my opinion, is one of their weakness. The price are too complicated and hard to fully capture, so if you are concerning something else, why just keep it exogenous and put other more realistic stuff.


texts: Heteroskedasticity assumption in fGLS into linear form?

texts:
I am following Chapter 8 ("Heteroskedasticity" p. 259) in the 6th edition of Woolridge Introductory Econometrics: A Modern Approach and I don't understand one piece of the transformation of our model.

For fGLS, we assume [1] $Var(u|\boldsymbol{x}) = \sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)$, where $x_i, x_2,...,x_k$ are the independent variables appearing in the regression model and the $\delta_j$ are unknown parameters.

Then, we use the definition of conditional variance to say $Var(u|\boldsymbol{x}) = E(u^2|\boldsymbol{x}$), since our zero conditional mean assumption tells us that $(E(u))^2$ is zero.

Now, here is where I'm stuck: Wooldridge says that our assumption [1] above allows us to write $u^2=\sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)v$, where $v$ has a mean equal to unity, conditional on $\boldsymbol{x}=x_1,x_2, ...,x_k$

Can someone please help me to develop an intuition for this last step that Wooldridge has taken?  Essentially, it seems like we've assumed that $E(u^2|\boldsymbol{x})=\frac{u^2}{v}$ and I don't understand why or the properties that allow us to do this.

I've found this paper https://www.econ.uzh.ch/dam/jcr:e3cddc1b-f89d-4fb4-9474-c2c380355d69/joe_2017.pdf to be useful (specifically, assumption #6 on p. 2), but it doesn't leave me with much intuition for what we're doing and why, especially because I'm fairly new to econometrics.

Thanks-
Maurus


texts: Effect on revenue of changing price of unitary demand elastic product

texts:
In my introductory microeconomics class, a problem set had the following question:

  If the price elasticity of demand for Snickers bars is 1, what will a 1% increase in its price do to the total amount spent on it (not quantity purchased, but total amount spent) each week?

The answer in the problem set solution released later was as follows:

  It will leave it unchanged because the percentage change in quantity demanded will exactly offset the percentage change in price.

My problem with this is that isn't total revenue (and therefore total expenditure) supposed to be maximum when the demand is unitary elastic? If so, shouldn't changing the price when demand is already unitary, decrease revenue/expenditure?

I've also tried numerical examples. If the price of a bar is \$2 and 100 units are being purchased, the expenditure is \$200. If the price increases to \$2.02, the quantity should fall to 99. Now the expenditure would be \$2.02 * 99 = \$199.98, which is lower than \$200.


texts: Reference Request: Cost Benefit Analysis of Conversion of Undeveloped Land for Housing

texts:
London is surrounded by a "green belt", a large area which government policy has protected from housing development. The current high cost of housing in London has led some to advocate a selective relaxation of the policy so that housing supply can be increased (there have been reports by London First, the Adam Smith Institute, and Shelter, although their economic analysis is in some respects not very deep).

Question   Can anyone give a reference to an academic paper or official report which provides, for a site anywhere in the world, a full cost-benefit analysis of the conversion of undeveloped land for housing development?

Within "undeveloped land" I include agricultural land, woodland, grassland or parkland, whether accessible to the public or not.  By "full" I mean a cost-benefit analysis which includes at least a serious attempt using environmental valuation techniques to quantify the value of the range of ecosystem services that undeveloped land may provide and may be lost on development, eg drainage, water purification, support for biodiversity, carbon sequestration, and opportunity for recreation.


texts: Which classical liberal economists promoted the privacy and secrecy of businesses?

texts:
Quinn Slobodian (2018) writes:

  the idea of businessmen opening their account books beyond the firm represented a revision of the classical liberal vision. The privacy of the businessman was no longer sacred.

(This quote is in the context of Hayek and Mises's efforts in trying to set up the Austrian Business Cycle Research Institute and "to overcome the life-threatening secretiveness of Austrian enterprises and organizations.")

I was surprised by the above quote. I don't think I've ever come across Adam Smith or other "classical" economists promoting the "sacred" privacy of the businessman.

So, which economists advocated ideas that would justify the above quote?


texts:
I'm using CPS monthly individual data which comes with wtfinl as a float weight.

I'm computing some annual statistic for unemployed. I do that by

Sum up wtfinl for all the unemployed observations for a given year
Divide all wtfinl values by the annual sum, and then multiply the variable with this relative share

For example, if the variable is income, this gives me average income of unemployed.

Now, I would like to bootstrap the standard errors. I'm in Python. I

draw samples from the full annual table, each row with equal probability
Stop when number of rows is equal to the actual data
I then apply the same estimator as before to the sample, each row weighted with wtfinl

Now, when I compute the confidence bands, they're not centered around my actual estimator. Even worse, for one or two data points, the estimator is outside of the bands.

I suppose a alternative way to do the bootstrapping would be to

i. Draw from the annual table, each row with probability relative to wtfinl/wtfinl.sum().
ii. Stop drawing once wtfinl.sum() is equal to wtfinl.sum() in original data?
iii. Then do all the computations without using weights.

I thought my way was better because (a) I use the exactly same estimator both times without changing weights, and (b) it is clearer: How would I do (ii) exactly? When I have room for wtfinl=1 left, do I only draw from rows with wtfinl <= 1?

However, given that my confidence bands dont line up with my original estimation, I'm befuddled. What should I do?


texts: Is there an economic rationale for wanting to know the gender of a child before it is born?

texts:
[Rewritten to express issues in economics terms:]

In terms of the classic economic rational actor (Aka homo economicus) is there some rationale to want to know the child's gender before it is born.

Potential  economic advantages of knowing ahead of time:

Smaller decisions space for choosing a name
Can purchase items in advance

Potential disadvantages of knowing ahead of time:

Is there a utility of surprise?
Are excess purchasing impulses easier to control if you don't know the gender?

I would like to understand this in the framework of the classic rational actor (Assuming they would ever want to have a child)


texts: Can one Calculate Fixed and Variable Cost From TC and Quantity Alone?

texts:
I have been asked a question and believe there is a mistake in the problem.

I have been given a table of values, Quantity and corresponding Total cost. From those numbers I can easily calculate the Average total cost and marginal cost.

I am asked to find the fixed and variable cost for each quantity. The question provides no other information. Is this possible?


texts: Has a market labor shortage ever occurred?

texts:
A true labor shortage is when no labor is available for a task at any price. Surely this occurs all of the time if you consider markets that don't exist or could never exist, but has this ever happened otherwise?

Has there ever been a situation where a particular type of labor existed, and then dissapeared, leading to a situation where none of the labor in that sector was available at any price?


texts: Deriving equation for income offer curve

texts: Sorry if this is a basic question, however I have no idea on how to derive an equation for an income offer curve. All the explanations I'm getting is the graphical one where you just connect the different optimum points. It would be really helpful if someone can explain how do you derive an equation for such given any utility function.


texts: Growth rate of variables on a balanced growth path (BGP)

texts:
Normally, in the very basic endogeneous model of growth. It is said that all variables grow at a constant rate.
Let's take the basic capital accumulation ;

$$\dot{K}=Y-C$$

If I write this in following way ;

$$g_{K}=\frac{\dot{K}}{K}=\frac{Y}{K}-\frac{C}{K}$$

Normally, at balanced growth path (BGP), $g_{K}$ grows at a constant value (an arbitrary constant)

In this case, this means that variation of $g_{K}$ according to time at BGP should be equal to zero.

So ;

$$\frac{dg_{K}^{BGP}}{dt}=\left(g_{Y}-g_{K}\right)-\left(g_{C}-g_{K}\right)=0$$

which implies at BGP ;

$$g_{Y}=g_{K}=g_{C}$$

Is this reasoning correct ?

Because in fact, it seems me weird to differentiate a growth rate $g_{K}$ according to time.


texts: Name for a slightly-stronger than Nash Equilibrium?

texts:
As I understand it, a Nash Equilibrium is a fixed point in strategy profile space, in the sense that it is not to any individual player's advantage to deviate from said strategy profile.

Is there a name for the (slightly stronger) equilibrium condition whereby it is to every individual player's disadvantage to deviate from said strategy profile? If so, what is it?


texts: How online payment services system work?

texts:
Nowadays, online payment services like Transferwise, Payoneer and Paysera have been widely used. It enables people outside US to receive payment from companies.
These services gives you a bank account details when you sign up to receive your payment.
They called it (virtual bank address) to receive payments. So this is not real account in the bank but just a virtual address? How these online payment services enables you to receive money from different countries as if you have a local account in those countries? Does this mean my payments goes through (let's say transferwise) real bank account and they give give me something like sub account details which is my virtual bank address?
I want to know how these companies operate the transfer process?


texts: Is there a difference between the two? If so can you intuitively explain it? I see internet resources saying these are equivalent, but I thought I remember someone telling me once shadow price was different than marginal cost, but I may be misremembering it. Bonus points if you can place the definition in the context of a non-equilibrium setting.


texts: If central banks become shareholders, where can investors go?

texts: The ECB is buying corporate bonds. It could eventually also buy shares. What would be left for investors to invest in? Letting bank shareholders pay for bailouts resulted in crashes of their shares. It was interesting to see how fast they went down. It seems like bank shares are relatively volatile. Letting lenders take hair-cuts is very impopular (maybe this is a separate question) but, would the ECB becoming a shareholder / bondholder amount to the same thing? Could it soften or break the opposition against taking hair cuts? (Who would be paying ultimately?)


texts: How to derive the Indirect Utility Function and Marshallian Demand from Homothetic Preferences

texts:
I need to prove the following relationships:
1 - If preferences are homothetic, then the indirect utility function can be written as
$v(p, w) = v(p) · w$.
2 - If preferences are homothetic, then the Marshallian demand functions take the form
$x_i(p, w) = x_i(p) · w$, i.e., they are linear functions of income.
I know that I can use the Roy's Identity and the connections below:
$$ e(p,v(p,w))=w$$ $$v(p,e(p,u))=u,$$
but I can't organize this answer.
Thanks!


texts: What is the Canonical Metric for Investment? (U.S.)

texts:
I'm currently taking a run-of-the-mill Intermediate Macro class and have coursework which asks to produce a vis that tracks U.S. Investment from 1970-2014. What is the salient/canonical National Accounts metric for this?

At present I'm using Gross Domestic Private Investment from the FRED database, but am uneasy about what exactly "Private" means/whether that excludes anything I need to include.

The class itself is mostly modelling so refers to investment as just 'I', not any specific metric so there's nothing from the actual class content for me to go on.


texts: Definition: Extractive Goods (Comtrades HS-Categorization)

texts:
I'm currently writing a paper on China in Africa and I'd like to compare Africas Exports to China with its exports to Europe and the USA. More specifically I'd like to find out if the Exports to China consist of more natural resources than those to Africas other trading partners. However I find it hard to distinguish between "extractive goods" and non-extractive ones. So far I used Comtrades HS-categorization and the categories:

5 mineral products
9 wood and articles of wood; wood charcoal; cork and articles of cork; manufactures of straw, of esparto or of other plaiting materials; basketware and wickerwork
14 natural or cultured pearls, precious or semi-precious stones, precious metals, metals clad with precious metal and articles thereof; imitation jewellery; coin
15 base metals and articles of base metal

Do you think this wouldd be ok, or do you have any sources that state which categories to define as "extractive"?


texts: derive value function from utility function

texts:
We have the utility function.

$$U_{t} = \ln{c_{t}} + E_{t}\sum_{s=1}^{\infty}(\beta^{s}\ln{c_{t+s}})$$
And I am trying to find the value function.

$U$ is utility function. $c_t$ is consumption at time $t$. $\beta$ is the discount factor.

My manual says multiply the right side with $1-\beta$ to get:

$$U_{t} = (1-\beta)\ln c_{t} + \beta E_{t}U_{t+1}$$

How? And multiply only the right side? I am unsure what is happening here and how.

For $s = 1$ we have

$$U_{t} = \ln c_{t} + \beta E_{t}\ln c_{t+1}$$

but this is as far as I can understand. I don't get anywhere multiplying the equation by $(1-\beta)$.


texts: Formulas or rules regarding End of Life for vehicle

texts:
Are there formulas or rules when keeping a vehicle is no longer financially beneficial?
I understand the below needs to be considered:

Every time a purchase is made, sales tax will need to be paid.
Keeping a vehicle longer reduces the number of sales tax
transactions.
A vehicle, especially new vehicles of certain models,
depreciate quickly - exponential depreciation.
The retail book value comes into play as well as the age of vehicle on whether a repair should be made; 10%, 20%, not certain.


texts: Why don't researchers use regularized probit model?

texts:
I know that a regularized logistic regression can be done to reduce training error, but I haven't found any economics research that uses a regularized probit model, only a regular probit model from what I have been able to find. Why don't economic researchers use a regularized probit model?

Thank you


texts: Can't solve this matrix for Nash Equilibrium?

texts:
So, I have the following 9 by 9 probability matrix. I want to solve it for a nash equilibrium.
https://docs.google.com/spreadsheets/d/16Y1FqxRIAHsHpgEz1ckxDt2sEOInOG3zz_wU8kBHvB4/edit?usp=sharing

For anyone who might recognize it, the probabilities are from Hearthstone tournament data.

We can eliminate 4 strategies by dominance, leaving us with a 5 by 5 matrix, but when we try to solve in mathematica:

data1 = {
{50, 56, 33, 44, 39},
{44, 50, 75, 69, 44},
{67, 25, 50, 25, 69},
{56, 31, 75, 50, 39},
{61, 56, 31, 61, 50}}
prob = List[m, pr, r, s, wr]

NSolve[{
data1[[All, 1]].prob == data1[[All, 2]].prob,
data1[[All, 2]].prob == data1[[All, 3]].prob,
data1[[All, 3]].prob == data1[[All, 4]].prob,
data1[[All, 4]].prob == data1[[All, 5]].prob,
Total[prob] == 1}, prob]

So I'm using the standard MSNE strategy, taking the dot product of the probability vector and player 2'd payoffs, then setting them equal. The output is:

{m -> 0.447102, pr -> 0.5299, r -> 0.286108, s -> -0.241951, wr -> -0.0211592}

But we can't have negative probabilities. This would mean an MSNE cannot occur, which would imply a PSNE, but that can't happen either with the way the matrix is set up.

So what's the deal? What's the NE in this matrix?


texts: Sequential Price Competition for Perfect Complements

texts:
There are two goods, $1$ and $2$ produced by two firms at zero marginal costs. The goods are perfect complements. The demand for each goods is: $Q_1=Q_2=a-(p_1+p_2)$. The prices are set sequentially, with the leader firm ($1$) credibly committing to a price which the follower takes as given. Determine the equilibrium prices, quantities and profits.

I understand that in standard Stackelberg games of prices, the follower has a second mover advantage. For the above question, I found that the reaction curves turned out to be downward sloping, i.e. prices are strategic substitutes. $(p^*_1,p^*_2)=(\frac{a}{2},\frac{a}{4})$.
Would the second mover advantage still hold? Evaluating the leader's profit function at Bertrand prices would show that the leader has an incentive to set a price above $p^B_1$ since prices are strategic substitutes and goods are perfect complements (evaluating $\frac{\partial\pi_1^L}{\partial p_1}$ at bertrand prices).
Is this the correct method to evaluate second mover/first mover advantage?


texts: How might the Swiss currency floor be unwound?

texts:
The Swiss National Bank has been enforcing a currency floor since 2011, not allowing the EUR/CHF rate to drop below 1.20 by buying unlimited amounts of foreign currency as needed with newly created CHF.

I'm having trouble finding exact amounts, but it seems from their balance sheet that their foreign currency reserves have increased by about CHF200bn since 2011.

How will they unwind this situation? They state that they still view CHF as overvalued at the 1.20 rate, so presumably they would let it drop some way from that before they start selling the reserves, leaving them with a gain in CHF. Will they just leave the money base permanently contracted to account for this? What long-term impacts will this have?


texts: Disruptions in Server / Data Center Market

texts:
With the advent of cloud computing, data storage and scaling has become extremely cheap when compared to the strictly physical server alternative (which require a dedicated facility and substantial fixed/variable costs). Implicitly, we could view cloud computing as having comparatively big ecological advantages over dedicated servers. From this perspective, companies with server/data center needs will have huge incentives to choose cloud computing.

My question is, is the verdict really this simple? Wouldn't some companies be reluctant to use cloud computing for security / conflict of interest reasons? Instead, might they prefer to be the sole custodians of their data? For example, investment banks, hedge funds, ect?

Are there any other compelling reasons that might hold the server / data center industry away from adopting the cloud?


texts: Cost Minimization of $f(x) = min(x_1,x_2) + x_3$

texts:
The following production function is given,
$f(X) = min\{x_1,x_2\} + x_3$
There is a solution here https://math.stackexchange.com/questions/605925/constrained-maximization-of-leontif-utility-function-minx-1-x-2, which is similar to this function. However, it does not include an additive $x_3$.
My initial solution attempt
Redefine the production function, such that,
$f(X) = x_1 + x_3$ if $x_2 < x_1$ and $f(x) = x_2 + x_3$ otherwise. This gives the following Lagrangian;
$L = p_1 x_1 + p_2 x_2 + p_3 x_3 - \lambda_1(x_1 +x_3 - Q) - \lambda_2(x_2 + x_3 - Q)$
With each $\lambda_i > 0$ both constraints are binding, such that,
$Q=x_1+x_3$ and $Q=x_2 + x_3$; and then the constraints reduces to
$x_1 - x_2 = 0$ implying that $x_1 = x_2$. However, this contradicts the initial conditions that I made on the relationship between $x_1$ and $x_2$ and, thereby, the arising production functions.
I'm caught in a bit of confusion here. How should I proceed with this problem?


texts: Profit maximizing, Quantity and Price with Dominant Firm and Competitive Fringe

texts:
A dominant firm operates in various markets. In one of these markets, it is a monopolist and produces with the following cost function: C(q1) = 5q1. The market demand is P = 1005 - Q.

(a) Find the profit maximizing P and q1 and profit.

(b) A new fringe firm with C = 28,900 + (qf^2)/4 enters the market. The fringe firm acts as a price taker and maximizes its profits. The dominant firm, after the entry , subtracts the fringe firm's supply and behaves as a monopolist for the residual demand. Find the new profit maximizing P, q1, qf and profits as well.

My attempt for (a):

P = 1005 - Q.

MR = 1005 - 2Q.

MR = MC.

1005 - 2Q = 5

Q = 500

P = 505

Profit = 505 x 500 - 5 x 505 = 249975

Hopefully I'm right.

My real problem is I'm stuck on (b). I'm not familiar with price taker. I did read my course book but it wasn't that helpful. I'd appreciate if anyone can help me, thank you. Please let me know if (a) was right as well


texts: Economies of scale v.s. technological change

texts:
In Greene's Econometric Analysis, 7th edition, page 355, it is written that:

  A long-standing problem in the analysis of production functions has been the inability to separate economies of scale and technological change.

I know what the boldfaced terms refer to but it's not clear to me what is the source of the described "inability to separate." Can you please illustrate via a simple model, preferably one (adopted) from an article / a book that studies this very issue.


texts: indifference curve slope from utility function

texts:
in the economics book that I'm reading right now it is written that this utility function:
$$u(x_1,x_2) = 2x_1 + x_2$$
yields indifference curves with a slope of $−2$.
Could someone please explain me how they found the $-2$?

Initially, I was thinking that they derivated the utility function in respect of $x_1$ and $x_2$ but this would give $2$ instead of $-2$. Thank you very much for your help


texts: Can't government experiment on price in the case of a monopoly?

texts:
In the lecture given by Jon Gruber at MIT, he talks about the governmental regulations on monopolies, and he states that

(in short)
for government to regulate a monopoly, it needs to know the price of
that good in the case of a perfectly competitive market.However, in
reality, the government does not know the demand and supply curve.
Nevertheless, to get the demand curve the government can do
experiments on the consumer and get the demand curve.

If so, can't the government do experiment on the monopolist ? I mean, it can set a price first, and then change the price. Doing so, observing how much the firm produce, we can learn the supply curve of the monopolist. Of course, this would in some sense be not logical, but in the long run, you the government could set all the monopolies in the optimal price.
Moreover, if we look from a broader picture, this can be accomplished more easily by cooperation of different governments on collecting the data.


texts: Experiments contradicting the expected utility model

texts:
This is a question I asked on the cognitive science beta which never got any answer there. I do not know what the policy should be for question migration/reposting (maybe worth discussing in the meta?), but I hoped it might get more answers (i.e. at least one ;)) here.

I am looking for a list of experiments which cannot be accounted for by the expected utility model. By the expected utility model, I mean the model of individual preferences over vectors of uncertain events (e.g. $\Big(P(rain) = 0.4, P(sunshine) = 0.6\Big)$ and $\Big(P(rain) = 0.6, P(sunshine) = 0.4\Big)$)  which satisfies a list of axioms proposed by Von Neuman and Morgernstern, namely

Completeness
Transitivity
Continuity
Independence

A rigorous formulation of these axioms can be found on page 8 of Axiomatic Foundations of Expected Utility and Subjective Probability, by Edi Karni, from the Handbook of Economics of risk and uncertainty..

Alternatively, by Von-Neuman and Morgenstern's representation theorem (page 9 of the same reference), these axioms are know to be equivalent to the fact that the preferences of the agent can be represented by a utility function of the form (in the discrete case):

$U(L) = \sum_{all~possible~events "e"} P(e)u(e)$

where $P(e)$ is again the probability that $e$ occurs and $u(e)$ is the utility of getting event $e$ for sure.

The violations of these axioms I am most interested in are the ones related to the Independence axiom (violations of completeness, transitivity and continuity would probably deserve a separate question. See this question for an example of intransitivity.).

I am looking for situations which cannot be accounted for by the expected utility model. Some well-known examples are the the Allais and Ellsberg paradoxes (although there is still a debate regarding Ellsberg paradox). On the other hand, I do not see the Saint-Peterborough paradox as contradicting expected utility theory, because it can be accounted for by the theory if one assumes an appropriate degree of risk aversion. But you are much welcome to argue against that.

I hope this question can serve as a repository of famous experiments contradicting expected utility theory, so feel free to add many.


texts: Inflation without Increase in Money Supply?

texts:
Is it possible to have inflation without increase in the supply of money?

For example, if workers demanded higher wages, and goods went up in price, but the money supply in circulation did not increase. Or is this an impossible paradox?


texts:
A consume has a preference relation on $\mathbb{R}^4_+$ with a utility function defined as
$$ U(x_1,x_2,x_3)=(\ln(3x_1+2x_2+x_3))^3$$
Find the demand at prices $p=(1,1,1)$ and wage $4$.
Attempt
I thought to either use Lagrange or condition
$$\frac{MU_{1}}{p_1}=\frac{MU_{2}}{p_2}=\frac{MU_{2}}{p_2}$$
but just considering the inner function i.e $ U(x_1,x_2,x_3)=\ln(3x_1+2x_2+x_3)$ since they represent the same preferences. I get the 3 partial derivatives
$$\frac{\partial U}{\partial x_1}=\frac{3}{3x_1+2x_2+x_3}$$
$$\frac{\partial U}{\partial x_2}=\frac{2}{3x_1+2x_2+x_3}$$
$$\frac{\partial U}{\partial x_3}=\frac{1}{3x_1+2x_2+x_3}$$
Now, i would isolate the variables in
$$\frac{MU_{1}}{p_1}=\frac{MU_{2}}{p_2}=\frac{MU_{2}}{p_2}$$
but a solution to that system does not exist since they are just
$MU_1=MU_2=MU_3$ which is of course not true (for any variables). Am I missunderstanding the approach?
*I would then use the expressions in the budget constrain and solve for the variables ones again.


texts: What is the best way to compare the price of a GB of internet across countries

texts:
I have the average price of a GB of data / internet across 45 different countries. I want to be able to compare the price of using data on the people in that country.
Let's say 1 GB of data costs 1.37 USD in the USA and the equivalent of 1.1 USD  (regular conversion rate) in China. I cannot state the the internet is "cheaper" in China than it is in the US, as 1.1 USD in China could buy so much more for a family living there and therefore is more taxing on their income than 1.37 USD would be on an American family.
How can I compare the effect that spending these 2 values could have on a family in these 2 countries? Would the purchasing power parity be the right way to go here? If so, can someone explain to me how to use it? I looked up the PPP in China, and it's 4.15.
I read online that to compare the price of the good across both countries we would calculate: 1.1 / 1.37 / 4.15 = 0.19. So the price of a GB of data is about a fifth of that in the US? And not almost the same? But that's not what I'm looking for, I'm looking for a number that would tell me that since life is so much cheaper in China, and spending a dollar is so much more taxing.
Wouldn't (1.1 / 1.37) * 4.15 = 3.33 make more sense? So spending 1 USD in the USA on internet would be equivalent to spending 3.33 USD in China for the same amount of internet?


texts: Coefficients of Cubic Total Cost Function

texts: Given a Total Cost equation $TC(Q) = a + bQ + cQ^2 + dQ^3$ what do the coefficients mean? For example $a$ is fixed costs, what are $b,c,d$ and how are they calculated?


texts: second order stochastic dominance without the same mean

texts:
Let $F$ and $G$ be two distributions with the same mean. $F$ is said to second order stochastically dominate (SOSD) $G$ if
$$\int u(x)\mathrm dF(x)\ge \int u(x)\mathrm dG(x)\tag{1}$$
for all increasing and concave $u(\cdot)$.

This above definition is equivalent to
$$\int_{-\infty}^x F(t)\mathrm dt\le \int_{-\infty}^xG(t)\mathrm dt,\qquad\forall x\in\mathbb R.\tag{2}$$

I was told that the requirement for $F$ and $G$ to have the same mean is not really necessary. Suppose $F$ and $G$ do not have the same mean. Can we then still have the equivalence between $(1)$ and $(2)$?

N.B. I was able to show $(2)\Rightarrow (1)$ without the same mean condition, but not the other way around.


texts:
If strict preferences over three outcomes x, y and z, do not satisfy transitivity, so that $x \succ y \succ z \succ x$, then these preferences cannot be represented by a utility function.

Is this statement true or false? Can anyone explain it to me?


texts: What should the value of a private sector company tell us?

texts:
At the highest level, would you say that regardless of market/economic environment (free/regulated), a company's value should reflect its ability to efficiently and effectively bring products and services to market that improve the lives of consumers?

Perhaps this is more of a philosophy/ethics question; cant think of any valid argument against this.

For some context, my train of thought is:
If the values of all companies do reflect their ability to improve the lives of consumers, then an equity index should therefore be an indication of how good the private sector is at improving life. The value of an equity index allows us to consider the health of a particular market. The financial markets are complex systems in which both physical and mental health are two large constituents. By physical health, I mean the bodies of employees, the buildings in which they work and the technology they use for example. By mental health, I refer to the emotional and psychological well-being of individuals, teams, whole companies and markets.

Thoughts please.


texts: What is equilibrium dependent upon in Generalized Second-Price Auctions?

texts:
Theory states that GSP auctions induce truthful bidding.  Is it the case that this is true ONLY IF

a) each of the bidders truthfully bids their value ($b_i = v_i$) (each bidder's optimal strategy) AND

b) each bidder assumes that all of the other bidders are also truthfully employing their own optimal strategy ?

My question arises out of the following possible example:

Two bidders bidding for a single item, Vickery sealed-bid second-price auction.

The bidders have equal values for the same item (say $v_1 = v_2 = 10$)

$b_1 = 7$

$b_2 = 9$

$b_2$ will win the auction and pay $7$; with a surplus payoff of $2= (9-7)$.  This outcome is equivalent to the example where:

$v_1 = b_1 = 7$

$v_2 = b_2 = 9$

$b_2$ wins in either example but neither bidder is using the optimal strategy in the first example.  What logic am I missing?


texts: Will SRAS curve definitely shift if LRAS curve shifts?

texts:
From what I know, a shift in LRAS is generally caused by a change in maximum productive capacity of an economy, which affects the full-employment output level. Such change in maximum productive capacity would also cause a shift in SRAS.

So does this mean whenever LRAS curve shifts SRAS curve will also shift? If not, are there any examples against this?


texts: I figured out how the economic order quantity (EOQ) formula comes out. I know it is quite similar with economic batch quantity (EBQ), sometimes termed economic production quantity (EPQ). I just don't understand why they are different. What makes the difference in holding cost part?


texts: Can mixed strategies actually predict behaviour of rational actors in non-constant sum games?

texts:
I understand how the concept of the mixed NE (mathematically) works. But I don’t understand how we can expect players to behave in a way that would arrive at such an equilibrium.
Consider the following example in which the four axioms of expected utility are met:
Two players play a coordination game of the following form:

(I believe the game is commonly called “meeting in New York”)
This game has a NE in mixed strategies, in which both players play E with a probability of $\frac{c}{1+c}$. This means that the higher the potential payoff of playing C is the lower the likelihood that a player will elect to go with this strategy. We arrive at this paradox, because a player always mixes in a way that makes her opponents indifferent.

But in my opinion, this is not how I would expect a rational, utility maximizing player to behave. In this example, a truly rational player (how knows that her opponents are also rational) should become more and more likely to play C the higher c is.

I have seen various examples of the mixed NE being useful in for example Binmore, but I don't understand why this concept is seen as generally useful? Could somebody help me out?


texts: Country specific economic recession/financial crisis data?

texts:
Many financial crises are at the global level, yet some of them can be country-specific, especially the ones connected with political instability.

For example, the 1990 recession of Russia, the 1958 recession in China, and the recent Brazil currency crisis is kind of independent of the global economic situation. The Eurozone crisis also only applies to a limit number of nations. Examples also include the Iceland bankruptcy.

So my question is, how could we identify those country-specific crises? Are there any established methods/datasets? Any references or ideas or suggests or guidelines will help!


texts: What does the value of an industry mean?

texts: In product pitches, a timeless line is "this is a $____ industry", but what does that really mean? Is that how much money the industry typically produces in a year? In a quarter? As some ratio of the annual/quarterly sales or profits? What does it mean?


texts: How to show average cost is falling if we have IRTS

texts:
Using maths how could I show this, I am able to show that AC>MC By differentiating AC with respect to q and assuming AC is falling , but how do show its falling in the first place if we have increasing returns to scale. Thanks

aso I know that IRTS means f(tz)>tf(z) where f is productions function gives us maximum amount of output for a given set of inputs Zi.


texts: How likely is a total economic collapse due to the potential coronavirus impact?

texts:
Most signs show that lockdown could easily stretch through the summer. A freeze in consumer spending would cause multiple industries to fail causing a ripple effect.

To be specific, if lockdown lasts through the summer, and a second virus wave occurs in the fall as expected, then lockdowns will continue further into the year. The timeframe for a vaccine is 12-18 months earliest. Then, the vaccine must be manufactured and distributed. Since the virus is so widespread that it is now assumed that it will reach a global critical mass, this essentially guarantees the collapse of the restaurant, airline, tourism, and hotel industries as they cannot sustain prolonged losses in a capitalistic structure. If they fail, their suppliers fail, and so on. History has shown that large systems are prone to failure time and time again, esp. when accountability is obfuscated (e.g. the Titanic, the World Wars/Holocaust, and now this). In the past Egypt fell, and then Rome fell. What is to say our current systems won’t fail, even if as a slowly sinking ship?

EDIT: This question was closed, before I received enough good, thoughtful answers. As of tonight (April 4th) Bernie Sanders held a virtual address on the situation. He's looking at the unemployment projections that were posted by the St. Louis Fed's models and has spoken with a number of economists. Finally a voice of reason in this media circus. He has confirmed that a potential collapse is possible as another 47 million Americans may become jobless - this is unprecedented and would be absolutely devastating to American civilization.


texts: nash equilibrium public good - is this correct?

texts:
Two players, 1 and 2, simultaneously choose their consumption of a public good. Given the consumption choices, g1 and g2, player 1 derives a marginal benefit of MB1 = 10 - (g1 + g2), while player 2's marginal benefit is given by MB2 = 8 - (g1 + g2). The unit price of the public good is equal to 4.

The question asks to find a Nash Equilibrium of the game, then calculate the efficient level of public good provision and compare it to the NE.

I can understand the efficient provision of public good which will be nothing but the sum of marginal benefits set equal to the marginal cost. In this case, it turns out to be 7. What will be the Nash equilibrium?

An update with my attempt:

Player 1's best response function: g1 = 6 - g2
Player 2's best response function: g2 = 4 - g1

Added these two to get the total level of public good - it comes to 5.

Then I equated the two response function to get: g1 = g2 - 2

Substituted it in g1 + g2 = 5 equation with getting g2 = 3.5 and g1 = 1.5

I don't know if this is correct.


texts: What is the importance of Epstein-Zin preferences?

texts:
I've heard that there is a lot of work being done recently that applies Epstein-Zin preferences. The Wikipedia page doesn't seem to be very full.

Why are Epstein-Zin preferences important?
How does recursive utility differ from other preference models in general? What do they capture that can't be captured otherwise?
What are some good resources to learn more about them?


texts: How much influence does the president really have on US economy?

texts: We hear a lot about how the economy changed under a certain president, but how much does the incumbent actually affect the economy? Are the fluctuations we see in economic growth due to natural market fluctuations or can they be attributed to policy changes?


texts: Questions regarding ordered probit model

texts:
I am currently working on a hypothetical research proposal for a course at my university. I am using data from three Afrobarometer surveys conducted in 34 African countries in the years 2011-2013, 2015 and 2019. I have to perform an ordered response model (i.e. ordered probit model) as my dependent variable comes from the following question:
Q26D: Here is a list of actions that people sometimes take as citizens when they are dissatisfied with government performance. For each of these, please tell me whether you, personally, have done any of these things during the past year. If not, would you do this if you had the chance: Refused to pay a tax or fee to the government.
With the answer possibilities ranging between: 0 = No, would never do this, 1 = No, but would do if I had the chance, 2 = Yes, once or twice, 3 = Yes, several times, 4 = Yes, often.
Until now, I came up with the regression displayed in the attached file. The X's stand for my four explanatory variables coming from four different questions, the Z display added covariates for which I control, the D_t is a country-level dummy variable to control for heterogeneity across different countries and the α_t is a year fixed effect.
However, I am uncertain about the following points because this is the first time I am doing something like this:

Is the ordered probit model built up correctly the way I did it?

When looking at γ'Z_(i,t,c), do I have to specify the γ with a subscript as I have 12 different control variables I am looking at, i.e having a notation like γ_k'Z_(i,t,c)? And do I have to transpose the γ such that γ'Z_(i,t,c) or don't I have to use a transpose such that γZ_(i,t,c)?

A just have a repeated cross-section dataset and not a panel dataset. Nevertheless, is it right to have the subscripts (i,t,c), or should I just account for (t,c) as I am not looking at the same individual in each of the three surveys because different individuals were asked in each survey?

My control variable accounts for the respondants’ age (Q1), mother tongue (Q2A), occupation (Q95A), religiosity (Q98), education (Q97), gender (Q101) and race (Q102) as well as the respondents’ present economic situation (Q4A), present living condition (Q4B), their free speech (Q14), satisfactory with democracy (Q36) and covariate to control for corruption (Q44D). However, now I am wondering if I can control for mother tongue, religiosity, gender and race in the way I am doing it because these variables are time-invariant and would drop out when applying year fixed effects α_t? Am I running into some problem here? How should I account for this? I want to urgently show which direct effect mother tongue, religiosity, gender and race have on the dependent variable, but is this possible with year fixed effects?

I really hope that you can help me!
Thanks to everyone!
[built-up ordered probit model] [1]: https://i.stack.imgur.com/86jlC.png


texts: Do trade policies have to change after Brexit?

texts: Being part of the EU is surely not the only way to participate in a free trade market. Could the UK continue with the same policies despite not being part of the EU?


texts: How can a citizen contribute to get his country out of the poverty trap?

texts:
I am from Madagascar. We are in what is called a "povery trap".
Building a business is very difficult because the population is agglomerating in the capital and the competition is very high. Moreover, there is a lack of public infrastructure that freezes the economy.

What do you suggest me to do as a citizen without any governmental control to have a good impact in the economy?


texts: When can one read the general theory of employment,interest and money?

texts:
I am a first-year undergrad econ student and was interested in reading Keynes' book. in the preface, Keynes pointed out that the text deals in the abstract and is meant for his fellow economists. After reading a few chapters its become quite clear that he wasn't kidding. there so many theories and ideas that I am not familiar with and most of the ideas are criticised more than they are explained.

So my question is: what prior knowledge do I need to possess to understand the book? Any books you can recommend to acquire said Prior knowledge?
and lastly is the book even worth reading?


texts:
I have the following problem that asks me to solve for the "maximal growth portfolio."

  Suppose that the equilibrium stochastic discount factor evolves as
  $$
\log S_{t+1} - \log S_t = \kappa_s(X_t, W_{t+1}).
$$Solve the following maximization problem:
  \begin{equation*}
\begin{aligned}
& \underset{x}{\text{maximize}}
& & E[\log(R_{t+1})] \\
& \text{subject to}
& & E\left[ \frac{S_{t+1}}{S_t} R_{t+1}\, \middle | X_t = x \right] = 1.
\end{aligned}
\end{equation*}

It seems clear how we would derive the following solution:
$R^*_{t+1} = \exp(-\kappa(X_t, W_{t+1})) = \frac{S_t}{S_{t+1}}$.
However, my question is related to understanding the economics behind this problem. The constraint in this problem is clearly saying that whatever portfolio we construct, it must be fairly priced (given the stochastic discount factor process $S_t$). However, I don't understand why there would be a portfolio that produces a "maximal expected return." So, there are my two questions:

Why isn't the objective here unbounded? Can't we always choose a portfolio with a higher expected return (with correspondingly higher risk)?
Also, why is there a log in the objective? Would this problem work just the same as having the objective be $E[R_{t+1}]$?


texts: If a currency crashes, does that effect the value of rare or collector coins?

texts:
I own lots of collectable coins from the 70's (mostly mint dollars and quarters.)  Some of my friends are telling me that the US economy is going to crash and the the dollar is going to lose its value.  This got me thinking.  In the unlikely event that this happens (hyper inflation, a drastic drop in value compared to other currencies or a complete loss of value), how would that effect the value on my coins?

This may not be the best place to ask this question.  Please help me get it to the right place.


texts: Optimal choice for a weird leontief function

texts:
Compute the optimal choice for a consumer with the following utility function:

$$u(x_1, x_2) =\max \{\min(2x_1, x_2), \min(x_1, 2x_2)\}$$

I'm familiar with computing optimal choice for perfect complements but this has 2 expressions and I'm stumped with how to go about doing this. I'd also appreciate if anyone could explain what exactly is happening in a function like this.


texts: Visualization tools for game theory: Game trees

texts:
There are many ways to draw a sequential game 'by hand'. By drawing the game I mean this:

Displaying players' decision points, available actions and payoffs.

Is there any way I can do this in R or a similar high level programming language? To be precise: I do not want to plot geometric equations, I want to define a structure (players, points, connections, payoffs) and have the program plot it.

I am currently browsing the 'igraph' package but I am having some difficulty labeling so I am wondering if there is a better way.


texts:
I am looking to merge the various core data files from SIPP - 1989 to 2014 - so that I can exploit its panel and cross section features.  Basically I want to create one dataset for all these years where I can identify the same household observed multiple times too. Does anyone have any guidelines on how to do this easily? I found some guidelines here: https://ceprdata.org/sipp-uniform-data-extracts/sipp-extraction-programs/#programlist but this is impossibly hard to get working.
Thanks in advance!


texts: which type of goods maximum utility function represent?

texts:
I am not sure, which type of goods does the maximum utility function represent i.e., $U(X_1, X_2) =\max(X_1, X_2)$.
As the $U(X_1, X_2) =\min(X_1, X_2)$ represent the complementary goods, and $U(X_1, X_2) =X_1+ X_2$ represent the substitute goods, I think it represents the substitute goods as the maximum of both matter. So am I correct?
Please clarify this doubt, thank you.


texts: Math basics for Macro&Micro economics and econometrics

texts:
I have just been admitted to a graduate school for studies in economics and I major in public administration during my undergraduate time. I have learnt linear algebra, single variable calculus, probability theory and mathematical statistics by myself(Otherwise I will not be admitted). After all I am a amateur in economics, and I have another 5 months to go before register to the graduate school.

So, I think I'd better to equip myself with solid mathematical knowledge to deal with the courses in the first year, which are showed in the title.

ps. The books I will use in these courses are:

  Microeconomic Theory, Andreu Mas-Colell

  Advanced Macroeconomics, David Romer

  And there is no prescribed textbook for econometrics.

Any ides are going to be appreciated, and if I didn't make a clear expression of my question, please tell me to edit my question.


texts: Are there Nash Equilibria that aren't mixed strategies?

texts: We can consider only finite games if it makes a difference, but are there nash equilibria that can't be characterized as mixed equilibria?


texts: Is there a proven, quantitative link between food wastage and food prices?

texts:
Reducing food wastage should in theory reduce demand for food, thereby driving food prices down. However, there are a lot more factors involved here (for example, the reduction in price of a product x due to lesser wastage in region A may not actually lead to lesser prices in region B because transportation costs may fully offset the price decrease).

Has there been a study that quantitatively links food wastage and food prices?


texts: Could be this picture be interpreteded as a pareto set?

texts: Hi, is there a way to interpret this picture as a Pareto set? What assumptions are necessary for such an interpretation?


texts: residential property shares trading (similar to REIT)

texts:
This year in the UK a residential property crowdfunding platform propertypartner.co went live and I would like to understand it from economic point of view.

The idea is that a flat/house is purchased and within couple of weeks the necessary amount will be collected from individuals and companies, that can invest 50+ gbp. A special purpose vehicle limited company will be created and investors will get shares in it, according to the amount they contributed. Let's say a 200k GBP property will be assigned to a limited company with 1m shares and so one share costs 20pence on the primary market. The property will be rented out and rental income will be distributed between the shareholders, with yield roughly 3%.

I heard about Real Estate Investment Trusts (REIT) and it seems similar, but in this case you can trade shares in one particular property and have several properties in your portfolio.

Several weeks after the purchase has been finalised, shares can be traded on the secondary market - shareholders put N shares on sale for price P and buyers can purchase 1 or more shares (or not, if they are not satisfied with the price).

After a long introduction couple of questions:
1. Share prices are denominated in pence, so a 19.95 pence share can go up to the nearest pence, 20 (and 21), so the potential profit will be 0.25% or  ~5% for 21p. I know about the effect of decimalization on the stock market increased volumes somewhat significantly. Would lowering the price increment always increase volumes?

Buyers have no way to signal how many shares they want to buy at what price, they can only buy at offered prices or wait. Is there a name for this type of marketplaces with only offer listings? Are there any advantages compared to the usual exchanges with bid/ask listings?
Every several months properties are reevaluated, currently property prices grow at about 10-20% per year in the UK. But interestingly shares of some properties on the secondary market cost already +20% compared to the last valuation, especially these with unusually high yield (3.5-3.8%). I understand like with fixed income securities, unusually high yield will drive up prices. Interesting that properties with similar yield and potential growth characteristics trade at somewhat different premiums. I presume such illiquid markets have lots of irrationalities?
Let's imagine the whole residential rental market will be securitised in such way, would it increase/decrease chances of bubbles? Are there any interesting papers about it?

Thanks, my question is rather long and I will try to rephrase it clearer later..


texts:
Literature: See Chang (1988) for theoretical part and Achdou et
  al. (2015) for numerical part respectively.

Model

Consider the following stochastic optimal growth problem in per capita notation.
\begin{align}
&\max_{c}\int^\infty_0 e^{-\rho t}u(c)dt\\
\text{s.t.}~~~&  dk = [f(k) - (n-\sigma^2) k - c]dt - \sigma kdz\\
&c\in[0,f(k)]\\
&k(0) = k_0
\end{align}
everthing is standard except for $dz$ which is the increment of a standard Wiener process, i.e. $z(t)\sim\mathcal{N}(0,t)$. The population growth rate has mean $n$ and variance $\sigma^2$.

Analytical Solution

We presume Cobb-Douglas technology
\begin{align}
f(k) = k^\alpha,\quad \alpha\in(0,1)
\end{align}

and CRRA utility
\begin{align}
u(c) = \frac{c^{1-\gamma}}{1-\gamma},\quad \gamma > 1.
\end{align}
Set up the Hamilton-Jacobi-Bellman equation (HJB-e)
\begin{align}
\rho v(k) = \max_c\left\{\frac{c^{1-\gamma}}{1-\gamma} + v'(k)(k^\alpha - (n - \sigma^2)k - c) + v''(k)\frac{k^2\sigma^2}{2}\right\}
\end{align}

The first order condition (FOC) reads
\begin{align}
c = v'(k)^{-\frac{1}{\gamma}}=:\pi(k)
\end{align}
where $\pi(\cdot)$ denotes the policy function.

Resubstitute FOC into HJB-e
\begin{align}
\rho v(k) = \frac{v'(k)^{\frac{\gamma-1}{\gamma}}}{1-\gamma} + v'(k)k^\alpha - v'(k)(n - \sigma^2)k  -  v'(k)^{\frac{\gamma-1}{\gamma}} + v''(k)\frac{k^2\sigma^2}{2}.
\end{align}

We guess a functional form of $v(k)$ with (Posch (2009, eq. 41))
\begin{align}
v(k) = \Psi \frac{k^{1-\alpha\gamma}}{1-\alpha\gamma}
\end{align}

where $\Psi$ is some constant. The first and second order derivative of $v$ are given by
\begin{align}
v'(k) &= \Psi k^{-\alpha\gamma}\\
v''(k) &= -\alpha\gamma\Psi k^{-1-\alpha\gamma}.
\end{align}

The HJB-e then reads
\begin{align}
&\rho \Psi\frac{k^{1-\alpha\gamma}}{1-\alpha\gamma} = \frac{\Psi^{\frac{\gamma-1}{\gamma}}k^{\alpha(1-\gamma)}}{1-\gamma} + \Psi k^{\alpha(1-\gamma)} - (n-\sigma^2) \Psi k^{1-\alpha\gamma} -  \Psi^{\frac{\gamma-1}{\gamma}} k^{\alpha(1-\gamma)}  - \alpha\gamma\Psi k^{1-\alpha\gamma}\frac{\sigma^2}{2}\\[2mm]
\Longleftrightarrow \quad &
k^{1-\alpha\gamma}\left(\frac{\rho}{1-\alpha\gamma} + n - \sigma^2\left(1 - \frac{\alpha\gamma}{2}\right)\right) = k^{\alpha(1-\gamma)}\left[1+\Psi^{-\frac{1}{\gamma}}\frac{\gamma}{1-\gamma}\right]
\end{align}

The maximized HJB-e is true iff the following conditions hold
\begin{align}
\rho = \left(-n + \sigma^2\left(1 - \frac{\alpha\gamma}{2}\right)\right)(1-\alpha\gamma)\quad \wedge \quad \Psi = \left(\frac{\gamma-1}{\gamma}\right)^{-\gamma}
\end{align}

Resubstitute $\Psi$ into $v$ which finally gives the true value function
\begin{align}
v(k) = \left(\frac{\gamma-1}{\gamma}\right)^{-\gamma} \frac{k^{1-\alpha\gamma}}{1-\alpha\gamma}.
\end{align}

How come that $v$ does not depend on $\sigma$?

So the deterministic and stochastic value function must be the same. The policy function is then readily given by (use FOC and derivative of value function)

\begin{align}
\pi(k) = \left(1-\frac{1}{\gamma}\right)k^\alpha.
\end{align}

Note that this function does not depend on $\sigma$ either.

Numerical Approximation

I solved the HJB-e by an upwind scheme. Error tolerance $\epsilon=1e-10$. In the figure below I plot the policy function for varying $\sigma$. For $\sigma\to 0$ I arrive at the true solution (purple). But for $\sigma>0$ the approximated policy function deviates from the true one. Which should not be the case, since $\pi(k)$ does not depend on $\sigma$, right?

Can anyone confirm that the approximated policy functions should be the same for any $\sigma$, since the true one is independent of $\sigma$?


texts: What would happen in the IS-LM model if there is a simultaneous decrease in tax and interest rate?

texts:
Since there is a fiscal expansion with a decrease in tax i'm not sure what the interaction would be with a decrease in interest too, would money supply and output both increase?
Thanks


texts:
My economics textbook says that demand curves slope downward - but then goes on to say that when demand increases, prices go up! Does anyone else find this confusing?

Edit: from the small number of answers I have received, it seems that this is not a well understood issue in economics. Is anyone aware of alternative approaches which avoid this contradiction (e.g. I have heard that the Austrian School does not use demand curves)?


texts:
If $\succsim$ is rational, then $B \mapsto C^*(B, \succsim)$ satisfies the weak axiom, and $\succsim=\succsim^*$

Previously in the same theorem actually, they proved the following:

  If $C$ is a choice rule satisfying the weak axiom, then $\succsim^*$ is rational, and for all $B \in \mathcal{P}(X), C(B) = C^*(B, \succsim^*).$

Note: $C^*(B) = C^*(B, \succsim) = \{ x \in B: \forall y \in B, x \succsim y \}$, and the weak axiom is referring to the weak axiom of revealed preference which a choice rule satisfies if $[x \succsim^* y ] \Rightarrow \neg (\exists B)[y \succ_B x]$

My try of the proof:

First suppose $B \mapsto C^*(B, \succsim)$ does not satisfy the weak axiom, then $\succsim^*$ is not rational by the earlier part of the theorem, so if we can prove $\succsim = \succsim^*$ we have a contradiction which will prove the statement.

As $\succsim$ is rational, then there is a utility function $u: X \to \mathbb{R}$ that represents $\succsim$, then $\{x \in B: \forall y \in B, u(x) \geq u(y) \} = C^*(B, \succsim)$ but then $\exists B$ s.t. $x,y \in B$ and since $B \mapsto C^*(B, \succsim)$ then $u(x) \in C^*(B, \succsim)$ so $x \in C(B)$ hence $\succsim = \succsim^*$


texts: Must a EU bank pay 500€ to the ECB, if I deposit 100k€ into that bank?

texts:
Given that the current ECB reserve rates are negative (-0.5%), I suspect that if I deposit 100k€ into a EU commercial bank, that bank must in turn deposit my money at the ECB and pay 500€/year to ECB (negative interests).
Is that correct? How does the mechanism work?


texts: What is the point of a constant (thus known) inflation rate?

texts:
I have read somewhere (attributed to Milton Friedman) that a good practice of monetary policy is to maintain a constant inflation rate (of 3% per annum, say). What is the point of that? If everyone knows the constant inflation rate, would they not factor that in when pricing goods and thereby effectively eliminate the inflation?

As a toy example, suppose the Feb maintains the money supply $M(t)=M(0)e^{at}$ at time $t$ for some constant $a$ known to people. Then people will price the goods (including debts) $P(t)=P(0)e^{at}$ at time $t$ where $P:=(p_1,p_2,\cdots,p_n)$ is a vector of prices for $n$ goods. Then the ratio of the prices $P/p(1)=(1,\frac{p_2}{p_1},\cdots,\frac{p_n}{p_1})$ remains the same. What is the point of the targeted inflation?

I can think of one justification in a particular scenario for setting a target but of the money supply rather than of inflation which is the increment in price. If we know the quantity, so to speak, of the economy is growing at $Q(t)=Q(0)e^{at}$. Then it makes sense to increase the money supply as described above, so that people can still price the goods at $P(t)=P(0)$. But this is no price inflation. Besides, if the money supply is held constant and the quantity grow rate is known, people can just price the goods at $P(t)=P(0)e^{-at}$ and the price ratio still remains unchanged. I do not see the harm in price deflation.

The possible flaw in this setup is that the "speed" of the diffusion of the physical monetary supply amongst the non-bank entities is no greater than the "speed" of the transaction. We can eliminate this flaw and achieve infinite monetary diffusion speed and simultaneity of inflation by bringing all transactions onto digital platforms. People can set their algorithms to increase the prices at the target rate.

This question is related but different from the question Is zero inflation desirable?. The latter asked about the effect of keeping inflation at zero. My question asks whether targetting an inflation rate not necessarily zero that is to be known to all people is any different from zero inflation and its desirability.


texts: What are the relationships between price stability and long term economic growth?

texts: I was wondering what the links are between price stability and economic growth on the long term.


texts: Do property values capture producer choice in agriculture?

texts:
I am interested in conducting research into how climate change impacts the social welfare of a country, particularly how it affects producers of agricultural product. My immediate thought was that as the climate changes, certain crops will fare better under these new conditions and would generate a substitution effect towards these crops.

e.g. As temperatures rise, soybean becomes relatively more attractive than wheat in terms of yields and farmers would, over time, switch towards growing soybean so as to maximize rents.

After a discussion with a colleague, they suggested looking into property values of farms as these would encompass information about farmers' choices over time. I am not sure how to understand this connection formally. How would farmers switching crops be reflected in the property value of a farm?


texts: What are the advantages and disadvantages of second price auctions?

texts:
I am reading https://en.wikipedia.org/wiki/Vickrey_auction about second price auctions.

It seems counterintuitive to me that the winning bidder pays the
bidding price of the runner-up bidder, rather than their own winning
bidding price as in first price auction. What is the purpose of
that?
What are the advantages and disadvantages of a second price auction?
Especially when it is compared to a first price auction?
The wikipedia article also says

  Vickrey auctions are much studied in economic literature but uncommon
  in practice. A slightly generalized variant of a Vickrey auction,
  named generalized second-price auction, is used in Google's and
  Yahoo!'s online advertisement programmes.

Why does the internet advertising industry use second price auction,
instead of other auction types e.g. first price auction?


texts: Do capital goods have to be valued so that (discounted) real expected return on capital goods equal current present value of capital goods?

texts:
Let $P_k$ be the value of 1 quantity of a capital good. If one does not sell the capital good and keep it, the good provides interests.

In such a case, does standard macro say that all expected discounted real expected returns (or net present value of all future and present returns) be equal to $P_k$?


texts: Ricardian vs Non-Ricardian policy identification

texts:
I am reading Sala (2004) and I think I have found a mistake in the paper. On page 7 the author argues that one can differentiate between Ricardian and Non-Ricardian policy regimes by considering correlations between primary surpluses and their effect on real debt. See this picture.

Where $s_t$ is current primary surplus, $\alpha_t$ is the discount factor and $b_t$ is the real debt.

He says:

  if the response of $b_t$
  to $s_t$ is negative, the regime is Ricardian; if the response of $b_t$ to $s_t$ is nonnegative,
  the regime is Non Ricardian

While I agree with this, I don't agree with what he wrote in the picture I linked to. I.e that case 1 represents the Ricardian regime and case 2 the non-RIcardian regime.

In case 1 there is no correlation between current primary surplus ($s_t$) and future surpluses ($s_{t+k})$, thus the real value of debt is constant. How is this consistent with the quote above? To me, case 3, i.e the one where $\text{corr}(s_{t},s_{t+k}) < 0$ should be the Ricardian regime because high surpluses today imply low surpluses tomorrow.

Have I misunderstood the author or did he mean to write 'Case 2 and 3 allow for regime identification'?


texts:
A student wishes to minimize the time required to gain a given expected average
grade, , in her end-of-semester examinations. Let $\displaystyle {t}_{i}$ be the time spent studying
subject i ∈ {1,2}.

Suppose that the expected grade functions are $\displaystyle {g}_{1} ({t}_{1})=40+8\sqrt{{t}_{1}}$ and  $\displaystyle {g}_{2} ({t}_{2}) = 2{t}_{2}$.

Thus the individual's optimization problems is to choose ${t}_{1}$ and ${t}_{2}$ to minimize total studying time $ = {t}_{1} + {t}_{2}$ subject to obtaining a mean grade of  where

$\displaystyle m-\frac{[{g}_{1}({t}_{1})+{g}_{2}({t}_{2})]}{2}=0$

I need to solve for the optimal choices of ${t}_{1} , {t}_{2}$ and $$ in the case where the student wishes to obtain an expected mean grade of 70.

Working through the problem I end with

${t}_{1}=4$

${t}_{2}=42$

$T=46$

$\displaystyle\lambda=-1$

How would I interpret the lagrange multiplier in this case?


texts: What would the consequences of an economy-wide 500EUR/tonne carbon tax be?

texts:
I recently calculated that Finnish car owners effectively pay 500 EUR per every tonne of carbon dioxide emitted from the tailpipe of a car. This payment is caused by three taxes that are in practice proportional to the emissions of a car:

Tax when buying a vehicle (it's practically proportional to the stated emissions)
Yearly tax when owning a vehicle (it's also practically proportional to the stated emissions)
Tax when refueling a vehicle (it's directly proportional to the real emissions)

A comment stated that it would be interesting to speculate what the consequences of economy-wide 500 EUR / tonne carbon tax would be. (Sorry @gerrit, I stole your question.)

So, what would the effects of such a tax be?

My understanding is that it would cause a massive transition to either nuclear or renewables. Power would be created by either nuclear power, or wind power and solar power, complementing each other. The very-short-term variability of wind power (wind can suddenly stop) would be balanced by massive lithium-ion batteries. The long-term variability of wind power and the variability of solar power would most likely be balanced by power-to-gas technology, where the gas can either be synthetic methane or synthetic hydrogen. If hydrogen, it would be stored to underground reservoirs. If methane, the carbon dioxide required to create it and emitted by burning it would not be a waste but rather something to be recycled, also stored to underground reservoirs separately from the methane.

The price of electricity would become extremely variable: sometimes, it's free (when there's lots of wind and/or sunshine), at other times it's so expensive that it makes sense to construct grid energy storage based on power-to-gas.

Fossil natural gas would no longer be treated as a clean fuel. Instead, synthetic methane created from water electrolysis and Sabatier reaction would be used.

Steel production would shift to using hydrogen (created by electrolysis of water) instead of using carbon. In areas that require heating, heat would be created from seawater or ground source, using massive heat pumps.

New cars would most likely be either based on electricity (passenger cars) and hydrogen (long-haul vehicles). The electric cars could be used to balance the short-term variability of wind power, using vehicle-to-grid (so the separate grid-connected batteries might not be needed). Old cars could be still used, as evidenced by the massive Finnish car fleet running mostly on gasoline and diesel, even though there is an effective 500 EUR per tonne carbon tax.

Aviation would use biofuels, the production of which would not be enough to displace all current oil uses, but would be enough to displace all current aviation oil use.

Forest owners would let the forest grow to a very high density, and when forest is chopped eventually after ending its growth, there would be lots of sawlogs that can be used to construct buildings in a manner that retains the carbon. The forest-based carbon sequestration could offset the emissions of cement production, which would still be necessary for a functioning world economy.

Thus, I believe it would not be a major disaster to world economy. In fact, it might be a good thing: it would cause a rapid mitigation of dangerous climate change.

It could be a disaster, however, to nations where the entire economy is built on export of fossil fuels.

Is my understanding correct? Or, would some of the technologies I listed be so expensive that it could still be a worldwide disaster?


texts: Why is the yield curve typically concave?

texts:
The normal yield curve is usually drawn concave. Why is this typically the case?
My current understanding is that long term bonds have higher interest rate risk because a higher percentage of its outflows come from coupon payments. For example, a 1 month bill price won't change much for a change in interest rates since its price is dominated by the par value which will be paid back in a month.
Applying the logic to convexity vs. concavity: as time to maturity increases, the percentage of a bond's price which comes from the final par value payout decreases slower and slower. Therefore, the risk premium should increase slower and slower creating a concave yield curve.
Is this logic correct or is there more to it?


texts: Why does a model that is used for policy analysis needs its shocks and parameters to be structural (= invariant) to the shock under consideration?

texts:
In their paper, " New Keynesian Models: Not Yet Useful for Policy Analysis"

V. V. Chari, Patrick J. Kehoe, and Ellen R. McGrattan

argue that one needs a structural model in order to analyse the effect of economic policy. More specifically, they argue that it needs enough microfoundations consistent with the data such that both the models's shocks and parameters are structural. But in my opinion, they don't really explain why that is the case.

I understand that IF it is the case, you can do policy analysis, and the results of this analysis will always apply, because the model is unchanged nevermind any policy. This was the Lucas critique, on models that used adaptive expectations.

Why is this the case? Isn't it reasonable to assume that, in addition to many economic variables, also many parameters that govern micro behaviour will be influenced by a policy shock? Which contradicts their claim? Or do they only say that those parameters related to the shock under consideration cannot change? Why not? Isn't it wishful thinking one can ever settle down on a structural, fixed, microfounded model, as too many parameters governing micro behaviour depend on too many things like institutions, policy, technology, ... ?

Additional question: expectation formation is a microfoundation I guess. So, if we use the adaptive/heterogeneous expectations approach instead of the rational expectation assumption: I guess if an agent switches from a fundamentalist rule to an trend following rule (see the book and papers by Cars Hommes and De Grauwe and Zi), this is a structural change to the model? Or is this not structural, because the switching is a structural part of the model? However, it is exactly this endogenous switching that happens in response to (policy) shocks. How does this switching relates to the condition that models should be structural in their shocks and parameters to be used for policy analysis?

Some more context below:

"We begin by clarifying the distinction between reduced form and structural shocks.
This distinction is critical in policy analysis. The reason is that in order to do policy analysis,
we need to predict the consequences of changes in policy both for outcomes of the standard
economic variables and for welfare. Such a prediction is possible only with a structural model.
Speci…cally, a structural model must have two ingredients. First, the relevant elements of
the model— including the shocks— must be invariant with respect to the policy interventions
considered. Second, the shocks must be interpretable, so that we know whether they are what
could be thought of as “good shocks”that policy should accommodate or “bad shocks”that
policy should o¤set. Shocks which have both of these properties are referred to as structural
shocks and ones that do not are referred to as reduced-form shocks.

Proponents of the New Keynesian model argue that it is promising for two reasons. It
represents a detailed economy that can generate the type of wedges we see in the data from
interpretable primitive shocks; and second, it has enough microfoundations that both their
shocks and parameters are structural, in that they can reasonably be argued to be invariant
to monetary policy shocks. A model with both of these features would potentially be useful
for monetary policy analysis."