What international payment systems do exist? I recently read up on the Society for Worldwide Interbank Financial Telecommunication (SWIFT). As faar as I understood it was up until recently the only provider of a system to exchange money internationaly between different entities.

(There are other national systems)

Now I saw that china is developing its own system called Cross-Border Inter-Bank Payments System (CIPS). This system is still using SWIFT to communicate with certain entities but can also connect them directly.

Also the Instrument in Support of Trade Exchanges (INSTEX) is beeing created by France, Germany and the UK. This system is not connected to SWIFT and currently only allows goods to be traded.

Did I understand it right that those systems are partwise competitors and are there more such systems?

SWIFT, as a private company, only provide secure transmission of financial messages between the participants. The message types or so vast from customer payments and cheques to financial institution transfers, treasury markets, commodity transactions, Letter of Credits etc. Providing instant, secure, without any disconnection messages together with standardization of these messages are a big job for smooth payments.
SWIFT does not hold your money, my money nor does it keep an account for the beneficiary bank or remitting bank.
The main underlying money exchange is done through correspondent banking accounts between financial institutions. These accounts are called as nostro and vostro accounts. The debit or credit from and to these account will be confirmed through SWIFT messages. Before SWIFT, the Telex system is used for communication.

Chinese, CIPS is used only for Renbinmi transactions and is not a competitor to SWIFT. The member banks to this system can use it as a small network but there may be still many banks who are not a member of the system.


Can we see the computer age in the productivity statistics? Robert Solow famously said:

  You can see the computer age everywhere but in the productivity statistics

This quote is often linked with the productivity paradox (https://en.wikipedia.org/wiki/Productivity_paradox), such that we don't see mayor productivity growth from new tech.

But there is something I don't understand. Economic growth is about percentage growth. A graph of GDP looks like an exponential function. So nominally a 5% growth is much much higher when the economy is that of the US than that of Malawi.

So we might not see an acceleration of economic growth, but we at least see continued growth, which allegedly becomes harder and harder as economies develop. This is the idea behind Solow's model, where without an exogenous percentage growth in A, output converges to the steady state.

So I don't really understand the problem. To me, computers are clearly visible in a growing economy. But this seems to be unsatisfactory for Solow, who wants to see what, a 10% growth rate?

What's wrong in my thinking?

It means that computers (or IT in general) contribute to the society (they make us better off and more productive at work), but this does not show up in GDP statistics. The reason is that many of these services are for free. As an example, the value of the Google Search is not reflected in a market price for running this search. The problem is related to the societal value of mothers raising their children at home. Other examples are environmental protection or caring for your parents. Since these services are not traded on markets, it does not enter GDP. Whether the Solow quote is actually true is however debatable. The value of the google search engine is to some extent reflected in the advertisement google is selling. And this enters GDP statistics. The relation with the productivity puzzle is whether productivity is actually falling or whether we need new concepts to measure productivity in the computer age.


Definition of covered market I do Industrial Organization course, and I've seen the phrase "market is covered" several times in my lecture slides, however, I'm struggling to find the formal definition of "covered market" and the condition when it's true. Can you please help me with that?

A market is covered if all consumers will choose to buy from at least one of the firms at the prevailing prices.

For example, consider a standard Hotelling model with two firms who are located at opposite ends of the unit interval. Suppose that each firm charges that same price $p$ and that consumers are uniformly located on $[0, 1]$. Finally, suppose that every consumer has unit demand and the same utility function $u = v - tx - p$ where $v$ is their valuation for the good, $t$ is the cost of transportation and $x$ is the distance that they travel to the firm from which they buy. In this example, every consumer will choose to buy a good if and only if the consumer located in the centre chooses to buy the good (since she has the furthest distance to travel). This is equivalent to asserting that

$$ v - 0.5t - p \geq 0 \iff v \geq 0.5t + p .$$

That is, the market is covered when the valuations of the consumers are sufficiently high relative to the price and cost of transportation.


Is risk aversion bounded in CRRA utility? For instance, Cagetti (2003) estimates ρ > 2 by targeting the median wealth of households,
Gourinchas and Parker (2002) find ρ < 2 by targeting the mean consumption of households,
Chetty (2006), using the effects of wage changes on labor supply, finds that ρ < 2.

Marginal utility of consumption is decreasing very fast when ρ > 2, still you can find in macro or finance even ρ = 10. In experimental or in labor ρ is close to 0.

Is there any bound on this coefficient?

A practical or mathematical bound? For a practical bound, people have argued that very large values of $\rho$ are impossible to reconcile with non-financial risk taking. Indeed, some values of $\rho$ may not be compatible with crossing the street.

Perhaps that's a bit glib, but consider Neilson and Winter (2001) which find that CRRA utility and observed wage premia for dangerous jobs are compatible with values of $\rho$ such that  $0<\rho<<1$. They then point out that if $\rho$ were very very large and the model properly specified then the dangerous job wage premium would also be large or alternatively (and implausibly) that people place a very, very low value on their own lives (like $3,000).

Generally speaking, data and models implying very high values of $\rho$ like a basic equity premium setup and the relative volatility of equity returns and consumption) are often taken as signs of model miss-specification instead of alternative measures of risk preferences.

While we can't talk about globally infinite risk aversion, we can consider what happens as If you take the limit $\rho\rightarrow\infty$ around a particular value of wealth $W_0$. As it goes to infinity you get a step-function utility function with $U(W) = -\infty, W < W_0$ and $U(W) = C, W \ge W_0$.


Finding economy's factor price for perfect complement production function Q.Consider an economy producing a single good by a production function
$$Y = min [K, L]$$
where Y is the output of the final good. K and L are input use of capital and labour respectively. Suppose this economy is endowed with 100 units of capital and labour supply is Ls is given by the function

Ls = 50w

where w is the wage rate.
Assuming that all markets are competitive find the equilibrium wage and rental
rate.

Actually I am having doubt in assessing if the economy would use its full capital endowment. Also how we are going to calculate marginal product of labour and capital for finding wage rate and rental rate. I think if we use isoquants and isocost lines, then optimal solution should come where $$K = L = Y$$. But I think I am missing something, please help.

The planner is trying to maximize:
$$\Pi = Y - r\cdot K - w\cdot L= min [K, L] - r\cdot K - w\cdot L $$

In perfect competition factors receive their marginal product as price. If $0<w <2$ then $0 < L_s < 100$. This means that the marginal product of capital (MPK) is zero and therefore the price of capital ($r$) should be zero. In this region the marginal product of labor (MPL) is 1, and so there is only one wage that represents a competitive equilibrium, $w*=1 \rightarrow L^* = 50, Y^* = 50, r^* = 0$.

What about of $w\geq 2$? In this region the MPL is 0 so this can't be a competitive equilibrium because $2< w \neq MPL$.


Deriving long-run cost function I'm a bit unsure about how to derive a long-run cost function. Suppose my production function was $X(L, K)=L^a K^b$, where $a+b>1$.

I'm thinking about doing the following, but I'm not sure it's correct. If it's not, what am I not considering?

The beginning of my solution:

Our production function is $X=L^a K^b$ and our cost equation is $C=wL+rK$. So, we must solve $\max L^a K^b \text{ s.t. } C=wL+rK$. Therefore, our Lagrangian function is $\mathcal{L}=L^a K^b + \lambda(C-wL-rK)$.

The first order conditions are: (1) $aL^{a-1}K^b-\lambda w=0$, (2) $bL^aK^{b-1} -\lambda r=0$, and (3) $C-wL-rK=0$.

Then, we solve the maximization problem (dividing conditions 1 and 2, solving for $L$ and $K$, and then plugging $L$ and $K$ into the cost equation). Does this seem like the right way to do it?

You're right. Divide Eq (1) by Eq (2):

$$
\frac{a L^{a-1}K^b}{bL^aK^{b-1}} = \frac{aK}{bL} = \frac{w}{r} ~~~\Rightarrow~~~ L = \frac{ar}{bw}K \tag{4}
$$

Now use this in Eq. (3)

$$
C = wL + rK = \left(\frac{a}{b} + 1\right)rK ~~~\Rightarrow~~~ K = \frac{C}{r(a/b + 1)} \tag{5}
$$

Replace this in Eq. (4) to get $L$


Pareto Optimality and Core I know this is a basic question. Can I get a mathematical proof for "Any allocation in the core of an economy is also Pareto optimal." I found this statement on some PPT online.

An allocation is defined as being a part of the "core" of an economy if there's no coalition of people that blocks the allocation. A coalition will block an allocation if all of its members could be made better off by another allocation (or, more weakly, if at least one of its members could be made better off without others being made worse off).

And so, by definition, for an allocation to be in the core of the economy, there must not be another allocation which any coalition prefers to the given allocation. And since one coalition that could be formed is the "grand coalition" (i.e. everyone in the economy), any allocation in the core must be Pareto optimal, or else the grand coalition would block it.

This probably isn't much more involved or mathematical than the PPT you pulled it from, but that's because it's basically true by definition.


On closedness: commodity space In Intriligator (2002, p. 143) we find the following statement:

  \begin{align}
 C = \{(x_1,x_2,\ldots,x_n) : x_j \geq 0,~j=1,2,\ldots,n\} \subset [0,\infty)^n
 \end{align}
  Thus  commodity  space is the  nonnegative  orthant  of  Euclidean
  $n$-space,  a closed,  convex set.

I'm rather confused why $C$ is supposed to be closed, because $x_j$ is not bounded from above. However, we may argue that $C$ is closed, because its complement
\begin{align}
C^c \subset (-\infty,0)^n
\end{align}
is open.

Still, isn't it appropriate to say that $C$ is half-closed? Am I hairsplitting here?

A closed set does not need to be bounded. For instance, the set $[0,\infty)$ is closed but unbounded.

Formally, a set is closed if it contains all its limit points. You can easily verify that it is the case for your $C$. Take a sequence of elements $x^m=(x_1^m,\cdots,x_n^m) \in C$ that converges to a vector $x^{*}=(x_1^{*},\cdots,x_n^{*})$ under any appropriate topology. The $j$-th coordinate of $x^{*}$, $x_j^{*}$, is the limit of the sequence $x_j^{m}$. Since all $x_j^{m}$ are nonnegative real numbers, so is the case for the limit $x_j^{*}$. Since this is true for all $j$, $x^{*}$ also belongs to $C$.


MSNE and the probability of encountering each payoff I'm currently setting up a model using data from the game "Hearthstone". Those familiar with the game know that it can (for the most part) be described as a zero-sum game, where players choose a deck before being randomly matched against another player. These decks have over-all winrates against all players, as well as winrates for each specific matchup (Deck A vs Deck B).

Let's assume there are only 5 decks that can be played (there are a lot more). We could then form a 5x5 expected payoff matrix for each matchup using the respective winrates of all decks.

My question is this: how would the probability of encountering a certain deck factor in? We could technically calculate an optimal strategy from the payoff matrix, but it doesn't seem like that takes into account the likelihood of encountering a certain deck more than another.

At first I thought it could be a type of signaling game, where the matchmaking process was a "type" drawn randomly, but that isn't the case here, since the players are making their decisions before this occurs.

Edit

I should have specified. I mention MSNE since I'm trying to see if you can better your chances of winning statistically by playing a number decks in a number of sequential games, rather than just choosing one deck and sticking with it.

Denoting your five decks by $d_1, d_2,...,d_5$, you will get a $5 \times 5$ matrix
$$
\begin{array}{|c|c|c|c|c|}
\hline
a_{11} & a_{12} & a_{13} & a_{14} & a_{15} \\
\hline
a_{21} & a_{22} & a_{23} & a_{24} & a_{25} \\
\hline
a_{31} & a_{32} & a_{33} & a_{34} & a_{35} \\
\hline
a_{41} & a_{42} & a_{43} & a_{44} & a_{45} \\
\hline
a_{51} & a_{52} & a_{53} & a_{54} & a_{55} \\
\hline
\end{array}
$$
where $a_{ij}$ denotes the the expected payoff of deck $i$ against deck $j$. I am guessing this is actually the probability of deck $i$ beating deck $j$ but I am not familiar with Heartstone or your exact intentions. If it is in fact a probability then the payoff of deck $j$ against deck $i$ is $a_{ji} = 1-a_{ij}$.

Which desk yields the highest expected payoff?
 There is no answer this question without some assumptions about your opponent. E.g. in rock-paper-scissors there is no best move unless you specify what your opponent will do. If your opponent plays $d_j$ with probability $p_j$ then your expected payoff for playing $d_i$ is
$$
\sum_{j=1}^5 p_j \cdot a_{ij}.
$$
Whichever $i$ (or $i$'s) maximize this is (are) the best deck(s) to play.

How does one derive the probabilites $p_j$?
 There is no clear answer to this. You can use the concept of Nash-equilibrium to calculate mutual best responses. Or you could rely on experience by calculating the actual frequency of opponents playing $d_j$.


General mathematical model of incomplete contracts? I have read various articles about incomplete contracts, like Hart's papers and Milgrom's papers.

But I have not found a paper that defines mathematically, in the most general way possible, what an contract is, and how a contract can be more, or less, "incomplete".

Is there a general model that has as special cases the incomplete contracts studied in the literature (e.g. by Hart, Incomplete Contracts and the Theory of the Firm, and others), and perhaps also as special case the complete contracts?

Note: I am not necessarily asking for a general model that can include all the reasons for incomplete contracts (thought that would be nice too). Just a model that can be used to state how (in)complete a particular contract is, whatever the reason.

Just a model that can be used to state how (in)complete a particular contract is, whatever the reason.

I remember a debate at the end of the 90's on Incomplete Contracts: Where do We Stand? by Jean Tirole and Foundations of Incomplete Contracts by Hart and Moore, where they develop a model that provides a rigorous foundation for the idea that contracts are incomplete, followed by Complexity and Renegotiation: A Foundation for Incomplete Contracts by Segal.
Check also this book The Impact of Incomplete Contracts on Economics (2006) by Aghion, Dewatripont, Legros, and Zingales, including Comments on the Foundations of Incomplete Contracts by Maskin.
An interesting paper by Tirole Cognition and Incomplete Contracts: Thinking  about  contingencies,  designing  covenants,  and  seeing  through  their implications is costly. Parties to a contract accordingly use heuristics and leave it incomplete. The paper develops a model of limited cognition and examines its consequences for contractual design.


How to interprete independence between treatment indicator and outcomes? In Woodridge's textbook "Econometric Analysis of Cross Section and Panel Data", page 907, it says

  ...the treatment indicator $w$ is statistically independent of ($y_0$, $y_1$), as would occur when treatment is randomized across agents.

In which $w$ would be 1 if the subject receive a treatment; $y_0$ is the outcome without treatment; $y_1$ is the outcome with treatment.

I found the statement a bit strange since this would mean that, e.g. in the case of double-blind experiment involving giving one group of patients placebo and the other group of patient real medication (i.e. randomized across agents), giving real medication or not is independent of the outcome of the patients taking the real medication and the outcome of the patients not taking the real medication (i.e. the real medication is assumed to have no effect if the agents is randomized, which does not make sense).

Furthermore, the book showed that when treatment is randomized, $E(y|w=1)=E(y_1|w=1) =E(y_1)$. However, it seems that randomizing treatment is not essential for this equation to be established as long as $y=(1-w)y_0+wy_1$ (showed on p. 906 at the buttom). What is the difference between $E(y|w=1)$ and $E(y_1)$? They seems to be the same (expected outcome with treatment). In what circumstance would $E(y|w=1)=E(y_1|w=1) =E(y_1)$ be not satisfied?

Or is there something wrong with my interpretation?

Note that this section in the book starts with the counterfactual that each agent has an outcome $y_0$ without treatment and an outcome $y_1$ with treatment. You observe only the $y_0$ of the untreated agents and only the $y_1$ of the treated agents, but both exist for each agent. If treatment is randomized across agents then $w$ is indeed independent of $(y_0,y_1)$, but of course not independent of the $y_i$ you actually observe.


What is the economic meaning of distribution parameter in a CES-production function? This is the production function (two input factors: $x_1$ and $x_2$)

$$q=A[δx_1^ρ+(1-δ)x_2^ρ]^{\frac{1}{ρ}} $$

If distribution factor $δ$ is set to increase, what are the economic impacts on these two input factors? Substitution elasticity remains unchanged.

In this answer you can see that $\delta$ becomes the exponent in the Cobb-Douglas function as $\rho \to 0$, i.e. as the elasticity of substitution becomes unity.
The exponent in the Cobb-Douglas production function is the output elasticity of the input(s), but also, it is the "output share" of each factor, under competitive conditions. This is why the scholars that introduced the C.E.S. function named this parameter "distribution parameter".
So you can start thinking from there.


Approximating the socially-optimal price in a monopolist market A monopoly firm has an incentive to increase the price and decrease the produced quantity in order to increase its revenues. But this decreases the social welfare. The government can intervene in several ways, one of which is to set a maximum price for the product.

Ideally, the price set by the government should be equal to the equilibrium price, because then the social welfare is maximized. However, in order to know this socially-optimal price, the government must know the cost curve of the seller. A monopolist seller might decide to hide the true cost curve and claim that the cost is higher than it is, in order to make the government raise the maximum price.

MY QUESTION IS: what can a government do in order to approximate the socially-optimal price? I am interested in references to both theoretical suggestions and practical case-studies.

NOTE: I am interested even in a very simple case, in which the monopolist's price per unit can be assumed to be constant, so that the only hidden information is that constant.

The following paper apparently deals with a very similar question:

  Regulating a Monopolist with Unknown Costs   In Ecnometrica (1982),
  pp. 911-930, doi:10.2307/1912769 by P. Baron, Roger B. Myerson

This and other similar papers can be found here.


Monetary policy optimization I was wondering if anyone could give me some advice / lectures / introduction to stochastic optimization that could be applied to monetary policy. I have heard of the Dynamic stochastic general equilibrium modeling (DSGE) but I think that this is more linked to the consumer theory and not really to monetary policy. Correct me if I am mistaking ...

Also, I am familiar with convexity and linear optimization, but a little bit shaky when it comes to stochastic optimization. Therefore I would welcome the opportunity to also get some recommendations on that if you have some, in order to deepen my understanding of it !

You are unfortunately mistaken. DSGE models are at the heart of monetary policy and the most widely used class of models in this field. To work in monetary there is no real way around learning DSGE.

A very good book to get started. is Walsh (2010) "Monetary Theory and Policy". I can also recommend Gali's book ("Monetary Policy, Inflation, and the Business Cycle", 2008), but he skips a lot of steps. These will give you a very good introduction to DSGE.

The mother of all books on monetary policy is "Interest and Prices:
Foundations of a Theory of Monetary Policy" by Woodford, but can be hard to read at times. I would start with Walsh.

Note that there are small, medium and large scale models. You can pretty much forget about large scale ones. I recommend starting to study small scale models. The small scale model should boil down to three equations and much of the intuition for it can even be understood from old keynesian type models such as IS-LM and AS-AD. You should also be familiar with basic Solow-Growth models.


Question about an interpretation of the MRS Given the marginal rate of substitution of $x$ for $y$ : $\frac{u'(x)}{u'(y)} $
I know one can interpret this as the amount of $y$ one is willing to give up for an additional unit of $x$, or the amount of $y$ that has to be given to compensate the consumer for a loss of $x$.
But mathematically, is it saying, how much the consumer values the next unit of $x$, in terms of the next unit of $y$? or the marginal valuation of $x$ in terms of additional units of $y$?

Writing out the expression with Leibniz notation, we get $\frac{\frac{du}{dx}}{\frac{du}{dy}}$, or the marginal utility of $x$ divided by the marginal utility $y$.
For example, let's imagine I get 10 utils from another apple and 5 utils from another cabbage. In that case, the MRS is therefore $\frac{\frac{10 utils}{1 apple}}{\frac{5 utils}{1 cabbage}}$, or, $\frac{2 cabbage}{1 apple}$, matching the marginal rate of substitution of 2 cabbages per apple.
A bit of simplification will easily get you $\frac{dy}{dx}$, which is the rate of change of $y$ with respect to $x$, the interpretation we're familiar with.


Why is the short run average cost curve not a tangent to the long run average cost curve at the lowest point on the short run average cost curve? The diagram from the Varian textbook shows that the SRAC curve is tangent to the LRAC curve at a point which is not the bottom of the SRAC curve. It would be really helpful if someone could explain this.

The diagram is fine as an illustration of a possible relation between the long run average cost curve and one particular short run average cost curve.

Long run in the context of a firm's cost functions means that all inputs are free to vary, so it makes sense to refer to the long run cost curve.  Short run means that one or more inputs (eg capital equipment) are fixed.  Since these inputs could be fixed at different levels, there are many different short run cost curves. The long run cost curve is the envelope of these curves. Unless it has been specified at what level they are considered fixed (which could implicitly be whatever is their current level), it makes no sense to refer to the short run average cost curve.

In most cases, the minimum point of a short run cost curve will be above the long run cost curve.  This should not be surprising: it just means that, for the relevant output, it's possible to obtain lower costs if all inputs are free to vary than if only some are free to vary.

There will however be one short run cost curve corresponding to the levels of fixed inputs at which the long run cost curve is at its minimum.  The lowest point of that particular short run cost curve will be tangent to the long run cost curve (and incidentally the short and long run marginal cost curves will also pass through the same point).

A diagram showing multiple short run average cost curves, with one having its lowest point tangent to the lowest point of the long run cost curve may be found in Nicholson W (9th edn 2005) Microeconomic Theory.  For an online source see here.


What are modern examples of established economic theories being used on a large scale in real life? I was thinking recently how economic theories (the stuff they teach you in college) affects real-life decisions. I found some examples (see below), but most of them are from the past and many of those theories are not "established"/respected today.

What are examples from the present or recent past, when an established economic theory affects real-life decisions, preferably on a large scale?

I'm interested in cases when some organization or individual decides what to do based on such theories and their decisions affect many people (e. g. it is known that the central bank of country X uses some monetary economics theory to decide what the interest rate should be). I'm looking for examples of established economic theories being widely used "in the wild" (in the real world).

Examples from the past:

Vulgar liberalism: Economic reforms in the post-Soviet Russia in the 1990es.
Marxism-Leninism: Soviet Russia
In the late 1990es many people believed that free trade between the US and China would benefit both sides. This belief was based on the experience with trade between the US and European countries (Germany, France). The US helped China join the WTO in 2001. 17 years thereafter it turned out that free trade with China was harmful to the US economy because China is very different from Germany and France. The methodology used by those economists was wrong and the decisions based on it affected about 400 000 people in the American manufacturing sector (source, passage starting with "We would conservatively estimate...").
Chicago school of economics: Milton Friedman's ideas influenced how Estonia's economy was reformed in post-Soviet times.
Input-output models were used, among other things, in the Soviet planning economy.
Linear programming/Operations research was used to optimize the output of factories (allegedly both in socialist and capitalist countries).
Demurrage proposed by Silvio Gesell was used in, among other things, the Austrian city of Wörgl (German) in 1932.

Spectrum auctions are generally designed by economists using results and insights from auction theory. For example, most modern spectrum auctions are at least somewhat related to the ascending clock proxy auction of Ausubel and Cramton. These auctions are used to sell hundreds of millions of dollars of radio spectrum licenses. A similar point can be made about the auction mechanisms used by other branches of the public section (such as central bank treasury auctions).

Matching theory has been widely applied in the design of many real-world markets and allocation mechanisms. Examples include the assignment of student doctors to medical residency, the assignment of students to high schools, and the pairing of kidney donors with patients.

Compeition (antitrust) policy is based to a very large extent on results from industrial organisation. This includes policy formulation informed by many comparatively recent results on topics including bundling, collusion, and vertical restraints.


Are the retirement plans insured in the USA? Are the retirement plans insured in the USA? Or the clients of the pension funds can lose their pensions completely in case the pension funds are going bankrupt?

The Pension Benefit Guaranty Corporation is the government entity responsible for insuring private sector pensions against the event that a corporation cannot pay their obligations.


Why does an increasing demand for dollars lead to the depreciation of a currency? I am self studying some slides of a course on monetary economics.

The source of the slides is Pilbeam, chapter 11 on the mechanism of the Bretton Woods system.

I don't understand the following reasoning:

Suppose there is an increasing demand for dollars in some country (because of a shortage on the current account).
This will lead to the depreciation of the currency.

I am by no means an expert in monetary policy, but this is how I understand it. An increasing demand for dollars implies that more people want to trade the local currency for dollars. The supply of the local currency then increases while demand for it decreases, implying that the currency will depreciate.


Quasi-linear utility functions I have the following quasi-linear utility function given: $u_0 = f(x_1) + x_2$ (with $f'>0$,$f''<0$).

I know that the indifference curves are vertically parallel, which means that the slope is independent of the consumption of $x_2$. I suppose that there is no income effect, but how can i show this?

Cheers

You can show this concerning the optimization problem with the objective function $U_0 = f(x_1) + x_2$ and the budget restriction $M - p_1 x_1 - p_2 x_2 = 0$. Using the Lagrangian, this leads you to
$$
f'(x_1) = \frac{p_1}{p_2} \quad \text{or} \quad f'^{-1}(\frac{p_1}{p_2}) = x_1^{*} = D_1(p)
$$
You can see that in this special case the optimum quantity of $x_1^{*}$ (Marshallian demand function) does not depend on the income $M$
$$
\frac{\partial D_1}{\partial M} = 0,
$$
The income effect is therefore zero, and you will not consume a different amount of $x_1^{*}$ if the income $M$ varies.

Some further considerations: Based on the Marshallian $D_i(p, M) = x_i^{*}$ and Hicksian $H_i(p, u) = x_i^{*}$ demand function, you can show some interesting properties of this particular utility function using the Slutsky equation:
$$
\frac{\partial D_i}{\partial p_i} = \frac{\partial H_i}{\partial p_i} - x_i^{*} \frac{\partial D_i}{\partial M}
$$
This shows that the derivative of the Marshallian demand function with respect to price equals the derivative of the Hicksian demand function with respect to price minus the optimal $x_i^{*}$ times the derivative of the Marshallian demand function with respect to income. In this special case, the Marshallian demand function equals the Hicksian demand function, as $\frac{\partial D_i}{\partial M} = 0$.


Government bonds and printing money Wikipedia: If a central bank purchases a government security, such as a bond or treasury bill, it increases the money supply, in effect creating money.

My question is: what is the difference between this (government issues bonds and the central bank buys them) and directly printing money? If any. If there is no difference, then why would a government chose one way or the other?

The difference is that in buying the bond, the central bank now owns a bond, and a fiscal deficit has not been directly monetised.

That means that:

the government will have to keep paying interest on the bond, to the central bank, and will have to redeem it if it's not a perpetual. Remember, some governments are completely distinct entities from central banks, with no guaranteed way to move money between them in a consequence-free manner: the Eurozone governments are a good example.
The central bank can sell that bond when it wants to, giving it an extra means of contracting the money supply.
Currency speculators are less likely to start circulating around the currency like vultures that have spotted dying prey.


Understanding the arithmetic in this 1690 text Nicholas Barbon (1690, A Discourse of Trade)

  Another use of Interest, is, It is the measure of the Value of the Rent of Land; it sets the Price in Buying and Selling of Land: For, by adding three Years Interest more than is in the Principle, Makes the usual Value of the Land of the Country; The difference of three Year is allowed; Because Land is more certain than Mony or Stock. Thus in Holland, where Mony is at three per. Cent. by reckoning how many times three is in a Hundred Pounds, which is Thirty Three; and Adding three Years more; makes Thirty Six Years Purchase; the Value of the Land in Holland: And by the same Rule, interest being at six per Cent. in England, Land is worth but Twenty Years Purchase; and in Ireland, but Thirteen; Interest being there at Ten per Cent: so that, according to the Rate of Interest, is that Value of the Land in the Country.

I do not quite understand what the above means.

In particular, what does for example "Thirty Six Years Purchase" mean? Does it mean that to buy a piece of land, one pays 36 times the (annual) rent?

It seems that the gentlemen is speaking in the english dialect of England.  The Years purchase phrase is still used today.

https://en.wiktionary.org/wiki/year%27s_purchase

Years Purchase: The amount yielded by the annual income of property; used in expressing the value of a thing in the number of years required for its income to yield its purchase price, in computing the amount to be paid for annuities, etc.

An example of its use is here: https://investmentproperty.co.uk/property-investment-calculators/years-purchase-single-rate/


What does "capital used as structure" means? I'm in the progress of reading a paper and I came across the fragment below:

Second, we assume that producers rent machines from a capital stock. Capital can also be used as structures in both automated and nonautomated firms.

My question is: what "structures" mean in economics ? These are just buildings or the definition is broader ?

This is not really an economic terminology. Many words can have multiple meaning in common English. According to the Oxford dictionary:

structure /ˈstrʌktʃə  /
▸ noun
1 the arrangement of and relations between the parts or elements of something complex.
...
2 a building or other object constructed from several parts.

In case of that article the first meaning of the word is used instead of second one.
To be more specific, the authors Hemous and Olsen (2018)  use that sentence when they talk about production process and production function of the company so what they mean is the that the capital can be used in the meaning 1 that is used in the arrangement of and relations between the parts of the production.


Choice of measure for unemployment There are six types of unemployment rates in the US (U1-U6). U6 provides the broadest measure of unemployment, taking into account not only the unemployed labour market participants who are actively seeking for jobs, but also the marginally affected, the discouraged, as well as the part-time workers who would like to have a full-time job (i.e. "underemployed" workers). This broad measure is deemed by numerous economists to be the "true" unemployment rate. However, what is usually popularised in the news media is in fact, the U3 unemployment rate, which only takes into account those unemployed that are actively seeking for jobs. What is the reason for the U3 rate being the more popularised and widely emphasised measure of unemployment in the United States and also for other developed economies?

What is the reason for the U3 rate being the more popularised and widely emphasised measure of unemployment in the United States and also for other developed economies?

Historically, data for U-3 have been collected for longer than U-6.

For example, in the US, the former have been collected since 1948, while the latter only since 1994. So, it is "traditional" to report the U-3 data.

In many other countries, the equivalent of U-6 data may not even be collected.

So, when making comparisons across time and countries, U-3 data are the best we've got.

  This broad measure is deemed by numerous economists to be the "true" unemployment rate.

This is incorrect. Economists do not consider any single measure to be the "true" unemployment rate. Instead, to arrive at any conclusion, economists try to look at a broad variety of measures and data, where available.

(But again, for reasons already given above about data availability, economists will often use only the U-3 data. This though should not be misconstrued as them thinking that this is the "true" unemployment rate. In fact, the deficiencies of the U-3 data is exactly why economists encourage collecting also other measures of unemployment.)


Incentive compatibility: Weakly dominant strategy versus Nash equilibrium? When it comes to proving that a mechanism e.g. auction is incentive compatible this is the approach I'm using:

I break down all the cases that might happen if the agent reports an untruthful value to achieve higher utility. Then I show that by lying about the valuation an agent will achieve a lower or at best the same utility as of truthful valuation reporting. I call this weakly dominant strategy truthfulness.

Now my question is that what is the difference between weakly dominant strategy and Nash equilibrium? I know that a strong dominant strategy equilibrium is stronger than the nash equilibrium. But what about the weakly dominant strategy equilibrium?

A Nash equilibrium that consists of weakly dominant strategies is a stronger solution concept than a NE itself.

Consider the following simple matrix game where best replies have been marked with *

\begin{array}{c|cc}
P1/P2&\text{left}&\text{right}\\
\hline
\text{Up}&1^*,1^*&0^*,0\\
\text{Down}&0,0^*&0^*,0^*
\end{array}

Both Up and left are weakly dominant strategies. They are always at least as good as Down and right respectively. That does not rule out, however that there are no other Nash equilibria as the game shows. The combination (Down, right) is also a Nash equilibrium because there is no gain from unilateral deviation. By deleting weakly dominated strategies we lose the latter Nash equilibrium so a Nash equilibrium that consists of weakly dominant strategies is a stronger solution concept.


Derivation of Surplus in Paul Romer's paper on "mathiness" In this paper by P. Romer https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.p20151066
I'm wondering the Surplus $S$ was derived.
By using the given condition I found that $$q_0=m^{-\tfrac{1}{a+b}}N^{-\tfrac{b}{a+b}}$$
By Surplus I assume he means total Surplus (Consumer Surplus + Producer Surplus) which can be calculated by the integral $$\displaystyle{S=\int_{0}^{q_0}[D(q)-S(q)]dq=\int_{0}^{q_0}[q^{-a}-N^{b}q^{b}]dq}$$
With a little bit of algebra I find $$S=C(a,b,m)N^{\tfrac{b(a-1)}{a+b}}$$ where $C(a,b,m)=\tfrac{1}{1-a}m^{\tfrac{a-1}{a+b}}-\tfrac{1}{b+1}m^{-\tfrac{b+1}{a+b}}$
So I'm probably wrong, is my idea of $S$ correct? I need to know because if it is then it's likely a mistake in my algebra. I also assumed that $b>0$ and $0\leq a<1$

I think you have a typo in your  $q_0$: the exponent of $N$ should be  $-\frac{b}{a+b}$. I did the whole calculus with this corrected type of $q_0$ and I was able to replicate your results (this is why assume $q_0$ has only a typo and you actually did the algebra with the correct $q_0$).
I suggest that the discrepancies to the paper are indeed connected to the Surplus function. But i cannot come up with any idea why this surplus function might be wrong.

Edit: Outside from the typo there was no error, @actuarialboi9 and my humble self calculated the individual surplus. If one multiplies that Surplus function with $N$ the number of people in the market results will be equal:
$\begin{equation} S= C(a,b,m) N^{\frac{b(a-1)}{a+b}} \;  \cdot \; N \;  = \; C(a,b,m)N^{\frac{a(1+b)}{a+b}} \end{equation}$


Question about misperception in IS-MP model Why is these steps happens one after another in IS-MP Model if MP curve is a horizontal line? Also, is this preventable?

a) Policymakers believe the slow-down in growth is caused by a
negative aggregate demand shock...

(b) ...so they lower the Real interest rate R.

(c) In truth, the IS curve never shifted...

(d) ...so the great inflation happened.

Consider the standard IS-MP model with horizontal MP. According to (c), the IS remains in the original level. Therefore, the fall in the real interest rate $R_t$ leads to an increase in the output gap $\tilde{Y}_t$. This happens because the opportunity cost of investing is lower. As such, for an unchanged marginal return to capital $r$, investment increases, leading to a deviation of actual output from potential output, and therefore to a positive short-term output gap $\tilde{Y}_t$.

In the IS-MP-PC model, inflation follows a simplified Phillips Curve, which is:

$$\Delta \pi_t = v\tilde{Y}_t + \bar{o}$$

(notation borrowed from Jones, Macroeconomics, 3rd edition).

Therefore, in the absence of a cost-push (or supply) shock ($\bar{o}$), deviations in inflation from the target are given by the positive output gap $\tilde{Y}_t$. In consequence, inflation increases.

I don't really get your second question (is this preventable?). Clearly, a first best is for central banks to correct their models in order to avoid mistakes. This is of course difficult. It requires to identify potential output and to distinguish between aggregate supply and aggregate demand shocks. Not an easy task.


Why are there not more competitive nonprofits? For example, when I go to the grocery, and peruse the various goods for sale on the shelves, there is at least a 99.9% chance that any given product is produced for-profit.  Even "Newman's Own", which gives all of it's profits to charity, is classified as being for-profit.

Why are there no non-profit brands of, e.g. breakfast cereal, whose goal is to simply provide consumers with a healthy and affordable morning meal, but not to make a profit?

There is a Hungarian economist by the name János Kornai, who has renowned work on eastern block socialist systems. He has devised a system theory on coordination mechanisms which guide the way people work together and allocate resources. Based on this theory you can explain different economic and political systems as well. The four coordination mechanisms are:

market (for-profit business - capitalism)
bureaucratic (the state - socialism)
ethical (non-profit, charity organizations, the church etc.)
aggressive (organized crime etc.)

From these four, the ethical is the mechanism which guides charity and non-profit organizations, which is actually the weakest in terms of efficiency. The guiding objectives are grounded on moral and altruistic behavior, but as humans are collectively more selfish in reality, this does not work too well. There is a crowding-out process, by which market coordination takes over in that certain field. Which is in your case the FMCG industry. Even if there are some moral initiatives to simply provide consumers with a healthy and affordable morning meal, but not to make a profit, slowly the enthusiasm erodes and people start to behave more selfish, and exploit the the brand and image to make money. Look at part III. section 1. of the article titled, Neither bureaucracy, nor market? for a good explanation.


Could massive derivatives exposures at banks lead to disaster? A while back I posted this question about the possible risks of banks having massive derivatives exposures.

The most upvoted answer (by BKay) said that there was little risk because banks mainly hold pairs of opposite bets. So for example it may simultaneously hold bets with two companies (A and B) where, if the price of oil goes up sharply then it has to pay out to A, but B has to pay the bank.

So this is all fine so long as both A and B are solvent after the oil price rise. Presumably if B goes bust then the bank is still liable to A.

So now my question is - couldn't there be some scenario where there is a sudden economic shock which simultaneously means that the banks will have to do a lot of paying out of bets but where the companies that are losing bets, and owe the banks money, go bust. With such enormous exposures it wouldn't take much of a fraction of the bet-losing companies going bust to cause an enormous loss for the banks.

Its possible, but, in principle, most non-financial companies use derivatives to "hedge risk", rather than to "bet". Hedging risk means that the firm will use derivatives to lower its chances of going bankrupt, for  example an oil company will buy a put option on its oil output, so that if the price of oil falls after the firm invested in producing it,  the firm can still sell the oil at a high price, and avoid bankruptcy. Other times, the bank is an intermediary in futures. futures allow a firm to sell its output forward in time, and another firm to buy the output forward in time. this reduces the risk for both of the firms. Of course, selling or buying  forward reduces the  chance of making  it big if the prices improve in your favor.

Also, financial regulation forces banks to consider multiple possible future scenarios and their effects on their balance sheet. These exercises result in a measure of the riskiness of the bank, and in turn let authorities ask the bank to hold more capital or unwind some of its positions if has too much risk of some sort. The exercises include dramatic swings in commodity prices, unemployment, or the failure of large corporations, or large financial counter-parties.

There are certainly some financial agents out there that hold tons of risk. They might be indeed betting on one view or another, but because of the regulatory environment, these can't be "banks". This is very important, because if they are not banks, then their collapse does not then create contagion. A big investor looses his money, but if its not a deposit taking, (or similarly, a highly leveraged institution), then the losses, or gains, are in sense expected.

Therefore, although you are right in principle when you say that if banks stand in the middle between two firms and one of them goes bankrupt then the bank gets hit, regulation is meant to push banks away from risk. Also, the possible losses to the banks owners move them towards avoiding risk. And "risk" here includes the one that comes from their clients on one leg or another of a deal collapsing...

Here's a more detailed analysis: Congressional Research Service article on Financial Regulation.
You could also do worse than by taking Nobel Prize winner Bob Shiller's  online course.


Why doesnt Law of Diminishing Marginal Utility not affect price effect? Ok so in my textbook, it is given that the downward slope of the demand-price curve is justified by three factors:

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

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

  price effect=income effect+substitution effect

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

This may just be a semantic misunderstanding. The Law of Diminishing Marginal Utility (LDMU) does "affect" the price in the sense that it is responsible for the convexity of preferences, which in turn guarantees a well-defined price effect. The formulation "price effect = income effect + substitution effect" is just a short way of saying that the change in consumption following a change in the price of a good can be decomposed into two different (consumption changing) effects called income effect and substitution effect. The LDMU itself is not a change in consumption and therefore not part of this identity; it is more like a prerequisite to be able to establish this identity in a unique way.

(PS: The LDMU only makes sense for cardinal utility functions which have long ago been replaced by ordinal ones, at least in deterministic contexts. It should be replaced by the Law of Diminishing Marginal Rate of Substitution. What I said above holds analogously then.)


How much average value does 1 working hour produce? ( are there reliable statistics?) This is a non-economist's question.

As a philosophy teacher ( in a french high school) , I have to study the theme of " labour" in class. I'm looking for factual data in order to assess the contemporary validity of some philosophical theories regarding the employee/ enterprise relation.

I suppose there is no single answer to the question : how much average value does 1 working hour produce?

Are there reliable statistics dealing with this subject?

Either statistics by country, or by enterprise, or by social category/profession?

Has also the profit generated by 1 working hour been studied?

Has the historical evolution of this profit through time been investigated?

One possible measure is "GDP (or productivity) per hour worked": OECD, EU28.


Are Complex Roots in Macroeconomics OK? I've been estimating some non-linear Macroeconomic models.

As a field, do we care about complex roots of the autoregressive matrix? Is there any reason to think the real word processes have real roots?

As regards dynamic convergence and stability, complex roots are associated either with a stable orbit around the fixed point, or with convergence to the fixed point by damped oscillations.

Check also https://wordpress.com/post/alecospapadopoulos.wordpress.com/197


Effect of the Bank Home Loans of Property Prices my name is Nick and I'm from Sydney, Australia.

In the last 5 years, our big cities such as Sydney and Melbourne has experienced rapid property price growth, they went so high and so fast that Sydney has been catapulted to top 5 least affordable cities. This rapid price growth has been accompanied by the extremely high quantity of mortgages issued by the various private banks, in fact, Australian banks are the most profitable banks in the world and currently, their main assets are home loans. I'm wondering of the correlation between high quantity of bank home loans and property prices.

As well how the inflation is influenced by the bank credits? Can the bank borrow more money in example from the overseas and therefore increase the money supply without increasing the actual production and purchasing power and driving the inflation upwards? Can same be applied to the property prices?

Are the prices rising so high as a result of increasing amount of affordable loans or vice versa, the demand for property has driven the supply of cheap loans?

As I understand this is actually a problem of the central bank (not corporate banks) not increasing the interest rates, they are at record level low right now. Actually, because the wages are as well at record level low as a percentage of GDP and stagnate the central bank afraid to increase the rates because people won't be able to repay the mortgage.

Regards,
Nick

This is a big question. I will just comment on one aspect.

  Are the prices rising so high as a result of increasing amount of
  affordable loans or vice versa, the demand for property has driven the
  supply of cheap loans?

We know that people can pay for a house in a few ways:

Use proceeds of the house that they are selling.
Use savings from wages and salary.
Sell other assets (e.g., equities) and use proceeds.
Get a mortgage.

Unless the other sources of cash (1-3) rise enough to cover higher house prices, mortgage lending has to rise. One can try to do a lot of statistical analysis, but the usual relationship is that mortgage borrowing rises at the same time as house prices going up.

Returning to the part of the question I highlighted above, one could argue either way.

One argument is that house prices rose (for some reason), and so mortgage borrowing has to rise in response. In this view, the amount of mortgage loans is not a driver of anything, it is just a mechanical response to higher house prices.

Going the other way is possible. However, we need to remember that mortgages are inanimate objects - in what sense can they drive behaviour? It is safer to say that some humans have changed their behaviour, and the rising loans is a consequence of that behavioural change. The driver is the behaviour change (a possibility not covered in the question.)

The likely suspect is that the behaviour of bankers has changed. Their "effective lending standards" have changed for any number of reasons, and so households can borrow more. (One possible factor is lower interest rates; although formal lending standards may not have changed, the same household can qualify to borrow more under the existing standard.) This extra mortgage borrowing capacity allows households to bid up the price of houses.

I do not think I have fully answered the question, but this discussion may help you rethink how to pose the question.  This website has a difficult time with extremely broad questions, so you may get more responses if you ask a few very specific questions.


What did Karl Marx mean by "the movement of this antithesis"? In a lecture about ancient and modern cities, a quote came up on the slides from Karl Marx's Capital where he writes

  "The foundation of every division of labor that is well developed, and brought about by the exchange of commodities, is the separation between town and country. It may be said that the whole economic history of society is summed up in the movement of this antithesis."

What does a movement of an antithesis mean ? And I don't understand what antithesis he is referring to in this excerpt; what is being contrasted; the well-established separation of divisions of labour and the exchange of their resulting specialised products ? Or the well-established foundations of divided labour and how that was brought about by exchanging commodities (or that commodities could be exchanged at all) ? Or am I missing something else completely ? Is this a translation thing, an English thing or an economics thing ?

Town represents manufacturing and it's where a lot exchanges taking place. Country represents farming. The movement of antithesis symbolizes the urbanization of civilizations as economy progresses.

As an economy progresses, people will move from rural area into the cities. Labour associated with agriculture will decrease, at the same time, workforce in manufacturing and services industries will increase.


Why does the incentive compatibility constraint bind (moral hazard)? Consider a very basic model of moral hazard with two possible effort levels $e_L<e_H$ and two possible levels of output $y_L<y_H$. If the agent doesn't participate, they get utility of $\bar{u}$. If they participate, they get $E[u(w)|e]-c(e)$ where $u'(w) > 0$, $u''(w) < 0$ and $c(e_L)<c(e_L)$. In other words, the agent is risk averse and dislikes effort. Putting in more effort raises the chance that output is high, i.e. $P(y=y_H)=p$ if $e=e_H$ and $P(y=y_H)=q$ if $e=e_L$ where $1>p>q>0$. The principal chooses a contract ${w_H, w_L}$ which specifies a wage following $y=y_H$ and $y=y_L$ respectively. Since they are risk neutral, they choose $w_H$ and $w_L$ to maximise $E[y - w]$.

Let us suppose that the principal wishes to induce $e=e_H$.

The optimal contract must satisfy an 'incentive compatibility' constraint:

$$pu(w_H)+(1-p)u(w_L)-e_H\geq qu(w_H)+(1-q)u(w_L)-e_L$$

In the optimal contract, this must hold with equality ('bind'). If I recall correctly, this has something to do with optimal risk sharing (more precisely, that the principal doesn't want to expose the agent to `unnecessary' risk). However, I would be very grateful if anyone could provide a more precise (but ideally still intuitive) explanation for why this must be the case.

The idea behind the incentive compatibility constraint is that the expected utility when doing the high effort level needs to be as least as large as the one the agent would obtain from doing the low effort level. There are many contracts that satisfy the IC. Given that the agent is risk averse, i.e., has strictly convex indiference curves, the further the asymmetric information contract deviates from the symmetric information contract, the higher will be the expected payoff the agent receives. Of course, the higher the expected payoff for the agent, the lower the expected payoff for the principal. Hence, the principal will choose that contract that a) provides the agent with just her reservation utility and b) the IC is satisfied as an equality.

Perhaps what you have in mind is that, since the expected utility for the agent is the same irrespective of the effort level she exerts, she may as well end up doing the low effort level anyway. But recall that the agent is indifferent between the two effort levels, and, therefore, we can assume that she chooses to do the high effort level.


Liquidity Trap Question? Return to equilibrium As far as I inderstand a liquidity trap occurs when increasing the money supply is not able to stimulate the economy because people prefer hoarding the cash rather then investing in debt securities because of low yields. However will that not in turn cause the bond prices to drop and conseqeintly yields to rise due to lack of demand. And if so shouldnt these rising yields provide more and more incentive for people to start putting their money in bonds or other securities and thus solve the liquidity trap?

Thus my question is why are we not seeing this occur in places where a liquidty trap exists?

However will that not in turn cause the bond prices to drop

Low yields provide incentives for people to sell bonds in exchange for cash. And they do. However, bond prices will not drop if there is a counter-acting amount of buying. Who is that buyer? The various central banks that are causing the liquidity trap in the first place. If that sounds counter-intuitive, remember central banks are trying to stimulate the economy instead of running a trading operating that tries to maximize profits, and so it is not always in their interest to do the same thing other market participants do. If you're skeptical that central banks could do enough bond buying to counter-act the selling, take a look at the central bank of Japan (Bank of Japan). According to this Reuters article, they own 45% of the Japanese government bond market.


Is personal produce counted in GDP? Good day. And sorry if it's a stupid question.
I came across a question on another q&a site earlier today. It was about a hypothetical scenario. The question was if everyone in a nation becomes self-sufficient, would GDP increase. There were answers where the answerers opined that it might actually reduce the GDP. Others had the opposite opinion.
I studied a bit about it and thought any product is counted in GDP. Am I correct?
Would personal produce (consumed by own) be counted in GDP calculation?

This is often called “home production.” By default, the answer is no, but different countries have different methodologies.
This US Bureau of Economic Analysis page has some information: BEA webpage.
They produce a “satellite account” that includes this information. (Not officially part of GDP, but official supplemental information.)


Distrubtion of a test statistic under the alternative hypothesis I have been reading Davidson's Econometric theory and methods and I cannot understand one particular paragraph about the distribution of a test statistic.In the paragraph below he says that under the alternative hypothesis if the true $\beta$ is equal to $\beta_1$ then $\hat b= \beta_1+\hat\gamma$. Then he defines $z=(\beta_1+\hat\gamma-\beta_0)/(\sigma^2/\nu)$ and finds the mean and variance as given by 4.04. Why is he doing that? I understand how he gets the mean and variance but I don't get why is he doing that because at the end we dont get a standard normal variable but a variable with mean $\lambda$ and variance 1.

I have been stuck here for a while so any help would be highly appreciated.

Reading the book, $z=\frac{\hat\beta-\beta_0}{(\sigma^2/n)^{(1/2)}}$

The distribution of $z$ under $H_0$ will determine the critical values for a given level of significance $\alpha$, i.e. it will determine the probability of Type I errors (prob of rejecting the null, when null is true).

The distribution of $z$ under $H_1$ (4.04) will define the probability of Type II errors(not rejecting null when alternative is the true hypothesis).

The closer - the averages are close - the distributions of z under the null and the alternative are, the higher is the probability of Type II errors.
In the picture below, we have several pdf for normal distributions. In blue, the distribution has zero mean; in red mean 1; and in yellow mean 2.

At the usual critical values of $1.96$ and $-1.96$ (for an $\alpha=0.05$), we can see a vertical line. When we're on the blue curve, i.e. under the null, we can calculate the prob of type I error, as the area to the right of the rightmost vertical line, to the left of the leftmost vertical line and below the blue line.

To calculate the type II error, we check in the interval between the vertical lines(not rejecting $H_0$ area), under the red or yellow curve, depending on the values that $\beta$ really takes.
Notice that the area below such a curve will increase the closer the curve is to the one under the null distribution. In this case, the prob of type II error is greatest is when the alternative is the true model and the mean of the distribution is 1.

By deducing the distribution of z under the alternative, the authors want to give an idea of the type of rejection region one will get, when doing inference in this setting.


Is the BEA double counting benefits in Personal Income? The BEA (US Bureau of Economic Analysis) that produces the GDP and GDI also prepares a summary of Personal Income for the nation.

In that it includes employer contributions for both private pensions and insurance as well as the employer contributions for government social insurance such as social security and medicare.

Later on "transfer payments" from both private and government programs are also added.

Finally, personal payments for social security etc are deducted.

To me it seems that including employer contributions that are not available as income and are counted later in transfers seems like double counting and also doesn't agree with elementary macro economic texts that define national personal income as not including such contributions. In fact these contributions are carried into "Disposable Personal Income" which seems clearly wrong. Am I missing something?

6/15

After reading the comments, part of the issue may simply be that I'm not good at accounting, but I understand part of this better. I agree there is no double counting. But, in the image below (just looking at social security)

I'm OK with gross "personal income" at the aggregate level including line 8 and the net of lines 18 and 25. But if one thinks of Social Security as a big savings account, then line 8 belongs in personal savings and not disposable personal income. No?

Statistical Agencies do not necessarily obey the habits of Economic Theory. There is no "mistake" here (certainly, there is no double-counting), but a different approach to what each concept means or "should mean" (which sometimes is also a consequence of historical precedence).

For the fun of it I post below how the same data could be arranged to conform with standard theoretical economics, where we make a point of distinguish between income earned, taxes in the broad sense, transfers, consumption, saving.

ALTERED/RE-ARRANGED BEA TABLE 2.1. "Personal Income and Its Distribution"


Fair voting procedure when there are many issues When several people have to decide about a single yes/no issue*, the natural decision rule to use is the majority rule.

But when there are many issues to decide upon, the majority rule is "unfair" in the following sense: it is possible that the majority's opinion will be accepted on all topics and the minority's opinion will not be accepted on any topic. As an extreme example, it is possible that 51% of the population will decide about 100% of the issues.

I am looking for a decision rule which prevents this unfairness.

Formally, define a "uniform group" as a group of people who always vote in the same way. Define the "acceptance rate" of a uniform group as the percentage of issues on which the opinion of the uniform group got accepted.

Define a "fair decision rule" as a rule for which, for every uniform group containing X percent of the population, the acceptance rate tends to X when the number of issues tends to infinity.

MY QUESTION IS: Does there exist a fair division rule as defined above?

(* I restrict the question to yes/no issues, since when the issues are not binary the problems are much more complicated).

That's interesting: the flavor of the frequentist approach to probability used for a socio-political fairness criterion: if my measure as a population group is $0<p<1$, and known, then my opinion should be accepted by the whole at the same measure, as number of issues goes to infinity. In other words, current observed acceptance rate should be a consistent estimator of theoretical acceptance rate, and equal to my measure.

Then it is very easy to create such a decision rule, while saving public money: no need to hold one referendum after another, just construct a die, with as many sides as there are "uniform groups", with the die's weight distributed in such a way that the side representing uniform group $i$ will have probability of turning up equal to $p_i$. It won't be difficult to construct, and publicly and objectively test it for the desired properties.

Then, wherever an issue comes up for voting, just roll the die. And ok, spend some money for a suitable public ceremony.

Whenever there is a census, the relative size of each uniform group can be re-measured and a new die can be constructed.

Why do I have the feeling though that no uniform group is likely to ever accept such a scheme?

(This of course puts aside the importance of each issue, in general, for each uniform group, etc, but I took that from the OP which concentrates on number of issues, irrespective of what the issues are about, and to whom they matter and how much they matter, and how do we measure that etc).


Book Value per Common Share Does book value per common share include intangible assets?
As far as I know, its formula is common stockholder's equity divided by shares outstanding? If shareholder's equity includes intangible assets, then book value per common share should also, right?

Shareholders equity does not include intangible assets per se. This is mainly bookkeeping not economics but generally in most double-entry bookkeeping systems all accounts will have two sides one is asset side and second is liability and equity. An aggregate of all these entries will end up in the balance sheet which will again have asset side and liabilities and stockholders equity side. The asset side of balance sheet tells you what firm owns and and liabilities and stockholders equity side where the sources to obtain those assets came from. An example of balance sheet would be:
Assets                              Liabilities & Stockholders equity
Cash              $100                     Stockholders Equity      $50
Intangible assets $100                     Bank Loan               $150

The formula for book value per common share is according to investopedia given by:
$$BV = \frac{\text{total equity} - \text{preferred equity}}{\text{Total Shares Outstanding}}$$
Note that neither the total equity or the book value in itself gives you any information what the amount of intangible assets is or they are included in calculation. The total equity can be calculated as Assets minus Liabilities but again you cant generally tell from total assets or liabilities what the intangible assets are.  In this case the total equity is $\\\$50$ but amount of intangible assets is $\\\$100$. The book value also does not give you any information or contain the intangible assets either.  To see what they are you would have to go back to balance sheet or some ratio that includes them.


What economics aggregate(s) could suggest an imminent change in exchange rates? I have read articles about the Swiss Franc breaking its peg with the dollar and I would like to understand what indicators people look at to determine whether a currency break/depegging is imminent. More which of these useful economic aggregates are most important in determining a currency peg break?

If they expected the peg to break then it is clear that the franc would gain in value. Since the currency has been held artifically cheap by the central bank, i.e. would have gained value if the central bank had not intervened, then the moment the central bank stops intervening (abandons the peg) the currency will appreciate.

Why would it have gone up otherwise, i.e. what are the factors driving exchange rates? We call these "fundamentals". Basically exchange rates are determined by supply and demand for a currency, just like for anything else. So basically anything influencing supply and demand for currencies would be cause for a change in exchange rates. Further expectations of changes in fundamentals cause them as well. These include the trade balance (typically governs the long run behavior of exchange rates in reality) and the difference between domestic and foreign interest rates (typically govern the short run behavior in reality).

Now one might ask, why did they expect the peg to be abandoned? That depends on the specifics about Switzerland. I'm not an expert there, so I'm sorry if I cannot give a very concrete answer. However pegs are typically unstable and usually abandoned eventually. This is because the longer the central bank keeps a currency at the "wrong" price, the more pressure from the market there is to correct it which means the central bank must fight harder and harder to keep it and eventually gives up or decides its not worth it anymore.


In US gov treasury auction, can the highest bidder force high prices for all others In US treasury auction (for bonds and notes), my understanding is that the highest bidder's price (and rate) is applied for all the buyers.

Assume a buyer 'A' who plans to buy a smaller number of bond shares. Let two other players 'B' and 'C' invest heavily compared to 'A. Let 'B' and 'C' be competitors of 'A'.

Is it possible for 'A' to invest low but bid high thus play spoilsport for 'B' and 'C'?

No. The auction uses the highest yield, which means the lowest price (for the same coupon). That is, for bonds, price up -> yield down (and vice versa). (The only tricky bit is that the coupon is not known until the auction concludes.)

For a discussion of U.S. Treasury bond structure: link to TreasuryDirect.

Not all bonds are issued via an auction process (one alternative is “tapping” issues). Sweden is an example of using a multi-price auction - link to Swedish auction description.


Why should Greece destroy their cash euros? Leading economists in my country (Sweden) recommend and predict that (in the case of default) the Greek government will destroy all the euro bills in the country. Making holes in them and stamp them to become drachmer which are maybe 80% or 90% less valuable than they were. There seems to be about €80 billion (M0) in euro bills in Greece, about a third of one year's GDP.

What would the upside be with destroying this fortune? Wouldn't it be better to for example use those €80 bn to pay the debts? Do any prominent non-Swedish speaking economists give the same advice?

In Sweden former heads of the central bank, the highest government officials, economists at several financial firms and the publicly profiled academic economists (including professors in the committee which chooses so called Nobel prize winners in economics) all talk about destroying the cash euros as if it was some kind of solution. Have they all gone raving mad, or what am i missing? How could it even be done? How force people to destroy their own cash? And I think they have to cut away more than 1/3 of the bill to maculate it, or else they can be exchanged for new euro bills.

Using Google translate I have read some of the articles you referred. It seems to me that the problem the Swedish economists are talking about is that Greece will need its own currency (this is debatable). However it takes a long time to get currency in sufficient amounts.

  Before the 2003 invasion of Iraq, citizens in many parts of the country began to ditch their own currency, believing that it would soon be worthless as all notes carried a depiction of Saddam Hussein, the country’s president. De La Rue, the world’s largest printer of banknotes, began work on new cash. “In the case of Iraq, the issues may not have been dramatically different from any other currency change; but the timescale was,” the company said. “Working out the details … is all very well when you have a year or two to think about it. Make that a month or two, and things start to get interesting.”

Source

Hence the recommendation is to use what they have at hand: euro bills. But if their euros would be the same as other euros, then the exchange rate between a Greek euro and a 'normal' euro could not go over 1, because you could always take a Greek euro abroad and use it there. So if the government wants the exchange rate to change (this would increase competitiveness and this is the biggest advantage Greece could get out of a new currency) they will have to modify the existing euros they have. For example they can stamp holes in them. You can read about such speculation in more detail

  During a “euro pause” the Greek Central Bank is granted a three-year licence by the European Central Bank to create euros that are non-exchangeable for other euros.
  The euros in Greek ATM machines have “GT” (Greek Transactions) stamped prominently on them. In Greece, these euros circulate normally but a Greek individual planning a transaction outside Greece will need to convert their GT euros to non-GT euros at a market rate.

here.

It is debatable whether having a national currency two months ahead of time is worth the cost of 80 billion euros. However it might also be that the ECB will demand 80 billion euros from Greece if it leaves the Eurozone. (I am not sure whose property the cash allocated to Greece is.) In this case, stamping the euros may satisfy the ECB and give Greece their temporary currency.


Why Keynesians prefer short run measures despite straight long-run Phillips curve? I was studying about the Monetarists' and Keynesians' view of the Phillips curve and natural rate theory of Friedman. It seems intuitive to me as to why Friedman argues that using an expansionary monetary policy in the short run will ultimately lead to no increase in output in the long run and will solely put pressure on the prices, thereby increasing inflation. Consequently, it seems that in the short run, monetary policy can't achieve much to change the natural rate of unemployment. The Keynesians too have a straight long-run Phillips curve, but still, they argue for going forward with activist policies in the short run.
The book I am referring (Richard T. Froyen's Macroeconomics: Theories and Policies) is pretty vague on this final part. It just says, " If we don't accept the other propositions of the monetarists - and Keynesians do not- there is a short-run role for stabilization policies, whether monetary or fiscal." I don't understand which assumptions it is talking about and why Keynesians believe, despite the straight long-run Phillips curve, that short-run measures can help stabilize the economy.

Actually both New Keynesians, Keynesians and Monetarists are advocating for short-run government activism, just the underlying mechanisms are different and Monetarists stress monetary over fiscal policy.  According to the New Palgrave Dictionary of Economics (Cagan 2017) monetarism is defined as:

Monetarism is the view that the quantity of money has a major influence on economic activity and the price level and that the objectives of monetary policy are best achieved by targeting the rate of growth of the money supply.

Actually Friedman (1968) and Phelps (1968) criticized the original Philips curve mainly because it posited permanent employment inflation trade-off.
The monetarist Phillips curve would  be very close to something like:
$$\pi_t = \pi_t^e + \lambda( \ln Y_t - \ln \bar{Y}_{t}) + \epsilon^s_t$$
where   $\pi_t$ is inflation, $\pi_t^e$  inflation expectation $\ln Y_t$ log of current output $\ln \bar{Y}_{t}$ log of the natural rate of output. The argument here is that if government follows inflationary policy and people are not grossly irrational then in the end $\pi_t = \pi_t^e$ and there is no inflation-output trade-off. However, even Friedman himself didn't argued against short-run trade-off. The problem in his view was that in order for there to be permanent trade-off government would always have to 'surprise' people by targeting ever increasing inflation in an unexpected way. However, the moment when the expectations would adjust $\pi_t= \pi^e_t$ and the Philips curve would be 'flat' in a sense output would be orthogonal on rate of inflation as the terms would cancel out.
Thus, if we would argue that $\pi_t= \pi^e_t$ will always hold then there would be no trade-off even in short-run - but that is not really what was ever argued by Monetarists or at least not by Friedman and Phelps. Friedman and co. were writing their research before the rational expectations revolution really took hold so their treatment of how rational expectations work was not really as rigorous as today which probably lead to some misconceptions. I think either this got somehow either not properly explained by the Froyen's book or there is some misunderstanding (I dont know the book So I can’t really comment on that).
Also from your question it’s not clear if the author of your textbook means New Keynesian Philips curve or something like  the accelerationist Philips curve.
The accelerationist Philips curve that cab be considered ‘Keynesian’ would look like this:
$$\pi_t = \pi_{t-1} + \lambda( \ln Y_t - \ln \bar{Y}_{t}) + \epsilon^s_t$$
The difference between this Philips curve and the previous one is that instead of inflation expectations $\pi^e_t$ we have there just past inflation $\pi_{t-1}$ (I am guessing that perhaps this is the assumption that was being alluded to in your textbook). This implies that there is always some short run trade-off between inflation and employment.
The New Keynesian Philips curve is yet even more different and given by:
$$ \pi _{{t}}=\beta E_{{t}}[\pi _{{t+1}}]+\kappa y_{{t}}.$$
The New Keynesian philips curve is actually based on ideas of Friedman and Phelps (see Roberts; 1995) where now the mechanism depends on current expectations on future inflation $ E_{{t}}[\pi _{{t+1}}]$. Here there is again always short-run trade-off between inflation and output with a caveat that the trade-off depends on not what past inflation was but what is the future expectation of inflation.
As you can see all three models allow for monetary policy to stimulate economy in short-run but the mechanisms are different:
In the Friedman & Phelps case short run inflation-output trade-off exists when the inflation expectation of people are not correct or if they are being surprised by government.
In the accelerationist case there is always short-run trade-off between inflation and employment because of the assumption of inflation expectations being just past inflation $\pi^e = \pi_{t-1}$.
In the New Keynesian Philips curve the mechanism depends on present expectations of future inflation and there is also always trade-off between inflation and employment with subtle difference that the trade-off depends on what the future inflation expectations are.
I think Romer Advanced Macroeconomics has a good treatment of the Philips curve so if you would like to know more about this that is the source I would recommend.


Instrumental Variable Paper for Minimum Wage I am trying to write a paper dealing with minimum wages and employment.  I understand there is simultaneity bias between these two variables so I must come up with an instrument.  Does anyone have any ideas for instruments?  I am also wondering if it is feasible to do a cross-sectional study instead of a time-series one in this scenario.  *Note:  The class requires using IVs and I am open to suggestions for other topics.

Neumark and Wascher did a lot of work on the minimum wage in the 90s and 00s, including their 1992 piece "Employment Effects of Minimum and Subminimum Wages: Panel Data on State Minimum Wage Laws". A non-paywalled version of the article can be found here. It includes use of panel data (cross sectional data that you are interested in can be considered a special case of panel data) to study the effects of the minimum wage on employment.

From page 65:

  "Another possible source of bias arises from the potential endogeneity of state minimum wage levels. If state legislators choose the timing of minimum wage increases to correspond to periods in which minimum wage increases will have the smallest (or perhaps least noticed) disemployment effects, the estimated minimum wage effects in Table 2 will be biased upward..."

They too were concerned with endogeneity between the minimum wage and employment, so their solution was to use a fixed-effects specification and put in state and year effects in the first stage of the regression, with the instrument being "the [adjusted] mean of the minimum wage level in all geographically bordering states" (p. 65). Their data was from US states. So the setup for their study could be a useful starting point for you, or those interested in a similar question to this.

As Tobias mentioned, you can also use political variables as an instrument. In Lemas (2004), Political Variables as Instruments for the Minimum Wage, lags for the endogenous variable (min. wage) can be used with serially uncorrelated errors, but if that does not hold, you can use political measures such as influence-weighted politicians' support for or against the minimum wage, among other measures that can be found in section 4.2. of the paper.


Actions in economics Mirowski 1989 argues economics and physics have frequently informed each other's theoretical development, and neoclassical economics has the same Lagrangian and Hamiltonian formalism frequently seen in physics. I don't know how mainstream this approach has ever been, but his account doesn't make explicit what would be an action in economics. For example, I can imagine a firm's profit maximization, or a portfolio's ROI variance minimization, being formalized as an extremal action principle, but only if such quantities are expressible in the form $\int_a^bL(t,\,q,\,\dot{q})dt$ or a suitable generalization. Are there any specific examples like that?

Select examples from a book suggestion due to @markleeds, Optimal Control Theory with applications in Economics:

Polluting growth has action $\int(bz-\dot{z}+\ddot{z})dt$.
Optimal extraction of a natural resource has action $\int(C(-\dot{x},\,t)+q\dot{x})e^{-st}dt$.
Consumption vs rapid attainment of production capacity has action $\int[\dot{x}-x+q-a]dt$.
Resource extraction in an open economy has action $\int-U(\bar{c}-e^{rt}\dot{x}+ay-\dot{y})dt$.
Consumption versus investment can give rise to many actions, including:

$\int(\dot{x}-1)U(x)dt$
$\int e^{-\rho t}(\dot{K}+\delta K-f)U(K)dt$
$\int\frac{dt}{K-\dot{K}}$
$\int e^{\dot{K}-aK}dt$
$\int(\dot{K}-cK)^ae^{-bt}dt$


Why does Bimetallism require international cooperation to have a chance at succeeding? I was reading the Britannica encylopedia's article about Bimetallism and under the arguments put forth against it, they cite that bimetallism doesn't work without international cooperation. Could anyone explain to me why this is? I can't seem to find a succinct answer to my question.

Quoting Wikipedia:

Bimetallism[a] is a monetary standard in which the value of the monetary unit is defined as equivalent to certain quantities of two metals, typically gold and silver, creating a fixed rate of exchange between them.[3]

Let's suppose that France says 1 ounce of silver is F1 (1 franc) and one ounce of gold is F80. And let's suppose that Germany says 1 ounce of silver is DM1 (1 Deutschmark) and one ounce of gold is DM79.
Anyone with an ounce of gold and a bit of common sense will go to France, convert it to francs (80 francs), convert it to silver (80 ounces), go to Germany, convert it to Deutschmarks (80 Deutschmarks) and convert it back to gold (1 ounce + 1 Deutschmark left over). Then they'll do it again. Over and over and over and over. Every time, they get an extra Deutschmark. Until France runs out of silver or Germany runs out of gold.
The only way this can be stopped, is if every country uses the exact same ratio - for example, if they all agree that 1 ounce gold = 80 ounces silver. That is international cooperation.


Composite Elasticities Consider the following composite function

$$ \lambda(\theta(J)) $$

If you want to think about it in more economic terms, think about it how values of firms $J$ affects market tightness $\theta$, and through that, job finding rates $\lambda$.

Let $\eta_{a,b}$ denote the elasticity of $a$ w.r.t. $b$. Then we have, under some abuse of notation,

$$ \eta_{\lambda, J} = \frac{\partial \lambda}{\partial \theta}\frac{\partial \theta}{\partial J} \cdot \frac{J}{\lambda} \\
\eta_{\lambda, J}= \frac{\partial \lambda}{\partial \theta} \frac{\theta}{\lambda}\frac{\partial \theta}{\partial J} \cdot \frac{J}{\lambda} \frac{\lambda}{\theta} \\
\eta_{\lambda, J}= \eta_{\lambda, \theta} \eta_{\theta, J} \frac{\lambda}{\theta}
$$

Could someone give me an intuition for $\lambda / \theta$ in the last expression? Why is the total elasticity not just the chain of elasticities, $\eta_{\lambda, \theta}\cdot \eta_{\theta, J}$?

But it is, there is just a simple oversight in your calculations:
We can indeed write identically

$$\eta_{\lambda, J} = \frac{\partial \lambda}{\partial \theta}\frac{\partial \theta}{\partial J} \cdot \frac{J}{\lambda} \\
\implies \eta_{\lambda, J}= \left\{\frac{\partial \lambda}{\partial \theta} \frac{\theta}{\lambda}\right\}\left\{\frac{\partial \theta}{\partial J} \cdot \frac{J}{\lambda}\right\} \frac{\lambda}{\theta} $$

But the term in the second curly brackets is not equal to $\eta_{\theta, J}$.
We have to re-arrange to get

$$\eta_{\lambda, J}= \left\{\frac{\partial \lambda}{\partial \theta} \frac{\theta}{\lambda}\right\}\cdot \left\{\frac{\partial \theta}{\partial J} \cdot \frac{J}{\theta}\right\} \frac{\lambda}{\lambda} $$

The fraction in the end now cancels and so
$$\eta_{\lambda, J}= \eta_{\lambda, \theta} \cdot\eta_{\theta, J} $$


Subgame Perfect Equilibrium for Pure and Mixed strategy In a game theory textbook there is something similar to the table below where there is one pure strategy nash equilibrium and multiple mixed strategy nash equilibria. It is a simultaneous game with the payoffs presented below.
If we assume that this game is played twice, How do I identify all subgame perfect equilibria for this game, as well as nash equilibrium that is not a subgame perfect equilibrium?
For a game with multiple pure strategy nash equilibrium I think I can find a solution by using backward induction, but for a game like this with just one pure strategy nash equilibrium and multiple mixed strategy nash equilibria, I have  no idea how to identify the subgame perfect equilibria and possibly a nash equilibrium that is not subgame perfect equilibrium, especially when there are mixed strategy equilibria included.
Any help in this would be appreciated.
\begin{array}{|c|c|c|c|}
\hline
  &  A    &  B    &  C \\\hline
A & (1,1) & (0,0) & (0,0)\\\hline
B & (0,0) & (2,1) & (1,2)\\\hline
C & (0,0) & (1,2) & (2,1)\\\hline
\end{array}

Check for the Nash equilibria (pure or mixed) of the one-shot game.
Repetition of the strategy profile of the Nash equilibria of the one-shot version yields one set of subgame perfect equilibria: For instance, play $(A,A)$ in the first stage and for any action profile played at the first stage, play $(A,A)$ in the second stage. The same holds true for the mixed (complete or otherwise) as well. For instance, the totally mixed SPNE is :Play $\left(\frac{3}{5},\frac{1}{5},\frac{1}{5}\right)$ in the first stage and for any action profile (assuming the randomisation is observable), play $\left(\frac{3}{5},\frac{1}{5},\frac{1}{5}\right)$ in the second stage.
Combinations of the Nash equilibria of the one-shot game yield another set of SPNE: For instance, Play $(A,A)$ in the first stage and play $\left(0,\frac{1}{2},\frac{1}{2}\right)$ for any action profile in the second stage and so on.
Use credible threats to play a non-Nash action profile in the first period: Play $(B,B)$ in the first stage. At the second stage, if $(B,B)$ was played, play $\left(0,\frac{1}{2},\frac{1}{2}\right)$. For any other action profile at the first stage, play the totally mixed Nash equilibrium of the one-shot game. Why does this work? There is no incentive for player 1 to deviate anyway because they're playing their best reply in the first stage. For player 2, if they were to deviate to $C$. they'd receive $2$ in the first stage and $1/3$ in the second stage. Assuming no discounting, they get $7/3$ while if they obeyed the strategy, they would get $(1+3/2)$ which is strictly greater. Similarly $(C,C)$, $(B,C)$ and $(C,B)$ can be played as first stage action profiles in a sub-game perfect equilibrium.


Binding constraints at second-best optimum I am dealing with ex-ante asymmetric information problems, i.e. adverse selection and in particular I cannot understand what's the intuition behind the fact that only two out of four constraints imposed in the second-best maximization problem are binding.

To be precise, when there is asymmetric information with two types of agents, the optimum is found maximizing the utility under two individual rationality (or participation) constraints and two incentive compatibility constraints. In order to simplify the computations, it can be proven that the IC for the high type agent and the IR for the low type agent are binding, whereas the other two constraints are redundant.

I have seen the proof and it is pretty clear but what I cannot understand is the economic intuition behind the proof; Is there someone that has this kind  of intuition?

I think its not a complex issue:

a) You need to keep the high type agent from pretending to be the ow type agent, so you give him an extra compensation from showing his high type. But this nice deal pays him more than necessary to keep him in the game so his IR is more than satisfied, i.e. not binding.

b) Similarly, you will make it painful to show that you are a low type, so that the high type doesn't go there, but you can;t make it so painful that the low type doesn't want to play so you pay him the minimum amount that he will take, i.e. his IR is binding, but  he would never choose to show himself as the high type anyway because with his low type, the incentives don't work in his favor, so the IC is not binding.


Are unemployment benefits considered to be an investment that may lead to a multiplier effect? I'm aware of the concept of the multiplier effect, and when I think about it, shouldn't it be possible that government spending on unemployment benefits create a multiplier effect?

With monetary offset by the central bank the fiscal multiplier is approximately zero for any government spending.

See eg Why the Fiscal Multiplier is Roughly Zero.

Basically, if any government spending pushes up inflation (or a similar measure targeted by the central bank) the central bank will 'print less money', eg by increasing interest rates.  If government austerity were to suppress total spending and thus inflation, the central bank 'prints more money', eg by lowering interest rates or doing more QE.

We can see that happening eg with the American fiscal cliff---the US federal deficit was cut in half, and pundits forecast the end-of-the-world, but if anything job growth accelerated.  Similarly, we can already see that Trumps promised extra spending just leads to the FED raising rates.  Inflation expectations both from the Feds forecasts and implied by spreads of inflation indexed treasury bonds over convention treasury bonds both stay relatively flat at 2%.

Under a gold standard or a central bank regime that targets things other than inflation or aggregate spending, government expenditures can have a non-zero fiscal multiplier.


Difference-in-Difference (DID) Regression with Non-Stationary (but Cointegrated) Treatment and Control Groups I would like to run a DID regression between two periods where each period spans multiple years. For example:
Period 1: 1970Q1-1990Q4
Period 2: 1991Q1-2010Q4.
My treatment and control variables are non-stationary, but they are cointegrated. Thus, the error term is stationary and normally distributed. All assumptions of OLS also hold for DID. However, in a standard setting where you have two cointegrated variables one would have to use a DOLS or FMOLS to properly estimate the standard errors. Yet, the setup of a DID regression is different than the standard assumptions of regressing Y on X (with both being I(1) and cointegrated) which is what all of the theory on cointegration (in levels) is based on.
My question is if the variables are non-stationary, but cointegrated is the DID estimation valid? If it is, then the estimates would be superconsistent as is the case with an OLS between cointegrated variables, however, I am not sure if one can correct for the standard errors in this setup.
Any help would be much appreciated!

If your question is the broad: "How do I estimate the differences between these two groups under these problematic contexts?" I recommend taking a look at event study literature, which has a lot of similarities to the DiD literature, but is frequently applied in the context of stocks (which can be non-stationary).
MacKinlay, A. Craig. "Event studies in economics and finance." Journal of economic literature 35.1 (1997): 13-39.


Question about Strict Preference Relation Strict Preference usually states that
x is strictly preferred to y if  :  < x is weakly preferred to y and not y is weakly preferred to x >.
Let me split the < > part into two segments:

x is weakly preferred to y

and

not y is weakly preferred to x

Why do you need the first condition to satisfy the strict preference relationship? The second condition seems to be enough to satisfy the strict preference relation. I mean, "not y is weakly preferred to x" means the same thing as "x is strictly preferred to y" right? So 1. seems to be unnecessary to me when trying to explain Strict Preference Relation.
Is it because we assume that "completeness" of preference isn't satisfied when we define strict preference relation? Therefore there is a third option of "I don't know" if we just write the 2nd condition which requires us to add the first condition as well to cover for "non-completeness"?

You are correct that the motivation regards issues surrounding completeness. As you point out, when $\succcurlyeq$ is complete $y \not\succcurlyeq x$ implies $x \succcurlyeq x$ (hence, $x \succ y$).
If, however, we do not want to assume complete preferences then (2) does not imply (1), but strict preference can still constructed from weak using the more complex definition. (One could also take the set difference of weak preference and indifference).


Lancaster's Characteristics Theory In 1966 Kevin Lancaster proposed a new Economic Theory based on product characteristics instead of product utility. I would like to know the status of this theory nowadays among economists specifically those dedicated to Economic Theory.
Thank You

Lancaster initiated what has come to be called "Hedonic Demand Analysis", or "Hedonic Price Analysis".

This field of analysis has been rigorously housed in microeconomic theory in the seminal paper

Rosen, S. (1974). Hedonic prices and implicit markets: product differentiation in pure competition. Journal of political economy, 82(1), 34-55.

It has also entered in a very important way applied economics and policy, since, for example, for many years now USA calculates the official Consumer Price Index using the "Hedonic" framework (mainly in order to accomodate changes in quality). There is, as one can understand, a vast literature on the matter.


If someone stays at home because they can't find the type of job they want, are they included in unemployment numbers? Say someone is looking for a job, but the ones they can find either don't give them the right compensation (businesses pay them too low) or is not the type of work they're looking for. So they stay at home until they find one.

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

This may vary depending on the country. But for the US, there are 3 criteria:

People are classified as unemployed if

they do not have a job;

have actively looked for work in the prior 4 weeks; and

are currently available for work.

Criteria #1 and #3 are fairly straightforward. Criterion #2 may be a little subjective and so we have the following clarification:

Actively looking for work may consist of any of the following activities:
Contacting:
    An employer directly or having a job interview
    A public or private employment agency
    Friends or relatives
    A school or university employment center
Submitting resumes or filling out applications
Placing or answering job advertisements
Checking union or professional registers
Some other means of active job search

So if your someone has actively looked for work in the prior 4 weeks (which includes the above activies), then she is counted as unemployed. Otherwise, she isn't.
Source: BLS, "Who is counted as unemployed?", which also gives some of the major questions (in the BLS survey) that determine employment status.