Do governments really need to tax us, when they can create money at will? I feel a contradiction between Prof. Howard Chernick's answer and Redditor "galivet"'s comment?  Who's correct? Chernick has

B.A., Johns Hopkins University, Economics, 1969
Ph.D., University of Pennsylvania, Economics, 1976

Here's What Would Happen if No One Paid Taxes

ICE: What would happen if no one filed a tax return?**
Howard Chernick: Well, the income tax is probably fifty or sixty-five percent of the federal government's money. Most people pay their income tax in the form of withholdings throughout the year. So the federal government has our money already, and what's happening on the end is just accounting reconciliations. But if no one filed his or her income tax, that would mean a huge increase in tax evasion, and much less money for the federal government, which already runs substantial deficits. So the government would have to borrow a lot more money, and the spending would have to go way down. After that, the US economy would begin to go into the tank. So as painful as it is, if you wind up owing taxes, as Oliver Wendell Holmes said, that's the price of civilization.

ELI5: When the US government uses emergency funding in the billions or even trillions, where is it getting the money from? : explainlikeimfive

The government does not need to fund its operation through revenue (e.g. tax revenue) because it create money at will. Taxes don't pay for government services; that's an illusion. Taxes accomplish two things: maintaining a mechanism whereby the government can uphold the value of the dollar by reducing the supply of dollars, and redistributing wealth. When the government taxes some people more than others while offering services to everyone (and more services to some), it's engaging in a kind of social engineering. The government could pay for all of its services and never tax anyone because it can create all the money it needs; the downside is that the dollar would decline in value over time and $\color{red}{\text{the government would have no way of stopping it (i.e. runaway inflation)}}$. When the government decides to destroy certain types of people's money to a greater extent than others, it's putting the burden of maintaining the value of the dollar on those who pay the greater share of the tax. And it turns out that those who pay more in taxes usually benefit more from the dollar maintaining its value anyway, so it's a reasonably fair deal.)

Is the red text true? Can't the government Quantitative Tightening?

It is true that government can print as much money as it wants but value of money is not constant. For example, under 101 econ quantity theory of money the price level is given by:
$$P = \frac{MV}{Y}$$
Where $P$ is the price level (with change in price level giving you inflation), $M$ money supply, $V$ velocity of money and $Y$ real output. Assuming $V$ constant government can increase money supply only by the growth rate of economy without incurring inflation. In more complex IS-LM AS-AD model the story is a bit more complex but the main message that government cant expand money supply freely without risking inflation holds (the equation above is actually an simplified equilibrium condition at money market in IS-LM).
Most modern governments run spending at a level of somewhere between $25\%-60\%$ GDP (see the OECD data) while real output grows at around $2\%$. There is no way that even the modest $25\%$ spending could be covered without government running two digits inflation in the best case scenario ignoring other issues this would create.

In fiat money system collecting taxes is what actually gives money value in the first place. See this thread that discuses this issue in greater detail (especially Holger's and Brian's +1 answers). If government will stop collecting taxes there is no guarantee that in the long term its currency will still be acceptable, especially since given the point 1 the currency would be rapidly loosing its value.

"Can't the government Quantitative Tightening?":
It can use it reduce the problem but it would not be any solution. Raising interest rates helps contract money supply itself but at the cost of  depressing economy and increasing unemployment. For example, prior to Volker disinflation the US inflation during late 70's and early 80's was even in the worst times below $12\%$ and to bring it down to low inflation it took interest rates that were almost as high as double the inflation rate with the funds rate reaching more than $19\%$ (see Goodfriend & King 2005).
Moreover, some point rising interest rates higher and higher would not help fighting inflation just due to the fact that $Y$, which varies negatively with interest rate $i$ (that is $\partial Y/ \partial i<0$ see for example Blanchard et al Macroeconomics an European perspective) would fall more than $M$. Furthermore, in the end raising interest rate can only reduce the broad money supply not actually the base money i.e. the actually printed coins and notes in circulation so if government will insist on continuing to print money to cover all its expenses raising interest rates would just slow the inevitable.

The view of those economists are not necessarily contradictory. One way how government could avoid some disastrous inflation is to slash its spending dramatically, borrow at rate that keeps debt to GDP stable due to growth and try to live of the seigniorage from some reasonable slow paced money supply expansion (assuming they would be still in demand due to issue covered in 2). According to Fed Dallas the US seigniorage revenue accounts for less than $2\%$ of real output so with some balanced borrowing my guesstimate is that US government could run spending on level $4-5\%$ of GDP in this scenario. That would be barely enough to cover US defense spending itself and not much else.  The second economist just assumes that government spending would not change and hence stresses the effect this would have on the value of money itself. There is no contradiction there both are valid options that government could pursue.


Why do we have to normalize the income of consumers when working with an Edgeworth Box in a simple trade model with Pareto optima? I was studying microeconomics and I confess I am not the brightest person for maths and sorry if this is very dumb but I get that we CAN normalize the income and I get where it comes from and how it is done, but I don't understand WHY do we have to do that. Can't we still do the maximization problem? I read further and understood that it is to "fix" a line in the box with slope Px/Py (with Py being the normalized price), I still don't understand why. What is the problem of finding the Pareto optimum in a freely moving point? Is it only to represent the budget constraint in the box?
I am probably missing a fundamental calculus/microeconomic fact.

If you by normalizing income mean normalizing one of the prices then yes you do not have to normalize it, but it makes everything easier since only the relative price matters.
All price vectors (2 dimensions) that solves the problem will have the same ratio. There are therefore usually infinitely many price vectors that solves the problem.

Regards


Which capital accumulation is right? $K_t = (1-\delta)K_{t-1} +I_t$ or $K_t = (1-\delta)K_{t-1}+I_{t-1}$? In a lot of models with capital, I find different variants of capital accumulation formula as follows:
$K_t = (1-\delta)K_{t-1} +I_t$ or

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

Which one is more economics-sound formula?

Both are economically sound. The notation is just a question of convention. The reason behind the ambiguity is that capital is a stock and investment is a flow variable. You are looking at capital in two different instants. Investment happens during the time between the two instants and its index is either the starting or the ending instant.


Correct way to measure Defence budget of a country like India I read that defence budget of the country is 2-3% of GDP, but isnt GDP  irrelevant when we are talking about expenditure? Shouldn't it be in a ratio of military import/total import?

So the budget is simply measured by adding up all the expenses.

The comparison to GDP that you reference is that we can measure how 'intensive' that sector is in the economy by what size of the economic pie is spent on that sector. So a country could spend a seemingly large amount of money, but if their overall economy is large enough, the military spending to GDP ratio would be small, indicating that the country isn't too devoted to that sector.

https://en.wikipedia.org/wiki/List_of_countries_by_military_expenditures

As we can see in the link, India spends 2.3% and the US spend 3.3%, while the actual number is different by an order of magnitude. So the ratio gives us a way to compare across countries as the absolute numbers ignore a country's size.


Does the demand for bad quality products increase when there is information asymmetry? Situation 1 In a situation where we have two markets one with good quality products and the other with bad quality products, if we are in a situation where the buyer knows which is the good product and which is the bad we can say that the demand for good quality products is superior to the bad quality ones.

Situation 2 Now if we go from situation 1 to situation 2 where the buyer does not know which is the good or the bad product we can say that the demand for good quality products decreases since the buyer is willing to pay less because he does not kbow if what he is buying is a good product.

Now what I dont understand is why do we say that the demand for bad quality products will increase when the demand for good quality products decreases?

Is it just because the decrease in demand for the good products is the same quantity as the increase in demand of bad product since the two products are the same type but not quality? Or is there another explanation for this ?

In the second case (information asymmetry) there is only a single market. This may be the market for the product with unknown quality or in case of adverse selection it may be a market for the bad quality product alone. Assuming there is no adverse selection the reservation price of a consumer w.r.t. the unknown good is the expected value of his reservation prices from the full information case. Thus it is a weighted average and will fall between the reservation prices of the good quality product and the bad quality product. Since this is true for all consumers, the demand function adjusts in the way you described.

What happens exactly (number of products sold) depends on the market structure, whether the seller of the goods is a monopoly or there is supply-side competition.


Generalization of the Heckscher-Ohlin Model The Heckscher-Ohlin Model is normally presented for the case of 2 countries, 2 factors of production and 2 traded goods, leading to statements that, subject to free trade and various other assumptions:

A country with a relative abundance of a factor will specialize in
and export the good whose production makes relatively intensive use
of that factor (the Heckscher-Ohlin Theorem).
The return to a factor will be equalized between the countries (the
Factor Price Equalization or Heckscher-Ohlin-Samuelson Theorem).

Do these results generalize, subject to the same assumptions, to cases with more than 2 countries, factors or traded goods, and what are good sources that treat this topic?  Of particular interest are cases with 3 factors: labour, man-made capital and natural capital.

I appreciate that the predictions of the Heckscher-Ohlin Model often differ from
empirical findings (eg the Leontief Paradox), but this question is about the model itself.

The HO model has been generalised. Vanek does a good job of it.

Instead of only two countries, there is an index of countries.

There are many industries.
Identical technology
Identical, homothetic tastes.

The HOV theorem states that if a country is abundant in a factor,
its factor content of trade in that factor should be positive, and
negative otherwise.

Empirically, this model is not that successful. Here is a good paper discussing the applications and results.

See below for that extension:
Vanek, Jaroslav, The Factor Proportions Theory: The N-Factor Case,” Kyklos, October 1968, 21, 749-755.


Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete? According to a textbook, in the context of uncertainty (e.g. in lottery), if the preference is complete, a monotone increasing but nonlinear transformation of a utility function would not represent the same preferences. Why is it so?

An example of such preference would be appreciated.

Consider lotteries over $\{x,y,z\}$. Let $u(x)=0, u(y)=\frac{1}{2}, u(z)=1$. Consider the nonlinear transformation f(t)=t^2. Let $v:=f\circ u$, so $v(x)=0,v(y)=\frac{1}{4}, v(z)=1$.

Consider two lotteries,  $P=(0,1,0)$ and $Q=(\frac{1}{2},0,\frac{1}{2})$.

$$E_P[u]=\frac{1}{2}=E_Q[u]$$

$$E_P[v]=\frac{1}{4}<\frac{1}{2}=E_Q[v]$$

In general, let $\succeq$ be a preference over lotteries $\Delta(X)$.  Let $U$ be a utility function of $\succeq$ that has the EU form, so $U(P)=E_P[u]$ for some $u$. Take any increasing transformation $f$ and define $V(P):=f(U(P))$ then $V$ will also be a utility function for $\succeq$, that is $V(P)\geq V(Q)\iff P\succeq Q$. However, unless $f$ is a positive affine transformation, that is $f(x)=Ax+B$ where $A>0$ then $V$ will not be an expected utility function. That is, there will not exists a $v$ such that $V(p)=E_p[v]$.


Endogenous Growth: Balanced Growth Path with CRRA Utility I've got a model of endogenous growth due to spillovers.

$\textbf{Model:}$
$$K_t=\frac{1}{n}\sum_{t=1}^nk_t$$
In this model, $k_t$ is chosen by agents, and $K_t=\bar{k}_t$ (the average of all $k_t$).

Now, agents want to dynamically maximize utility (under certain constraints) and they have CRRA (constant relative risk aversion) utility, so the maximization looks like:
$$\sum_{t=0}^\infty\beta^t\bigg(\frac{c_t^{1-\gamma}}{1-\gamma}\bigg)$$
$$s.t.\;Y_t=k_t^\alpha(E_tL)^{1-\alpha}$$
$$c_t+i_t=Y_t$$
$$k_{t+1}=(1-\delta)k_t+i_t$$
$$c_t,i_t\geq0$$

$E_tL$ is effective labor and the rest of the variables are typical  (I can give their definitions if requested).

One last addition to the model is that there are two equilibrium constraints:
$$E_t=\frac{K_t}{L}$$
$$k_t=K_t$$
$\textbf{Solution:}$

Using an Euler equation approach, two terms in the objective:
$$...\frac{\beta^t[k_t^\alpha K_t^{1-\alpha}+(1-\delta)k_t-k_{t+1}]^{1-\gamma}}{1-\gamma}+\frac{\beta^{t+1}[k_{t+1}^\alpha K_{t+1}^{1-\alpha}+(1-\delta)k_{t+1}-k_{t+2}]^{1-\gamma}}{1-\gamma}...$$
FOC:

w.r.t  $k_{t+1}$ and substituting in consumption:

$$\beta^tc_t^{-\gamma}=\beta^{t+1}c_{t+1}^{-\gamma}[\alpha k_{t+1}^{\alpha-1}K_{t+1}^{1-\alpha}+1-\delta]$$
Substituting in the equilibrium constraints:
$$c_t^{-\gamma}=\beta c_{t+1}^{-\gamma}[\alpha+1-\delta]$$
$$\implies \frac{c_{t+1}}{c_t}=[\beta(\alpha+1-\delta)]^{\frac{1}{\gamma}}$$
This implies that consumption grows at a constant rate which depends on preference parameters.

The next thing I want to prove that we have a balanced growth path. By this I mean that all variables grow at the same constant rate. $$\frac{k_{t+1}}{k_t}=\frac{c_{t+1}}{c_t}?$$
I have started to answer the question, but I have gotten stuck. Here is what I have so far:
$$k_{t+1}=k_t^\alpha K_t^{1-\alpha}+(1-\delta)k_t-c_t$$
In equilibrium $K_t=k_t$:
$$k_{t+1}=k_t+(1-\delta)k_t-c_t$$
$$\implies \frac{k_{t+1}}{k_t}=1+(1-\delta)-\frac{c_t}{k_t}$$
If we have a constant rate of capital growth, suppose:
$$\frac{k_{t+1}}{k_t}<\frac{c_{t+1}}{c_t}$$
If this is true:
$$\underset{t\rightarrow \infty}{lim}\;\frac{k_{t+1}}{k_t}=\underset{t\rightarrow \infty}{lim}\;1+(1-\delta)-\frac{c_t}{k_t}=-\infty$$
This means that the growth rate will continue decreasing. Now there are two ways this can happen. The first way is if $\underset{t\rightarrow \infty}{lim}\;k_t=-\infty$, which would clearly show that it couldn't be the case because capital cannot be negative. The second way which this could happen is if $\underset{t\rightarrow \infty}{lim}\;k_t=D$ where $D$ is some positive horizontal asymptote. If it did approach some asymptote, there is no reason why it could not be the case that consumption grows at a faster rate than capital. This is where I am stuck. How can I show that it cannot converge to some asymptote, and that $\underset{t\rightarrow \infty}{lim}\;k_t=-\infty$? Also, if there is an easier way to show that this model exhibits balanced growth paths, what is it? Any help would be greatly appreciated!

You have obtained

$$ \frac{c_{t+1}}{c_t}=[\beta(\alpha+1-\delta)]^{\frac{1}{\gamma}} \equiv 1+g$$

and

$$\frac{k_{t+1}}{k_t}=1+(1-\delta)-\frac{c_t}{k_t}$$

By equating you can show that there is a unique rule that maintains a balanced growth path

$$\frac{k_{t+1}}{k_t}=\frac{c_{t+1}}{c_t} \implies c_t =( 1-\delta-g)k_t$$

(too much consumption, by the way). This shows that the model has a unique balanced growth path.

If you want further to argue that the economy will indeed choose this path, you have to invoke the Transversality condition (which constraints the consequences that a chosen path should have  on capital accumulation), and maybe the Inada condition that your chosen utility function satisfies.


How do stock index futures help an economy? It seems that stock index futures affect economic growth, but I don't know how they work. Please can someone explain?
Thanks in advance~

Actually empirically there is causality going both ways there (i.e. economic growth helps stock index futures to grow but also stock index futures help economy to grow). However, focusing only on the effect going from futures to the economy, the reason for this relationship is the fact that capital markets (including the futures market), help to ensure efficient allocation of capital and this empirically has first order effect on economic growth (e.g. see Levine, 2005).
As summarized by Şendeniz-Yüncü, Akdeniz, & Aydoğan (2018):

... well-functioning futures markets
allow for greater and more efficient risk sharing, thereby making it possible for firms to
undertake relatively riskier projects and, hence, promote growth. On the other hand,
futures markets widely distribute equilibrium prices that reflect demand and supply
conditions, and knowledge of those prices allows investors, consumers, and producers
to make informed decisions. Consequently, the amelioration of information and
transaction costs fosters efficient resource allocation, thus leading to economic growth.

In addition note that literature overall suggest that the effect from the direction of stock futures gets weaker for high income economies. This is thought to be due to the fact that capital in high income economies is already more or less efficiently allocated.


Example production function with increasing returns to scale but diminishing marginal product I know that diminishing marginal returns even to all factors of production doesn't imply decreasing returns to scale. But could you please give me just an example of such production function?

Decreasing marginal returns to a factor means that keeping the other factors fixed, the marginal output generated by this factor is decreasing. When looking at returns to scale, we change all outputs. Increasing a factor with decreasing marginal returns can have an indirect effect in increasing the marginal productivity of other factors. If we increase all factors at the same time, the indirect effects may outweigh the direct effect. The production function $F:\mathbb{R}_+^2$ given by
$$F(x,y)=(x+1)^{2/3}(y+1)^{2/3}$$
has decreasing marginal factor productivities everywhere but not decreasing returns to scale (it doesn't have increasing returns to scale either).


The relationship between the expenditure function and many others! I dont understand the relationships between Hicksian demand, walrasian demand (marshallian), the expenditure function and the indirect utility function (including the value function V(b)).  I have found this subject very difficult and cannot comprehend how they relate to each other due to the formality that is used in the books I have available!

I understand how to derive the indirect utility, however, I need to be comfortable to show how I can use it to derive the expenditure function and the rest and how they differ in dualities!

Following up on the excellent MWG diagram in Amstell's answer, the fundamental observation needed is that holding $p$ fixed, $e$ and $v$ are inverses of each other. $e$ tells us the amount we need to spend to get a certain amount of utility $u$, while $v$ tells us the maximum amount of utility we can get from a certain expenditure $w$. Whenever we want to convert from utility to wealth, we use $e$; and whenever we want to convert from wealth to utility, we use $v$.

All the key identities can be derived from this observation. For instance, suppose we want to derive an identity for $\partial v(p,w)/\partial p_i$. We already know the corresponding identity for the expenditure function, $\partial e(p,u)/\partial p_i=h_i(p,u)$. To turn this into an identity for $v$, we substitute $w=e(p,u)$, obtaining $v(p,e(p,u))=u$, and differentiate with respect to $p_i$. The chain rule implies
$$\frac{\partial v(p,e(p,u))}{\partial p_i} + \frac{\partial v(p,e(p,u))}{\partial w}\cdot\frac{\partial e(p,u)}{\partial p_i} =0\\
\Longleftrightarrow \frac{\partial v(p,w)}{\partial p_i} = -\frac{\partial v(p,w)}{\partial w}\cdot x_i(p,w)$$
which, if we divide by $-\partial v/\partial w$ on both sides, becomes Roy's identity.

Or, suppose that we want to derive the Slutsky equation, which gives the relationship between the derivatives of Marshallian and Hicksian demand (decomposing a Marshallian demand change into substitution and income effects). Analogously to above, we can substitute $w=e(p,u)$ into Marshallian demand $x(p,w)$ to obtain $x(p,e(p,u))=h(p,u)$. Then, differentiating with respect to $p_i$ on both sides and applying the chain rule gives
$$\frac{\partial x(p,e(p,u))}{\partial p_i} + \frac{\partial x(p,e(p,u))}{\partial w}\cdot \frac{\partial e(p,u)}{\partial p_i} = \frac{\partial h(p,u)}{\partial p_i}\\
\Longleftrightarrow \frac{\partial x(p,w)}{\partial p_i}=\frac{\partial h(p,u)}{\partial p_i} - \frac{\partial x(p,w)}{\partial w}\cdot x_i(p,w)
$$
In general, I think the heuristic "switch between $w$ and $u$ as needed using $v$ and $e$" allows you to get pretty much everything here. (A similar heuristic is also useful if you ever deal with Frisch demand systems, where marginal utility $\lambda$ plays the same role that $w$ and $u$ do in Marshallian and Hicksian demand systems.)

Of course, there is one other key fact used above, which is $\partial e(p,u)/\partial p_i = h_i(p,u)$, which for $w=e(p,u)$ becomes $\partial e(p,u)/\partial p_i = x_i(p,w)$. This is best viewed, instead, as a direct consequence of the venerable envelope theorem.

($\partial v/\partial p_i$ can also be derived from the slightly more advanced version of the envelope theorem, where constraints as well as the objective are allowed to depend on a parameter. Since varying $p_i$ in the utility maximization problem changes the budget  constraint rather than the objective, the envelope theorem says that its effect will depend on the Lagrange multiplier on that constraint, which is the marginal utility $\partial v/\partial w$ of wealth. This is a good intuition for why the expression for $\partial v/\partial p_i$ is more complicated than the expression for $\partial e/\partial p_i$, picking up an extra factor.)


Game theory - Definition problem - Strategy vs Action A one definition is given by :

  Strategy is one of the possible actions of a player

But I'm having a trouble. When working with games, We specify a strategy set $S$ and a strategy $s \epsilon S$. For instance consider a typical normal form game, battle of sexes for instance. We have $2$ strategies for each player so the set $S$ has two elements. According to the definition here what would be the actions? What is a "possible action"?

I'm asking this because in the definition of Bayesian games we are given an Action set instead of a strategy set. Can anyone clear things up to me?

I had the same question few weeks ago. I attach the link below that may help you, but here is the approach I took to solidify the difference.

When action and strategy differ in game theory

Don't associate the distinction between action and strategy with whether the game is in normal form or extensive form or sequential or not. This can cause more confusion.

When you want to define strategy, always think of "contingency".

Action is a set of possible things you can do when you are called upon to move. For example, suppose you want to sell a used car as dealer. As seller, what is it that you CAN DO when you are "called upon to move"? Simple: offer high price or low price.

But you immediately realize things can get complicated if, say, dealer has more information on the car's condition. You might suspect that car behind the dealer is a good used card or lemon. Although you still get to offer high price or low price at the end of the day, as player of the game, you must set a contingency plan when the car is good or lemon.

Harsanyi introduces "nature" to do exactly this. The condition of car is simple: good or lemon. This is described as the state space of the game. Both players, seller and buyer, understand the ex-ante probability distribution over this state space, meaning you and potential buyer know the probability you get good car or lemon. Therefore, as dealer, you would have action space $A_1=\{H,L\}$ indicating offering high or low price. However, your strategy space would be $S_1=\{(H,h),(H,l),(L,h),(L,l)\}$ where first entry of the pair is your action when the car is good and second entry is your action when the car is lemon. It is a game plan laid out for you in every possible scenario.

One good exercise may be to see if you can construct the strategy set for buyer if she doesn't observe the condition (i.e. state) of the car the nature draws.


Are there economic policies that help countries fight corruption? Are there particular taxes or subsidies or public goods that a country's economic authority could implement to help in the fight against corruption? While the rule of law seems to be the first order issue, and often government is where a large part of corruption exists,  it's still seems like it's  phenomenon that could be affected by economic policy.  Taxes, expenditure rules, purchasing rules, etc, are potentially useful. Maybe!

Kaushik Basu has proposed (Why, for a Class of Bribes, the Act of Giving a Bribe should  be Treated as Legal) legalizing paying bribes to separate the ties of criminality between the bribe payer and receiver. This allows the bribe payer to pay the bribe and report the bribe taker. If bribe paying is illegal then the shared criminality prevents this.
Dina Pomeranz empirically examines the widely held belief that VAT taxes discourage tax evasion (No Taxation without Information Deterrence and Self-Enforcement in the Value Added Tax) and finds that they do indeed discourage tax evasion:

Claims that the VAT facilitates tax enforcement by generating paper
trails on transactions between  firms contributed to widespread VAT
adoption worldwide, but there is  surprisingly  little  evidence. This  paper  analyzes  the  role  of  third  party  information for
VAT enforcement through two randomized experiments among over 400,000
Chilean  firms.  Announcing additional monitoring has less impact on
transactions that are subject to a paper trail, indicating the paper
trail's preventive deterrence effect. This leads to strong enforcement
spillovers up the VAT chain.  These  findings confirm that when taking
evasion into account, significant differences emerge between otherwise
equivalent forms of taxation.
Other forms of taxation that are harder to monitor and enforce provide more opportunities for corruption and so switching to a broad VAT may reduce corruption.

Another possibility is outsourcing corruption enforcement:

The International Commission against Impunity in Guatemala (Spanish:
Comisión Internacional contra la Impunidad en Guatemala, CICIG) is an
international body charged with investigating and prosecuting serious
crime in Guatemala. It was created on December 12, 2006, when the
United Nations and Guatemala, under the government of Óscar Berger,
signed a treaty-level agreement setting up CICIG as an independent
body to support the Public Prosecutor's Office (Procuraduría General
de la Nación), the National Civilian Police (Policía Nacional Civil)
and other state institutions in the investigation of a limited number
of sensitive and difficult cases. The ultimate goal is that through
CICIG's work, national judicial sector institutions will be
strengthened to continue to confront illegal groups and organized
crime in the future.

Wikipedia: International Commission Against Impunity in Guatemala (CICIG)
Civil service exams (as opposed to the spoils system which still has defenders) were, among other reasons, adopted as an anti-corruption mechanism. Perhaps these countries could also adopt such exams.

This article traces a number of cases of graft in Zambia to show the
importance of this practice within the political system. Graft is
treated as one element of a spoils system through which clientelism
operates and through which, more generally, the state is used as a
resource for private ends. Graft and patronage are shown to have
negative consequences for the state through undermining efficiency and
legitimacy and displacing policy ends. But perhaps most importantly,
it is argued that graft ultimately involves a transfer of wealth
between classes and more specifically is an important factor in the
growth of an indigenous owning class.

Political graft and the spoils system in Zambia — the state as a resource in itself
Well defined property rights provide fewer opportunities for regulatory discretion and therefore fewer opportunities for bribe takers to exert influence. Easier said that done.
Restrict financial privacy of and gift taking, side-employment, and post-employment by government employees. May be hard to enforce in low-development societies.


Measuring macroeconomic variables more frequently What would be the costs and benefits of collecting and releasing macroeconomic data, say, monthly instead of quarterly, or weekly instead of monthly? And what are the barriers to doing so?

Looking at the US Economy,  the US Bureau of Economic Analysis (BEA) and specifically ch. 3 p. 49 of the Handbok of NIPA (National Income and Product Accounts), we read

  "The data that BEA uses are collected from a variety of sources and are
  usually collected for purposes other than for incorporation into BEA's
  estimates. Data collected by federal government agencies provide the
  backbone of the estimates; these data are supplemented by data from
  trade associations, businesses, international organizations, and other
  sources. The Government data are from a number of agencies, including
  the Commerce Department's Census Bureau, the Labor Department's Bureau
  of Labor Statistics (BLS), the Treasury Department, the Office of
  Management and Budget, and the Agriculture Department.
  “Administrative” data are data that are tabulated by federal
  government and by state and local government agencies as a byproduct
  of administering their programs—such as processing corporate tax
  returns, regulating public utilities, and issuing building permits.
  “Statistical” data are data collected by the federal statistical
  agencies, such as the Census Bureau and BLS. These data consist of
  periodic economic and population censuses and a wide range of sample
  surveys, such as those that collect data on manufacturing and trade,
  employment, and prices. The relatively few surveys that BEA conducts
  cover international trade in services and international direct
  investment, both by foreign companies in the United States and by U.S.
  companies in foreign countries. The source data available to BEA are not always ideal for the preparation of the
  NIPAs. BEA must develop methods that transform the best available data into estimates that are consistent with the NIPA concepts and framework and that fill gaps in the
  coverage of the source data."

Macro-data are not just micro-data simply sitting out there and only needing adding up. So "collecting macroeconomic data" is a misleading term : "laboriously producing macroeconomic data", where collection is just a first step, moving on to selection, clean-up, adjustment, homogenization, and estimation, is more like it. This is a vast enterprise, even with today's Information Technology capabilities, even for smaller economies than US.

Increasing the frequency of macro-data amounts to increasing the total output from this data-production function, which looks convincingly like a huge increase in input factors absorption. So to do it, it would increase costs substantially.

Moreover, the "collected for reasons other than..." part, indicates that a lot of procedures should be disrupted and changed in order to achieve that. Also, the number of different primary sources implies too many people and institutions should change their way of doing things. These are significant barriers on their own, irrespective of cost-issues.

What could be the benefits?
One could think that it would permit a "better" fine-tuning of the economy? -to the degree that one believes that an economy can really be fine-tuned by its Government (it can certainly be affected, but fine-tuning is a whole different game).

What about the benefits to the private sector? It is indeed the case that, say, Gross Domestic Output is produced every day. Assume that in some magical way, GDP was recorded and published every day. So we could follow GDP as we follow the Stock Market. We will be able to observe the everyday variability of output. Would that be beneficial? No, on the contrary, it would be misleading. Why? Because, although GDP is produced everyday, it mostly is produced based on structural relations (contracts, technologies, customs, knowledge etc) that have a lower frequency of change -and for reasons other than lack of data. So its everyday variability would be mostly due to pure randomness or exogenous factors like the weather -and observing it would only torment us towards trying futilely to do something about it (at our own micro-level).

What about the benefits to the discipline of Economics? Presumably, more data is always better. Is it? By increasing the number of instances of "asking for" and recording data about an economic variable, we increase the instances for which we may have measurement error - and this may very well degrade the overall quality of our data. It is a standard wisdom departed in undergraduate statistics classes, that even if we could conceivably run a census than just collecting a sample from the population under study, it would be better to have just the sample, because the error of representability would most likely be smaller than the error of measurement we would have if we attempted to record the whole population.

That would offset the perceived benefits of having pushed the magnifying glass closer to the object of study. And sometimes, it is better to look from a certain distance, anyway.

Closing, by a "Laffer-curve" style of argument, one could argue that there must exist some optimal frequency to have available macro-data. I am not saying that what we do have now is this optimal frequency, but I doubt making the frequency higher is the way to go (my opinion is that modern economies of the western world at least would be tracked better under a three four-month cycle - Jan-Apr, May-Aug, Sep-Dec -it seems to me that this scheme combines better the seasons with the social aspects of life and economic activity).


If banks create money by lending it out, how are they taking any risk? When I lend money to someone and they don't pay it back, I lose my money.  I can only lend out money that I own (or borrow).  I understand that when a bank lends money, that money is created the moment they lend it out.  If that is so, how does the bank take any risk in lending it out, considering they didn't own it in the first place?

Try the magic of double entry bookkeeping to see that creating money does not immediately make a bank more valuable. Initially the loan is matched by a deposit, and this is creation of what is effectively money:

Bank A has an asset: a newly created loan to customer B
Bank A has a liability:  B's newly created deposit with Bank A, which B can spend

B then spends the amount with C, who banks with D, and the deposit is transferred on B's instruction to C's account. Now

Bank A has an asset: a loan to B
Bank A has a liability:  Bank A owes money to Bank D
Bank D has an asset: Bank A owes money to Bank D
Bank D has a liability:  C's deposit with Bank D

Bank A now needs to settle with Bank D: this can happen through clearing if other customers are moving money to Bank A, but it is easier to imagine that Bank A tells the central bank to give some of A's reserve deposits there to Bank D. So Bank A has an asset, namely a loan to B, but this has been offset by an increase in liabilities or a reduction in other assets.  Similarly Bank D has an increase in assets, offset by a liability to C. The created money is now C's deposit with D, which C can spend.

Suppose the loan to B then goes bad and is never likely to be repaid.  From Bank A's point of view, the value of that asset falls to zero, while the associated increase in liabilities or reduction in other assets remains, and Bank A has to take this as a loss (negative profit), with the side effect of destroying that amount of money.  Bank A is now worth less (net) than when it started the loan to B.  This is the risk for Bank A from creating new financial assets and liabilities (i.e. new money).

If instead nothing goes wrong, B makes some money selling to E, pays A some interest, and possibly repays the loan (in which case the total amount of money in the economy reduces again).  In this case Bank A is more valuable (net), not directly from the creation of the loan or from its repayment or from use or return of the corresponding deposit, but from receiving the interest on the loan.

When Bank A makes too many loans, it may run out of reserve deposits at the central bank after its customers spend the new money.  The solution to this is to take deposits from other customers, as Bank D does in the example above.  But these deposits may need interest to attract them, at a cost to the bank.

So Bank A's overall profit on loans and deposits is the difference between the interest it receives from the loans it makes and the interest it pays on deposits it takes, allowing for the cost of bad loans; it may also make money from fees and have to pay for staff and other expenses.  The creation and destruction of money by making the initial loan and it being repaid is not Bank A's particular concern, though it is for the macroeconomic policy of the central bank and the government; if the economy grows and more loans are made, then the money supply also rises and the hope it that will happen neither too quickly nor too slowly.  Ultimately Bank A cares about the risk from bad loans, the interest rate margin and its administrative costs.


What are some of the good textbooks on Modern Monetary Theory and the Development of Monetary Theory? I am trying to study modern monetary theory for my research. Recommendations, please? Thank you!

You ask for sources on MMT and then sources on development of monetary theory. I don't know about the former (but I know there are some users here who are fans of MMT so hopefully they will hook you up with some good sources) but when it comes to the latter then a classic text that covers development of contemporary monetary theory is Walsh Monetary Theory and Policy (The MIT Press).
It is probably one of the most comprehensive textbooks that cover monetary theory all the way  to the most recent advances. It unfortunately does not cover MMT because it is not an accepted theory in profession but has very good treatment of development of monetary theory all the way from canonical models to present day state of the art models.


Is it possible to derive indifference curves given marshallian demand function? In a two good world, will a marshallian demand function the likes of D(p,m) where p is the price of one good and m the income yield a utility function or indifference curve function? If so, how does one go about solving this?

Yes, under some conditions. This is the classic integrability problem: for detailed discussion, see some excellent notes by Kim Border.

Several other technical conditions are required, but the most economically substantive condition is that the Slutsky matrix must always be symmetric and negative semidefinite. To be concrete, if we define the $ij$th element of the Slutsky matrix at $(p,m)$ to be
$$\sigma_{ij}(p,m)=\frac{\partial D_i(p,m)}{\partial p_j}+D_j(p,m)\frac{\partial D_i(p,m)}{\partial m}$$
then we must have $\sigma_{ij}(p,m)=\sigma_{ji}(p,m)$ for all $(p,m)$, and also for any vector $v$ we must have for all $(p,m)$
$$\sum_i \sum_j \sigma_{ij}(p,m)v_iv_j \leq 0$$
The necessity of these conditions follows immediately from basic consumer theory, which shows that if Marshallian demand is derived from constrained maximization of a utility function, then the Slutsky matrix is symmetric and negative semidefinite. But the sufficiency of these conditions (in conjunction with some other technical assumptions) for us to back out a utility function is a more complicated matter, and to get the details I recommend Border's notes or some other advanced micro source.

If, assuming that the Slutsky conditions hold, you want a rough practical way (ignoring the technical subtleties) to back out indifference curves in the typical two-good case, the simplest way is probably to use your knowledge of demand to determine the compensating change in expenditure that is necessary to adjust for a given change in prices. Specifically, for either $i=1,2$ use the identity
$$\frac{\partial e(p,u)}{\partial p_i} = h_i(p,u) = D_i(p,e(p,u))$$
which, given knowledge of the Marshallian demand function $D$, is a differential equation in the expenditure function $e$. Starting with some initial values $(\bar{p},\bar{m})$ that produce some unknown utility $\bar{u}$, we know that $e(\bar{p},\bar{u})=\bar{m}$. Then, varying $p_1$, we can integrate the above differential equation for $i=1$ to obtain $e(p_1,\bar{p}_2,\bar{u})$ for any $p_1$. And then we can get the Hicksian demand vector
$$h(p_1,\bar{p}_2,\bar{u})=D(p_1,\bar{p}_2,e(p_1,\bar{p}_2,\bar{u}))$$
for any $p_1$.

Since these Hicksian demands all correspond to the same utility $\bar{u}$, they are on the same indifference curve. By varying $p_1$, we will be able to trace out many different points on this indifference curve. In fact, if demand is sufficiently well-behaved, then we can trace out the entire indifference curve by varying $p_1$ enough in either direction. (By the way, "tracing indifference curves" is all we can do in any event: since the cardinality of utility is irrelevant to Marshallian demand, we can only retrieve ordinal properties like indifference curves and their ordering.)


What's the speed of convergence to the potential GDP? (Empirical estimates) Suppose a reform makes potential GDP higher, at what speed does actual GDP close the gap? I'm looking preferentially for empirical estimates, but anything that allows me to narrow it down will be helpful.

Dietz Vollrath says (https://growthecon.wordpress.com/2014/12/03/insert-policy-here-wont-boost-growth-rates/) that there's copious empirical evidence saying that the rate is about 2% (2% of the gap is closed each year); he doesn't provide sources and it seems awfully slow, but he is very confident on that. I've tried to find such an estimate, and failed.

Thanks!

First of all the speed is not constant, it declines as one gets closer (at least according to the text book predictions).

A classic paper on among others this issue is the one by Mankiw, Romer and Weil in the 1992 QJE "A Contribution to the Empirics of Economic Growth" They find convergence rates of about 1 to 2%. The paper is cited 16,000 times in Google scholar, so no doubt you'll find some material there too. I'm no macro-economist, but it seems an area of active research.


Best micro/macroeconomics books Does anyone of you could recommend me some good Macroeconomics and Microeconomics books based on your personal experience. I am an engineer and I do not have a background in Economics. I am planning to apply for a graduate school in Economics (MA if I am not qualified for a PhD as I already have a MSc in Engineering).

What would be the best way for me to learn some principles of economics and not to struggle if I get accepted into a graduate program while other graduate students have lots of experience and/or background in Economics? I just want to be on the same level with them at least during classes and be able to understand what is being given or taught.

I have looked it up on the internet, but people suggested all kind of books, but mostly intermediate and/or for those who already have background either in Economics or business related subjects.  The future graduate programs want me to have a background in Microeconomics , Macroeconomics, and Econometrics at least...

Although this question will be flagged and closed I assume, I would recommend getting a variety of texts. Mankiw has a good intermediate macro book, that can get you from zero to a foundation, however his introductory book isn't as good.

For econometrics, Woolridge gives a good bang for your buck, but I like Gujarati's basic econometrics as well. For time series, Enders' "Applied econometric time series" is my bible.

For micro I'm not as sure, I didn't have any great experiences with introductory texts. I can't really give a good opinion on the intermediate level either, as I've only used Varian's.

Once you get an idea of the concepts the best thing to do is to delve right into academic journals, so that you can start learning how to read them. Just that skill will help you be able to catch up fast.

I assume you're already strong in linear algebra and your other math, and some of your engineering will carry over to economics, especially your ability to think about minimizing and maximizing.

Good luck!


Lecture note recommendations for the endogenous growth model (EGM) I'm curious if anyone has a recommended lecture notes, slides, or book, anything really, that goes through evolutions of basic models like $y=AK$, to $y=AK^aL^{1-a}$, to $y_t=A_tK_t$, to $y_t=A_tK^{a}_tL_t^{1-a}$, etc. such that the models get more complex. I'm following along with the lectures in class but all the asides, comments on real-world examples, aren't helping me solidify the intuition for the big-ideas that are underlying some of the evolutions. Basically, why some models are too simple, and what adding more variables does to the model.

Previous threads focus on discrete models in econometrics (hit markets for ideas I'm concerned with lead me here), so not that relevant.

I think that the notes closely resembling what you are looking for - a gradual explanation of how the growth theories develop - are those from Acemoglu. Check his web page for slides and look in your school library for Intro to Modern Economic Growth. The slides are very detailed I think.

Growth models are, I believe, presented very rigorously. Additionally, in my opinion, it is discussed how they are connected.


(Ricardian model)Is it correct that complete specialization in comparative advantage CAN lead to DECREASE in total production? I have the model in my electronic spreadsheet (created by me) and its results quite suprised me. In short, complete specialization (I just call it specialization) in good where a country has comparative advantage CAN lead to inefficiency, to decrease of production of one of the goods (cheese in this case). This result suprised me and I would like it checked in case a mistake (in my reasoning or calculations) was made. (I can also share the spreadsheet if you want)

Suppose there are two countries, USA and France. Each country has industries: cheese production industry and wine production industry. Each industry in each country has exactly 1000 workers(the top is the American workforce, the bottom is the French workforce)

But technologies are different.

From this we conclude that opportunity costs are following:

France has comparative advantage in cheese, while USA hold comparative advantage in wine. So France should concentrate all its laborforce in its chesee industry while USA should concentrate all its labor force in wine industry.

... except it will be bad news for world cheese production.

Production of cheese and wine in both countries before trade and (complete) specialization (the top is the American production, the bottom is the French production):

Production of cheese and wine in both countries after trade and (complete) specialization (the top is the American production, the bottom is the French production):

Now France produces all cheese in the world. But its cheese production technologies are too labor-intensive to produce enough cheese to compensate for fall of cheese production in USA. In order to avoid this USA will have to employ at the least 500 of its workers in cheese production, despite it beign American comparative disadvantage.

Thus we can conclude that in this case full specialization in cheese is a bad idea.

Its not correct to say that production will be lower in the solution to the Ricardian model (in your case full specialization of US is not equilibrium outcome). In general in Ricardian model the production after specialization will always be either the same (if the relative opportunity costs are exactly same) or production will be higher. The reason why you got it lower in your case is that your model omits demands for the two goods and by your assumption on production technology US is economically big country while France is economically small (meaning the production possibility frontier (PPF) of US severely outstrips the PPF of France).

In situations like these you will find that only small country fully specializes while the big country specializes only partially. The reason for this is that even if the small country produces on full capacity it simply wont be able to satisfy the world demand, so once the US produces enough wine to fill up the word demand it will be also allocating the rest of the resources to cheese.

Fully deriving the optimum solution with adding utilities would take too much space so instead of full proof consider the following numerical simulation with your own example.

As you have shown in autarky we will have the following production:

US Cheese: 500 US Wine:  1000
France Ch: 250 France W:  333
World  Ch: 750 World  W: 1333

Now consider possible scenario with full specialization France (all in cheese) and partial US (1500 labor in wine and 500 in cheese):

US Cheese: 250 US wine: 1500
France Ch: 500 France W:   0
world Ch:  750 world W: 1500

Now you can see the production of cheese is exactly the same as before plus world has more wine. With just one extra unit of labor in cheese in US you would still get more cheese and also more wine compared to autarky.

Now to get an exact optimal solution you need to explicitly include consumer utility and demand, and you would see that in this case there would be excess demand that France could not satisfy which would be allocated to US. For the full treatment see Feenstra, R. C. (2015). Advanced international trade: theory and evidence. Princeton university press.

The undergraduate treatment of Ricardian model does not include demand functions explicitly because as long as none of the two countries have production frontiers that do not strictly outstrips the PPF of the other at all points you will always get full and never partial specialization so the exact nature of demand function does not matter (notice that in undergraduate Ricardian model you wont even find the final distribution of the goods unless the final demands are assumed in the question - this is to simplify the model to make it easier to solve but it does not represent the full model in its modern specification)

PS: of course on off equilibrium path any combination of outputs that satisfies the resource constraint is possible


Creating a tailored sample from panel data As a small part of a project, I have been asked to tailor a large panel dataset I have built into a form that is more comparable to one specific country.

So I have done the following:

Look at the ranges of my dependent variable, explanatory variables and controls for the country of interest.

Drop any firm-time observations that fall outside the ranges of any of these variables.

Run my regression on the truncated sample.

I was wondering whether there are any serious cons of this approach - particularly given that my method will include only a subset of the observations for some firms. Bear in mind that this is meant to provide a rough and ready indication rather than be a super robust exercise.

Many thanks for your help.

Your approach seems no good. Let us make it really simple: You have only the dependent variable and you want to compare the averages across countries. You keep the firms whose $y$ values are inside the range. By doing this, you are (sort of) equating $y$ values, which you aimed to compare. This is strange. In fact, this leads to endogenous sample-selection.

It seems, however, acceptable to keep only comparable firms (rather than firm-year) based on the exogenous variables.


Quality Provision Game A seller owns a single unit of an invisible good. It is worth $v(s)$ to a buyer, where
$s ∈ R^+$ is the quality of the good. The function $v(·)$ is strictly increasing and strictly concave with
$v(0) = 0$. Quality is chosen by the seller, and the cost of providing a good of quality $s$ is given by a
function $c(s)$, which is strictly increasing and strictly convex with $c(0) = c
'(0) = 0$ and $c'(0) < v'(0)$.
(Implicit in this description is the assumption that the buyer’s preferences are quasilinear is some good
other than the one being traded.)

There are many parts to this question, but I'm most concerned about the step up. Which asks write down the first-order conditions to find the pareto optimal quality that maximizes the sum of the utilities and confirm that it is positive.

I'm thinking that the utility functions are as follows:

$u_B(x,s)=x+v(s)$

Where $x$ is dollars spent on anything besides the good that is being traded (like the composite commodity theorem)

$u_S(s)=v(s)-c(s)$

The utility of the seller would just be the value they can sell the good for minus it's cost?

Thus,
$max_s(u_B+u_S)=v'(s)+v'(s)-c'(s)=0$

This results in the following equation:

$2v'(s)=c'(s)$

Which doesn't make sense because of the assumptions of the first derivatives in the statement of the problem. So I'm not quite sure what I am doing wrong. Any assistance would be greatly appreciated. Thanks in advance!

Maybe I'm missing some information about this model, but the intuitive interpretation to me is that $$u_B = v(s) - p $$ and $$u_S = p - c(s)$$ where $p$ is the price paid by the buyer for the good.

Pareto optimality is obvious, and it's easy to check that the Pareto optimal quality is positive.


Where can I find data on market capitalization? I am working on Home Equity/Bond Bias and need data to calculate the indicators of Home Equity Bias. So where can I find data on market capitalization (stocks and bonds) by year for each country?

Many thanks for your help.

Market capitalization of listed domestic companies (% of GDP) across years and countries from the World Development Indicators in the World Bank data website or the United Nations one.
FRED economic data on market capitalization.
Focusing on European Countries: the ECB website.


Is the European Single Market a Free Trade Area? The European Single Market is (obviously) a Single Market.

Are Single Markets also free trade areas?

Free trade area means there's no customs checking goods traded within that area.

From Wikipedia:

  The European Single Market, Internal Market or Common Market is a single market which seeks to guarantee the free movement of goods, capital, services, and labour – the "four freedoms" – within the European Union (EU).

So goods are traded freely within the EU, and hence EU is an FTA.


Common Knowledge and the Red Hats Puzzle Here is a puzzle that is supposed to help illuminate common knowledge in game theory. Three girls are sitting in a circle, each wearing a red or white hat. Each can see the color of all hats except their own. Now suppose they are all wearing red hats.

It is said that if the teacher announces that at least one of the hats is red, and then sequentially asks each girl if she knows the color of her hat, the third girl questioned will know her hat is red. I understand the reasoning there. The first must have seen at least one red hat on the other two to say I don't know. And the second girl must have seen a red hat on the third, or else she would deduce that the first girl saw a red hat on her.

What I don't understand is the necessity of the teacher. Everyone knows there is at least one red hat. And, if we start with common knowlege, they should figure out that everyone else knows that. So is the teacher only introduced if common knowledge is not an assumption?

Source: http://cowles.econ.yale.edu/~gean/art/p0882.pdf

Without the teacher, everyone knows that there is at least a red hat, but nobody knows that everyone knows - the fact is not common knowledge.

With the introduction of the teacher,

Girl 1 doesn't answer. Due to common knowledge, 2 and 3 can reason: "1 knows there is at least one red hat, and since she doesn't know her hat color, 2 and/or 3 must have a red hat.

Without the introduction of the teacher,

Girl 1 doesn't answer. Without common knowledge, there is nothing 2 and 3 can reason on top of their prior knowledge: 2 will keep knowing that 3 has a red hat, and 3 will keep knowing that 2 has a red hat. Nothing more.

In other words: Without the teacher, the set of knowledge is:

1: 2+3 have red hats
2: 1+3 have red hats
3: 1+2 have red hats

The teacher works as an injector of additional knowledge:

1: 2+3 both know that there is at least one red hat
2: 1+3 both know that there is at least one red hat
3: 1+2 both know that there is at least one red hat

And, common knowledge means that in the next level, everyone knows that everyone knows

1: 2+3 both know that I know that there is at least one red hat

etc, ad infinitum. This additional information is required to solve the puzzle.


Where does investment originate from in the circular flow model? The above image is from my macroeconomics textbook.
I’m struggling to understand the “financial markets” corner. If financial markets refers to banking and perhaps the stock market, is it true that its only input is savings from households? Don’t firms also participate?
And if investment refers strictly to capital goods and additions to inventory, then shouldn’t the I arrow originate from firms, who make the investments?
If everything that a firm makes becomes income, then where does it get money for investment? It seems from the diagram that all of the firm’s profit goes straight to the resource market—paying employees, etc.
(On a more basic level, how does wealth ever actually increase/the economy ever grow if everything is a cycle? I understand that a central bank could do things in the financial market to increase money supply, but assuming such a system as a gold standard, is it even possible for the economy to grow?)
I appreciate your answers.

Investment ultimately comes from households through savings. From a macroeconomic perspective savings is equal to to investment ($S=I$).
Investment comes from income because saving is portion of income that is not consumed. For example, if your income is $\\\$1000$ and you consume $\\\$700$ of it the $\\\$300$ you are left it is by definition saving and saving is ultimately equal to investment.
For example, when you put $\\\$300$ into your bank account you are actually inserting it into financial sector and bank will actually use the money on your deposit account to finance loans for investment even if you might not know about it.
This is why the arrows are as they are. Households supply saving to financial markets where firms who need money to make investments get it from.
The economy grows because even though everything is a circle the income increases each year as economy becomes more productive thanks to improvements in technology. For example, if today you can make 100 widgets then your income will be equal to the value of those 100 widgets. If thanks to increase in technology you can produce 200 widgets your new income is equal to the value of those 200 widgets.


Solving a LRE model in King-Watson form using alternative algorithms I have a linear rational expectation model that is in the King-Watson form:

AE_{t}y{t+1} = By_{t} + C_{0}x_{t} + C_{1}x{t+1}  (1)

with the driving process

x_{t}     = Q \delta_{t}                          (2)
delta_{t} = \rho \delta_{t-1} + G \espilson_{t}   (3)

I have a fairly large system and would like to solve it using a different algorithm than the King-Watson one, such as the Anderson-Moore algorithm (but am completely open to anything fast). However, I have so far failed in implementing the KW in Anderson-Moore. Any ideas on (i) how to solve the problem using the Anderson-Moore algo, or (ii) a different algorithm that can be used?

Note, my system of equations in (1) is about 1000 lines.

Here is a toy example for parameterization

A  = [1,0,0,0;0,1,0,0;0,0,-1,-1;0,0,0,0];
B  = [0,0,1,0;0,0,0,1;0,0,-1.1,0;0,-0.7,0,1];
C  = [0,0;0,0;4,1;3,-2];
Q  = [1,0;0,1];
RHO= [0.9,0.1;0.05,0.2];
G  = [1,0;0,1];

which should yield

\Pi = [1,0,0,0; 0,1,0,0;0,1.225, -21.0857, 3.15714; 0, 0.7, -3, 2];
M   = [0,1.225, -21.0857, 3.15714; 0, 0.7, -3, 2; 0,0,0.9,0.1; 0,0,0.05,0.2];

The two approaches specify the linear rational expectations problem somewhat differently, but one can reconcile the solutions they produce.  In addition to the difference in the equation system specification, KW use the "predetermined variables" concept while AM does not.

King and Watson (KW) address a model of the form

$$
  A E_t y_{t+1} = B y_t + C_0E_t x_t +C_1 x_{t+1}\\
  x_t=Q \delta_t +G \epsilon_t\\
  \delta_t=\rho \delta_{t-1}\\
  y_t=
  \begin{bmatrix}
    \Lambda_t\\k_t
  \end{bmatrix}
$$

the $k_t$ are predetermined variables.

The algorithm produces solutions of the form
$$
 y_t=\Pi s_t\\
  s_t=M s_{t-1} + \bar{G} \epsilon_t\\
  s_t=
  \begin{bmatrix}
    k_t\\ \delta_t
  \end{bmatrix}
$$

Anderson Moore (AM) cast the problem as

$$
  H_{-1} w_{t-1} + H_0 w_t + H_{+1} E_t{w_{t+1}} = \psi_{\epsilon} \epsilon_t + \psi_c
$$

and produce solutions of the form

$$
  w_t=R w_{t-1}+ \phi \psi_\epsilon \epsilon_t + (I-F)^{-1}\phi\psi_c
$$

where
$$  \phi=(H_0+H_{+1}R)^{-1}\,\, \text{and} \,\, F=-\phi H_{+1}
$$

In the AM setup, the $w_{t-1} $ are given as data and cannot be affected by the $\epsilon_t$ or
the  current or future values of $w_{t+i}\in, \{w_t,w_{t+1},\ldots\}$.
  In KW,  the ``predetermined'' variables at time t depend only on the already realized shocks.  So the
$\epsilon_t$ only influences future $k_{t+i} \in \{k_{t+1},k_{t+2},\ldots\}$  Consequently, to square AM and KW, the dating of some of the model variables
and their time subscripts  will differ.

Set

$$
 w_t=
  \begin{bmatrix}
\Lambda_{t}\\    k_{t+1}\\x_t\\  \delta_t
  \end{bmatrix}
$$

We will need to partition the KW $A=
\begin{bmatrix}
  A_1&A_2
\end{bmatrix}
$ and $B=\begin{bmatrix}
  B_1&B_2
\end{bmatrix}$
 matrices to accomodate  these differences.

Construct the AMA $H$ as

$$
H_{-1}=\begin{bmatrix}
  0&-B_1&0&0  \\
  0&0&0&-Q\\
  0&0&0&-\rho
\end{bmatrix}\\
H_{0}=\begin{bmatrix}
  -B_2&A_1&-C_0&0  \\
  0&0&I&0\\
  0&0&0&I
\end{bmatrix}\\
H_{+1}=\begin{bmatrix}
  A_2&0&-C_1&0  \\
  0&0&0&0\\
  0&0&0&0
\end{bmatrix}$$ and
$$\psi_c=0 \,\, \psi_\epsilon=
\begin{bmatrix}
0\\  0\\G\\0
\end{bmatrix}
$$

Then, we will find that
$$
  R=
  \begin{bmatrix}
    0&M_{\Lambda,k}&0&M_{\Lambda,\delta}\\
    0&M_{k,k}&0&M_{k,\delta}\\
    0&0&0&M_{x,\delta}\\
    0&0&0&M_{\delta,\delta}\\
  \end{bmatrix}
$$

So that for KW
$$
  M=
  \begin{bmatrix}
    M_{k,k}&M_{k,\delta}\\
    0&M_{\delta,\delta}\\
  \end{bmatrix}
$$

$$
\phi \psi_\epsilon=
\begin{bmatrix}
\bar{\bar{G}}\\
  \bar{G}
\end{bmatrix}
$$

The KW solution for $\Lambda_t$, $\Pi_\Lambda$ can be found by expressing the first few rows of R as a linear combination of the next few rows of R.

$$
  \begin{bmatrix}
      M_{\Lambda,k}&M_{\Lambda,\delta}
  \end{bmatrix}= \Pi_\Lambda
\begin{bmatrix}
      M_{k,k}&M_{k,\delta}\\
\end{bmatrix}
$$

See also
Gary Anderson. Solving linear rational expections models: A horse race. Computational Economics, 31:95–113, March 2008.


Different terminology for discrete vs. continuous "marginal" concepts? e.g. Marginal Utility.

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

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

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

Do they also have different names?

I found an answer that satisfies me in Preston McAffee's Introduction to Economic Analysis (2006):

  Marginal is just economist’s jargon for “the derivative of.” For
  example, marginal cost is the derivative of cost; marginal value is
  the derivative of value. Because introductory economics is usually
  taught to students who have not yet studied calculus or can’t be
  trusted to remember even the most basic elements of it, economists
  tend to avoid using derivatives and instead talk about the value of
  the next unit purchased, or the cost of the next unit, and describe
  that as the marginal value or cost.

So it looks like economists don't have a terminological distinction, because in their own work they tend to treat all goods as near enough to continuous anyway (I suppose because it's easier and because markets are often large). The only reason they talk about e.g. the price of "one more unit" of a good, in introductory classes and textbooks, is that they don't expect the students to be comfortable with calculus yet.


Does ownership determine efficiency in an economic system? what determines efficiency in an economic system?
a) ownership
b) competition
c)both
d) none

I am confused between option (C) and option (B) because I am not sure about whether ownership can be said to be determining efficiency although it is often argued that private ownership brings efficiency. so if you can lend me some clarity would be grateful.
competition is certainly a force that brings forth efficiency so no doubt about it.

It's not unusual - in many real-world subjects - for there to be questions for which the right answer at one level of learning, under one teaching framework, is the wrong answer in a different context. This is one such question. It will depend as much on what the teaching framework's objectives are, and what its position is within normative economics.

As such, for your homework question, the right answer is whatever you've been taught is the right answer. You know what you've been taught. We do not.

So, given that, let's deal with the reality, rather than the homework question.

Ownership can matter ... but it's complicated.

Ultimately, competition matters most when it drives under-performing competitors out of the market. If a competitor can afford losses and still stay in business, then competition won't be fully effective: although the customers will benefit from lower prices, the push to greater efficiency won't flow up the supply chain. In theory, state-owned enterprises may be more able to sustain losses than private-owned ones, so ownership should matter. However, there are cases where private-owned enterprises have sustained losses for many years; just as there have been state-owned enterprises that do not tolerate losses and have cultivated economic efficiency.

Furthermore, if there are externalities, then one way to get a more efficient market is to have a state-owned enterprise rebalancing the market to price in those externalities. Indeed, one could take that further, and say that when externalities are the dominant part of the costs or benefits, and the lowest-cost supply is easy to establish, then a state-owned monopoly can provide the highest level of efficiency: in this case, there is neither competition nor private ownership in the most efficient market.


Citing non-economics studies in an economics research paper I am currently working on a paper in economics that has some dimensions that discuss women's social value. As is the case in developing countries a lot of economic studies do not exist whereas there are tons in Sociology. While I am not convinced by the sociology results, is it ok (from the perspective of a reviewer) to borrow from that to build a narrative.
For example, if I am looking at fertility levels in a country and there is a sociological study that speaks of the link of women's perceived value and her fertility which is rarely discussed in econ literature, could I potentially use this to discuss a point in my paper? Ergo, there is anthropological/sociological arguments that indicate that a woman's value in country x is linked to her fertility? Or is that too speculative from the standpoint of an economist?
As an economist myself, I am confused but then again I would use this to argue my point.

As long as the main results/conclusions of your paper don't rely solely on the non-economics literature you cite, you should be okay. In other words, it's perfectly fine to use non-economics literature to motivate or even as part of the support for your thesis, as long as you also include proper economic arguments, i.e. theoretical models or econometric analyses.
For example, Bidner and Eswaran (2015) theorized about the origin of the Indian caste system and cited quite a few sociological, anthropological, and biological literature to motivate their model.
Likewise, Caplan and Dean (2008), which provides axiomatic foundations for a neuroscientific hypothesis (that dopamine encodes the "reward prediction error"), is full of references to the psychology and neuroscience literature. The paper even includes an extended review of the non-economic literature and explains how they are relevant for economic decision-making.
Similar examples are plentiful, and they end up in high-rank journals because, notwithstanding their non-economics citations, those papers contain substantive economic contributions.


What is the necessity of the FDIC in the US banking system? A bank's basic function is to "borrow short and lend long". In other words, it borrows money from depositors over the short term, promising to repay it on demand, while it lends most of that money out over the long term to borrowers, for instance in the form of 30-year mortgages. This difference between these time frames, known as maturity mismatch, leads to systematic problems for banking. It makes banks vulnerable to crises, because if all the depositors show up one day asking for their money, the bank can't give it to them, because it's been lent out to borrowers, so the bank becomes instantly insolvent, even if it had no financial troubles before the depositors were worried about the bank's solvency.

Indeed, this used to happen frequently in the 1800's and early 1900's, most prominently in the Great Depression, until the FDIC came about. The FDIC makes all the banks pay a premium, and in exchange, whenever there's a run on a bank, the FDIC gives the bank money so that it can meet all its depositors' demands (at least up to a cap, like a hundred thousand dollars per account).

My question is, in the absence of the FDIC, why wouldn't banks just obtain private deposit insurance? Whenever people have significant risks, even if they're small, they tend to buy insurance. You don't have a very great risk of dying tomorrow, or having a car accident, or having a flood in your house, but still you buy insurance just in case. Companies of all kinds do the same: stores buy liability insurance, fire insurance, etc. So why wouldn't banks insure their risks similarly?

And it's not like banks don't buy private insurance already. For instance, when they lend out money, they buy insurance in case the borrower defaults on a loan - it's called a credit default swap. (Those were partially responsible for the financial crisis of 2008.) So what reason would they have for not buying insurance in case their depositors' demands exceed their reserves?

Is the problem that the premiums they would have to pay on the free market would be too high to make banking profitable anymore? If that's the case, then does that mean that the FDIC is not charging actuarially fair premiums to banks right now?

Any help would be greatly appreciated.

Thank You in Advance.

You provide a generally correct impression of history (i.e., there were lots of runs on banks by depositors in the US until federal deposit insurance was established— a good history is provided by Gorton (2012)), and then ask three questions: why isn't deposit insurance provided through the private sector, is it because the free market equilibrium premiums would be too high, and if so, does this mean that the FDIC premiums are set too low?

To answer, we should first back up to the reason for deposit insurance generally, which is twofold:

Monitoring costs
Bank runs are a stable equilibrium

Then, we can discuss the reasons for government provision of deposit insurance specifically, which are:

Externalities
Monitoring costs (still)
Moral hazard
Systemic crises

The monitoring costs issue is a real one, and has been discussed in the literature by Diamond (1984), among others. It's derived from a prinicpal-agent issue: foremost, depositors want bank management to make safe investments that ensure that their deposits can be returned with certainty, while bank management is encouraged by its equity holders to take on as much risk as possible (for a general discussion of this principal-agent problem in the theory of the firm, see Hart (2001)). In short, management isn't looking out for depositors, and it's really expensive to ask all depositors to be aware at all times about the state of a bank's investments. This is additionally difficult as a practical matter, as bank balance sheets are not paragons of transparency.

Further, as Diamond and Dybvig (1983) showed, even if one ignores monitoring costs, bank runs are one stable equilibrium of a system without deposit insurance. The logic for this is described in your question: if an institution that holds illiquid assets is forced to liquidate them prior to maturity and within a short time period, it may face solvency issues as a result of that forced liquidation. This is known as the "solvency-liquidity nexus" and is discussed in a context including wholesale funding, as opposed to only deposit funding, in Pierret (2015). As a result, if depositors believe that a bank may face a run, it's rational for depositors to run on that bank even if it is fundamentally solvent. In fact, if one considers that a depositor's only recourse (in the event that monitoring reveals that management is taking on too much risk) is to withdraw his or her deposits, it should be clear that zero-cost monitoring of banks does not eliminate the possibility of runs.

So, why government-provided deposit insurance?

Perhaps the simplest reason, but the one that is least discussed in the literature, is that bank failures tend to occur together, as widespread episodes with significant externalities. For this reason alone, it's easy to understand why society (and on behalf of society, government) would have an interest in ensuring that they don't occur. But that doesn't really answer your question, which is, why doesn't the private sector handle the problem of bank runs through private insurance (and, contra another answer to this question, the private sector has never handled this issue well) so that the problem never becomes one that the government must address?

Well, a second reason would be that depositors would still face monitoring costs, as the value of the liquidity guarantee provided by a private insurer would only be as good as that entity's capacity to make good on its guarantees, which would require monitoring in turn. So that problem would still exist.

A third reason, as Diamond and Dybvig (1983) discussed in their conclusion, is that an insurer must be able to regulate the bank it's guaranteeing, because otherwise, the bank managers again have an incentive to make riskier choices:

  The riskless technology used in the model isolates the rationale for
  deposit insurance, but in addition it abstracts from the choice of bank
  loan portfolio risk. If the risk of bank portfolios could be selected by a
  bank manager, unobserved by outsiders (to some extent), then a
  moral hazard problem would exist. In this case there is a trade-off
  between optimal risk sharing and proper incentives for portfolio
  choice, and introducing deposit insurance can influence the portfolio
  choice. [...]
  Introducing risky assets and moral hazard would be an interesting
  extension of our model. It appears likely that some form of government
  deposit insurance could again be desirable but that it would be
  accompanied by some sort of bank regulation. Such bank regulation
  would serve a function similar to restrictive covenants in bond indentures.
  Interesting but hard to model are questions of regulator "discretion"
  which then arise.

Given this need for a regulator where deposit insurance exists, it makes quite a bit of sense to build a legal framework around a single regulator-insurer, which we've done in the US in the form of the FDIC and related entities (including Federal Reserve supervision and the OCC). This is largely because market-based regulation of banks by private deposit insurers (such as by allowing insurers to cancel coverage if banks breach certain risk limits) would be difficult (at best) to structure without the broad legal authority the government has to seize control of an institution that breaches risk limits and make necessary changes. If private deposit insurers can't rescind coverage, their ability to discipline banks is limited; if they can, then banks face a likely run if their coverage is rescinded, which solves nothing. It is also, of course, difficult as a practical matter because of the aforementioned opacity of bank balance sheets.

Fourth and finally, as discussed by Caballero (2009a, 2009b), bank failures don't occur in isolation; institutions tend to be impaired at exactly the same moment that other institutions and markets are impaired. While you correctly note that a form of partial insurance is in use (in the form of credit-default swaps) today, it's worth considering what happened during the crisis, when outstanding CDS contracts caused the failure of the insurer AIG.

This leads us to a reasonable question: what would a private deposit insurer look like? We know at least two things. One, it would have to be very well-capitalized, for if it were not, the Diamond-Dybvig "run" equilibrium would still exist. Two, it would have to hold its significant reserves in the form of information-insensitive "safe" assets, most likely government-guaranteed securities, or else it may not be able to liquidate those assets under the conditions that lead to bank failures (which can be accompanied by fire sales and other phenomena that impair asset values).

This leads us to an answer to your second question, which is yes, this would be relatively expensive, as you'd have to insure the whole stack of deposits, rather than allowing the government to provide a tail risk guarantee as it does with the Deposit Insurance Fund (if the FDIC's DIF is run to zero during a crisis, the US government will make up the difference). That tail risk guarantee provided by the government is a conditional put— it costs nothing until the DIF needs a bailout, at which point the government can fund it by issuing debt at the very low rates that prevail (for safe assets) during times of financial distress.

To answer your third question, the DIF has never required a bailout, and its rates are adjusted to prevent it from holding reserves that are too great, so— the FDIC is probably charging an actuarially fair rate over a long time horizon, though the rate may be too high or too low at certain points in time.


Is there an externality if someone buys all stock of some merchandise? Is there an externality if someone buys all stock of some merchandise? On one hand, if they buy all of everything and there's still demand then they've taken it away from other people. On the other hand, it kind of feels like that should be accounted for in the supply curve, and it's not an externality so much as the producers not having known the correct supply curve?

From the Oxford dictionary: (emphasis added by me)

  externality (noun)

  A consequence of an industrial or commercial activity which affects other parties without this being reflected in market prices...

Another way to put this is that externalities are not the results of market rivalry. So if you and I are bidding on the same item on e-Bay, and you are buying it, I kind of suffer, but this is within the market context, this is not abnormal. Whereas if you buy a new stereo system on e-Bay and then keep me up all night by listening to loud music, this happens outside of the market context (unless I sold you the right to listen to loud music) and is an externality.

In case of a Cournot-oligopolies one firm's increased production would also harm other firms by lowering the price. But this is not an externality either, as it is the result of normal market rivalry for the consumers.

It seems like in the situation you are describing you are not facing an externality, as it everything happens in a market context. Perhaps there is information asymmetry, as the store was understocked. (This would require additional assumptions and is not the only possible explanation.)


If $X$ is a Giffen good then $Y$ must be a normal good While going through some problems as part of self-study I encountered the following True/False question:

Q. Steven only consumes two goods: $X$ and $Y$. If $X$ is a Giffen good for Steven, then $Y$ must be a normal good for Steven.

The given answer is True.

I am unable to understand why it is necessary for the other good to be normal. Why can't it be inferior/Giffen?

Reason: Both goods cannot be inferior.

Let's say originally you consume $x$ and $y$. So your budget constraint looks like

$$p_x x + p_y y = I.$$

If both X and Y are inferior, when income goes down from $I_0$ to $I'$, the quantity demanded for both has to go up (by definition) from $x$ to $x'$ and $y$ to $y'$. This implies

$$p_x x' + p_y y' = I' < I = p_x x + p_y y.$$

This is a contradiction, since $x' > x$ and $y' > y$.

Your question is a bit more specific. But since a Giffen good must be inferior, this answers your question as well.


Solow Model: Steady State v Balanced Growth Path Okay, so I'm having real problems distinguishing between the Steady State concept and the balanced growth path in this model:

$$ Y = K^\beta (AL)^{1-\beta} $$

I have been asked to derive the steady state values for capital per effective worker:

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

As well as the steady state ratio of capital to output (K/Y):

$$ \frac{K^{SS}}{Y^{SS}} = \frac{s}{n+g+\delta } $$

I found both of these fine, but I have been also asked to find the "steady-state value of the marginal product of capital, dY/dK". Here is what I did:

$$ Y = K^\beta (AL)^{1-\beta} $$
$$ MPK = \frac{dY}{dK} = \beta K^{\beta -1}(AL)^{1-\beta } $$

Substituting in for K in the steady state (calculated when working out steady state for K/Y ratio above):

$$ K^{SS} = AL\left(\frac{s}{n+g+\delta }\right)^{\frac{1}{1-\beta }} $$

$$ MPK^{SS} = \beta (AL)^{1-\beta }\left[AL\left(\frac{s}{n+g+\delta }\right)^{\frac{1}{1-\beta }}\right]^{\beta -1} $$

$$ MPK^{SS} = \beta \left(\frac{s}{n+g+\delta }\right)^{\frac{\beta -1}{1-\beta }} $$

Firstly I need to know whether this calculation for the steady state value of MPK is correct?

Secondly, I have been asked to Sketch the time paths of the capital-output ratio and the marginal product of capital, for an economy that converges to its balanced growth path "from below".

I am having problems understanding exactly what the balanced growth path is, as opposed to the steady state, and how to use my calculations to figure out what these graphs should look like.

Sorry for the mammoth post, any help is greatly appreciated! Thanks in advance.

This is when the attempt at accuracy creates confusion and misunderstanding.

Back in the day, growth models were not incorporating technological progress, and led to a long-run equilibrium characterized by constant per capita magnitudes. Verbally, the term "steady-state" seemed appropriate to describe such a situation.

Then Romer and endogenous growth models came along, which also pushed the older models to start including as a routine feature exogenous growth factors (apart from population). And "suddenly", per capita terms were not constant in the long-run equilibrium, but growing at a constant rate. Initially the literature described such a situation as "steady state in growth rates".

Then it appears the profession thought something like "it is inaccurate to use the word "steady" here because per capita magnitudes are growing. What happens is that all magnitudes grow at a balanced rate (i.e at the same rate, and so their ratios remain constant). And since they grow, they follow a path..." Eureka!: the term "balanced growth path" was born.

...To the frustration of students (at least), which have now to remember that for example, the "saddle path" is indeed a path in the Phase diagram, but the "balanced growth path" is only a point! (because in order to actually draw a Phase diagram and obtain a good old long-run equilibrium, we express magnitudes per effective worker, and these magnitudes do have a traditional steady-state. But we continue to call it "balanced growth path", because per capita magnitudes, which is what we are interested in, in our individualistic approach), continue to grow).

So "balanced growth path" = "steady state of magnitudes per efficiency unit of labor", and I guess you can figure out the rest for your phase diagram.


Seemingly simple consumer theory problem A function $v: \mathbb{R}^K_+ \xrightarrow{} \mathbb{R}_+$ is is said to be a valuation function if

The value of function $v$ at $x = \textbf{0}$ is $0$: $v(\textbf{0}) = 0$
$v$ is continuous on the domain $\mathbb{R}^K_+$, strictly increasing and strictly concave on $\mathbb{R}^K_{++}$
For any $p \in \mathbb{R}^K_{++}$, the set $A(p) = \{x \in \mathbb{R}^K_+| v(x) \geq p \cdot x\}$ is compact, the set $A^*(p) = A (p)-\{\bf{0}\}$ is nonempty and lies inside $\mathbb{R}^K_{++}$.

Show that a if $v$ is a valuation function, for every $p \in \mathbb{R}^K_{++}$, for every $x \in \mathbb{R}^K_{++}$, there exist $t>0$ small enough that
$$
v(tx) > p\cdot tx
$$
In other word, for every $p>\bf{0}$, if you zoom the set $A(p)$ sufficiently close at the origin, it contains all the points near the origin in first quadrant.
Remark 1: This is the problem I reduce from a microeconomics problem I am working on.  I want to extend the Inada condition to multivariate case in a topological way. My prototype function is $f(x,y)=x^{\alpha}y^{\beta}$ where $\alpha+\beta <1, \alpha>0,\beta>0$.
This family of functions satisfy (1),(2),(3) and the property I want to prove, say (4). I am trying to show either (1),(2),(3) => (4) or should I include (4) as an additional axiom?
Remark 2: A few examples of $A(p)$

An example of A(p) when p is small

An example of A(p) when p is large

(4) is demonstrated by the geometric fact that the contours approach vertical and horizontal axis near $0$.

It follows indeed from the first three conditions, though I did not find a simple proof. Here is a messy one:
Observe first that, $v(tx)>p\cdot tx$ with $t>0$ is equivalent to $v(tx)/t>px$. By replacing $p$ by some multiple, we can see that the right-side can take any value without changing the left value. The function $t\mapsto v(tx)$ is strictly concave, strictly increasing, and has value $0$ at $0$. The problem is then equivalent to showing that its right derivative is infinite for all $x\gg 0$. That the right derivative exists follows from the concavity of $v$.
As it turns out, it is enough to find a single $x^*\gg0$ such that $t\mapsto v(tx^*)$ has an infinite right derivative at $0$.
To see this, let $x\gg 0$. There is some $\delta>0$ such that $x\gg \delta x^*$. Take some $K>0$. For $t>0$ small enough, we have $v\big(\delta t~x^*\big)/(\delta t)>K/\delta $ or $v(\delta t x^*)/t>K.$
Since $v$ is strictly increasing on the interior,
$v(tx)/t>v(t\delta x^*)/t>K$ for $t>0$ small enough. Therefore, the function $t\mapsto v(tx)$ must have infinite right derivative at $0$.
It remains to find the damn $x^*$. Let $\Delta$ be the $K-1$-dimensional unit simplex. For each $N$, there must exist some $x\in\Delta$ such that the function $t\mapsto v(tx)$ has a right derivative of at least $N$ at $0$. Otherwise, for $p=(N,N,\ldots,N)$ we would have $A(p)-\{0\}=\emptyset.$ Also, $A(p)-\{0\}\subseteq\mathbb{R}^K_{++}$ implies that such an $x$ must be positive in each coordinate. So let $x_n\in\Delta$ be such that $t\mapsto v(tx_n)$ has a right derivative of at least $n$ at $0$. Now let
$$x^*=\sum_{i=1}^\infty\frac{1}{2^i}x_{2^i}.$$
That the relevant series converges follows from any norm being bounded on the compact set $\Delta$ and absolute convergence implying convergence. Clearly, $x^*\gg 0$ since $x_{2^i}\gg 0$ for all $i$. It remains to show that $t\mapsto v(tx^*)$ has an infinite right derivative at $0$. Since
$$t^{-1}~v\bigg(t\sum_{i=1}^\infty\frac{1}{2^i}x_{2^i}\bigg)>t^{-1}~v\bigg(t\sum_{i=1}^n\frac{1}{2^i}x_{2^i}\bigg)$$
for all $n$ by $v$ being strictly increasing on the interior, it suffices to show that for each $K>0$, there exists some $n$ such that
$$t^{-1}~v\bigg(t\sum_{i=1}^n\frac{1}{2^i}x_{2^i}\bigg)>K$$ for $t>0$ small enough. Let $S_n=\big(\sum_{i=1}^n 1/2^i\big)^{-1}$ and note that
$$t^{-1}v\bigg(tS_n\sum_{i=1}^n\frac{1}{2^i}x_{2^i}\bigg)=t^{-1}v\bigg(\sum_{i=1}^n S_n\frac{1}{2^i}t x_{2^i}\bigg)\geq\sum_{i=1}^n S_n\frac{1}{2^i}t^{-1}v(tx_{2^i})$$
by the concavity of $v$. Since $\lim_{t\downarrow 0}t^{-1}v(t x_{2^i})\geq 2^i$, this sum is almost $S_n n$ for $t>0$ small enough. Now $S_n$ converges to $1$, so $S_n n$ is larger than $K$ for $n$ large enough and $t>0$ small enough.


Why is there a positive risk-free interest rate? I've been told that the interest rate is the price needed to be willing to take on the risk associated with lending. This is why personal loans have higher interest rates than bank deposits, for example. So why is there a positive (as opposed to zero) risk-free rate? It is usually assumed that government bonds are risk-free, yet they have a positive return. If there is no risk, how can there be a positive rate?

The interest rate is (1) the price needed to take on risk and (2) the price needed to delay consumption.

The reason there is a positive risk free rate, even though there is no risk, is because of the time preference typical of any economic agent. It is preferable to consume today, than to consume tomorrow. To put off consumption today and invest in the risk free asset instead, the agents want to earn interest, otherwise they will consume instead of saving.

Normally, if the risk free rate was zero, nobody would buy the risk free asset, but spend everything on consumption. E.g. nobody would buy government bonds. The government has to offer a positive interest rate to find buyers.

Current negative interest rates are actually a reflection of how our classical assumption, that agents prefer to consume today rather than tomorrow, has been turned on its head. Nobody wants to consume today despite zero or negative interest rates contrary to the classic theory above (and people buy government bonds with negative interest rates). This can happen if agents are apprehensive enough of the future to want to increase their precautionary savings instead of consuming. If they are worried enough, they will do this even if they lose money on their savings (due to the negative interest rate).


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

$p\cdot z(p)$ is total revenue (price times quantity), and so its derivative $\frac{\mathrm d}{\mathrm dp}pz(p)=pz'(p)+z(p)$ is marginal revenue.


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

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

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

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

No, but the correct ratio is

$$\frac{\text{Assets} }{ \text{Equity}}$$

Reasoning: with "leverage" we want to obtain information on how much a company uses debt for financing. And we want to have the correspondence "higher leverage $\to$ more debt financing".

Moreover, in order to be consistent with the definition of "leverage" ("the exertion of force by means of a lever"), we want the information on debt to be in the denominator, since we want to form a ratio.

In order to achieve all these together, we need to put equity on the denominator, so that lower equity (implying higher debt for same level of assets) increases the value of the ratio, and we get the higher leverage.


What does "sample period" in this case mean? Dasgupta,2019 documented that

the treated group comprises all firms that are headquartered in
countries that have passed a leniency law by year t. The control group
comprises firms in countries that never adopted a leniency law in our
sample period and firms headquartered in countries that adopted a
leniency law at some later point of time.

I am wondering "sample period" here is the whole period of the study or the window [-2;+5] around the law implementation of a specific country. For example, Korea passed the law in 1997, so "sample period" means "1990-2012"(the whole dataset Dasgupta,2019 consider in their analysis) or "1995-2002"?

It is definitely hard to interpret, and I wish the authors had been more clear.
However I think "sample period" refers to the whole dataset.  There is actually nothing in the identification or data sections that suggests that the authors are using the [-2,+5] window around law implementation in the main regression results. I could be missing something but I only see this window mentioned describing the graphical analysis at the very beginning of the results section.  It is not very clear to have a graphical analysis that doesn't actually correspond to the regression being run, but I think maybe that is what is going on.  If the authors were running a regression based on offsetting the data around the law passed I think they would have described the "t" index in the regression equations as referring to "years since passage of the lenience law" rather than simply "years".
A way to confirm with certainty that the authors are not using the seven year window in the main regression analysis would be to check the sample size under the regression tables. Seven years of data per country will generate a very different N to 22 years of data per country.


Negative real rates on yield curve If you look at information on the Treasury website, you will notice that currently, the real interest rate on the entire yield curve is negative.

If you check the nominal rates in the short term, you can verify for the shorter period bills.

Thus, an interesting question for laypeople to learn from us on this site may be why this is the case? How can it be that investors are essentially paying the government to hold onto money for them?

Investors are not paying to hold Treasury bonds (yet), nominal yields are still positive (but that could change...). All that is happening is that inflation-protected securities are guaranteeing a return less than CPI inflation.

This is not that much of a mystery: there is no way to buy the CPI index (other than trading inflation derivatives). You can buy some goods, but you cannot lock in prices for services. As such, there is no guaranteed way to lock in the CPI inflation rate.

Investors try to make money trading bonds. As long as the nominal returns are greater than the nominal cost of holding positions - which is approximately equal to the policy rate - buying bonds is profitable. Current U.S. Treasury pricing is consistent with the belief that the Fed will cut rates.

The interesting question is why investors would hold bonds with negative nominal yields. The reasoning is more complex, but as we see in Japan and the euro area, they can be forced to do so - since holding large amounts of currency notes is not an option for institutional investors for security reasons.