Why do indebted governments fear deflation?

They don't or shouldn't, fear deflation absolutely. But it's a complicated issue because there are two causes of deflation/inflation. One is changes in the money supply, the other is changes in production.

Changes in production that cause prices to fall are beneficial to everybody. Society becomes materially richer, and this is the great economic success of the last 100 years.

However, prices will also shrink if the money supply falls, since there is less money to buy things with. That in and of itself wouldn't be such a big problem in a market based environment where prices could adjust up and down. However the one thing that can't adjust its price is debt, debtors have made a commitment to  re-payments irrespective of whatever the money supply and deflationary situation is.

It depends where you are in the world right now, as to whether the money supply is expanding or contracting. The situation in Greece is particularly problematic:

This is very similar to the Great Depression pattern in the US which saw a 30% drop in the money supply 1929-1932. Once something like this gets established, it creates self-reinforcing negative feedback loops throughout the economy. For example, part of the reason for the drop is Greeks moving money to banks in other countries that they expect to stay in the Euro. But because of that, Greek banks can't make new loans without violating their regulatory requirements, and that further causes the money supply to shrink.


How to find a firm's cost function based on its production function

A firm's production function is a relationship between inputs and outputs (thus what are the combinations of input and out that can be obtained given the available technology). y-axis is Output and x-axis is for inputs.
A firm's cost function is a relationship between costs (expressed in monetary terms) and output. Thus, for every level of output, and market prices for inputs, what is the cheapest way to produce it. Output on the x-axis and Cost (monetary units) on the y-axis.

This relationship isn't as straight forward if prices aren't linear. However, most models will assume linear prices. If that is the case, you can kind of see the cost function as the inverse of the production function (essentially flipping the axes), because more inputs for an unit of output imply more costs.

As far as actually getting the cost function from the production function, you have to start by finding the argmin for this cost minimization problem:
$$\min (w \cdot k + r \cdot k)$$
s.t:
$$
q=L^{1/4}K^{1/4}
$$
F.O.C.

$w={\partial{F}\over{\partial{L}}}=f_{L}(L,K)$

$r={\partial{F}\over{\partial{K}}}=f_{K}(L,K)$

So wages will be equal to marginal productivity of Labor and interest rate will be equal to marginal productivity of capital in equilibrium.
Let me know if you don't know how to keep going from here.


In 1991, when the Bureau of Economic Analysis made the switch from GNP to GDP as "their primary measure of U.S. production," they indicated the continued importance of GNP this way:

  GNP, however, continues to be a useful concept. Because it refers to the income available to U.S. residents as the result of their contribution to production, it is appropriate for analyses related to sources and uses of income. For example, saving rates are normally expressed as a percentage of income, and GNP is the more appropriate measure for this propose. In addition, GNP is better than GDP for analyses that focus on the availability of resources, such as the Nation’s ability to finance expenditures on education.


Maximum price a consumer is willing to offer?

There is indeed and it is called a bid function. Consider a standard set up where preferences of the agent are given by the utility function $$u(c,h) = \bar u$$ with $c$ being a composite good and where the budget constraint is given as $$c + ph = I.$$ In this case the price $p$ must satisfy $$p = \frac{I-c}{h}$$ and the maximal price $\phi(\bar u,I)$ that the consumer can offer for a unit of $h$ conditional on attaining a utility level of at least $\bar u$ given the income $I$ can be defined as
$$\phi(\bar u,I):=\max_{c,h} \left\{\ \frac{I-c}{h} \ \Bigg\lvert \ u(c,h) \geq \bar u \right\}, $$
under standard assumptions on $u(c,h)$ the constraint is binding and therefore using that $h = u^{-1}(c,\bar u)$ the optimization problem can be reformulated to
$$\phi(\bar u,I):=\max_{c,h} \ \frac{I-u^{-1}(c,\bar u)}{h}.$$
The bid function complements duality by satisfying
$$V(\phi(\bar u,I),I) = \bar u \phantom{xxx} \wedge \phantom{xxx}\ \phi(V(p,I),I) = p,$$
in relation to the indirect utility function $V(p,I) :=\max_{c,h}\{u(c,h)\lvert c+ph=I\}$ as well as the relations
$$E(\phi(\bar u,I),\bar u) = I \phantom{xxx} \wedge \phantom{xxx}\ \phi(\bar u,E(p,\bar u)) = p,$$
in relation to the expenditure function $E(p,\bar u) :=\min_{c,h}\{c + ph\lvert u(c,h) = \bar u\}$.
This implies that the bid-function can be found by inverting the indirect utility function or the expenditure function. So with Cobb-Douglas preferences
$$u(c,h) = \left( \frac{c}{\alpha}\right)^\alpha\left(\frac{h}{1-\alpha} \right)^{1-\alpha},$$
the indirect utility function is given as $V(p,I) = I/p^\alpha$ implying that the bid function is
$$\phi(\bar u,I) = \left(\frac{I}{\bar u} \right)^{1/\alpha}.$$
For an overview of the more well-known duality relations see this post duality and for the perhaps most important application of the bid function see this post monocentric city dealing with the monocentric city model.


Why is oil being traded in U.S. dollars?

why would they force to trade in U.S. dollars instead of just taking the oil from their country by force?

One of the basic tenets of power is that $control$ is superior to $ownership$.  War is expensive, oil must be stored before it is used, and any captured production assets must be defended and maintained at great cost.

Rather than own all of this through waging successful war, it is far cheaper to simply control it.  This is accomplished precisely because the $USD is the world's reserve currency.  It is cheaper for any given sovereign nation to hold one currency in reserve, rather than to hold an adequate amount of all world currencies in reserve.  Much of US global policy in the past has been in support of the US' perceived role as a stable nation supported by rule of law, which builds the necessary trust for most other nations to put their economic "eggs" into the USD basket.

But how does control enter in? As a simple picture, any time international trade is conducted, there are three transactions that take place: the buyer converts home currency into USD; then the USD is exchanged for the goods/services; and finally the seller converts the USD into home or other currencies as required.  Thus there are two points of leverage in this transaction chain where the US can exert control, up to and including blocking transactions altogether.

Have you ever wondered how trade sanctions are actually enforced?  This is how.  Sanctioned nations are simply blocked from using USD to engage in global trade, severely curtailing their ability to transact with other nations.  In the extreme, the US is able to unilaterally exclude any nation not already holding substantial reserves of USD from participating in global trade altogether.  In a global economy, this is often a much more consequential tool than the threat of war.


Could the Troika's economic plan work for Greece?

The short answer is "No", if by "small number" we mean something no more than "five".

The two characteristics you mention are rather different: "high growth" describes a rate of evolution. Now, it is standard corporate speak to say "we are in an excellent position to grow" to express in a diplomatic way the fact that you have hit rock-bottom. Given the unprecedented fall in Greece's GDP, to obtain some positive growth rate it is not that hard, since the base has shrunk so much.

As for "high employment", if by that we mean reverting back to the country's "natural rate of unemployment" (which was $7-8\%$ for decades), to do that in $10$ years, back-of-the-envelope calculations show that one would need $50$ billion euros additional investments yearly for $10$ years in a row to achieve that. This represents a $128\%$ increase in yearly investments from current level, or almost "two times and a half more" than now. Yearly.

From a structural point of view, what is required is a massive increase in Greek exports, or a massive increase in import-substituting economic activities. These things do not happen "in a small number of years".  The first has to deal with international competition, the second requires extended geographical and sectoral relocation of productive resources.

But Greece returning to "high growth-high employment" was not and is not the main concern of the creditors -not unsurprisingly, and perhaps rightfully, since it should be the main concern of the Greeks and their (our) political system.

As to whether the approach taken by the creditors do indeed serve their own interests, is a totally different question, and a very complex to answer -because we would have first to clearly identify "their interests".


How does Net Foreign Assets (NFA) differ from Net Foreign Investment (NCO)?

One is a stock another is a flow.
Net Foreign Assets are:

Net foreign assets (NFA) determines whether a country is a creditor or debtor nation by measuring the difference in its external assets and liabilities. Net foreign assets (NFA) refer to the value of overseas assets owned by a nation, minus the value of its domestic assets that are owned by foreigners, adjusted for changes in valuation and exchange rates.

Net Foreign Investment is:

Foreign investment involves capital flows from one country to another, granting the foreign investors extensive ownership stakes in domestic companies and assets.


Jordi Gali Markup Marginal Cost Relation

The problem is the maximization of profit of a firm that produces a differentiated good $i$ using labor $N_i$ as unique input, under the demand function of the consumers (or final goods producers) and the production function.

The first three steps are computed by substituting the two constraints and the market clearing condition for goods market $Y_t=C_t$ into the objective function in order to have a free maximization problem in one unknown, $P_{it}$.

The FOC for $P_{it}$ is right and the same is true for the next step, where the left hand side is positive because he has divided for $-(1-\epsilon)$, i.e. $(\epsilon-1)$ that you see at the denominator of $\epsilon$. The highlighted part is correct too: this is the derivative of the function nested in the square brackets; he added $\frac{1}{P_t}$ because he kept $\frac{P_{it}}{P_t}$ all elevated at $-\epsilon-1$, this means that $P_t^{-1}$ and $P_t$ goes away. You could also have written
\begin{gather}
\epsilon\frac{\frac{P_{it}^{-\epsilon-1}}{P_t^{-\epsilon}}C_t}{A_t}=\epsilon\frac{\big(\frac{P_{it}}{P_t}\big)^{-\epsilon-1}C_t}{A_t}\frac{1}{P_t}
\end{gather}

After the "Continue...", he just sum the two expressions in square brackets because they are exponentials with the same base and in the second step he notice that
\begin{gather}
\bigg[\frac{\frac{P_{it}}{P_t}^{-\epsilon}C_t}{A_t}\bigg]^{\frac{1}{1-\alpha}}=N_t
\end{gather}
using again the demand for $Y_{it}$, $Y_t=C_t$ and the production function.

The last step is a rearrangement of the previous one (simple algebra) and it is still the FOC for $P_{it}$. If you rearrange it as in Gali, you obtain the optimal pricing condition for the monopolistic firm in flexible price setting.


Why does China buy so much U.S. Treasury debt?

As was said above, buying debt to affect the exchange rate and make Chinese exports more attractive may be one reason to buy these Treasuries. Surely all of these are not reinvested into buying more debt and some of it is put into other civic projects.

The other reason to buy debt is to have a string of payments over time that may become more valuable later on. Since the US is a large nation and powerful nation, China probably feels it is very unlikely that the USA will default, and if they did, that would give China a legitimate complaint against the US, that might help them in foreign relations. It may even be that they want the US to be stable so as not to crash the global economy and so that they can still sell lots of products to the US, so they buy up the debt to keep the USA stable.

The more important part of that whole paragraph though is to have a string of payments. For the same reason that governments like to hold debt even when they have the ability to pay it off, China might find that investing into debt will provide a better rate of return than infrastructure at the moment, and later on, once infrastructure has a better rate of return (capital steady state changes) then they can take a stream of income from interest payments from the US and taxes and then invest into that.

Finally, I couldn't help but notice that you see China as needing to lift itself out of poverty. That may be true, but why would investments into infrastructure be the solution to helping the rural poor--places that don't need as much infrstructure? Most of the poor in China are in rural areas, so there's something to think about.


The justification goes back to the work of Pigou in the early 20th century. The essence is this: the burning of fossil fuels creates a negative externality: a cost that is incurred, but not by that consumer, but by the general population, and for a century or so.

This in essence creates a kind of "social subsidy": the price does not fully reflect the costs. This means that fossil fuels are over-consumed, relative to the economically efficient quantity.

As I wrote on that other answer: the "Economics Help" site explains the issue

The deadweight loss from fossil fuel consumption is the red striped triangle: this comes about because fossil fuel producers do not have to pay for their pollution, leading to a competitive advantage, and an artificially high quantity sold Q1 at price P1.

This inefficiency can be corrected (in long-run equilibrium) if the externality is priced back in - which is what the carbon price is intended to do.

Given the presence of fossil-fuel incumbents, their lobbying power, and their decades of direct and indirect subsidies, it is highly likely that a carbon price set at the marginal social cost of carbon would be an insufficient signal. A very helpful one, but insufficient on its own.


Economics: inductive or deductive? Verificationism or falsificationism?

As regards the induction/deduction division, economics uses both, and they usually start by some induction followed by mathematizing it and then using deduction.

In the older days, economists were based more on their own personal experience and observation as to how people behave economically. Just browse any classic economics book from the 18th, 19th and even pre-war 20th century and this becomes obvious. They then embarked on lengthy verbal arguments to connect these instances of experience (in the modern era this approach has partly survived, but formalized into the "representative agent" analytical framework).

In modern days, both stages have changed:
At least for fundamental advances, what can be detected as long-term trend is that solid empirical evidence (being statistical or other), that can claim some generality, has become a required springboard for induction and a new theoretical economic model. Just one example of a seminal such paper,

Aiyagari, S.R. (1994). Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics, 109(3): pp.659-684.

is a paper where the author packs considerable statistical evidence and theoretical and empirical references in two pages before presenting his model of (what the paper title says), as a way of validating his approach.

The second stage has become mainly mathematical rather than verbal: one lets its model roll and see what results it will produce (this is the deduction step). This synthetic approach is necessitated because social phenomena do not have the repeatability observed in the natural world (although I would dare to say that there are many aspects of economic behavior that have remained virtually unchanged for at least all written history, and around the globe).

Of course since nowadays science is produced in an industrialized way, a million economics papers out there are purely works on existing theoretical frameworks, so this strand is pure deduction.

As regards the verificationism/falsificationism contrast, it appears that the OP uses the words in a rather relaxed manner, away from their stern meaning and the philosophical schools behind them. In that sense then, yes, economics looks for "adequate representations of reality", i.e. it sides with "verificationism": an inside joke is that "no economic theory was ever abandoned because it did not conform with the data"...

For such matters, Mark Blaug's inside polemic The methodology of economics: Or, how economists explain has not lost its bite.

The helpful comment below suggested also looking at abductive inference for how economists go methodologically about understanding the world.


The classic paper on preferences over the timing of information revelation is Kreps and Porteus (1978). This seems to capture at least a little, if not most, of what you seem to be describing, so you should definitely have a look.

Strzalecki also has a nice paper connecting Kreps-Porteus to the various modern approaches to preferences under ambiguity.


Decision to make one side of a multisided platform the subsidy side

Yes. For example, in Armstrong (2006), a monopoly platform sets the price for side 1, $p_1$, such that

$$\frac{p_1-f_1+n_2\alpha_2}{p_1}=\frac{1}{\eta_1}$$

where $f_1$ is the unit cost on side 1, $n_2$ is the number of consumers on side 2, $\alpha_2$ is the cross-side externality created by each side 1 consumer, and $\eta_1$ is the conditional price elasticity of demand on side 1.

Thus, side 1 consumers get subsidised (i.e. $p_1<f_1$) if

their demand is very elastic
they create a big externality for the other side.

That's the basic principle. Subsidise the guys who create a lot of value and who would run away if the price were high.

Thus, for example, nightclubs offer free entry to females rather than males if the owners believe that females are more price sensitive and that men care more than women about meeting members of the opposite sex (I let you decide for yourself whether that's true or not).

By the way, we can compere this equation to the one a normal monopolist would use:

$$\frac{p-f}{p}=\frac{1}{\eta}.$$

The reduction in price to internalise the network externality can clearly be seen.


Two-year difference-in-difference model design

Is there some literature about two-year difference-in-difference (DiD) models?

Of course.
The traditional two-group/two-period DiD design was quite popular 25 years ago, though it's less common today to find evaluations where entities are observed in only one time period pre- and post-shock. DiD methods hinge on the graphical exhibition of common group trends before program exposure. You cannot possibly demonstrate this, visually or statistically, with less than three pre-treatment time periods. Serial observations pre- and post-treatment is not necessary, but is very much preferred. In my opinion, your study is likely to be met with skepticism if you do not observe individuals for a sufficient number of time periods before your treatment of interest.

Suppose a policy was implemented in 1982, but not strictly enforced among all people. Can I still estimate a DiD model using the data only from 2012 to 2016?

No.
Unless I misunderstood your question, the immediate policy adoption year is 1982. If you were to restrict your time series to the years from 2012 to 2016, then by definition, you're only observing entities in the post-policy phase. This assumes the policy has persisted until 2016. Unless the policy was rescinded and reintroduced in the interval you referenced, then you cannot possibly conduct a DiD evaluation. Assessing treated and untreated entities post-policy is a posttest-only evaluation. A posttest-only design is not considered a DiD evaluation; you must observe entities pre- and post-shock.
But suppose, for example, a completely new policy is introduced in between the years you referenced (e.g., 2014). Before its introduction, all individuals are untreated. Once it is instituted, only a subset of individuals will be eligible. The individuals affected by the policy comprise your treatment group, while all non-affected persons comprise your control group. At a basic level, the 'classical' DiD approach requires you to observe a treatment group and a control group at least one year before and at least one year after your policy. If you do not observe any pre-event data, then you must model the effect of the policy in a different way.


Deriving demand function from utility function

This is an example of quasilinear utility. In general, a quasilinear utility function takes the form
$$u(x,y)=f(x)+y.$$
The perfect substitutes utility function, for example, is a special case of the quasilinear utility function. One feature of quasilinear utility is that the MRS is independent of at least one of the two goods:
$$\frac{\frac{\partial u(x,y)}{\partial x}}{\frac{\partial u(x,y)}{\partial y}}=f'(x),$$
meaning the slope of indifference curves is independent of the quantity of good $y$.

The Marshallian demand functions satisfy the equations:
$$ f'(x)=\frac{P_x}{P_y}$$
$$I=P_xx+P_yy,$$

which come from the first-order conditions of the constrained maximization problem. We can solve for the Marshallian demand function for $x$ directly from the first equation:
$$x^*=f'^{-1}(\frac{P_x}{P_y}).$$
Substituting this into your second equation gives
$$I=P_xf'^{-1}(\frac{P_x}{P_y})+P_yy$$
$$y^*=\frac{I-P_xf'^{-1}(\frac{P_x}{P_y})}{P_y}.$$

In your example, we get
$$x^*=(\frac{P_y}{P_x})^2.$$
$$y^*=\frac{I-P_x(\frac{P_y}{P_x})^2}{P_y}.$$

There is a fundamental problem with your solution. You write a demand function for $x$ that depends on the quantity of $y$. Demand functions depend either on $(P_x,P_y,I)$, if Marshallian, or $(P_x,P_y,U)$, if Hicksian.


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

The statement
"In the short run, only the minimum point on the SRAC curve is productively efficient"
is false.

Suppose producing 1 unit of a good costs 5 dollars. 2 unit costs 8, x>2 units costs 5x. Clearly AC is minimal if you produce 2 units.
But perhaps I do not want two units of the good, only one. Why spend the extra 3 dollars on the second good? Producing only 1 unit is also efficient in this case.

Note that this does not contradict your definition
"The definition of productive efficiency is that any given output is produced for the lowest possible cost."
The given output is 1 unit, and it is produced for 5 dollars, not 7 or 8, so there is no waste. Your definition does not say anything about per unit costs.

My example is also consistent with the definition of productive efficiency that I know.

  Productive efficiency is a situation in which the economy could not produce any more of one good without sacrificing production of another good.

Sidenote:
 Perhaps you are confusing productive efficiency and minimum efficient scale of production?


Yes, $\Pi^n_{i=1}$ refers to the product of a sequence.

Regarding Lucas' solution, the Lagrangian of the problem is:

$$ L (c_1,...,c_n) = U(c_1,...,c_n) - (c-\sum c_i) $$

The FOC with respect to $c_i$ and $c_j$ are:

$$ \frac{\partial L}{\partial c_i} = \frac{\partial U}{\partial c_i} +1 = 0 $$

$$ \frac{\partial L}{\partial c_j} = \frac{\partial U}{\partial c_j} +1 = 0$$

From here you get (the MRS):

$$\frac{\partial U}{\partial c_i} = \frac{\partial U}{\partial c_j} $$

Since

$$ \frac{\partial U}{\partial c_i} = \left(\frac{c_i}{\alpha_i}\right)^{-1} \Pi^n_{i=1} \left(\frac{c_i}{\alpha_i}\right)^{\alpha_i} = \left(\frac{c_i}{\alpha_i}\right)^{-1} U(c_1,...,c_n) $$

from the MRS you get that:

$$ \frac{c_i}{\alpha_i} = \frac{c_j}{\alpha_j} $$

Using these, the definition of $c=\sum c_i$, and the fact that $\sum \alpha_i =1$, you can obtain Lucas's solution (I leave the last bit of the solution to you).

Finally, regarding weights, I think that is just to make the model interesting, as it means consumers might prefer some colors more than others (they spend $\alpha_i$% of their income in colour $i$). If not, they would spend $1/n$ of their income on each, to which any loyal disciple of William of Ockham would rightly observe "they why to bother with multiple colours at all"?


Search and matching model: effect of hiring cost on wage curve

It depends on what you define as wage curve. I did not check in the textbooks, but you suggest that Pissarides and Cahuc et al. do not use the same mathemaical expression for the "wage curve".

1) In Cahuc et al., the expression combines the surplus sharing equation with the Bellman equations without using the free entry condition of firms. The wage $w$ is increasing in $\theta$ because a tighter market tightness improves the worker's bargaining position. There is no labor demand effect in this wage equation. Therefore, the vacancy cost does not appear.

2) The Pissarides' wage curve is less straightforward to interpret. Given the positive relationship between $w$ and $c$, one could erroneously think that the vacancy cost increases the wage. The interpretation is the following.
At $\theta$ fixed, a higher vacancy cost means that firms spend more to recruit. More spendings capture the fact that firms make larger job profits (free-entry condition). When firms make larger profits, workers also obtain a larger surplus due to the Nash bargaining. Thus, the wage is higher.

This definition of the wage curve does not depend on the matching technology ($m$). To understand this result, we can write the model with an abstract matching market.
With your notations, we define the value of unemployment $U$, the value of employment $W$ and the value of a job for a firm $J$.
We can write the three Bellman equations, and the Nash bargaining condition with the wage:
\begin{align}
    & rU = z + R\\
    & rW = w+q(U-W)\\
    & rJ = y-w-qJ\\
    & w=\gamma y + (1-\gamma)rU
\end{align}
If a worker is employed, she produces $y$ and receive $w$, with a risk to lose the job $q$.
If the worker is not employed, she receives $z$ plus the returns from participating to a matching market $R$.

In the full model $R=\theta m(\theta) (W-U)$. Here, we do not use this structure.

We assume that each unemployed worker participating to the "matching market" produces $G$ and obtain $R$. To participate to the market and obtain part of the gains, firms have to pay a cost $c$. If we assume that $G$ is Nash-bargained, each worker obtains $R=\gamma G$, and recruiting firms share $(1-\gamma)Gu$. The average returns for a firm is $\frac{(1-\gamma)G u}{v}=(1-\gamma)\frac{G}{\theta}$.
The free entry condition implies that firms make no profits from participating to the market. Therefore, $(1-\gamma)\frac{G}{\theta}=c$.
Using the wage bargaining solution, we obtain Pissarides' wage curve using the wage bargaining solution and eliminating $rU$, $R$ and $G$.

The wage curve holds without assuming how the "matching market" works, we only assume that the outcome is Nash-bargained. To come back to a change in $c$. An increase in the vacancy cost $c$ necessarily implies that the gain $G$ is higher, ans so the wage.

3) This is partial equilibrium analysis. If you solve for the equilibrium level of wages, you will find that $c$ actually reduces the equilibrium level of wages.


Does the money's "Store of value" function actually exists?

What is value? Ultimately, value flows from the utility people get from consuming goods and services.

Now, suppose, in your example world, I am a farmer and it is Autumn so I have the product of a large harvest. Here are three things I could do with it:

Consume (and thereby enjoy the value of) my entire harvest immediately. But this would leave me hungry in the winter.
Store some food for later: Put some of the grain I produced into a silo and take it out of the silo to eat in the winter.
Sell some of my food to the bank in return for pebbles. Then, later in the winter, use those pebbles to buy back some food when my supply has run out.

Notice that points 2 and 3 are essentially equivalent (they result in the same distribution of consumption across time). In the former, I am directly storing food. In the latter, I am using the pebbles to store the value associated with the food until I want to claim that value back.

Although the store of value is really just an abstract implementation of the physical storage of the goods generating that value, this distinction becomes important in more sophisticated economies. Storing value rather than storing the goods that generate that value is attractive for a few reasons.

Many goods and services are hard to store. For example, as an economics professor it is impossible for me to "store" lectures during the autumn for use in the summer when I can't find any students to teach. How do I avoid starving during these long, studentless summer months? I take the (hopefully positive) value my lectures produce during the autumn and store this value in money. I can then claim this value back during the summer when I need it.
Storage of physical stuff takes up a lot of space and is expensive. Storage of money is much less so. Similarly, transporting stuff is expensive. With a bank card it becomes unnecessary to transport money at all.
Storage is often wasteful because it involves stuff sitting around doing nothing when it could be generating utility for someone.


What are the advantages and disadvantages of the IS LM model?

The best economic models make useful predictions with as little complexity as possible -- in other words, they make assumptions that aren't "true" in the real world, but make predictions that nevertheless turn out to be true.

For instance, advocates of the day-to-day use of the IS-LM model such as Paul Krugman point to the analysis of liquidity traps as an important case where its users have proved to be right where many other analysts have made bad predictions.

From "What I Mean When I Talk About IS-LM (Wonkish)":

  Those of us who understood IS-LM and took it seriously declared in advance — in late 2008 and early 2009 — that big deficits and huge increases in the monetary base would lead neither to soaring interest rates nor to soaring inflation. This was very much not what many influential people were saying: there were widespread forecasts of soaring rates and soaring inflation. Later, there were many people denying that austerity would have negative effects on output.

He provides a more detailed explanation of an IS-LM analysis of liquidity traps (and a few other insights that the model provides).


This demand function is just normalized to unit. If you are not interested in the concrete quantity of your demand function, but you are interested how the demand of the specific market is distributed between firms, you can use this simple demand function.

For example, you can consider a normalized demand function in a Bertrand's game. Let's assume the firms are symmetric, there's no capacity constraints. The demand ($D(p_i,p_{-i})$) of firm $i$ is the following:

$$ D(p_i,p_{-i}) =
\begin{cases}
    0       & \quad \text{if } p_i > p_{-i} \\
    1/2  & \quad \text{if } p_i = p_{-i} \\
    1  & \quad \text{if } p_i < p_{-i} \\
  \end{cases} $$


Why is Mises "permitted" to define "Economics is an a priori science", if a priori is not trustworthy?

Although I disagree with von Mises, he was reacting to what he saw as a very real problem, which was the use of relatively primitive statistical methods to describe behavior.  In fact, Leonard Jimmie Savage's work on probability and statistics should have been sufficient to meet his objections, although the computational speed would not have yet existed for that to have been worthwhile.

The challenge the Austrians have is that they are really arguing that no regularities exist in human behavior.  They do not see it that way, but probability and statistics are about the discovery of regularities.  Their position is that humans are too unique to be subject to statistical measurement.  All of economics could be solved axiomatically, in his understanding.

I would agree with him, as long as you got every axiom correct and the set was complete and properly partitioned for all possible cases.  Of course, the only way you could know that would be empirically and that would defeat his argument.

Although other branches of economics use axiomatic assertions, they then check to see if the predicted behavior really happens that way.  If so the axioms are at least not disconfirmed.  Most assumptions are also things nobody would disagree with.

For example, there is a proposition that humans prefer some things to other things.  If you also assume that for any pairing of goods, we will call them x and y, then either y is not dispreferred to x or x is not dispreferred to y, or neither or dispreferred to each other. If you add transitivity where for all triples x,y,z then if x is not dispreferred to y and y is not dispreferred to z then z is not dispreferred to x.

If those conditions hold, then it can be shown by theorem that it must be true that a utility function exists such that if the utility of x is not less than the utility of y then y is not dispreferred to x.

If those assumptions do not hold, then something else is true, but if they do hold then the entire mathematical theory of functions opens up to economics.  With the addition of some other mild assumptions, then calculus becomes available.

These do not need empirical checking because it is the only possible outcome, by force of math.  To go much past this point, however, becomes tenuous.  For example, must some of these functions be concave or are there circumstances where they could be convex.  If they can be convex, do real-world examples of this convexity exist?  Do real-world examples of the concave case exist?  Are there forced implications from either case or the existence of both cases?

These questions can only be approached empirically.


Is there an economic interpretation of the envelope theorem?

First, let's consider a standard "economic interpretation" of the envelope theorem for unconstrained maximization:
if $x^*(b)$ solves $\max_x f(b,x)$, then $\frac{d f(b,x^*(b))}{d b_k} = \frac{\partial f(b,x^*(b))}{\partial bk},$ i.e., the total derivative of $f$ w.r.t. $b_k$ equals the partial derivative of $f$ w.r.t. $b_k$.
The economic interpretation (in the given problem): Let $\pi^*(p,w) = p f(x^∗) − w·x^*$ be the maximized value of profits given output price $p$ and input price vector $w$. Then the $i$'th input demand function is $x^*_i(·) = −\frac{\partial \pi^*(·,·)}{\partial w_i}$, known as Hotelling's Lemma, after Harold Hotelling, (1895–1973). This derivative is negative: if the price of the input increases, then the firm's maximal profit decreases.

Second, let's consider a standard "economic interpretation" of the envelope theorem for constrained maximization:
if $x^*(b), \lambda^*$ solves $\max_x f(b,x)$ s.t. $h^j(b,x) = 0$, $j= 1, ...m,$ then
$$\frac{d f(b,x^*(b))}{d b_k} = \frac{\partial f(b,x^*(b))}{\partial b_k} + \sum_{j=1}^m \lambda_j^*(b)\frac{\partial h^j(b,x^*(b))}{\partial b_k}, $$
i.e., the total derivative of $f$ w.r.t. $b_k$ equals the partial derivative of $f$ w.r.t. $b_k$, plus the $\lambda^*$-weighted sum of the partial derivatives of the $h^j$'s w.r.t. $b_k$.
The economic interpretation (in the given problem): Let $\hat c(\bar q, p, w) = w·\hat x$ be the minimized level of costs given prices $(p,w)$ and output level $\bar q$. Then the $i$'th conditional input demand function is $\hat x_i(·) = −\frac{\partial \hat c(·,·,.)}{\partial w_i}$,  known as Shepard's Lemma, after Ronald Shephard  (1912-1982). The partial derivatives of the expenditure function with respect to the prices of goods equal the Hicksian demand functions for the relevant goods.


Why does allocative efficiency occur when P=MC rather than MB=MC

Question: If I set a price of $p$, which consumers will buy the good?

Answer: a consumer will buy the good if and only if his benefit from consuming it is bigger than his cost, $p$, of buying it. This means that the last (i.e. marginal) consumer who buys will be the one for whom the benefit is just equal to the cost. In other words, for any price, $\text{MB}=p$ must hold.

For efficiency, we know that we need $\text{MB}=\text{MC}$.

Putting these two equations together yields $\text{MB}=\text{MC}=p$.

What is going on here? We know (as you pointed out) that  we need $\text{MB}=\text{MC}$ for allocative efficiency. But we can't just go out and tell consumers whether to buy or not. We have to give them the incentive to make the efficient choice on their own. The way this is achieved is by setting the price such that only consumers for whom purchasing is efficient will be willing to buy.


Why the difference in productivity and wage trend in the UK economy?

Blundell, et. al (2014) offer an explanation. According to them, the UK economy experienced a positive labour supply shock over that period.

First, they present the facts in a very intuitive fashion (graph taken from the working paper version):

They argue that the supply shock was due to two factors:

changes in welfare policies that made work more attractive and tightened job-search conditions attached to the receipt of unemployment insurance beneﬁts
an increase in statutory pension age for women that strengthened their labor force attachment

I don't want to infringe copyrights so I won't include more figures, but look at Figure 14 (showing an increase in employment of older workers after the Great Recession), and Figure 15 and 16 (showing an increase in employment participation of Lone Mothers). As the authors state:

  "The age limit for youngest child was set at twelve in November 2008 for all new claimants of Income Support and was lowered to ten in October 2009, seven in October 2010 and five in October 2011." (p. 392)

That is an example of a policy fostering employment participation and a positive supply shock.


Homogeneous of Degree Two Utility Functions and Homothetic Preferences.

First of all, in order to provide a counterexample, you need to construct a utility function that is homogeneous of degree two, but is not homothetic. Therefore, the counterexample you gave in your solution doesn't work.

To prove the statement directly, let $u(x)$ be a utility representation that is homogeneous of degree two. That is, $u(\alpha x)=\alpha^2 u(x)$. Therefore, if $x\sim y$, which means $u(x)=u(y)$, we have
$$u(\alpha x)= \alpha^2 u(x)=\alpha^2 u(y)=u(\alpha y).$$
This means $\alpha x\sim \alpha y$, and hence the preferences are homothetic.

We can also use the proposition in MWG: A continuous $\succeq$ is homothetic if and only if it admits a utility function $u(x)$ that is homogeneous of degree one. One caveat is that the utility representation is unique up to monotone transformations, so even if one representation $u(x)$ is not homogeneous of degree one, the preferences could still be homothetic if a monotone transformation of the representation, $\phi(u(x))$, is.

In this question, if we consider a monotone transformation $\hat{u} (x)=(u(x))^\frac{1}{2}$, this $\hat{u}(x)$ still represents the preferences $\succeq$. Notice that
$$\hat{u} (\alpha x)=(u(\alpha x))^\frac{1}{2}=(\alpha^2 u(x))^\frac{1}{2}=\alpha (u(x))^\frac{1}{2}=\alpha\hat{u} (x),$$
meaning that this new representation is homogeneous of degree one. Therefore, by the proposition above, the preferences are homothetic.


Interpretation of Interesting Utility Function

This is the CES production function, where CES stands for constant elasticity of substitution.

The parameter $\sigma$ captures the (constant) elasticity of substitution and $\alpha$ is the share parameter.

The Cobb-Douglas production function can be obtained as a special case of the CES class by taking $\sigma\to1$. For proof, I'd refer you to this post.


For simplicity, numbers are in millions.

We assume that markets are efficient, and that the value of equity and liabilities equals that of assets. So debt + equity = 300. We want to solve for the value of the debt, and get equity as the residual.

The valuation debt $=\frac{200}{1.05}$ assumes no default. We model default by the probability of the value of the assets dropping below 200 (redemption value of debt) after one year.

We can value the default risk by nothing that it could be cancelled out by buying a put on the asset values, with a strike at 200. I leave to the reader the determination of this value. Buying the bond and the put creates a default risk free bond, which has the discounted value above.

The value of bond with default is therefore the value of the default free bond less the value of the put.


If we add up all the income while finding GDP of a country, is income counted multiple times?

There is no contradiction here. All these incomes are part of the GDP. In theory all incomes show the value of something. In your example this would be the value of the work done. Since all 10 government employees and the shopkeeper are working they all create value, the size of which is measured by adding up their salaries.

Here you can find an explanation of what GDP exactly is.


If all Banks in the world are emptied..?

The thing with these economics questions that never happened empirically is always the same: nobody really knows.
Befor Creditanstalt 1931 nobody thought that a bank can go bancrupt, during BrettonWoods/Goldstandard freely floating exchange rates were sought of being detrimental and dumb....

But in theory everything should collapse due to our fractional reserve system that requires banks to have a certain amount of money stored in their books for every granted loan.
But thats not going to happen because centralbanks would intervene and convince people that they are going to do anything to keep the banking system working. If the CB is able to make a trustworthy commitment that should work. Because a rational individual should have no incentive to have so much cash... The costs of carrying so much money are simply too high...

Once there was this Eric Canton attempt....


When a tax is imposed on the sellers, the price of the good rises. So, why doesn't the demand curve shift?

I think you're confusing quantity demanded, and the demand curve.

The demand curve tells you how much quantity should be demanded at each price point. Therefore changes in price should change the quantity demanded, not shift the curve. You want to think of this in terms of demand and supply shocks.

For example:

Imagine it was discovered that bananas gave you super powers. Now the ability to supply bananas hasn't changed (no supply shock), but the desirability of bananas at any given price point has increased (demand shock).

An increase in price due to taxation has not impacted the desirability of goods at any given price point. It simply changes the price point.


Hidden information concerns characteristics that are unobservable by one side of the market. For example, a consumer's willingness to pay, a worker's productivity, the quality of a used car all fall under this category. The characteristics in question are typically assumed to be fixed or very costly to modify.

Moral hazard concerns actions that are unobservable by one side of the market. For example, the effort that a CEO puts into managing a company and the care that an insured driver takes to maintain the condition of his car both fall under this category. By their very nature, the (unobservable) actions can be easily changed to suit the incentive structure of the problem.


Applying real growth rate to nominal value

This will provide you with a GDP in constant prices of the previous year. "Real GDP" only make sense if you mention which is you basis year. It is not an absolute figure.

Indeed, it would not make sense (beside research purposes) to display a real GDP in terms of the first year in which GDP was recorded. Accumulating 50 years on inflation in your figure would produce a tremendous discrepancy between your real GDP and your nominal GDP, resulting in confusion.


Effect of Promotional Sales on a Demand Curve

Your textbook is correct. I believe you are confusing an increase in demand and a shift in the demand curve and conflating the quantity demanded with the demand curve.

The quantity demanded is just how much of the good the consumers want in one particular case (e.g. for one given price). The demand curve tells you the quantity that would be demanded in all cases (for any given price).

Demand can increase without a shift in the curve, as there can be a movement along the original curve itself.

A shift in the demand curve, would mean that there is a different (in your case higher) demand at all prices. For example, if the income of the consumers increases, you might expect there to be more demand for the good at any given price. Concretely, a shift would mean that previously there were two pairs of shoes being demanded at a price of 50\$ and after the shift there are three pairs of shoes being demanded at a price of 50\$.

The sale on shoes in your example does not cause such an effect. The sale lowers prices, which increases demand (the quantity demanded). It is equivalent to a movement along the demand curve. Before there were e.g. two pairs of shoes being demanded at 50\$ and now the price is e.g. 25\$ so the demanded quantity equals 4 pairs of shoes.

In other words, take a demand curve and use any point on the curve as the situation before the sale. After the sale you have a lower price. Finding the quantity that corresponds to that price on that same curve will yield a higher demand, without shifting the curve.


Solving for Pareto Efficient Utility Possibility Frontier using constrained optimisation

The first constraint you have, $U_2(x_2)=x_2$, is not really a constraint.

Since points on the UPF is Pareto optimal, you should instead have $U_2(x_2)\ge \bar u$ or $x_2\ge \bar u$ as a constraint, where $\bar u$ is some arbitrary level of utility for individual 2 on the UPF. In other words, given that we're keeping individual 2's utility to be no lower than $\bar u$, how best can we make individual 1's utility as high as possible with the available resources.


What are good mathematics books to learn decision theory?

I do not know about social choice, but for utility representations I think the two most cited books are "Convex analysis" by Rockafellar and "Infinite Dimensional Analysis: A Hitchhiker's Guide" by Alliprantis and Border. They contain most (if not all) results on convex analysis and functional analysis used by economists.


As a disclaimer, I think the Austrian business cycle is incorrect. I will try to explain in a sympathetic fashion. Mises.org has a great deal of resources on Austrian economics, much of it free.
From a quick watch of the beginning of the video, the distinction is between a market rate of interest, and the “artificial” interest rate set by the central bank.
In the case of a market rate of interest, the belief is that prices for everything will set to some balanced arrangement: the demand for investment goods will balance the supply, and there will be a matching balance in lending activity (with the interest rate on loans being the price that clears the market). In classical economics, this balance would be described as an equilibrium. However, different Austrians disagree on how to describe this, but they generally reject using “equilibrium.” You would need to find another source to explain their terminology.
Getting to your question, Classical authors can explain why the balance in lending markets coincides with the balance in physical resource markets in equilibrium. Roughly speaking, if any market is unbalanced, this would unbalance other markets, so all of them have to end up in equilibrium. The Austrians somehow end up with the same conclusion, but different authors appear to explain it differently.
(The issue with “artificial” interest rates is that Austrians argue that central banks invariably set interest rates too low, and thus there is excessive investment - “mal-investment.”)


The OECD has nearly the exact data you are looking for. I haven't figured out how to get it into a raw data dump. I am pretty confident that this problem has more to do with me than it does with the data available.
The WTO holds similar quality information. I think somewhere a UK govt body is publishing this. Not sure where exactly though.
The UN has everything you need but you need to sign up.

See this question for other trade related sources:

Can anyone recommend a resource for monthly trade data for Mexico from before 2010?


If production function is concave, then demonstrate that profit function will also be concave

The "hint" is wrong and misleading.
It is wrong, because first-order conditions are sufficient for a maximum when the objective function is strictly concave, or at least strictly-quasi-concave, under some conditions. For example, a linear function is also concave (as well as convex), and in such a case, the first-order conditions are not sufficient for a maximum.
It is misleading, because concavity of a multivariate function depends on the signs of its Hessian matrix of second-order derivatives.  So the OP should compute the second derivatives of the profit function, with respect to capital and labor, since I guess the presumption here is that we maximize with respect to input quantities only, treating prices as exogenous constants.
Both of the above are standard material in many microeconomics books or "math for economics" books, so the OP should look them up there.
The proper "hint" would be that costs are linear in capital and labor...
...so the profit function has a non-linear part that relates to production function, and a linear part that relates to costs. And what happens to the second derivative when linearity is present ?


Is there any mechanism to prevent tariff 'exile'?

No, there is no mechanism or force that prevents the USA's (current/former) trading partners from cooperating amongst themselves to ramp-up trade amongst themselves to compensate for reduced trading with the USA.

And the USA offers very few goods or services that couldn't be substituted with goods or services from elsewhere: but note that supply chains don't grow overnight - it takes time and investment to expand supply chains outside the USA.

And as Adam Bailey notes in the comments, countries generally tend to trade more with those closest to them. To replace that trade, with trade with more distant countries, means higher transport costs, longer transport times, and possibly larger cultural and/or linguistic differences to overcome.


Is the standard of living of poor & middle class people higher than in the past?

I think you are looking for data on real median incomes. If this concept is unknown to you, you can read about it on wikipedia.

According to the data the real income of most households decreased after the financial crisis but is still above the 1995 level. This means that most households do live better.

I don't know if the number of people on welfare would be a good indicator of economic prosperity as there have been some changes in the US welfare system recently, drastically reducing the number of recipients.


Does Pareto-efficency take into account growth?

It seems to me that as long as every person likes wealth any allocation $W_t$ will be Pareto-optimal.

Even if this was not the case, so supposing that $w_1, w_2,...$ are not real numbers representing wealth but vectors representing bundles of goods the distribution from one time to another can change drastically if you do not specify how growth occurs. At $t=1$ someone might have everything, then at $t=2$ someone else might have everything. Both of these states are Pareto-optimal, but the distributions are quite different.

So no, it does not follow from your conditions that $D_t$ necessarily equals $D_{t+1}$.


Why would investors from other countries want to invest in a country with a large CA deficit?

Its all relative when evaluating investments:

A) It might be risky but pay a relatively high return. It could be the case that the local interest rates are high even taking into account a potential devaluation, or it could be the case that the investment is denominated in foreign currency, in which case the devaluation doesn't change the principal (although it does change the likelihood of default). Typically currencies appreciate after the central bank increases the rates in local currency, as foreigners are willing to tolerate more risk when the return goes up. (The "Sharpie ratio" is one way to measure the return relative to riskiness.)

B) The country can be temporarily uncompetitive. That is, if investors think it will be relatively better later on (less uncompetitive ), then they will be willing to bet on the country. (In other words, $R=(Dividend +Future Price)/Current Price$, which means that even if you expect low dividends or interest payments, your expected return could be high because the expected future price is high.


How did 'crisis' spread through the financial system in '07-'08?

Essentially, there was a bank run in the repo market.

The repo market is where big institutions (like, say, Fidelity) deposit large amounts of cash for short periods of time with institutions like, say, Bear Stearns.  Bear Stearns, in order to guarantee that it won't run away with the money, allows Fidelity to hold some valuable assets belonging to Bear Stearns in the meantime --- say some bonds.

Now Fidelity comes to believe that these bonds are worth only, say, 80% as much as it previously believed, and therefore asks for more bonds by way of collateral.  So, at around the same time, does everyone else.  But Bear Stearns only owns so many bonds, so it can't satisfy everyone.  If you've ever seen "It's A Wonderful Life", you know what happens next.

That, at least, is Gary Gorton's story, and it seems very plausible and is widely endorsed.  Of course there are many competing stories as well.


Bond pricing, compute YTM ... why t not = 2?

A better symbolism might be as follows.

T : periods to maturity from issuance,
t : periods remaining to maturity,
n : periods lapsed

Then t = T - n.

In your case, because the 1st coupon was paid the day in question, n = 1. T = 2. Thus, t = 2 - 1 = 1 period remaining to maturity.

You will only discount from the "current" time, in your example the end of year 1, across the remaining periods.


Arrow’s impossibility theorem and voting schemes

The answer is no in the following sense.

Suppose there are $N = \{1,\dots,n\}$ individuals, and $M$ alternatives, where $|M|\geq 3$.

Let $\mathcal{P}$ be the space of strict preferences over $M$, each individual has preferences $P_i \in \mathcal{P}$, and let $P = \{P_1,\dots,P_n\}$ be the profile of preferences.

We look for a social choice function $f:\mathcal{P}^N \rightarrow M$.

$f$ satsifies Unanimity (Weak Pareto) if all individuals rank $a$ first, then $f(P) = a.$
$f$ is Strategy-Proof if it is a dominant strategy to tell the truth about your preference.
$f$ is Dictatorial if there exists an individual $i$ such that whenever $f(P) = a$, then $a$ is ranked first according to $i$.

  Theorem (Gibbard–Satterthwaite) A social choice function $f$ is Unanimous and Strategy-Proof if and only if it is Dictatorial.


How a country is categorized as developed or developing?

The terms developed and developing are UNDP terms.

Read the paper at the link below - it goes through the UNDP, World bank and IMF classifications and it's an IMF working paper so i'd class that as referenceable. At the very least it will point you to better sources.

https://www.imf.org/external/pubs/ft/wp/2011/wp1131.pdf


Why are bond yields so low when Fed is cutting rates?

Perhaps you are confusing bond prices with yields? When bond prices go up, payments relative to the price the bonds are purchased will go down, and thus by definition yields go down.

The Fed mainly controls rates through open market operations, and more recently quantitative easing. In short, when attempting to cut rates, the Fed purchases securities such as US government bonds and in turn injects Federal Reserve Notes into the system. This has the two simultaneous effects: it raises the prices of bonds purchased and thus lowers their yields, and increases the money supply, lowering interest rates.


When first differences contradict a regular regression regarding Investment vs Output relationship

It's hard to say. Presumably you think you have some fixed (unobservable) omitted variables, which is why you ran fixed effects (FE) / first differences. So I see one of two things going on here:

The fixed omitted variables caused significance in the first regression, which means you do not have a significant effect. Do you have fixed omitted variables? If not, go with the first regression instead.
A quadratic model fits the data much better and hence you have significance in the first model, but not the second. In that case, you probably do have a significant effect. Is that true though? Why did you choose a quadratic specification? Does theory or the scatter plot suggest that is a good idea? If not go with the second regression.

My suggestion would be to try fixed effects/first differences  with the qudratic terms if you have good reason for both. Otherwise use the specification you think has the most merit.

Unfortunately, I am not familiar with R and cannot comment on the code.


I think the "first stage" would be $L_{it}$ on $\tilde{L_{it}}$. In the Peri paper above, the Bartik instrument is actually just included directly as $\tilde{L_{it}}$ as a control variable because it is an exogenous regressor in that form. If you are running labor supply elasticity regressions (and thus want to see the effect of $L_{it}$ itself on labor supply), if you can argue that the Bartik instrument is in fact exogenous, you can use it as an instrument for $L_{it}$. But, putting it directly in, as you suggested, would amount to something very similar (i.e., the Reduced Form rather than the Structural Eq.).


Is it possible that the minimum point of a short run cost curve does not touch the long run cost curve?

The idea that the long run average cost curve (LRAC) must pass through the minimum points of the short run average cost curves (SRAC) is a fallacy, but it seems to be a remarkably plausible one.  It was the source of a famous error by the economist Jacob Viner, referred to in this paper by Silberberg.  Underlying the fallacy is perhaps an assumption that the points of tangency with the LRAC must be the minimum points of the SRAC’s.  These points are coincident in the special case of a SRAC tangent to the LRAC at the minimum point of the latter.  But usually they are distinct, as in the numerical example below.

Suppose a firm has a Cobb-Douglas production function with increasing returns  $y = x_1^{0.6}x_2^{0.6}$.  The inputs are bought in markets in which supply is not perfectly elastic, so that costs are increasing functions of quantities:

$\quad c_1(x_1)  =  20x_1 + x_1^2$

$\quad c_2(x_2)  =  20x_2 + x_2^2$

The symmetry between the two inputs in respect of both technology and costs is not necessary to obtain a suitable example, but it is convenient because it implies that every point on the LRAC must satisfy $x_1=x_2$ (see Appendix below for proof).  This simplifies the derivation of  the equation of the LRAC.

LRAC

Writing $c(a,b)$ for the total cost function with inputs $a, b$ and given $x_1=x_2$ we have:

$\quad c(x_1,x_2) = 40x_1 + 2x_1^2\qquad(1)$

$\quad y = x_1^{1.2}\qquad(2)$

Hence:

$\quad x_1 = y^{5/6}\qquad(3)$

$\quad c(x_1,x_2)  =  40y^{5/6} + y^{5/3}\qquad(4)$

and so:

$\quad LRAC = \frac{40y^{5/6} + 2y^{5/3}}{y}  =  40y^{-1/6}+2y^{2/3}\qquad(5)$

To find the minimum point:

$\quad \frac{dLRAC}{dy}  =  (-40/6)y^{-7/6} + (4/3)y^{-1/3} = 0\qquad(6)$

$\quad -40/6 + (4/3)y^{5/6} = 0\qquad(7)$

$\quad y^{5/6} = 5\qquad(8)$

$\quad y=6.90\qquad(9)$

To confirm this is a minimum:

$\quad \frac{d^2LRAC}{dy^2} = (280/36)y^{-13/6} + (-4/9)y^{-4/3}$
$\quad = (280/36)0.0152 – (4/9)0.0761 = 0.118 – 0.034 = 0.084 \boldsymbol{> 0}\qquad(10)$

The inputs at this minimum, using (3), are:

$\quad x_1 = x_2 = 6.90^{5/6} = 5.00\qquad(11)$

SRAC

Suppose now that $x_1$ is freely variable but $x_2$ is fixed in the short run at a value other than $5.00$, say $2$.  Then:

$\quad y = x_1^{0.6}(2^{0.6})\qquad(12)$

$\quad c(x_1,x_2)  =  20x_1 + x_1^2 + 44\qquad(13)$

Hence:

$\quad x_1 = (2^{-0.6}y)^{5/3} =  (1/2)y^{5/3}\qquad(14)$

$\quad c(x_1,x_2) = 10y^{5/3} + (1/4)y^{10/3} + 44\qquad(15)$

and so:

$\quad SRAC(x_2 = 2) = \frac{10y^{5/3} + (1/4)y^{10/3} + 44}{y} = 10y^{2/3} + (1/4)y^{7/3} + 44y^{-1}\qquad(16)$

The first derivative is:

$\quad \frac{dSRAC}{dy}  =  (20/3)y^{-1/3} + (7/12)y^{4/3} – 44y^{-2}\qquad(17)$

Relation between LRAC and SRAC

The two curves meet when $x_1=x_2=2$ implying $y = 2^{1.2} =  2.2974$ since at that point, using (5) and (16):

$\quad LRAC = 40(2.2974^{-1/6}) + 2(2.2974^{2/3}) = 34.822 + 3.482 = \boldsymbol{38.30}\qquad(18)$

$\quad SRAC = 10(2.2974^{2/3}) + (1/4)(2.2974^{7/3}) + 44(2.2974^{-1})$
$\quad = 17.411 + 1.741 + 19.152 = \boldsymbol{38.30}\qquad(19)$

Moreover they are tangential at that point since using (6) and (17) the respective slopes are:

$\quad \frac{dLRAC}{dy} = (-40/6)(2.2974^{-7/6}) + (4/3)(2.2974^{-1/3})$
$\quad = -2.526 + 1.010 = \boldsymbol{-1.52}\qquad(20)$

$\quad \frac{dSRAC}{dy}  =  (20/3)2.2974^{-1/3} + (7/12)2.2974^{4/3} + (-44)2.2974^{-2}$
$\quad = 5.052 + 1.768 – 8.336 = \boldsymbol{-1.52}\qquad(21)$

However, this point of tangency is not the minimum point of the SRAC.  Using (17) to find the minimum:

$\quad \frac{dSRAC}{dy}  =  (20/3)y^{-1/3} + (7/12)y^{4/3} – 44y^{-2}  =  0\qquad(22)$

$\quad (20/3)y^{5/3} + (7/12)y^{10/3} – 44 = 0\qquad(23)$

Treating this as a quadratic equation in $y^{5/3}$, or by trial and error, it can be found that $y$ is approximately $2.525$.  To confirm this is a minimum:

$\quad \frac{d^2SRAC}{dy^2}  =  (-20/9)2.525^{-4/3} + (28/36)2.525^{1/3} + (88)2.525^{-1}  =  -0.646 + 1.059 + 34.851 = 35.26 \boldsymbol{> 0}\qquad(24)$

At this minimum point:

$\quad SRAC = 10(2.525^{2/3}) + (1/4)2.525^{7/3} + 44(2.525^{-1})$
$\quad = 18.543 + 2.170 + 17.426 = \boldsymbol{38.14}\qquad(25)$

This is lower than the point of tangency with the LRAC ($\boldsymbol{38.30}$), but above the LRAC at $y = 2.525$ which using (5) is:

$\quad LRAC = 40(2.525^{-1/6}) + 2(2.525^{2/3}) = 34.278 + 3.709 = \boldsymbol{37.99}\qquad(26)$

Appendix

Suppose $x_1\neq x_2$ and let $x* = \sqrt{x_1x_2}$.  Then:

$\quad y(x_1,x_2) = (x_1x_2)^{0.6} = (x*^2)^{0.6} = y(x*,x*)\qquad(27)$

$\quad c(x_1,x_2) = 20(x_1 + x_2) + x_1^2 + x_2^2$
$\quad = 20[(\sqrt{x_1} - \sqrt{x_2})^2 + 2\sqrt{x_1x_2}] + (x_1 – x_2)^2 + 2x_1x_2$
$\quad \boldsymbol{>} 2[20\sqrt{x_1x_2}) + (\sqrt{x_1x_2})^2] = c(x*,x*)\qquad(28)$

Thus the input combination $(x*,x*)$ yields the same output at lower cost than $(x_1,x_2)$, and so the latter does not correspond to a point on the LRAC.


Any drawback from printing money to pay for national services such as the NHS?

Because increasing money supply will eventually lead to inflation. Consider standard monetary model:

$$MV=PY$$

Where M is the money supply, V velocity of money, P price level and Y real GDP. Velocity of money can be thought of as constant - it’s especially the number of times one euro is used. Moreover, real output can in short run respond to money supply but in the long run money is neutral. Hence when you increase M only thing that changes in the long run is P. You are left with the same output just with higher prices.

Now this simple monetary model is oversimplified- in more modern models it’s expected money supply what matters but the main message stays same.

Also note that in the short run money is not neutral and monetary expansion can boost output but the channel is not really through public investment but through the fact that it helps to put “grease” on the wheels of economy in presence of sticky wages. Hence it might make sometimes sense to just print new money and buy government bonds which will fund also infrastructure or hospitals etc. But most economists believe it has to be done carefully and preferably during recessions.


Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences?

One reason I could think of is regarding convexity of the function (and hence risk aversion). For example, $u(x) = x$ is risk neutral, but $v(x) = \ln(u(x)) = \ln(x)$ is risk averse.

See also this.


Negative interest rates - Monetary Policy

Real interest rates can be negative without a negative benchmark rate set by the central bank (inflation is higher than nominal interest rates) so in that sense we won't see any new effects.

Regarding the interest rate set by the Central Bank, it does decrease the real interest rate as the banks won't deposit money and have more incentive to give out loans but effectively it is not different from a zero rate (you can't force the bank not to sit on the cash) though I guess the bank has to pay the interest on the mandatory deposits.


Stiglitz: movement capital vs labor, effect on living standars

The Roy model ( a much celebrated model in labor economics) deals with this issue. It can be arguably be directly mapped to this issue.


Contribution to change of a ratio with 3 terms

Suppose we want to find the contributions of the variables to the given function:

$$f(x,y)= {x\over{y}}$$

To find the growth rates of the given variables first take the logarithm of the function $f(x,y)$:
$$ln(f(x,y))=ln\left({x\over{y}}\right)=ln(x)-ln(y)$$

And then take the partial derivative of the variable you would like to analyze:

$${\partial ln\left({x\over{y}}\right)\over{\partial x}}={\dot{x}\over{x}}$$

$${\partial ln \left({x \over{y}} \right)\over{\partial y}}=-{\dot{y}\over{y}}$$

Where $\dot{x}$ and $\dot{y}$ are the derivatives of $x$ and $y$ respectively

Thus in your case if you would like to find the contributions to growth to leverage you can simply do the same thing as above.

i.e.

$$\mathfrak{L}={{l+b}\over{l+b+e}}$$

Where:

$\mathfrak{L}=$ leverage

$l=$ loans

$b=$ bonds

$e=$ equity

Thus

$$ln \left( \mathfrak{L} \right)= ln(l+b) -ln(l+b+e)$$

you can thus find the contributions to growth by the variables involved by taking the partial derivative of the variable you wish to examine.

Hope this is helpful!!


Finding Marshallian demands for Leontief production function with different powers

As Amit said, your answer is correct. As Toby said, you can rule out negative output.

There is no much insight to add as an answer really. However, I was also fairly puzzled that such a simple problem gives a complex answer. As it turns out, you get a linear demand (on income) only if the exponents on both components is the same.

Consider the more general case:

$$ U(x,y) = \text{min}\{ax^\alpha,by^\beta\} $$

Optimality requires (* notation for optimal values omitted)

$$ ax^\alpha = by^\beta\ $$

Replacing one of these in the budget constraint leads to:

$$ p_x x + p_y \left(\frac{a}{b}\right)^{\frac{1}{\beta}} x^{\frac{\alpha}{\beta}} = w $$

Here we see that only when $\alpha=\beta$, demand will be linear (on income). In this case:

$$ x = \frac{w}{p_x + p_y\left(\frac{a}{b}\right)^{\frac{1}{\alpha}}} $$

It seems an algebraic solution for the general (unrestricted) case cannot be derived, as the polynomial you get might have irrational powers.


How do U.S. treasury yields impact yields of other sovereign debt markets?

For free-floating sovereign borrowers (e.g., Japan, Canada, UK, and the euro as a bloc (the member countries are pegged versus each other), short-term bond yields are largely determined by the expected path of the policy rate (plus a small term premium).
For longer-term bonds, one can debate how value is determined, but forward rates are generally smooth, so they can be interpreted as rate expectations and a term premium as well.
This means that bond yields ca diverge: e.g. look at Japanese bonds versus other sovereigns from 1995-2008 (at which point other countries converged at levels near Japan’s).
However, we see correlations between markets, which is not unexpected.

Central bankers might set domestic rates as a spread versus another currency, like the USD.
The business cycle is global, and new information about the outlook is thus correlated across markets.

This explains why short-term movements often are in the same direction, yet there are no reliable “rules” (since that would imply guaranteed trading profits).


The effect of trade would normally only partly counter-act the dampening policy.

It is of course possible that a change in net exports is greater than the effect of the dampening policy if multiple things are changing at once (like in the real world). I will just discuss what happens if all else is assumed to be unchanged.

My discussion is based on model OPEN, from “Monetary Economics” by Wynne Godley and Marc Lavoie (Link to code at sfc-models.net). I will just do some back-of-the-envelope approximations.

We assume that imports are a fixed percentage of demand (20%), and we have two identical economies (which start out with balanced trade). We then assume that Country A enacts a policy that reduces domestic demand by 5%.

Exports would be (roughly) unchanged, since Country B kept policies unchanged. (This is an approximation, since the drop in growth in A would also reduce growth in B via its export industry.)
Imports drop by 5% relative to their previous level, which is an amount that is 1% of total demand (since imports are 20% of domestic demand).

The net result is that there is only a 1% offset from trade against the 5% demand contraction from policy.

In order for there to be no effect, we would need the entire drop in domestic demand to come from imports. There might be some special cases where this happens (e.g., the government stops importing foreign equipment), but such selectivity would not be possible with something like interest rate policy.


Does lowering consumption help reduce inflation rates?

Lowering consumption, and increasing savings can increase net exports. Since savings increase relative to consumption, there is more money to lend out to the world (in an open economy), and less investment domestically. The decrease in demand for your currency due to the reduction in investment and rise in savings can lead to a reduction in the real exchange rate for your currency relative to other currencies. NX (net exports) = S - I (Savings - Investment). S = Y-C-G (income - consumption - government spending). As you can see, the level of consumption directly impacts savings. A decrease in consumption increases savings, which in turn decreases the real exchange rate for your currency, which can make imports more expensive, creating nominal price inflation.

Another determinant of inflation however is also the money supply, and this is the biggest factor. The central bank in your country has the largest impact on money supply. This is because Y (output) is fixed based on the factors of production. % change in M (money supply) + % change in V (velocity of money) = % change in P (price level) + % change in Y (output). That is (% change M + % change V = % change P + % change Y). As you can see, the price level directly has to increase proportionately to the change in the money supply that the central bank can manipulate. So even if consumption decreases, nominal inflation rates will rise if the central bank is expanding the money supply. That is how it’s possible to see a decrease in consumption, and still potentially see inflation.


In the Cournot Duopoly Model,why is the Equilibrium achieved at 1/3 Rd of the Market Share?

It is not always necessarily 1/3rd. That just happens to be the outcome in the standard textbook example.


Nash equilibrium of a Bertrand game with different marginal costs

Yes, there is no equilibrium in pure strategies. For any price charged by firm 2 above $c_1$, firm one could only best respond by charging the largest price that is strictly smaller. which is impossible. If both firms charge at most $c_1$, one of these firms must make a loss, which cannot be a best response. So there is no Nash equilibrium in pure strategies.

There are, however, equilibria in mixed strategies. Consider an equilibrium in which firm 1 chooses a price of $c_2$, while firm two randomizes uniformly over the interval $[c_2,c_2+\epsilon]$ for some $\epsilon>0$. For $\epsilon<c_2-c_1$, this is a Nash equilibrium and, moreover, it uses no weakly dominated strategies. Firm 1 is making a profit of $c_2-c_1$ and firm 2 a profit of $0$. Clearly, firm 2 has no profitable deviation. To see that firm $1$ has no profitable deviation, recall that there can be no profitable deviation in mixed strategies if there is no profitable deviation in pure strategies (a very general game-theoretic fact), and observe that firm $1$ cannot profit from deviating to a price strictly below $c_2$ or weakly above $c_2+\epsilon$. So take any $\delta$ satisfying $0<\delta<\epsilon$ and assume that firm 1 charges $c_2+\delta$ (note that $\delta=0$ would be no deviation.) The probability that firm 2 charges a lower price is $\delta/\epsilon$, so the expected profit of firm 1 is
$$(1-\delta/\epsilon)(c_2-c_1+\delta)+\delta/\epsilon~ 0.$$
Write $K$ for $c_2-c_1$. We have a profitable deviation if
$$(1-\delta/\epsilon)(K+\delta)>K,$$
which we can rearrange to get
$$\delta(1-K/\epsilon-\delta/\epsilon)>0,$$
which is equivalent to
$$K/\epsilon+\delta/\epsilon<1.$$ If $\epsilon< c_2-c_1=K$, this can never be the case, so we obtain a Nash equilibrium if $\epsilon>c_2-c_1$.

One can actually use the same construction to construct equilibria in which firm 1 charges less than $c_2$, but in the resulting equilibrium, firm 2 must play a weakly dominated strategy.

The construction in this answer is taken from the following short paper:

Blume, Andreas. "Bertrand without fudge." Economics Letters 78.2
  (2003): 167-168.


There are too many applications of the concepts and results you mention for a list to be of any use. As a first introduction, look at:

Real Analysis with Economic Applications, Efe A. Ok (here, here, and here)

There used to be pdfs of (reasonably high quality) working version of the book available online, but they are harder to find now that the book is out (I believe the author put these working versions online as a way to get feedback and typo-reports but removed them since then). If you look hard enough, some of these working version might still live in corners of the internet though.

Also have a look at this related question: What are some applications of Real Analysis in Graduate Economics?


Because the notion of pairwise stability is so important in the theory of network formation and equilibrium, there has been a few attempts to test it in experimental setups. I know at least two papers:

Myopic or farsighted? An experiment on network formation, by Georg KIRCHSTEIGER1, Marco MANTOVANI, Ana MAULEON and Vincent VANNETELBOSCH.
Departures from Best Response in Market-like Link Formation: An experimental study, by Margherita Comola and Marcel Fafchamps.

The first is a discussion paper. A word of warning regarding the second : the version of the paper that is linked is very much a draft. You might want to have a look to get an idea of what the authors plan on doing, but don't rely on it too much. I attended a talk where Fafchamps presented the paper this week, and he told us that they initially got the wrong data from their experiment. They only realized it rather recently and had to revise the whole paper. Because the linked draft is from February 2014, there are chances it is still based on the the old data (I did not read it).

For some field experiments on networks in development economics, you might want to have a look at other papers by Fafchamps :
http://web.stanford.edu/~fafchamp/index.html. I am not sure these explicitly test equilibrium concepts though, but they might.


Does comparative advantage sustain over long periods of time?

The theory of comparative advantage, like Ricardo/Rybczynski/Stolper-Samuleson, is classically a static theory, but you seem to be worried about dynamics.

You seem to think specialization and "unlearning by not doing" might be bad bad.  The question is why?

Specialization is almost a necessary condition for trade: if we are all equally good at all tasks, what is the point of trading?  We could just produce whatever we wanted in autarky. Specialization is about learning and seems to take place over time. This goes in the direction of innovation, perhaps like Schumpeter: the country that makes pens might innovate a new writing tool that makes pencils and pens obsolete, and then A will regret specializing. Similarly, in the theory of firms, there is an idea of Absorptive Capacity of ideas.  If no one at Tesla knows anything about combustion engines, they might miss out on breakthroughs in that technology that would benefit Tesla. Maybe it's because the breakthroughs are valuable in themselves, or maybe it's because having an open mind means you can have more creative ideas.  So perhaps firms should keep some capacity to do things in which they do not have a comparative advantage in order to expand their R&D capacity.

But you talk about countries.  The US subsidizes food production because it wants to have its own food supply for national security reasons; look at the medical mask shortage right now.  So perhaps it makes sense to subsidize production of things in which a country does not have a comparative advantage in order to avoid becoming completely dependent on other countries.

So, given the information provided, perhaps you are mixing together the short-run classical theory with concerns about innovation, uncertainty, or long-run fitness?


$L^{\infty}$: the (Banach, usually) space of bounded measurable functions modulo the equality almost everywhere. Like all function spaces not involving holomorphic functions, it's really a space of equivalence classes.

weak-$^*$ topology: the topology on the dual $X^*$ of any topological vector space $X$ induced by the $(X, X^*)$-pairing.

"embedded in $L^{\infty}$": a (say) topological vector space $Y$ is said to be embedded in $L^{\infty}$ if there is an injective continuous linear map from $Y$ to $L^{\infty}$.

(This is the usual meaning. In your paragraph, "embedded" just means viewing those indicator functions as representatives of their classes. The weak-$^*$ topology on $L^{\infty}$ is given by the identification $L^{\infty} = (C_0)^*$.)


British inflation up again, but crisis might come. What should the BoE do?

You could say what the chart represents.

It is in fact the changes in the input Producer Price Index http://www.ons.gov.uk/economy/inflationandpriceindices/bulletins/producerpriceinflation/july2016 with a headline statement of

  the total input price index rose 4.3%  in the year to July 2016, compared with a fall of 0.5% in the year to June 2016

But this effect is smaller as it affects the economy as a whole.  For the output Producer Price Index the headline statement is less dramatic:

  Factory gate prices (output prices) for goods produced by UK manufacturers rose 0.3% in the year to July 2016, compared with a fall of 0.2% in the year to June 2016.

This has not yet had a substantial effect on consumers, where for the Consumer Prices Index http://www.ons.gov.uk/economy/inflationandpriceindices/bulletins/consumerpriceinflation/july2016 the headline statement is:

  The Consumer Prices Index (CPI) rose by 0.6% in the year to July 2016, compared with a 0.5% rise in the year to June.

I would be surprised if any of today's data surprised the Bank of England:

Imported inputs for UK producers now cost more due to a weaker Pound sterling
This has a relatively smaller effect on output prices, meaning British exporters are potentially more competitive internationally
This has not yet had a substantial impact on consumers

What the central bank does not yet know includes:

how much of an effect this will have on consumer prices in the longer term
how negative this will allow real interest rates to be if nominal interest rates are kept close to zero
how much of an effect this will have on imports and exports
how much of an effect this will have on consumption
how much of an effect this will have on investment

though it might try informed guesses.  Investment, consumption and exports in particular will be affected by broader factors including predictions about the long-term impact of a future Brexit.


It is the difference between total general government revenue and total general government expenditure defined in the National Accounts system.  You can find some sort of explanation at http://ec.europa.eu/eurostat/statistics-explained/index.php/Government_finance_statistics_-_quarterly_data#Government_revenue_and_expenditure

For Greece, Eurostat's underlying figures look like this

UNIT    NA_ITEM/TIME            2015Q1  2015Q2  2015Q3  2015Q4  2016Q1  2016Q2  2016Q3
M euro  Total GGov revenue      16,945  19,711  19,970  27,484  18,430  20,598  23,780
M euro  Total GGov expenditure  20,925  21,336  20,796  34,290  20,222  20,368  20,982
M euro  Net lend(+)/borrow(-)   -3,980  -1,625    -826  -6,806  -1,792     230   2,798
% GDP   Total GGov revenue        42.0    44.5    43.3    61.3    46.2    46.3    50.9
% GDP   Total GGov expenditure    51.8    48.1    45.1    76.5    50.7    45.8    44.9
% GDP   Net lend(+)/borrow(-)     -9.9    -3.7    -1.8   -15.2    -4.5     0.5     6.0

The percentages are of quarterly GDP.  If you wanted exact annual percentages then you should add up the four quarterly figures in Euros and divide by the sum of the four quarterly figures for GDP in Euros (from a different Eurostat table), but you will get a close approximation if you take the average of the four quarterly percentages.  So for Greece it might represent a government deficit of around 7.7% in 2015

Be aware that the numbers are not seasonally adjusted: it looks as if a lot of Greek government revenue and expenditure comes in Q4.


Link between Productivity and Labour Force?

Output per capita is $\dfrac{Y}{N}$. This can be decomposed as:

$$ \frac{Y}{N} \equiv \frac{Y}{h} \times \frac{h}{L} \times \frac{L}{A} \times\frac{A}{N} $$

where $h$ are aggregate hours of work, $L$ is number of employed, and $A$ is active population. $\frac{Y}{h}$ is aggregate labour productivity, $\frac{h}{L}$ is "work intensity", $\frac{L}{A}$ is the employment rate and $\frac{A}{N}$ is the participation rate.

The above equality can be turned into growth rates, which means in approximation, the growth of output per capita is the sum of the growth rates of each of the subcomponents.


There are not just rules but whole theories. Namely cardinal utility allows you to make interpersonal utility comparisons (as opposed to ordinal utility). A common cardinal utility framework is the one based on  von Neumann-Morgenstern.
Von Neumann-Morgenstern cardinal utility requires that axioms of completeness, transitivity, continuity and independence are satisfied (see von Neumann-Morgenstern (1944) Theory of Games and Economic Behavior), so you can view them as 'conditions' for interpersonal utility comparison (although there are also other approaches to cardinal utility that might have different conditions).
Furthermore, note these rather necessary conditions for interpersonal utility comparisons not sufficient ones, as mentioned in the comments a good book that discusses this in greater detail is Roemer Theories of Distributive Justice.


Can implicit costs make every option not worth doing?

As correctly pointed out by @Herr K., the opportunity cost of forgoing a movie (bowling) and going bowling (to a movie) is $2.
Hence, the net payoff from going to a movie = benefit - cost = 12 - (10+2) =0.
Similarly, the net payoff from going bowling is 17-(15+2) = 0
Hence the consumer should be indifferent between bowling and going to a movie.


Is there any evidence for consumer utility-maximising behaviour, at individual or market level?

Since utility by definition measures something very innate or subjective, it is difficult to obtain any non-experimental data on it. Hence researchers focus on choice, which is something observed in practice. This is where WARP, GARP and SARP comes in. Of which, GARP is the most relevant.
Any data generated by a utility maximising agent (with well behaved preferences) will satisfy GARP. The converse is true as well through Afriat's theorem - for any data satisfying GARP, there exists a utility function that rationalises it.
Note that it is difficult to study aggregate demand for such conclusions as well. The Sonnenchein-Mantel-Debreu Theorem basically kills any predictive power in this regard. So I would suggest you look up papers that empirically test GARP from choice data. Here's one such paper: Echenique et al
P.S. Mentioning @MichaelGreinecker here since I just noticed his comment that gave the same answer. :)


Induced jobs are those created by the spending of those employed directly by the primary source or indirectly by suppliers to the source.  For example, you have a project to build a bridge.  That project hires a worker.  That worker stops at a convenience store every morning and buys a coffee and a bagel.  The people responsible for selling the coffee and bagel are induced jobs.  This includes the cashier, the stock person, the delivery person, the baker, etc.

Obviously this particular worker is only responsible for a small fraction of the overall cost of these others.  However, if you aggregate all the effects across all the workers on the project, you may find that the convenience store has to hire an extra cashier, that the part-time stock person has to work full-time, that an additional delivery person has to be hired to share the stops, that another baker needs to be hired, etc.

The multiplier is simply an estimate of how much spending on the project will then be respent on labor indirectly.  It can be given either in terms of jobs or in money.  Economists use survey information and other studies to estimate how much this will be.


I think this is just a reflection of the casual language of the popular press. What appears to be in dispute in this question is if profits can be negative or if that case is properly referred to as losses.  I agree that in many contexts this is at best a confusing usage. Most dictionary definitions are clearly implying that profits must be positive (e.g., "A financial gain", "Advantage", "Benefit", or "income in excess of costs").

I'm comfortable thinking about negative profits as being a synonym for losses. Industry profits can be thought of as the sum of profits and losses of individual firms just like a firm's profits can be thought of as the sum of profits and losses of subsidiary firms. That seems uncontroversial, at least if this total is positive but that doesn't seem like a standard usage. If we accept that profits can be negative and this aggregate is negative we have weird things happening like firms with positive profits making a negative fraction of total profits. Nothing wrong with the math here, but the math may be telling you something difficult to translate into words. If firm level profits were by definition positive then in @denesp's example Apple and Samsung's share of profits would be 100 percent.

The more technical term for a variable that when positive is profits and when negative is losses is Net Income. Wikipedia's page on Net Income says:

  In the context of the presentation of financial statements, the IFRS
  Foundation defines net income as synonymous with profit and loss.

I'd avoid the confusion and not refer to losses as negative profits. Instead I would use the term Net Income.  Let's fix that Business Insider quote to use net income:

  Apple and Samsung account for more than 100% of industry net income
  because other makers broke even or lost money

  Samsung and Apple combined to take 106% percent of the industry's
  net income. How do they take more than 100%? Well, it's a quirk of the
  fact that everyone else in the industry is losing money, or breaking
  even. Apple has 65% of the industry's net income, and Samsung has 41%.

Now let's use @denesp's example:

Company / Net Income
Apple / \$53
Samsung / \$53
Other / -\$6
Total / \$100

Everything looks good to me here after the change in terms.


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

I’d go with (2j, something with how they calculate exchange rates. If you note the scale, the blips are abeolutely small, so there was just some small glitches.

I am only somewhat familiar with currencies, but the spot markets use market makers. (Currency futures are traded on exchanges, but the chart should be labelled as futures if that were the case.) Series like this are based on some kind of “average” of quotes. The period shown is outside “normal” trading hours (currency markets are global, so trading hours reflect that), and there is no reason to update quotes, so the level is mainly stable.

Any number of things could cause the small glitches. For example, if one of the dealers shuts down their system temporarily, it could move the average. Or there could have been some out-of-hours activity that caused one dealer to move quotes, and then snap back into line with the other dealers after the activity passed.


The relationship between structural budget balance and cyclically adjusted budget balance?

After searching, I found out that Structural Budget is OECD nomenclature for Cyclically Adjusted Budget.

Here's a link.


What you are after

The value of a good should be the highest possible utility that it would give anyone in the economy. If you care differently about different people, you are interested in the highest possible adjusted utility that it would give anyone in your economy, where you have adjust the utility with a weight that indicates how much you comparatively care about that person

It doesn't exist

This is almost what a price is: It is the highest possible utility that it would give anyone in the economy who can afford it, under frictions. These frictions could be informational (someone who benefits most from the new iPhone isn't aware of its existence) or other (some people/groups are restricted from purchasing a good, for example due to trade sanctions).

There is no other objective way that we are aware of. At the cost of sounding dogmatic, this is the superior part of capitalism compared to other economic systems: Allowing prices to judge the value of goods.

In alternative systems, you need committees or similar to do this job. While there is no theoretical reason why human's couldn't do a better job than prices do (unless you allow for hand waving the system is too complex), it turns out they don't.

Do you need real world cash for prices?

There is three properties of money: It is

a storage of value
a unit of exchange
unit of account

Introduction of money into your economy doesn't need to connect it to real world cash, but you need to make it valuable. Connecting it to real world cash at some rate would immediately determine its value. Say, if you allow modwizdollar at 1-to-1 rate to the USD, your dollar has immediately the same value as the dollar, and also its inflation rate.

In Diablo, players find gold and items over time, as they kill enemies. Therefore, the objective value of gold is the time it takes a player to earn that much gold, devalued by how much that time is worth to the player. The more time it takes for players to find items, the more valuable these are. For money to be work as a store of value, it is sufficient to keep finding modwizdollars costly in terms of time.

How to set prices

It depends on what your goals are, and I suppose people could write Bachelor papers on the complexity of these systems, and in fact, an economist of late publicity did exactly that for Valve.

One simple way to set up prices

One simple way would to allow the measure of goods (items) grow constantly over time. This would imply a new supply of a specific item $i$ of $S_i$. Let time be denoted by $t$.

Compute, at any time, the actual demand for goods by players given the current prices $D_i(p_{i,t})$. Given initial $p_{i,t}$,

Increase $p_{i,t+i}$ if $D_i(p_{i,t}) > S_i$
Decrease $p_{i,t+i}$ if $D_i(p_{i,t}) < S_i$

How much you want to increase or decrease these depends on many things, and I can't possibly spell out the whole model for you. Assuming that demands are stable over time, you could try a bijection.


Depreciating companies intangible assets

All assets which have a finite useful life are depreciated. For example, your patents or copyright might hold for 5 or 10 years but no more. Thus, it is quite coherent to reflect the loss of value through depreciation and amortization. Same goes for a software for example: in 5 years time, a software might be obsolete, so we need to reflect this in the financial statements.

However, the intangible assets which do not have a finite useful life (e.g. goodwill) will not be depreciated, though its value can be impaired. A great example was provided last summer by Microsoft.

The way it is done is the very same as for tangible assets.

Under IFRS, the relevant IAS is the IAS 38


Why real wage equals marginal product of labor when return to scale is constant?

Consider that the following production function $Y=F(K,L)$ excibits constant returns to scale ie $F(x K, x L)=x F(K,L)$, for any arbitrary scalar $x$. This means in plain English that eg for $x=2$, doubling the inputs will produce double the output. The intuition behind constant returns to scale is that inputs and outputs are directly proportionate.

In technical terms, an $F$ like that, is called linearly homogeneous. Such functions display the following characteristic, by virtue of their definition: $Y=K\frac{\partial F}{\partial K}+L\frac{\partial F}{\partial L}$. The total value of F can be decomposed into a sum of products; each product is made up of the quantity of the relevant factor and its corresponding marginal product.

Now consider how a firm that is using a constant returns to scale technology and is also a pricetaker in product and labor markets will solve its profit maximization problem; standard treatment proposes that it will find it profitable to employ each production factor up to the point where the value marginal product equals the factor's price or $P_Y MP_X = P_X$, where $X=K,L$.

Therefore, under constant returns to scale and price taking behaviour, linear homogeneity will ensure that (the value) of (optimaly produced) output is exactly offset by payments to production factors hence we are left with zero economic profits.


Measuring growth rate when values are negative

For negative values alone you can define relative change as:
$$\frac{X_t-X_{t-1}}{|X_{t-1}|}$$
This is quite common way to deal with rates of change when you have negative numbers. However, when the denominator is zero then the growth rate is not defined. This can solve any issue when zero is not a base.
When zero is the base unfortunately there is no way how you can calculate growth rate while keeping the zero there. This is because if you start from zero any change represents $\infty$ increase. Going from 0 to 1 is $\infty$ growth rate as well as going from 0 to 10 or 0 to 1000. You have to either get rid of a zero in some way or another or simply do not calculate growth rate but some other measure of change (e.g. simple change $X_t -X_{t-1}$).

I have already thought of adding an arbitrary but reasonable positive number to data points, to bring everything into a positive domain. But this is a very crude and not an elegant way to do this.

Yes, this is very crude way of doing it but perhaps there are more elegant alternatives. Using the temperature as an example a solution would be to convert degrees Celsius to Kelvin (with $T_{(K)} = T_{(°C)} + 273.15$) which would solve the problem.
Perhaps there is an another way to measure the quantity you want. Otherwise, adding an arbitrary constant would be a solution. It is hard to recommend any specific way without knowing all the details of the research.


Is First Order Stochastic Dominance (FOSD) relation convex?

The first order stochastic dominance relation is convex.

An easy way to prove this is to use the property that a cdf $F$ FOSD another cdf $G$ if and only if $F(x)\le G(x)$ for all $x$. That is, $F$ FOSD $G$ if and only if the graph of $F$ is never above the graph of $G$. It is then easy to show that $F$ is never above any convex combination $H(x)=\alpha F(x)+(1-\alpha)G(x)$, which in turn is never above $G$.


Is IS-LM still used in research or we learn it just to understand basic macro?

Yes, it is still used a recent example of IS-LM model used in literature is (Bonyah et al. 2019).
Also, it is important to understand those two are not substitutes for each other. IS-LM is a general equilibrium (GE) model. The way how you get dynamic stochastic general equilibrium (DSGE) model is that you take a general equilibrium model and add dynamism and uncertainty there.
As a student you were probably exposed more to the DSGE model based on real business cycle (RBC) model (which is based on Neoclassical GE models) as they are simpler, but New Keynesian DSGE models which are in essence DSGE version of IS-LM exists as well (see discussion of New Keynesian DSGE in Frische & Größl, 2010) and are relatively widely used (in fact I would say that after 2008 they became increasingly popular in the literature).
You will see DSGE models dominating over GE models in the literature, but this is because GE models are mostly used to derive some theoretical insights into how economy works, whereas DSGE can be used for actual practical simulations or even forecasting. You can't make any serious forecasts  with theoretical GE model - no matter whether it is IS-LM GE model or some other one (only predictions about variables and relationship but that should not be confused with forecasting). Consequently, you will see DSGE models dominating because it makes sense to make separate paper about DSGE model calibrated for let's say economy of the Netherlands as in Lafourcade and de Wind (2012) (coincidentally they actually apply IS-LM based DSGE), whereas applying any GE whether IS-LM or some Neoclassical one to a particular country would not be very useful (at least not much beyond what you can learn from the general version already). So for every one theoretical GE model, no matter what variety, you can easily find more than dozen DSGE models.