Is there a school of thought or concept that acknowledges that people aren't rational actors when it comes to economic decisions? People are subject to all sorts of cognitive biases.

For example:

Advertising works, and not just by making people aware of a product,
but by appealing to emotional quirks.

People are subject to psychological pricing.

It seems clear that people aren't entirely cold calculating rational agents, calculating the maximum utility and acting accordingly.

Is this acknowledged in any economic theories, or is it more or less ignored?

Yes this is a blossoming area of research in economics and it spans approaches from psychology to game theory, social theory, and cultural biases.

A lot of these approaches fall under the rubric of "Behavioral Economics".  Unlike classical market economics which often begins with assumptions around individual and collective rationality, behavioral economics seeks to study how economic decisions are actually made by individuals and groups (i.e. it does not take utility-maximizing rationality as an assumption but instead studies its role in animating economic decisions and systems).

"Irrational" behavior should not be confused with unexplainable or unpredictable behavior.  A simple example is why people buy lottery tickets.  This may be irrational under classical utility theory, but it is explainable and can be modeled, tested, and incorporated into larger economic frameworks like market options pricing by using behavioral economics.


Continuation value versus utility in asset pricing Is there a difference between continuation value ($V_t$) and utility ($U_t$) except for a possible scaling / difference in units? My question refers to the consumption-based asset pricing literature.

In standard time additive power utility settings, people seem to only talk about utility (e.g. $U_t=u(C_t)+\beta E_t[u(C_{t+1}]$). In recursive utility / Epstein-Zin-Weil settings, people often refer to a continuation value (e.g. $V_t=((1-\beta)C_t^{1-\rho}+\beta (\mathcal{R}_t(V_{t+1}))^{1-\rho})^{1/(1-\rho)}$).

It seems to me that both are fairly similar. The only reference I could find on the topic is the asset pricing book from Back (2010), in which (intuitive definitions) utility seems to be a utility measure in "utility units" while continuation value seems to be a utility measure in "consumption good units", and both are related via $U_t=u(V_t)=\frac{V_t^{1-\gamma}}{1-\gamma}$.

(Please note: Back confusingly talks about a continuation utility and uses a different notation, the one posted here is inherited from standard references. Also, you can find his book with this link.)

The term "continuation value" is usually used to refer to an aggregation of utility in future periods. In the case of $U_t = u(C_t) + \beta E_t[u(C_{t+1})]$,
$u_t$ is the flow of utility per period and $U_t$ is an aggregate of $u_t$ over all time periods $t$ and $t+1$. The quantity $\beta E_t[u(C_{t+1})]$ is the expected discounted continuation value and is in the same units as $u(C_t)$.
Recursive utility works similarly. The difference is that utility over multiple time periods can't be easily aggregated. In the expected utility case, it's aggregated using a weighted sum of expectations. To see this, I'll show how you can write an expected utility function in recursive form. This should make the continuation value used in discussions of recursive utility easier to understand.
Again, let $u_t$ be the flow of utility per period. Suppose that
$U_t$ is an aggregate of $u_t$ over all time periods from time $t$ into the future.
Sometimes $u_t$ is referred to as the "per-period utility function". An economic actor making decisions in time $t$ maximizes $U_t$, where $u_\tau$ for $\tau = t, t+1, t+2,...$ are simply the components that make up $U_t$.
Consider the case of CRRA utility:
$$
U_0 \equiv E_0 \sum_{t=0}^\infty \beta^t \frac{C_t^{1-\gamma}}{1-\gamma}.
$$
Let $u_t = \frac{C_t^{1-\gamma}}{1-\gamma}$ and let
$$
U_t = E_t \sum_{\tau=t}^\infty \beta^{\tau-t} \frac{C_\tau^{1-\gamma}}{1-\gamma}.
$$
Then,
$$
U_t =
E_t \sum_{\tau=t}^\infty \beta^{\tau-t} u_\tau
$$
and we can represent utility here recursively,
$$
U_t = u_t + \beta U_{t+1}.
$$
In the expected utility case of CRRA, $U_t$ is simply a weighted sum of future per-period utility. Epstein-Zin utility is a case in which $U_t$ is an aggregate of future per-period utility, but it cannot be expressed as a simple weighted sum.
Rather, $U_t=((1-\beta)C_t^{1-\rho}+\beta (\mathcal{R}_t(U_{t+1}))^{1-\rho})^{1/(1-\rho)}$,
where $\mathcal R$ is a "certainty equivalent" operator.


Economic schools of thought VS Econometrics From  Wikipedia:

  In the history of economic thought, a school of economic thought is a group of economic thinkers who share or shared a common perspective on the way economies work

Why is it that different economic schools of thought are  still taught in spite of the fact that we now have data to test their ideas and philosophies of the economy and see if they really line up with reality?

I think I can explain the problem as to why the schools persist.  For simplicity we will limit ourselves to the Marxist, Austrian, Neoclassical and Neo Keynsian schools.  I am not sure where to put the Feminist school except under the broad heading of heterodox with Marxists and Austrians as I don't think of it as a school so much as an attitude or direction of thinking.  The same thing would be true for Green economics, it isn't so much a school as a domain.  There are many small groups out there.

For starters, economics is a broad umbrella that prefers dissent and maybe even vocal and extensive dissent.  Part of economics is part of the humanities and part of economics is in the sciences.

Austrian economics as thought through by von Mises argues that there can be no way to measure what they are saying and so they are part of the humanities.  The neoclassical and the neo Keynesian school say any claim that is stated should be measurable and falsifiable, so it is in the sciences.

That said, any serious review of von Mises and related writers would tend to drive one down the path well laid by Leonard Jimmie Savage and his personalistic statistics and in doing so would have a complete empirical methodology.  I believe the branch of the Austrian school that says things cannot be measured simply hasn't read enough statistics.

The two primary schools, the modern Keynesian and Classical forms, are empirical and the reason you cannot rule one out is that both are empirically supported even though they are contradictory.  This is similar to the problem between quantum physics and relativistic physics.  They make contradictory assertions.  It is impossible that both are true, except where they don't overlap.  Yet they both work everywhere else.

The best tool for model selection in that it is both disciplined and founded on well understood mathematical principles is Bayesian model selection.  Non-Bayesian methods assume that you know the null model and you assert the model is true.  This works great for binary problems but is terrible for non-binary problems.

If we define a model space as indexed on the set $I$, with $i\in{I}$ and a set of models, $M$, so that $\mathcal{M_i}\in{M}$ and with vectors of parameters $\theta_i\in\Theta_i$ in a parameter space $(\theta_i,\mathcal{M}_i)\in\Theta\times{M}$ then we can solve the problem of the best model.  Best in this case being understood as being most probably close to the data generating function.

The probability that a model is the true model, from a set of models and given a data set, $X$, is $$\Pr(\mathcal{M_i}|X)=\int_{\theta_i\in\Theta_i}\frac{\Pr(X|\theta_i;\mathcal{M}_i)\Pr(\theta_i;\mathcal{M}_i)}{\sum_{\mathcal{M}_i\in{M}}\int_{\theta_i\in\Theta_i}\Pr(X|\theta_i;\mathcal{M}_i)\Pr(\theta_i;\mathcal{M}_i)\mathrm{d}\theta_i}\mathrm{d}\theta_i$$.

While this methodology works generally and works especially well on a problem by problem basis it won't answer which school is best since it will provide contradictory solutions across specific problems.

What is really needed is a better, overarching explanation of what triggers Keynesian-like effects and what triggers Classical-like effects.  My suspicion is that it is stochastic shocks in the planetary budget constraint compared to where that constraint is expected to be at by the individual actors.


Is there a general name for the setup in which payoffs are not known exactly but players try to influence each other's perception of the payoffs? A recent question elsewhere made me look at the "madman strategy" which actually consists of trying to make the opposite player think that he is playing a game of chicken instead of prisoner's dilemma. This can only work, of course, because in reality the payoffs are not known apriori, so an inversion of the non-cooperation payoff with the "tentation" payoff does this game switch.

Is there a general name for a "meta-game" (my term) situation in which the payoffs are not known exactly and players are trying to influence each others' perception of the payoffs?

What players are trying to do is always up for interpretation, it is not coded into the mathematics of game theory.

The madman strategy can be modelled as a Bayesian game, with different types having different payoffs, and one player sending a signal about their type, the other player observing the signal. A situation in which types are indistinguishable based on their signals is called a pooling equilibrium.


If $x \succsim_i x_i^*$ then $p \cdot x_i\ge w_i.$ (MWG 16.C.2) (MWG 16.C.2) Suppose that the preference relation $\succsim_i$ is locally nonsatiated and that $x_i^*$ is maximal for $\succsim_i$ in set $\{x_i \in X_i: p \cdot x_i \le w_i\}$. Prove that the following property holds: "If $x \succsim_i x_i^*$ then $p \cdot x_i\ge w_i.$"

Locally nonsatiation means that for every $x_i \in X_i$ and $\epsilon >0$, there exists $x_i' \in X_i$ such that $||x_i - x_i'|| < \epsilon$ and $x_i' \succ x_i$.
I think that I need to prove that if $x_i \sim_i x^*_i $ for $x_i \not= x_i^*$, then it is possible that $p\cdot x_i = w_i$ because I already know that if $x_i \succ x_i^*$, then $p\cdot x_i > w_i$.
I am stuck and  cannot proceed. Can anyone give me some hint for this question?

Hint: Prove by contradiction. That is, suppose $x_i\succsim_ix_i^*$ but $p\cdot x_i<w_i$, show that this would lead to a contradiction of $x_i^*$ being maximal for the feasible set.


Concentration Measures There are several metrics used to identify market power. Such as ...

the 'n' concentration ratio (the proportion of overall sales given by the top n firms) and the Herfindhal index.

However, there is also the Price cost margin (Lerner index).

These indicators may not always agree with one another.

Is there some way we can understand which of them is most relevant as an indicator of market power? For example by examining the local characteristics such as what kind of imperfect competition is present, and consumer demand patterns?

Unfortunately, I'm not sure there's a clear answer to your question, since it so often depends on what the specific needs are for the specific project. Overall, there are a number of different ways to try and measure concentration and market power (as you note in the question).

That said, there's definitely a lot of interplay between different measures, but often these measures can be reworked to allow for looser (or different) assumptions. For example, one of the more well known merger analysis tools currently used by the DOJ and FTC, the Upward Pricing Pressure test is traditionally linked to Bertrand competition. However, as the creators of the measure note, that link is often overstated, and the test can be used in cases where Cournot competition is assumed.

Moreover, UPP is closely linked to other measures, such as diversion analysis, for which there are many different tools to use to measure it. One method is to use a survey of consumers, (seen, for example, here,) though that of course comes with drawbacks. Instead, market shares can be used, but so can historiical data from switching patterns. Alternatively, you can look at second choice data and/or price and demand elasticity properties, or more abstractly data from stock-out events.

I'm sorry to get stuck in the weeds of merger analysis there, but I think it's an informative example of how many different ways there are to get at the same underlying ideas. Ultimately, what's "best" really depends on the specifics of your project, the data available, and how well you can defend the choice made.

Let me know if there's something more directly relevant that you'd like addressed, but a lot of the theoretical complementarities can be seen only when one particular interest is isolated and examined.


Proof that stochastic discount factor is positive in complete markets I am looking for a reference (with a proof possibly) to understand why the completeness of markets implies that the stochastic discount factor is strictly positive in the context of intertemporal consumption, i.e. when a agent FOC implies
$$
p_t = \mathbb{E}\left[\beta \frac{u'(c_{t+1})}{u'(c_t)} x_{t+1}\right]
$$
where $p_t$ is the price of an asset giving $x_{t+1}$ in the following period.

...the completeness of markets implies that the stochastic discount
factor is strictly positive...

This statement is not quite correct.
Rather, the agent's optimality condition implies that market is complete with respect to the agent's consumption-relevant states, and that the SDF must be strictly positive on those states.
The SDF is, more or less, same as Arrow-Debreu prices on consumption-relevant states, which must be strictly positive. Otherwise equilibrium would not exist. Marginal utility cannot be zero in equilibrium.
(SDF is the Radon-Nikodym derivative of AD prices with respect to the physical measure. SDF is strictly positive if and only if AD prices are.)
For simplicity, assume agent's consumption is $\omega$-contingent, where $\omega$ belongs to a finite set $\Omega$.
Then the FOC
$$
p_t = \mathbb{E}\left[\beta \frac{u'(c_{t+1})}{u'(c_t)} x_{t+1}\right]
$$
becomes
$$
p_t = \sum_{\omega \in \Omega}  \beta \frac{u'(c_{t+1}(\omega))}{u'(c_t (\omega))} \cdot x_{t+1} (\omega) \cdot P(\omega).
$$
The quantity
$$
\beta \frac{u'(c_{t+1}(\omega))}{u'(c_t (\omega))} \cdot P(\omega)
$$
can be viewed as the price of a claim with payoff $1_{\{ \omega' =\omega\}}(\omega')$ (i.e. a digital option that pays 1 if $\omega$ realizes and 0 otherwise).
Such claims are exactly the Arrow-Debreu securities in the market of $\omega$-contingent claims.
(If the payoff $x_{t+1}$ is contingent on, say, state $(\omega, \nu)$, where agent's consumption is invariant with respect to $\nu$, then market is complete only with respect to $\omega$-contingent claims.
Claims whose payoffs depend on $\nu$ cannot be replicated, i.e. market is not complete with respect to such claims.
In the FOC, the $\nu$-coordinate would be integrated out.)
In equilibrium, the FOC becomes the asset pricing equation
$$
p_t = \mathbb{E}\left[\beta \frac{u'(c_{t+1})}{u'(c_t)} p_{t+1}\right].
$$
This means, in the market of AD securities of $\omega$-contingent claims, the (representative) agent holds the portfolio that is the asset itself.


How do stockbrokers purchase shares? Do they use "Direct Stock Plans," or some other method?

Not sure if this is the right place to ask, but I'm curious.

Technically, a stock broker brokers stock purchases: they execute transactions for clients. That is, they buy on the behalf of clients. (This is not true for bonds, where the practice is that they sell clients bonds from their inventories.)

Direct stock purchase plans are aimed at individuals, to the best of my knowledge. Brokers might help set up such purchases, but historically they existed as a way to buy equities without using a broker.

A broker will transact in two forms.

Primary market: buying shares directly from the company, such as in an initial public offering (IPO) or secondary offering.
Secondary market: buying shares from other entities on stock exchanges or other markets (“dark pools”, etc.).


Do circular invoices count in GDP? I'm trying to understand GDP and what it means.
Say that there are two US software companies, Foo Inc and Bar Inc. Foo Inc produces software and charges Bar \$1 million for its usage, while Bar Inc produces its own software product and charges Foo Inc the same amount of \$1 million.
While money did change hands, the profits of both companies remained the same, as they both incurred the same amount in revenue and expenses.
Would the national GDP increase by \$2 million because of these transactions?

A firm's contribution to GDP isn't revenues. A firm's contribution to GDP is roughly the sum of the wage bill and the money earned by capital (debt (interest) and equity (economic and not accounting profits)). That is, profits + interest payments + wages (look elsewhere for a more precise definition). Your example doesn't really have enough to go on to estimate the GDP impact.
The contribution could be zero. This can and did happen in the dot com bubble when companies would agree to buy advertisements on each other's sites of equal amounts to boost sales figures. This increases revenues and expenses by the same amount with no changes in wages, profits, or interest expense (maybe minimal changes in practice).
The contribution could also be arbitrarily large. Imagine a firm that makes a buys a piece of software for \$2 million that allows them to make \$10 billion in sales (no other expenses and sales and no profit without this expense). That would make a GDP contribution $9.998 billion. Now imagine splitting that company in half so that two different firms each make \$5 billion in additional sales after buying \$1m in software.
In summary, the impact on GDP depends and there isn't enough detail here to be more specific.


Does economic growth always implies investments in infrastructure? For my course I'm analysing the problem of empty retail stores. I need to analyse how my alternatives to solve the problem would change the important factors about the problem in uncertain scenarios.
We chose to analyse how our solutions(investment in training, knowledge platforms and strategic growth) would affect the factors(investment in IT, average revenue and the amount of empty m2) in the doom scenarios with positive and negative economic growth and positive and negative investment in infrastructure.
One of my teachers that saw the presentation about the analysis said that he couldn't see economic growth happening without investment in infrastructure. Don't mind him if he's wrong because he actually teaches us how to give presentations.
But the following question arose: Does economic growth always implies that there will be significant investments in infrastructure, or can I see both factors as enough decoupled to analyse them separately?

In economics, we commonly use the formula for GDP as a Indicator of "economic growth"

The GDP formula is: GDP=C+G+I+NX

Where C is equal to all private consumption, or consumer spending, in a nation's economy, G is the sum of government spending, I is the sum of all the country's investment, including businesses capital expenditures and NX is the nation's total net exports, calculated as total exports minus total imports (NX = Exports - Imports).

Notice how we can have an increase in GDP by increased consumption or government spending. So technically we can see economic growth without any  investment in structure (which would be represented by an increase in I) from a mathematical perspective.

Note how this is a static measurement of economic activity, which we cannot make any predictions regarding the future. However you may want to look at the Solow-Swan Model regarding economic growth with capital accumulation and technological change.

Hope this helps.


$\alpha$ condition and choice structure I am trying to prove a statement that if $c_R$ is a choice structure, then it must satisfy Sen's $\alpha$ condition.

However, if $X=\{a,b,c \}$, I can construct some choice structure like $c(\{a\})=a,c(\{b\})=b, c(\{c\})=c, c(\{a,b\})=a,c(\{b,c\})=b,c(\{c,a\})=c,c(\{a,b,c\})=a$.

Such choice structure clearly violates the $\alpha$ (shrinking) condition.

So can someone point out where do I make a mistake? Or is the statement assuming the relation $R$ to be rational?

Thanks!

A choice structure can be whatever it wants to be. A choice structure that is rationalizable by a preference relation must (among other things) satisfy Sen's $\alpha$.

So if you want to show that a rationalizable choice structure satisfies $\alpha$ then you can show that any that satisfies WARP will also satisfy $
\alpha$.

I recommend Kreps or the UPitt notes for more info on the relationship between choice structures and preference.

http://www.pitt.edu/~luca/ECON2100/lecture_02.pdf


Alternative normalisation to triangular restriction on cointegrating vectors Johansen recommends that cointegrating vectors must be normalised for inference making purposes. All software packages use triangular normalisation of the cointegrating vectors i.e. the top $r$ by $r$ block of the estimated $\beta$ matrix is an identity matrix. Usually, this is achieved by deriving the row echelon form of the estimated long-run equations (cointegrating equations matrix).

Does any one know of any other normalisation forms? or methods to formulate different normalisation?
Thanks

The issue is not so much normalization as it is identification of the parameters of the co-integration vectors. The estimated co-integration vectors define the co-integration space, but many other sets of vectors span this same space.

In the case where you have a single co-integration vector, normalization is sufficient for identification. This is not the case when you have more than one vector in which case you need to impose restrictions, the most common set of identifying restrictions being the triangular normalization you mention.

Johansen (1995, section 2 theorem 3) provides a set of algebraic conditions which are fairly easy to compute (but tedious to type) to verify that a set of restrictions imposed on the co-integration vectors is identifying.

It is also possible to identify the co-integration vectors by imposing restrictions on the adjustment matrix ($\alpha$). This fairly recent overview by Johansen might be useful.

Reference: Johansen, Søren. "Identifying restrictions of linear equations with applications to simultaneous equations and cointegration." Journal of econometrics 69.1 (1995): 111-132.


Having trouble solving system of equations through matrix approach So I have this system of reaction functions:

$$s_1 = 2 + \frac{1}{3} s_2$$
$$s_2 = 7 + \frac{1}{8} s_1$$

I have to solve this through inverse matrix and confirm the result through Cramer's rule. The result is I'm getting awkward values:

$$ \begin{bmatrix} s1 \\ s_2 \end{bmatrix} = \begin{bmatrix} 52.6 & 2.6 \\ 54.6 & 15.6 \end{bmatrix}$$

I don't think so this is the correct result since Cramer's rule cannot really be applied to this system. Any suggestions?

You may find better help in the Math SE, but let's see if we can help here.

So we can arrange your system as such:

\begin{align}
 s_1 - \frac{1}{3} s_2 & = 2 \\
 -\frac{1}{8} s_1 + s_2& = 7 \\
\end{align}

So we form the matrix setup:

$$\begin{bmatrix}
        1 & -1/3  \\
        -1/8 & 1  \\
        \end{bmatrix}
\begin{bmatrix}
        s_1 \\
        s_2 \\
        \end{bmatrix}
=
\begin{bmatrix}
        2 \\
        7 \\
        \end{bmatrix}
$$

You can multiply the matrices out to see that you get the same system.

The first step of solving any system, regardless of method, is to always check for linear dependence of the coefficient matrix.

$$
\det
\begin{bmatrix}
        1 & -1/3  \\
        -1/8 & 1  \\
        \end{bmatrix}
=
(1 \cdot 1) - (-1/3 \cdot -1/8) = \frac{23}{24} \neq 0
$$

So Cramer's rule is indeed useable here. To solve for $s_1$. You replace the column for $s_1$ with the answer matrix and divide the determinant of that by the determinant of the original coefficient matrix. Use a similar process for $s_2$

$$
s_1^* =
\frac
{\det
\begin{bmatrix}
        2 & -1/3  \\
        7 & 1  \\
        \end{bmatrix}}
{\det
\begin{bmatrix}
        1 & -1/3  \\
        -1/8 & 1  \\
        \end{bmatrix}}
= \frac{\frac{13}{3}}{\frac{23}{24}} = \frac{104}{23}
$$

$$
s_2^* =
\frac
{\det
\begin{bmatrix}
        1 & 2  \\
        -1/8 & 7  \\
        \end{bmatrix}}
{\det
\begin{bmatrix}
        1 & -1/3  \\
        -1/8 & 1  \\
        \end{bmatrix}}
= \frac{\frac{29}{4}}{\frac{23}{24}} = \frac{174}{23}
$$

And then we're done. Plug in the answers and make sure they work.


The instrument in "The Colonial Origins of Comparative Development" I am hoping to understand when an instrument is appropriate. For the purposes of this question, I'm considering a simplied version of the model in AJR (2000):
$$\begin{aligned}\text{GDP} &\sim \text{Exprop} + \text{Latitude} \\
\text{Exprop} &\sim \log{\text{Mortality}} + \text{Latitude}\end{aligned}$$
My questions are:

Does latitude need to be included? (If we believe that latitude has a causal effect on settler mortality, expropriation, and GDP, then my guess would be yes, since leaving it out would leave a correlation between log mortality and the residuals of GDP, through the effect of latitude?). Similarly/in general, would we need to control for anything that could possibly affect both the instrument and the outcome?
Do we need to assume that the entire causal effect of log mortality on GDP is mediated through expropriation? Would it not be an appropriate instrument if the log mortality -> GDP causality could be mediated through something else (e.g. genetic diversity, folk traditions not related to institutions, etc)?

You should include all controls in the second stage, even if they are not instruments.
The entire effect of log(mortality) should be mediated through Exprop.  This does not mean there cannot be other things causing GDP or Exprop, but log mortality cannot have a effect on GDP except through Exprop.


Does investing in the stock market contribute to economic growth? I am morally opposed to economic growth:  I think that for the good of our planet we need to be shrinking human impact in pretty much every way, not increasing it.
If I invest in the stock market, I am placing a bet that growth will continue for some time.  I think this is a reasonable bet to place, despite my opposition to it.
However, does my investment actually contribute to economic growth?  In particular, could anyone give an analysis of the likely impacts of either

Debt elimination (ex: paying off mortgage early)
Keeping the money in a savings account.
Buying government bonds.
Buying index funds.

on economic growth?

tl;dr
Yes, investing into stock market has positive impact on growth. First, before going any further, investing into stocks is from an economic perspective just a form of saving. Consequently, following the literature this answer will be repeatedly referring to saving in general.
In economics, there are two main theories of economic growth. An exogenous Solow-Swan growth theory and endogenous (eg Romer model) - see Romer Advanced Macroeconomics Ch 1-3. In both of these strands of literaterature saving impacts economic growth positively but under Solow-Swan increase in saving rate causes level increase in economic output which will show up as higher economic growth but in order to raise economic growth permanently a one would have to continuously increase. On the other hand under endogenous growth models increase in savings rate can have permanent positive effect on economic growth.
Effects of Savings Under Exogenous Growth
To illustrate the mechanisms at play consider augmented Mankiw-Weil-Romer (1992) Solow-Swan model given by:
$$ Y(t) = K(t)^{\alpha}H(t)^{\beta}(A(t)L(t))^{1-\alpha - \beta} \tag{1}$$
Where $Y$ is economic output (change of which is economic growth), and economic output varies positively $K$ is stock of capital, $H$ is stock of human capital (i.e. education) $A$ is the stock of technology (assumed to be growing at an exogenously given rate $(A (t) = A (0)e^{gt})$ and $L$ the stock of labor (growing at exogenously given rate $(L(t) = L (0)e^{nt})$. The Greek letters are exogenously given parameters that depend on the nature of society's production function (with $\alpha +\beta <1$). Hence, when stock of capital, education, technology level or labor force expands economy will experience economic growth.
Now in order to see how savings plays a role in all this we can first define everything in terms of effective labor (e.g. $Y/AL= y$, $K/AL=k$ and $h/AL=h$), and using the fact that capital (and human capital as well) is determined by investment which is macroeconomically equivalent to saving we get that:
$$ \dot{k}(t) = s_k y(t) - (n + g + \delta_k)k(t), \tag{2}$$
$$ \dot{h}(t) = s_h y(t) - (n + g + \delta_h)h(t) \tag{3}$$
where $s_k$ is share of saving invested in physical capital and $s_h$ share of saving invested in education, whereas $\delta_k$ is depreciation of physical capital and $\delta_h$ erosion of human capital (e.g. loss skills over time). For simplicity it will be further assumed that $\delta_h = \delta_k=\delta$. Substituting the evolution of capital and human capital into the per capita version of (1) we get:
$$\ln y =  \ln A(0) + gt -  \frac{\alpha + \beta}{1-\alpha -\beta} \ln(n + g + \delta) +  \frac{\alpha }{1-\alpha -\beta} \ln s_k + \frac{ \beta}{1-\alpha -\beta} \ln s_h$$
Now stock market is stereotypically associated with investments into physical capital so I will focus mainly on relationship between output and physical capital. Hence, let us set growth rate of technology, population and to simplify calculation also depreciation to zero and let us assume technology stock and saving rate for human capital are fixed so their time derivates are zero. We end up with expression:
$$\ln y = \ln \bar{A} +  \frac{\alpha }{1-\alpha -\beta} \ln s_k + \frac{ \beta}{1-\alpha -\beta} \ln \bar{s_h} $$
Taking time derivative gives us:
$$ \frac{\dot{y}}{y} = \frac{\alpha }{1-\alpha -\beta} \frac{\dot{s_k}}{s_k}  $$
$\frac{\dot{y}}{y} $ is just continuous version of growth rate and consequently we can see that output growth depends on growth in savings rate. Furthermore, since $\alpha + \beta<1$ the relationship will be strictly positive}.  However, a caveat here is that saving rate cannot growth forever as it has to be between $0\leq s \leq1$ since it is a proportion of income not consumed, so any increase in saving rate will increase the growth rate but you can only increase your saving rate to the point you devote your whole income to it. Visually a simulation of an increase in savings rate would produce the following result (see Romer Advanced Macroeconomics pp 20 - please note the simulation is based on simplified version of an above model so the precise shape of those curves might be different but the point carries over):

However, this being said  higher level of saving will still increase level of output which will lead to temporarily higher growth just the effect won't be permanent and the only thing that can permanently increase the per capita growth rate in exogenous growth rate model is an increase in rate of technological progress.
Effects of Savings Under Endogenous Growth
While the theory above is more widely accepted, recently this theory was expanded on by endogenous growth theory. I won't go into such deep detail into endogenous growth theory as models there get far more complicated, but I will try to explain in in relation to the exogenous growth model above.
In short, the gist of endogenous growth theory is that it rejects the exogenous growth theory assumption that technology develops at some exogenously given rate and society cannot do anything to speed up technological progress. Endogenous theory rejects that view and argues that investments in capital, education, or having larger labor force (and thus be able to devote more labor to R&D projects) can increase the rate at which technology accumulates and so $g$ will be also function of investments into capital, education and share of labor devoted to R&D (see discussion in Romer Advanced Macroeconomics Ch 3).
Now since you are interested primarily in saving via stock market the first relationship will be of greatest interest to you.  Now endogenous growth literature argues that the link between growth and saving here is mediated by either learning by doing it (e.g. investing money into building a cargo ship allows firms to learn how to better produce cargo ships - see Arrow, 1962). Next there will be link because firms can use portion of that investment to finance R&D that then improves productivity of either capital or labor depending on what sort of production function industry has (e.g. see Romer 1990).
In economics there is still debate between the exogenous and endogenous growth camp, because given data we have it is very hard to statistically distinguish between endogenous and exogenous growth empirically (we have solid evidence for Solow-Swan model but it is difficult to distinguish transitory effect of saving from a permanent one with limited data), but recent Nobel Prize in Economics awarded to Romer in 2018 for his work on endogenous growth theory shows that this theory is becoming more dominant.
Summary
To sum it up, both major strands of economic literature shows saving whether through investment in stocks or in various other ways (putting your money in bank etc) has positive effect on economic growth. However, under exogenous growth theory this effect is just transitory whereas under endogenous growth theory there might be long lasting effect.
However, given that the economic literature on endogenous growth suggest that the link between saving and economic growth is mediated via investments in R&D and learning by doing, if you want to minimize economic growth of society you can do your research and invest exclusively into stocks of companies that devote as little of their budget to new research as possible. This won't avoid effect due to learning by doing but it would almost certainly result in lower long term economic growth than investing into stock of companies that invest heavily into research.


In a competitive equilibrium, can price of a commodity ever be zero? I don't think they can be, but I'm not very sure. Are their special cases where the equilibrium is competitive even when prices are zero?

It depends on the assumptions you make.

If you assume that preferences are locally insatiable then no.

Without this assumption, it is easy to construct counterexamples.  Consider an economy with two consumers ($A,B$) and two goods ($x,y$). Both consumers have preferences represented by their utility function
$$
U_i(x_i,y_i) = \min(x_i,1) + y_i.
$$
If the initial endowments are such that the total supply of $x$ is larger than 2 then the equilibrium price of $x$ is 0. (The numeraire is the good $y$.)


Help me understand scarcity I'm struggling with what should be a simple concept: scarcity. For some reason, I just can't wrap my head around the fact that in this highly advanced technological society of ours, we can't fix scarcity.

Sure, we might not be able to produce an "infinite" amount of things. But then again, nobody wants an infinite amount of things. That's an absurd notion, and an even more absurd foundation to build a principle on.

Say, everybody wanted 4 cars on average. Some people might want less, some more. Can we really not ramp up production to facilitate this wish? Couldn't we ramp up production to dig out even more gold? To mine for even more diamonds? To grow even more food? To collect even more water?

We live in an age of advanced technology. Of algorithms, artificial intelligence and of highly automated large-scale production. How am I to believe that, given all these abilities, we couldn't achieve a solution to a reasonable form of scarcity? By reasonable I mean scarcity that makes sense within a human context: nobody wants an "infinite amount of cars", at least the vast, vast majority of people don't, and the few outliers that do shouldn't be relevant in an economic principle of this significance.

This seems like an idea that would have made sense a century ago, but not anymore. How and why does is still hold up, considering our unprecedented potential to produce goods?

What you are saying is that the marginal utility of one additional good (car, or coconut) decreases and tends to zero. I believe everyone agrees with that.

The reason why scarcity matters is not that people can't be satisfied with a finite consumption, but that most individuals currently consume below their satiation level and would be happier with one additional unit. Most people would prefer a bigger house, a more luxurious car, more clothes, etc., even if they would finally be satisfied with some finite level.

Regarding your observation "Can we really not ramp up production to facilitate this wish?", the answer is no: it is still too costly to produce cars, houses, clothes etc. to accommodate everyone's wishes. If we were able to produce costlessly the amount of goods required to satisfy everyone's satiation level, the problem of scarcity would be solved (and economics would disappear as a science), but we are clearly far from this situation.


Confidence Intervals for Elasticity in Simple Linear Regression I'm pretty sure this is a very simple question that I am missing something obvious. I have a simple linear regression with multiple independent variables. I want to calculate the elasticity (no problem - $\frac{\partial y}{\partial x} \cdot \frac{x}{y}$), but also report the confidence interval for the elasticity. I know it's straightforward to compute the confidence interval for $\beta$ ($\hat{\beta} \pm t^{*}_{\alpha} \cdot \sigma_{\beta}$ ). But for the confidence interval for the elasticity, would it be the same range? Or do I need to account for the transformation ($\beta * x/y$)?

If I understand correctly, what you are proposing is estimating:
$$y = \gamma_0 + \gamma_1 \cdot x + \xi $$
and then using the confidence interval of $\gamma_1$ to estimate the range of elasticities:
$$ [\frac{\gamma_1 - 2 \cdot \sigma{\gamma_1}}{y} \cdot x, \frac{\gamma_1 + 2 \cdot \sigma{\gamma_1}}{y} \cdot x] $$

This is wrong, essentially because of Jensen's inequality ($E[f(x)]\neq f(E[x])$). You should absolutely take into account the non-linear uncertainty when calculating the confidence interval. Fortunately, this is easy. If you run the regression estimate of $$\ln(y) = \beta_0 + \beta_1 \cdot \ln(x) + \epsilon$$
then the confidence interval of $\beta_1$ is the confidence interval of the elasticity.

In follow up discussion, the questioner asks if it is possible to do this with the linear regression coefficient ($\gamma_1$), along with $\bar{x},\bar{y}$ and the associated standard errors? Why would you want to know the elasticity at the average values instead of the average implied elasticity over all x-y pairs? The beta parameter is estimated on the full population so why not the elasticity too? Because all we only know the average values and the linear regression coefficient.

In principle, you can do a Monte Carlo simulation like the following:
$$ \hat{elasticity}= (\hat{\gamma} + SE_{\gamma} * N(0,1)) * (\bar{x}+ SE_{\bar{x}} * N(0,1)) / (\bar{y}+ SE_{\bar{y}} * N(0,1))$$
do a bunch of simulations, and use this to make a confidence interval around the elasticity estimate.

In simulations that I ran, this did result in 95% standard errors that included the true value, but that might simply be a function of the parameters I tried. Unsurprisingly, the resulting standard errors on the elasticity are much larger than in log specification.


Book Recommendation: Price Theory Can someone please recommend a book or a chapter from a book which provides a good and clear explanation of price theory. How prices are determined what they reflect and how they serve as allocaters of resources.

The Applied Theory of Price

by Donald N. McCloskey

McCloskey published the book (pdf) for free now.

The Chicago school's other economists also published their books on price theory (see Milton Friedman's and George Stigler's).


Are there import taxes between US states? In the USA, are there import taxes (or equivalent) between states? Or is it in effect a customs union?

No. Such interstate taxes are prohibited by the Commerce Clause as they would be "undue burdens on interstate commerce".

The Commerce Clause is an evolving doctrine that has been largely developed by the courts (in particular the US Supreme Court).

The most recent development was South Dakota v. Wayfair (2018). Section A gives a summary of this doctrine's development and states:

  Modern precedents rest upon two primary principles that mark the boundaries of a State’s authority to regulate interstate commerce. First, state regulations may not discriminate against interstate commerce; and second, States may not impose undue burdens on interstate commerce.


Is money mostly created (out of nothing) by banks making loans? In the Bank of England's Quarterly Bulletin, 2014 Q1, McLeay, Radia, & Thomas write a pair of articles titled:

"Money in the modern economy: an introduction" and
"Money creation in the modern economy".

I believe they subscribe to what Werner (2014) calls the credit creation theory of banking. From their Overview:

In the modern economy, most money takes the form of bank deposits. But how those bank deposits are created is often misunderstood: the principal way is through commercial banks making loans. Whenever a bank makes a loan, it simultaneously creates a matching deposit in the borrower’s bank account, thereby creating new money.
The reality of how money is created today differs from the description found in some economics textbooks:
• Rather than banks receiving deposits when households save and then lending them out, bank lending creates deposits.
• In normal times, the central bank does not fix the amount of money in circulation, nor is central bank money ‘multiplied up’ into more loans and deposits.

These two articles were published in the BoE's Quarterly Bulletin, so I had initially assumed that what they were saying was the mainstream/widely-accepted/orthodox view. On further reading (e.g. of Werner, 2014), I discovered though that this might not be so and am now slightly confused as to what, if any, the mainstream view is.
My main question is this: Is the above description of money creation largely accurate?
Follow-up questions: Does this description differ from what is written in most textbooks and academic papers and books? (And if so, why? Is it because the above description is a relatively recent development? Or the above description has been true for a long time now, but has simply not been incorporated into textbooks and economists' models?)

The monetary base (MB) contains what might be called "public money creation", Notes and coins in circulation (outside Federal Reserve Banks and the vaults of depository institutions), Notes and coins in bank vaults (vault cash), and Federal Reserve Bank credit (required reserves and excess reserves not physically present in banks). The broadest available government measured US monetary measure is M2, which does not contain all the elements of MB, but still is an approximation of the total of private and public money creation, which includes currency, plus time, savings, and demand deposit accounts. So, what is MB/M2? What fraction of money is created by the government of the total?

FRED: (Monetary Base; Total)/(M2 Money Stock*1000)
The answer is less than half. Crudely, money is mostly privately created in the US. The "out of nothing" aspect of your question is more complex. In my personal view, and I guess that's only an opinion, is that because banks are government regulated and insured institutions, forced to back each loan with reserves, and regulated to have capital for each of those loans, they cannot really be said to make this private money out of nothing.


Is Artificial Intelligence a completely new (and underestimated) production factor? Accenture research defines Artificial Intelligence as completely new production factor along labour and capital. Is such notion acceptable by economists?

As far as I understand then every asset of AI - patented algorithms and software, proprietary knowledge bases and data bases - has its owner and therefore those assets can be considered simply as some form of capital and one should not make special conclusions about AI.

My guess is that it is not a new factor of production, but simply a type of total factor productivity. This is because:

factors of production are a stock, which produce services. What is the stock of AI? The stock of labour is easy to calculate. The stock of capital is more complex, but at least all capital goods (even robots) have a market price. As such, the heterogenous capital in an economy can be converted into a unique variable, via prices. Does different AI components have prices? I don't think so.
factors of production are rival goods. A machine cannot be used simultaneously by the same firm. Same for workers. Instead, AI are knowledge, codes, algorithms, which are non-rival.
AI is produced by labour. As such, from a endogenous growth perspective (a lá Romer), resources need to be invested in order to augment the level of AI in the economy.
factors of production get paid. How do you pay an algorithm? Even more, why would you pay an algorithm at all?

Therefore, if I were to model AI, I would do so as part of TFP, and not as a new factor of production. In my view, the report is highlighting is that AI is a different and new component of TFP, one which could revitalise growth.


How much money is wire transferred every year worldwide? How much money is wire transferred every year worldwide? Estimates are fine.

If you're just trying to understand the volume of electronic transactions generally to an order of magnitude, it's in the quadrillions of dollars per year. According to this document from the US Treasury, SWIFT handles about \$5 trillion per day, or given about 250 business days per year, about \$1.25 quadrillion dollars a year.

Similarly, CHIPS handles about \$400 trillion per year, and Fedwire handles around \$900 trillion per year (most of both of these arise out of SWIFT messages). These transactions make up a large fraction of electronic transactions in the world, so it's safe to assume that the global total isn't much more than a few quadrillion dollars a year.

SWIFT payment message volumes are usually around 11.5 million per day, giving an average payment size of around \$45,000— though if one considers the structure of the payments system, it's evident that there's a very wide distribution of payments sizes, so this average isn't particularly representative.


NE equilibrium with lobbying of cournot producers I have had an exam (exam is now past and submitted, but I want to now understand the solution without waiting) with the following questions:

GAME

Consider two firms playing the following two-stage game:

Firm face the following inverse demand:

$$
P(Q) = \frac{S+s_1 + s_2}{(Q+k)^{\alpha}}, Q=q_1 + q_2.
$$

in the first stage, firms can simultaneously lobby to ease trade restrictions by increasing $s_i$, for each unit of $s_i$ each firm pays $\frac{s_i^3}{9}$.

In the second stage they observe each other lobbying choice and set quantity simultaneously. Production costs are zero.

Let $\alpha = 3$ and $k=1$. Show that there is a NE with $S+s_1 +s_2 > S + s_1^{spne} + s_2^{spne}$ and explain why this is NOT a subgame perfect.

SPNE

SPNE is easy to find by backward induction, we know that in the second stage firms profits are

$$\pi_i = \frac{S'}{(Q+k)^{\alpha}}q_i - \frac{s_i^3}{9},$$

$S'$ is a fixed constant at this stage, so by differentiating we find the best responses and the optimal quantities

$$
q_1 = (q_2 + k)/(\alpha-1)\to  q^*_i = \frac{k}{\alpha-1}.
$$.

Anticipating this, at stage one, firm will want to maximize

$$\pi_i = \frac{S'}{(Q^*+k)^{\alpha}}q^*_i - \frac{s_i^3}{9},$$

deriving in $s_i$ we find the solution to be

$$
s^*_i = \sqrt{\frac{3q^*_i}{(Q^* +k)^{\alpha}}}
$$

Another SPNE?

I have tried finding an NE, but could not. Only thing I can find is what I think is another SPNE in which strategies are:

Both play $(\hat{s}, q_i^*)$ where $\hat{s} > s_i^*$ . If the other player deviates in the first stage, then the other will punish the other in the second stage by producing some

$$ q^p $$

such that $$\pi_1(\hat{s},s_2^* ,q^p,q_2^*) = \pi^{spne}$$ while
$$\pi_2(\hat{s},s_2^* ,q^p,q_2^*) < \pi_2(\hat{s},\hat{s} ,q_1^* ,q_2^*) $$ This should be -- assuming there is such a $q^p$ -- a credible threat since the player can get the same as the previous SPNE payoff and effective since it lowers player 2 profits by lowering the demand it receives.

Is this is an equilibrium at all and is it an SPNE or just a NE?

Since the choice of $q_i$ can be conditioned on $(s_i,s_j)$, strategies in this game are of the form $(\hat s_i, \hat q_i(s_i,s_j))$. For the given values $\alpha=3$ and $k=1$, the SPNE can be calculated as the profile where $s^*_i=1/3$ and $q^*_i\equiv 1$. Indeed, production levels $q_i^*=1$ are the unique NE in all subgames, independently of the chosen $s_i$-levels in the first stage. Therefore your suggested "other SPNE" is not an SPNE.

But consider the following strategy of player 1: $\hat s_1=1/3$ and $\hat q_1(s_1,s_2)=\left\{
\begin{array}\ 1 & \ldots & s_2 = 1/3+\epsilon \\ 2 & \ldots & s_2 \ne 1/3+\epsilon \end{array}
\right\}$, where $\epsilon>0$. Let player 2's strategy be $\hat s_2=1/3+\epsilon$ and $\hat q_2(s_1,s_2)\equiv 1$. Then $(\hat s_1,\hat q_1)$ is a best response to $(\hat s_2,\hat q_2)$, and provided $\epsilon$ is small enough that deviating in the first stage doesn't pay for player 2, $(\hat s_2,\hat q_2)$ is also a best response to $(\hat s_1,\hat q_1)$. Therefore the corresponding strategy profile is a NE with higher total lobbying than in the SPNE (but with the same production levels), benefiting player 1.

However, it is not subgame perfect, since if player 2 deviated in the first stage, player 1 would not carry out his threat to double production in the second stage. Technically speaking, the NE induces production levels $\hat q_1=2$ and $\hat q_2=1$ in all subgames following a deviation of player 2 in the first stage, but these production levels are not in equilibrium in these subgames.


Taylor Series Approximation around steady state in Solow In my Advanced Macro script, the professor says take TSA1 of the following equation:

$(1+g)(1+n)k_{t+1} = sk^\alpha_{t+1} + (1-\delta)k_t$

where $g$ is technological progress, $n$ population growth, $k$ capital per effective labour (AL).

In the class we work with discrete time. The results don't seem to make sense to me - could anyone guide me how to take the TSA in this particular case?

The $k_{t+1}$ means subscript and thus capital per AL at time $t+1$.

EDIT: TSA around the steady state.

Many thanks!

The steady-state value $k^*$ must be a fixed point :

$(1+g)(1+n)k^* = s(k^*)^{\alpha} +(1 - \delta) k^*$

Taking the difference between this equation and the dynamic one :

$(1+g)(1+n)(k_{t+1} - k^*) = s((k_{t+1})^{\alpha} - (k^*)^{\alpha}) +(1 - \delta) (k_t - k^*)$

Now if you denote by $d_t = k_t - k^*$ the distance to steady-state, this gives :

$(1+g)(1+n)d_{t+1} = s((k_{t+1})^{\alpha} - (k^*)^{\alpha}) +(1 - \delta) d_t$

But :

$(k_{t+1})^{\alpha} = (k^* + d_{t+1})^\alpha = (k^*)^\alpha + \alpha d_{t+1} (k^*)^{\alpha - 1} + o (d_{t+1})$

(Here was the Taylor development.) So that finally, this equality holds approximately around steady state ($d_t$ small):

$(1+g)(1+n)d_{t+1} = \alpha s (k^*)^{\alpha - 1} d_{t+1} +(1 - \delta) d_t$

From the steady state condition you can also compute (assuming that $ng << n+g$):

$(k^*)^{\alpha -1} = \frac{n+g+\delta}{s}$


Can the major indice of an exporting nation decrease at the same time the currency devalues? In the UK, the FTSE100 is achieving record highs at the same time the currency (GBP) is depreciating rapidly.

The media often correlate the two events by reporting that since the indice is made of 100 multinational companies who trade primarily in foreign currencies; a weak pound allows them to book larger profits after they trade back into the GBP domestically.

However, can the FTSE100 decrease at the same time the currency also decreases in value or must the two levers always go in separate directions?

Yes, the FTSE 100 can decrease at the same time as the currency. It depends on what is causing the depreciation of the currency or what is affecting the FTSE at the time. It is hard to establish which way the effects are going in real time, however.

Suppose the currency is depreciating due to loose monetary policy. If the Marshall-Lerner condition is fulfilled, this means companies will export more and have more profit. In that case, we could expect the FTSE to go up. On the other hand, if the condition is not fulfilled, exports may actually go down and the FTSE with it. This is the case where the currency depreciation affects the FTSE.

On the other hand, the FTSE may affect the currency. If firms are facing a crisis or other problems, the FTSE goes down. This may prompt the central bank to attempt to depreciate the currency or it may prompt investments to flow out of the country, which depreciates the currency. The currency may depreciate for a while, before the monetary policy has any positive effects on the FTSE. The loss of investment will have a direct negative effect on the FTSE, as there is less capital supply and interest rates for firms may go up. Here again both the FTSE and the currency may go down.

There could also be third factors that affect both the FTSE and the currency. Suppose the currency is depreciating because of other  factors, e.g. an increase in uncertainty. This may cause investments to flow out of the U.K. thereby depreciating the currency. Further, that same economic uncertainty and reduction of investment could hurt profits and therefore the FTSE could go down.

Moreover, a simultaneous crisis in the banking industry and a currency crisis is very possible. These are called "twin crises". See the 1999 Kaminsky and Reinhart paper in the AER for a reference. In that case, the FTSE and the currency can go down simultaneously. Twin crises are more relevant for fixed exchange rate regimes, however, so this possibility may not apply to the U.K. as much as to other countries.


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

Well you do not provide any source for the $dM+dV = dP+dY$ so it is hard to say why someone written that. That is certainly not normal total derivative of QTM.
You are right that the correct total derivative of QTM will be given by:
$$VdM+MdV=YdP+PdY $$
Possible explanation why you saw it somewhere written differently:

Note the above can be divided by $MV=PY$ to get:

$$(M dV)/(MV) + (V dM)/(MV) = (P dY)/(PY) + (Y dP)/(PY)$$
which after simplification yields:
$$\frac{dV}{V} + \frac{dM}{M} = \frac{dY}{Y} + \frac{dP}{P}$$
the above expression is quite common in the literature and it is possible someone just decided to substitute $dx = \frac{dX}{X}$ to clean up the expression: $dv + dm = dy +dp$,

Alternatively it is possible that the 'unnamed source' wanted to express the equation in percentage changes via log linearization and just used the same symbol for change as differential symbol. Log linearizing QTM yields:

$$\ln M + \ln V = \ln P + \ln Y$$
which is equivalent to:
$$\Delta \% M + \Delta \% V = \Delta \% P + \Delta \% Y$$
Some people will use $d$ or $\delta$ instead of $\Delta$ and omit $%$ sign.

There are some missing assumptions transformations that would make it right.

Source you got it from made a mistake.


Is an alternative other than negative interest rate possible? Currently there is a lot of talk about negative interest rate and possibly US would be adopting that. Denmark was the first country in the world which has "successfully" applied negative interest rate. How do Danish banks make their money there?

A lot of people in finance in US say that negative interest rate would not work in US and would cause a collapse of the banking sector. Given that we are currently in one of the biggest bond bubble in history, is an alternative other than negative interest rate possible because any rise in interest rate would cause a massive debt sell off. The last time FED tried to raise the interest rate by .25% the markets dropped by 20%. So i am trying to understand if we are in trouble, because if the interest rate is increased, we are looking at a deep recession but if the interest rates go negative we are looking at stagflation. Have I understood this right?

Negative interest rates means that if you take a 1.000 loan, you will pay 900 to the lender. At the same time, if you deposit this same 1.000 in a savings accounts, you will withdraw 900. This is an expansionary monetary policy. In other words, low or negative interest rates estimulates the consumption and destimulates the savings.

It also weaken a country’s currency, which boost the exports and pushing up import costs. Like Japan and USA, Denmark is a big exporter. One of Trump strategies - along with direct taxations into imported goods - is to decrease interest rates to gain advantage against China.

The stimulus for comsumption is to boost the economy and increase the aggregate demand. An investor would prefer to invest in a company or enterprise rather than government bonds, and a family would rather buy a new house today than save for 5 years.

Other monetary policies could be the reduction of the reserve ratio or quantitative easing, but all expansionary policies can lead to bad consequences in the future, like high inflation rates.


Why does raising interest rates work? Why does the federal raising interest rates actually have an effect on the economy? The typical answer is that it reduces money supply by incentivizing saving and increasing cost of loans.

But couldn't market participants just react by adjusting FX rates, inflation, etc. by the appropriate amount? Then even though the money supply is reduced, the real rates are unchanged, resulting in no net effect. What are the factors preventing this from actually happening?

The typical answer is that it reduces money supply by incentivizing saving and increasing cost of loans.

This is backwards.  The Federal Reserve (the United States' central bank) sets a target for the federal funds rate.  The rate itself is a weighted average based on market activity.  The Fed encourages the average rate to match the target by buying and selling bonds in what are called open market operations.  Buying bonds puts money into circulation, increasing the money supply.  Selling bonds takes money out of circulation.  The Fed changes the money supply to change the interest rate, not the other way around.

  But couldn't market participants just react by adjusting FX rates, inflation, etc. by the appropriate amount?

Only if all (or even most) of the participants worked together.  If only one or a small portion of participants attempt this, then it creates arbitrage opportunities for the remainder.  Currency exchange rates and inflation are both set based on market actions.  They aren't so easy to adjust.


Why can't I use TMoLM for this bliss point problem? I am having difficulty with a particular bliss point problem. The basic issue I have is my approaches seem flawed and I can't tell why.

The equation is

$$U(x,y) = 36x -4x^2 + 6y-2y^2$$

subject to

$$ 5x + 7y=40$$

My first instinct was to use the method of Lagrangian multipliers. But I had this on an exam this afternoon and my professor said I shouldn't use it here. I don't understand why. I tried it using wolfram alpha and also solved it by hand and got the same results

$$(4.78,2.29)$$

approximately as the optimum bundle. But seemingly this isn't the train of thought I was supposed to use.

I then had another idea. I can solve for $$U_x=U_y=0$$ because at the bliss point you should have MU equal to zero.

\begin{align*}
36-8x &= 0 \\
x&=\frac{36}{8}=4.5\\
6-4y&=0\\
 y&=\frac{6}{4}=1.5
\end{align*}

But this lead to different results than just using TMoLM.

My Question:

Can someone explain why TMoLM isn't the right approach? Why does it lead to different results then what my professor suggested and what others have said in the comments?

It all depends on whether you treat the budget constraint as an equality or inequality constraint. These are two different problems, with two different solutions in this case.

One version of the problem (rewriting the objective in the form suggested by denesp, and dropping the constant, for clarity) is
\begin{align}
\max~&-4(x-4.5)^2 -2(y-1.5)^2\\\text{s.t. }&5x+7y=40
\end{align}
With this equality constraint, the optimum is $(x,y)=(4.78,2.29)$ as you found using the method of Lagrange multipliers and Wolfram alpha. It's true that you would prefer consuming less and staying at the bliss point, but if we assume that the budget constraint is an equality then you aren't allowed to consume less.

Another version of the problem is
\begin{align}
\max~&-4(x-4.5)^2 -2(y-1.5)^2\\\text{s.t. }&5x+7y\leq40
\end{align}
with an inequality in the budget constraint. Here, as you point out, it's clear that the optimum is $(x,y)=(4.5,1.5)$, because that's the consumption profile that globally maximizes the utility function (and it obeys the budget inequality).

Assuming that the budget constraint is an inequality is usually more appropriate (presuming that you can always "throw away" extra wealth).

When solving constrained optimization problems where some of the constraints are inequalities, we need a generalization of the basic method of Lagrange multipliers called the Karesh-Kuhn-Tucker (KKT) conditions, which has probably not been covered in your course. You can read about this in more detail in the linked wikipedia article, but the basic idea is simple: we can still set up the Lagrangian, where we write the constraint as $g(x,y)=5x+7x-40\leq 0$ and then subtract $\lambda g(x,y)$ from the objective:
$$\mathcal{L} = -4(x-4.5)^2 -2(y-1.5)^2 - \lambda(5x+7y-40)$$
We can then equate the partial derivatives to 0 ($\partial\mathcal{L}/\partial x = 0$ and $\partial\mathcal{L}/\partial y=0$) to get two conditions
\begin{align}
\frac{\partial\mathcal{L}}{\partial x}&=0 \Longleftrightarrow 8(x-4.5)=-5\lambda\tag{1}\\
\frac{\partial\mathcal{L}}{\partial y}&=0 \Longleftrightarrow 4(y-1.5)=-7\lambda\tag{2}
\end{align}
The question, then, is how to pin down $\lambda$. You're probably used to finding $\lambda$ by seeing which value causes the budget constraint to hold with equality. In this case, however, that implies $\lambda<0$. This is not allowed for an inequality constraint under the KKT conditions, which require $\lambda\geq 0$.** Since $\lambda$ turns out to be the marginal utility of wealth, this constraint is tantamount to saying that more wealth (which relaxes the inequality) shouldn't hurt us.

The KKT conditions also have a requirement called complementary slackness, which states that either the inequality must bind (holding with equality) at the optimum, or else $\lambda$ must be 0. (Since $\lambda$ measures the "cost" of the constraint, this is logical: if the constraint isn't binding, then the cost must be 0, and it shouldn't be affecting your local optimization problem.) We already saw that if the budget constraint holds with equality, we get $\lambda<0$, which isn't allowed, so complementary slackness implies our only remaining option is $\lambda=0$. Plugging this into (1) and (2) above, we get $(x,y) = (4.5,1.5)$, which is the solution you already found intuitively.

Usually, there is no need in introductory micro to use the full KKT conditions, because we work with utility functions that are monotonic, where you'll always want to exhaust your budget constraint. Simple concave quadratic utility with an interior bliss point, like in this case, is an exception where we need a very simple case of the KKT conditions to do the optimization properly.

**Note: of course, if we add $\lambda g(x)$ rather than subtract it to the Lagrangian, the signs reverse. I've seen many different conventions, and I'm going with the one that makes $\lambda$ nonnegative. The Wikipedia article uses the opposite convention.


Repositories for working papers in economics and finance I would like to post my working paper (broadly defined as theoretical work in finance) on a repository.

Goals

Primary: to get a time stamp for a new idea that I have, such that I could establish the authorship and the date.
Secondary: to get some attention to my new idea, receive comments and discussions, so that I could improve the paper.

Conditions

I would like to be able to post the paper myself and to have good control over updating it when I wish to, provided that a track record is kept (see my primary goal).
(The reason for focusing on easy updates is that the paper is still rather preliminary and changes will be needed. You could say, I should finalize it first and submit only then, and I get the point. But it has been sitting around for too long, and I do not want the idea in it to get stale. Perhaps receiving good comments on the preliminary version will quicken my progress.)

Situation so far

I have considered posting it in my institution's working paper series, but that process goes through a secretary which is always busy and would not normally accommodate requests of updating the paper in a timely manner.
I have considered posting it on my own website, but then I do not get an official time stamp on the idea, and the visibility is low.

What could you recommend?

How about MPRA? After acceptance it would be cross-posted to REPEC, Ideas and Econpapers.


Quarterly GDP growth terminology: YoY vs QoQ Quarterly GDP growth can be calculated either in terms of YoY change or — in the case of seasonally adjusted data — in terms of QoQ change. (A third option would be to annualize the QoQ rate.)

To start with a current example: In the U.S., GDP in Q1 2018 grew by 2.9% compared to Q1 2017 (= YoY), whereas it grew by 0.7% compared to Q4 2017 (= QoQ).

In Q4 2017, however, YoY growth was at 2.6%, whereas QoQ growth was at 0.7%. So GDP growth in Q1 2018 was higher compared to the previous quarter in terms of YoY (2.6% -> 2.9%), whereas it was slightly lower compared to the previous quarter in terms of QoQ (0.7% -> 0.6%).

Now in judging an economy's growth momentum, analysts typically focus on changes in QoQ growth rates - in the example above coming to a conclusion like "growth in the U.S. slightly lost momentum in Q1 2018".

My question is: Is there a different term to express changes in the YoY rate? To stay with the example above, if I comment on the fact that the U.S. YoY rate is up to 2.9% from 2.6%, concluding that there was a “strengthening of growth momentum” might be misleading (especially given the diverging picture based on changes in the QoQ rate).

As long as you clearly label what you are doing, there’s probably a lot of ways of phrasing the change in the year-on-year growth rate. However, anyone with experience will take those changes with a large grain of salt, as a result of “base effects.”

For relatively low growth rates, the annual rate of change is roughly equal to the sum of non-annualised quarterly growth rates over the last four quarters (or the average of annualised growth rates for 4 quarters). The change in the annual growth rate on quarter is therefore driven by the difference between the latest quarter, and the quarter that dropped out of the annual average. If that previous period was abnormally low, the current annual growth rate will jump higher, even if the quarterly growth rate is unchanged.

Since that hardly represents new information about the economy, that jump is not providing a lot of new information - we knew about that weak quarter for a long time.

Year-on-year changes are a great for time series plots, but you need to dig further if you want to discuss acceleration/deceleration.


Signalling Game, Multiple Signals I am solving a three-stage game in a supply chain with one buyer and one supplier. The supplier has private information on its production capacity. The supplier also has the option to sell to the market directly. As of now, the game sequences are as follows. In the first stage, the supplier decides on the wholesale price, then the buyer takes the wholesale price as a signal, updates its belief about the production capacity of the supplier and order some of that capacity. In the last stage, the buyer decides, how much it wants to sell to the market directly, and the supplier decides how much to sell to the market if any capacity remains.
For now, the only signal is the wholesale price. I want to add a second signal to the first stage. In other words, the supplier not only sets the wholesale price but also puts a limit on the buyer's order quantity. In the next stage, the buyer solves its expected utility by considering two signals.

Has someone heard about a similar story with 2 signals at one stage?
Thanks

From the perspective of the buyer, he is receiving 1 two-dimensional signal. After observing a combination of the wholesale price and limit order, the buyer can update their beliefs about the supplier's capacity using Bayes rule. Let me show it:

Let $c\in [0,1]$ be the supplier's capacity (just for simplicity of notation I assumed it is in the interval from 0 to 1) and assume $c$ is distributed according to $\mu_0(c)$, thus $\mu_0$ is prior belief of the buyer that the capacity is $c$.
Then each type of supplier will optimally choose a signal $(p_w(c), \bar o(c))$ of the wholesale price and the limit on buyer's order. These are functions from the production capacity $c$ (or more generally, the  suppler's private information) into $\mathbb{R}^2$ (if some types of suppliers use mixed strategies, then $(p_w(c), \bar o(c))$ are functions that return distributions supported in  $\mathbb{R}^2$.

After receiving a signal say $(p_w, \bar o)$ the buyer's posterior belief, denoted  $\mu_1(c)$, is given by:

$$\mu_1(c|(p_w, \bar o))=\frac{Prob((p_w(c), \bar o(c))=(p_w, \bar o))\mu_0(c)}{\int_{[0,1]} Prob((p_w(t), \bar o(t))=(p_w, \bar o))\mu_0(t)dt}$$

That is the ratio of the probability of receiving signal $(p_w, \bar o)$ from a supplier with capacity $c$ over the total probability of receiving the same signal; from any type of supplier. Note that if the supplier with capacity $c$ is using a pure strategy, then $Prob((p_w(c), \bar o(c))=(p_w, \bar o)$ is either $0$ or $1$.

Given the 2 dimensional signal, I would  suspect that one of the following 3 scenarios will occur:

The buyer learns the capacity form the signal (for example if the function $f(c)=(p_w(c), \bar o(c))$ is injective from $\mathbb{R}$ into $\mathbb{R}^2$. (notice that this can occur even if one or both of the functions $p_w(c), \bar o(c)$ are not injective).
The function $\bar o(c)$ is constant, so you revert back to the case with a 1-D signal since the buyer learns nothing from $\bar o(c)$.
Suppliers choose mixed strategies. In that case, finding $(p_w(c), \bar o(c))$ will be a challenge because the set of distributions supported in $\mathbb{R}^2$ is quite large.

Good luck!


How can we estimate the tax incidence from a 20% tariff on Mexican goods? President Trump has proposed a 20% tariff on some Mexican imports to the US. Is there a good way to estimate the incidence of this proposal between the Mexican producers and American consumers, as well as the deadweight losses? Perhaps some analyses have already been done?

I know it's hard since there are no real details on the proposal.

Due to the tariff, the supply of any product being imported from Mexico to the U.S will shift back. This would mean that prices of goods will increase in the U.S itself and most of the tariff will eventually be paid by U.S citizens who buy the goods. As the price increases, consumer surplus decreases and the market will not be at equilibrium, therefore a deadweight loss will be present.If the selling price of a product is 10.5$.The new selling price is 12. There will also be a deadweight loss as the society will not receive the quantity it demands.


Has the natural rate of unemployment decreased with modern travel and the Internet? The natural rate of unemployment is a combination of structural unemployment and frictional unemployment.
Structural unemployment is caused by a surplus of labor at a given wage in a given area.
Frictional unemployment is caused by workers searching for or transitioning between jobs.
However, modern travel (airplanes, automobiles, etc.) would reduce structural unemployment and frictional unemployment by allowing for faster movement of excess labor to transfer to areas with a shortage of labor; similarly, the Internet (specifically search engines, online jobs fairs, etc.) would reduce frictional unemployment by allowing for workers to search for and find jobs more easily.

Does this imply that the natural rate of employment decreased with modern travel and the Internet?

To me, it seems that it has increased, not decreased, due to the factors you mention. Yes, transportation and information networks enable workforce movement. But they also enable movement of goods and information - and because goods and information are more mobile than humans, they profit more, and the results of their portability outpaces the results of the workforce's increased mobility.

When goods were hard to move, a local demand had to be met by local suppliers. If a manufacturer lost a deal, it went to a local competitor instead, and the workforce could adapt easily. Now, if a manufacturer loses a deal, it goes to a competitor 5000 km away. Take for example the Ruhr area: it's still the most densely populated area in Germany, even though the steel industry which attracted workforce in the mid-20th century is gone. The Germans literally shipped one of their steel mills around the globe to China - but the workers stayed.

So, because the workforce cannot adapt to structural changes with the speed at which they are happening, the structural unemployment is higher than before networks which enabled such changes. But the increased speed of change also means more frictional unemployment. A large part of the adaptation which is happening requires people to change jobs. Also, your observation of an increased commute radius contributes to frictional unemployment too - when a person is unhappy with his job, he has more opportunities in his now increased commute area, and is more likely to change jobs.

There are lots of indirect effects too. The Internet and the transport networks enable changes in culture (e.g. today people move out of their birth town early, so may be more willing to relocate again later), business models (e.g. movie streaming) and market structure (today's trend towards ever larger corporations is enabled through, among other things, efficient information and people movement, which reduces overhead costs of giant companies, and global knowledge - I doubt that 50 years ago, an American chain for mediocre coffee in fancy large cups would have been able to establish itself in Europe. Nowadays, the culture export means that the trendy European teenager recognized the brand before they had one of the shops in their location). And they go both ways - a giant corporation may actually be more stable, and afford to keep workforce during short-term demand slumps which would have capsized a tiny manufacturer.

Whatever globalization (spearheaded by more exchange of information and goods, and even people on their respective networks) may bring in the future, it currently seems to create more unemployment - not because it's a bad thing in itself, but because in a more dynamic market, there is less job stability.


Why does marginal cost slope upwards after the minimum point? My textbook writes this on marginal cost:

"The law of diminishing returns refers to the idea that as more of a factor (input) is used, with at least one fixed factor, there is some point at which the increase in output will be at a decreasing rate. Each variable unit produces less when diminishing returns are occurring, so the production of extra units of output will require more of the variable inputs, so MC must increase."

I've got some questions about this

What is meant by variable unit?
Does marginal cost increase because there is more variable input, or does each worker become less productive when there are too many workers, so there needs to be more variable inputs (so increasing the variable input doesn't decrease productivity, it increases because more input is needed when the workers are less productive).

The variable unit in the quotation is the factor of production that is varied keeping the others fixed. For example it could be the amount of workers hired, while keeping the amount of machinery (capital) fixed. Or it could be the amount of machines reented, keeping the amount of workers fixed.

As for your other question diminishing returns does not refer to workers specifically, although it can.

Suppose we do consider workers as variable input and keep capital fixed. In the beginning usually adding workers will increase output a lot, so the costs of producing an additional unit are low, and might even be decreasing.

However, at some point adding extra workers will increase output only a little. After all the amount of capital is fixed so adding extra workers mean that they e.g. have to wait for another at the machines or get in another's way. So at that point whereas earlier you only needed say 1/2 a worker to produce an additional unit of output, now you need 2 extra workers to produce that one extra unit. That means that the costs of producing an additional unit (the marginal costs) have risen.


Contract theory: Incentive contracts (when agents have multiple tasks) models by G. Baker and Holmstrom & Milgrom So my question is the following:

In both Baker's (2002) and H & M (1991) models we have a problem that a principal is trying to design a stimulating contract in such way that the agent will choose such an effort that maximizes his utility or profit.

The contract usually looks like this: W = s + b * V(agent's_effort, some_stochastic_stuff).
s - is, of course, some base payment.
So the goal is to find the right "b".

In both models the first step is to find a "Best response function" of an agent - his choice for an effort vector in response to any value of "b".
Great, no problems with that.

But then happens the magic (for me at least).

The next step in both models is to maximize the total surplus of agent and principal:
EUagent + EProfit -> max for 'b' subject to {effort is a function of 'b'}.

So the thing that is a mystery for me here is why do we maximize total surplus? Isn't it me logically correct to maximize the principal's Expected profit since that him who is designing the contract....

Of course I understand that those models are classic, there cannot really be a mistake by authors, but I really cannot get the logic here...

If someone could shed some light over this, it would be quite great!

Thanks a lot in advance...

Holmström and Milgrom assume that the agent exhibits constant absolute risk aversion. This implies that if you change the total wage of the agent with a lump sum transfer (that does not depend on effort), you will not change the incentives. Hence, to find the optimal contract, you can find the contract that maximizes total surplus subject to incentive compatibility, and then subtract a lump sum amount to make the agent indifferent between accepting and not.


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

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

It is very unclear what you are asking. But in most regressions it is assumed that the error term (I assume "e" is the error term) is assumed to be iid for all values of x. In particular, in the discrete case $E[\epsilon|d=1]=E[\epsilon|d=0]$, but this can be generalized by saying $E[\epsilon|x]=E[\epsilon|x']$ for all $x, x'$. Now if your regression also includes a constant term, it is without loss of generality to assume that the expected value of $\epsilon$ (which is the same for all values of x) is equal to zero. Thus, the importance of the assumption $E[\epsilon|x]=0$ is not so much the "equal to zero" part, but the fact that is the same for all values of x.


Nelson-Siegel-Svensson method I am a college student and I have recently learned about Nelson-Siegel-Svensson method which is used by the German Federal Bank to determine the yield curve. I have to generate yield curves of different shapes using historical data (β0, β1, β2, β3, τ1 and τ2) which I am free to choose myself. On the website of the German Federal Bank I see the monthly and daily estimated parameters for the period from September 1972 until today. I have the formula but I am not sure which numbers to use. Could somebody please explain to me, whether the monthly estimated parameters are suitable to generate an yield curve for the next 10 years? I am sorry, if the question is too easy. I would be very grateful, if anyone could help me to understand which parameters I can use.
Thank you very much!
Kind regards,
Amy

If anyone ever wonders the same, I´ve just tried weighting the monthly parameters and that leads to the correct interest rates :) you take 1 / 12 * ∑ (12 values of the respective parameter for the respective year). The answer was way easier than I thought :D


What textbook can I use to understand engineering economics? I'm an Engineering Physics student and this semester I took the course "Engineering Economics" as a requirement to complete the management sciences credits in my program, I need a good textbook to understand engineering economics, thanks.

These are the recommended books for our Engineering Economics university course:

Main Textbook

N. M. Fraser and E. M. Jewkes, Engineering Economics: Financial Decision Making for Engineers, 5th edition, Pearson, Toronto, Ontario, 2013

Supplementary Resources

D. G. Newnan, J. Whittaker, T. G. Eschenbach and J. P. Lavelle, Engineering Economic Analysis, 3rd
edition, Don Mills, Toronto, Ontario, 2014.

J. A. White, K. E. Case and D. B. Pratt, Principles of Engineering Economic Analysis, 5th edition, Hoboken,
NJ, USA, 2010.

I found the main textbook easy to follow. Hope this helps!


Can the amount of loans and deposits in entire banking system differ significantly? Can the amount of loans and deposits in entire banking system differ significantly?
When regarding the entire banking system, what factors impact the loans to deposits ratio?  Is it roughly constant or can change dramatically? Dose the amount of nonperforming loans play a rule in its determination? Can a straightforward equation be drawn for difference between the amount of loans and deposits in entire banking sector by variable like money supply, base money etc.?
Based on my understanding of money multiplier concept, there must be a one-to-one relationship between amount of loans and deposits in entire banking system and so the loan to deposit ratio must be roughly constant. Is it true?

The only thing we know for sure is that for banks, the two sides of the balance sheet balance. That is, assets = liabilities + equity.

In simplistic money multiplier discussions, the only bank assets are loans, the only liabilities are deposits, and there is no equity. So in that case, loans = deposits.

In the real world, equity is fairly small as a percentage. However, there are other large entries on the balance sheets.

On the asset side, banks hold securities for liquidity management, have fixed assets (buildings and computers, etc.).
Deposits are not the only liabilities (and we would need to distinguish between demand deposits and term deposits). Banks issue bonds and short-term debt.

As the mix of assets and liabilities change, so will the loan/deposit ratio.


Why would overemployment mean that labor is used inefficiently? If labor is being used efficiently, there is no excess unemployment
  or over employment.

This phrase from Khan Academy struck me as quite strange. Why on Earth would over employment mean that labor is NOT used efficiently? Labor is a resource. And if we can use more of a resource without increasing its size, then it would seem that we are using it more efficiently, we are using bigger share of it.

For an example, land is recourse. If we will drain swamps we will be able to use more of land for commerical purposes, meaning that we will use land more efficiently. I believe that similiar reasoning can be applied to labor.

P.S. What I understood from comments: Overemployment is inefficient because it happens due to sticky wages/prices in short run equalibrium. Sticky prices/wages create inefficiency in the market, thus it should be nothing suprising that overemployment caused by sticky wages/prices leads to inefficient use of labor.

Because using efficiently does not mean that all labor is used (this holds also for any other factor of production). This is so because on the margin at some point additional inputs might not produce enough value to justify the cost.

Consider simple supply and demand on perfectly competitive labor market with no market failures and all standard background assumptions.

Supply is: $S_L=10+w$ where $w$ is wage. Also let’s suppose there are enough people so that maximum 100 labor hours ($S_L \leq 100$) could be supplied after that there simply is no more labor hours due to lack of people.

Demand for labor hours is: $D_L=100-w$.

Now given the supply and demand it’s trivial to calculate that equilibrium wage is $w=45$ and equilibrium employment will be: $S_L=D_L=55$.

This equilibrium is completely efficient yet only 55 hours of labor is demanded. Employing 60 or 70 or 100 hours of labor would just reduce total welfare as measured by total surplus, and hence it would be inefficient.

Intuition is that because given the firms demand which is derived based on their own optimal production decisions given the prices they face for their product the equilibrium wage is too high to justify employing everyone. Employing more than 55h of labor would start destroying value as those workers would have to be applied to activities where simply the value of output is not sufficient to cover the cost of that labor. Of course, there could be situations where all labors would be employed if equilibrium demand is equal to maximum number of labor hours there is or exceeds it.


Why does a higher risk aversion leads to a lower intertemporal elasticity of substitution? Mathematically, a higher risk aversion leads to a lower intertemporal elasticity of substitution (there is an inverse relationship). But why?
If I become more risk-averse, I would like to smooth my consumption. So I will increase my participation in the financial market to avoid or reduce the risk. But how does that lower my intertemporal elasticity of substitution? Like why would I become less responsive to changes in the interest rate if I become more risk-averse? What's the intuition here?
Or because I just wanna smooth my consumption, I don't really care about changes in the interest rate?
Risk-lovers, on the other hand, although also participate in the financial market, do not care about smoothing their consumption? Like if the interest rate increases, they can drastically reduce their current consumption for more consumption in the future, but risk-aversers do not care about the higher interest rate?

Mathematically, a higher risk aversion leads to a lower intertemporal elasticity of substitution (there is an inverse relationship). But why?

The (relative) measure of risk aversion is measured as:
$$
r(x) = -x\frac{u''(x)}{u'(x)}
$$
Consider an intertemporal utility function $u(x_1) + \beta u(x_2)$. Maximising this with respect to an intertemporal budget constraint gives the following first order condition:
$$
\frac{u'(x_2)}{u'(x_1)} = \frac{1+r}{\beta}.
$$
where $r$ is the interest rate. This states that the marginal rate of substitution should equal the interest rate.
Now, for a given utility level, the indifference curve $x_1(x_2)$ can be implicitly defined as:
$$
u(x_1(x_2)) + u(x_2) = \bar u.
$$
Using the implicit function theorem, we can compute its slope:
$$
\frac{\partial x_1}{\partial x_2} = - \frac{u'(x_2)}{u'(x_1)}.
$$
The slope of the indifference curve is therefore equal to the negative of the marginal rate of substitution. Now, differentiate this again with respect to $x_2$ :
$$
\begin{align*}
\frac{\partial^2 x_1}{\partial x_2 \partial x_2} &= - \frac{u''(x_2) u'(x_1) - u'(x_2) u''(x_1) \dfrac{\partial x_1}{\partial x_2}}{(u'(x_1))^2},\\
&= - \frac{u''(x_2)}{u'(x_1)} - \frac{u'(x_2)}{u'(x_1)} \frac{u''(x_1)}{u'(x_1)}\dfrac{ u'(x_2)}{u'(x_1)},\\
&= -\frac{u''(x_2)}{u'(x_2)}\frac{u'(x_2)}{u'(x_1)} - \left(\frac{u'(x_2)}{u'(x_1)}\right)^2 \frac{u''(x_1)}{u'(x_1)},\\
&= \frac{r(x_2)}{x_2} \frac{(1+r)}{\beta} + \left(\frac{(1+r)}{\beta}\right)^2 \frac{r(x_1)}{x_1}.
\end{align*}
$$
This shows that the curvature of the indifference curve at the optimum is increasing in the measure of risk aversion.
Concerning it's relationship to the elasticity of intertemporal substitution, we intuitively see that the higher the relative risk aversion, the higher the curvature of the indifference curve, so the more the slope at the indifference curve, $\frac{u'(x_2)}{u'(x_1)}$,  will change as a response to a change in the ratio $\frac{x_2}{x_1}$. Vice versa, the higher the relative risk aversion, the less the ratio $\frac{x_2}{x_1}$ will change in response to a change in the slope $\frac{u'(x_2)}{u'(x_1)}$ (e.g. due to a change in interest rates).
To see this mathematically, consider he intertemporal elasticity of subsitution:
$$
\varepsilon_s = -\frac{\partial \ln(x_2/x_1)}{\partial \ln(u'(x_2)/u'(x_1))}
$$
This measures the percentage change in $x_2/x_1$ due to a one percentage point change in the marginal rate of substitution.
We can write everything in terms of $x_2$ (as we did above), then take derivatives of the numerator and denominator with respect to $x_2$ and finally evaluate it at the optimum:
$$
\begin{align*}
\varepsilon_s &= -\frac{\dfrac{x_1}{x_2}\left(\dfrac{x_1 - x_2 \dfrac{\partial x_1}{\partial x_2}}{(x_1)^2}\right)}{-\dfrac{1}{\dfrac{u'(x_2)}{u'(x_1)}} \left(\dfrac{r(x_2)}{x_2} \dfrac{1+r)}{\beta} + \left(\frac{1+r}{\beta}\right)^2 \dfrac{r(x_1)}{x_1}\right)},\\
&= -\frac{\dfrac{1}{x_2} - \dfrac{\dfrac{\partial x_1}{\partial x_2}}{x_1} }{\dfrac{1}{\dfrac{\partial x_1}{\partial x_2}} \left(\dfrac{r(x_2)}{x_2} \dfrac{1+r}{\beta} + \left(\frac{1+r}{\beta}\right)^2 \dfrac{r(x_1)}{x_1}\right)},\\
&= -\frac{\dfrac{1}{x_2} - \dfrac{- \dfrac{1+r}{\beta}}{x_1} }{ -\dfrac{\beta}{1+r} \left(\dfrac{r(x_2)}{x_2} \dfrac{1+r}{\beta} + \left(\frac{1+r}{\beta}\right)^2 \dfrac{r(x_1)}{\beta}\right)},\\
&= \frac{\dfrac{x_1}{x_2} + \dfrac{1+r}{\beta}}{ \left(\dfrac{x_1}{x_2}r(x_2) + \dfrac{1+r}{\beta} r(x_1)\right)},\\
\end{align*}
$$
The last expression gives the elasticity as a function of the relative slope $x_2/x_1$ and the relative risk aversions. Now, if the relative risk aversion is constant, say $r(x_2) = r(x_1) = \sigma$ this simplifies to $\varepsilon_s = 1/\sigma$.
Nevertheless, we see that if the risk aversion increases, i.e. $r(x_2)$ and $r(x_1)$ increase, then $\varepsilon_s$ decreases.

If I become more risk-averse, I would like to smooth my consumption. So I will increase my participation in the financial market to avoid or reduce the risk. But how does that lower my intertemporal elasticity of substitution? Like why would I become less responsive to changes in the interest rate if I become more risk-averse? What's the intuition here?

There is a difference between consumption and saving. The higher your risk aversion, the bigger the curvature of the indifference curve, i.e. the lower $\varepsilon_s$. And so the smaller the change of $x_2/x_1$ due to a change in, for example the interest rate $r$.
You can think of the curvature of the indifference curve as the degree of complementarity between $x_1$ and $x_2$. The higher the risk aversion the more $x_1$ and $x_2$ become complements. So I will try to consume $x_1$ and $x_2$ together which is equal to increasing consumption smoothing.
In order to smooth my consumption, I will need to lend and borrow on the financial market. So if my income over time changes a lot, I will have to save and borrow a lot. On the other hand, if my income is reasonable smooth over time, I will not need to borrow or save a lot in order to smooth out out my consumption.

Or because I just wanna smooth my consumption, I don't really care about changes in the interest rate?

This is a mis-understanding, risk averse consumers actually do care about changes in the interest rate.

First of all, a change in interest rates affects their saving decision. It is true, however, that changes in the interest rate will not change $x_2/x_1$ a lot. So although my relative consumption over time will not be affected a lot by changes in the interest rate, the amount that I save or borrow can change substantially.

A change in the interest rates also changes my utility. Assume for simplicity that I am infinitely risk aversion, so I will always always choose to set $x_1 = x_2$. In this case, my intertemporal budget constraint becomes:

$$
\begin{align*}
&x_1 + \frac{x_2}{(1+r)} = y_1  + \frac{y_2}{(1+r)},\\
\to &x_1\frac{2+r}{1+r} = y_1 + \frac{y_2}{1+r},\\
\to &x_1 = \frac{(1+r)y_1 + y_2}{2+r}
\end{align*}
$$
Then:
$$
\frac{\partial x_1}{\partial r} = \frac{y_1(2+r) - [(1+r)y_2 + y_2]}{(2+r)^2} = \frac{y_1-x}{2+r}.
$$
So if my consumption $x_1$ is smaller than my income in period 1 $y_1$ (i.e. I save in period 1), I will be able to consume more if interest rates increase. On the other hand, if $x_1 > y_1$ (So I borrow in period 1), then I will be worse of if interest rates increase. So changing interest rates will change my utility depending on whether I am a net saver or borrower.

Risk-lovers, on the other hand, although also participate in the financial market, do not care about smoothing their consumption? Like if the interest rate increases, they can drastically reduce their current consumption for more consumption in the future, but risk-aversers do not care about the higher interest rate?

Again risk loving (or neutral) consumers also care about interest rates. Consider for simplicity a risk neutral consumer with utility function $u(x_1, x_2) = x_1 + \beta x_2$. Then it is clear to see that if:

$\beta < \frac{1}{1+r}$, I will consume everything in period 1, so $x_1 = y_1 + \frac{y_2}{1+r}$ and $x_2 = 0$. Utility will be equal to $y_1 + \frac{y_2}{1+r}$,  which is decreasing in $r$. Higher interest rates lower my discounted future income, so I will be worse off.
$\beta > \frac{1}{1+r}$, then I will consume everything in period 2, so $x_1 = 0$ and $x_2 = (1+r) y_1 + y_2$. Then utility is equal to $\beta (1+r)y_1 + \beta y_2$ which is increasing in $r$. Higher interest rates increase my consumption in period 2.

As a conclusion, the consumer will gain by an interest rate increase if she is a net saver and will loose if she is a net borrower.
It is true that normally a risk neutral consumer will not respond her saving decisions by a lot if interest rates change. However if, for example due to the interest rate increase we shift from a situation where $\beta < 1/(1+r)$ to a situation where $\beta > 1/(1+r)$ then suddenly she will move all consumption from period 1 to period 2, which will mean a big shift from borrowing to saving.


GNP, GDP, GNI, GNDI and their relationships? GDP - Gross Domestic Product

GNP - Gross National Product

GNI - Gross National Income

GNDI - Gross National Disposable Income

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

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

GNI is simply a new name for GNP.  It is GDP plus net primary income from abroad (i.e. with primary income paid abroad treated as negative). Primary income is described in Chapter 11 of the IMF BOP manual

GNDI is GNI plus net secondary income from abroad (and similarly secondary income paid abroad is treated as negative).  Net secondary income from abroad is the same thing as is meant by net current transfers from abroad: see Chapter 12 of the IMF BOP manual