Question about the "No Dictator" Criterion in Arrow's Impossibility Theorem

Arrow's Theorem concerns a social preference function ---that is, a function that produces a group preference order for every possible profile of individual preferences.  The axioms "Nondictatorship", "Independence of Irrelevant Alternatives", etc. must then be satisfied by the function at every profile.  (To be more precise, an axiom like IIA involves a comparison between the behaviour of the function at two different profiles.  So it must be satisfied by the function for every pair of profiles.)   Your counterexample only shows me the outcome at two particular profiles;  it does not specify the function itself.  Until you specify a function, we can't know whether the axioms are satisfied.  Arrow's Theorem says that, when you try to extend your example to completely specify the outcome at every profile, sooner or later you will run into a situation where you must violate one of the axioms.


Looking for a term that explains market participants that lie about their participation to gain access to said market

What about a meme agent? (e.g. an agent mimics the qualities of another agent to "fool" regulators, competitors, consumers.)


Impulse Response Functions for non-linear models?


This looks like a quotation from The Indian Express

WPI is likely to mean "Wholesale Price Index", similar to what is sometimes called the "Producer Price Index" and related to GDP deflators, but distinct from the "Consumer Price Index".

The exclusion of indirect taxes is presumably designed to avoid measuring price changes directly associated with India's introduction of a national Goods and Services Tax in 2017.


Can the amount of loans and deposits in entire banking system differ significantly?

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

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

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

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

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


Wages in Solow growth model with savings = 0

Let
$$Q = F(K,L)$$
Assume
a) $F(K,L)$ exhibits consant returns to scale.

We need this to aggregate from the individual firms to the total.

b) Price taking behavior  and

c) Profit maximizing behavior

from the part of the firms.

Then, throughout the dynamic process,
$$w = \frac {\partial F(K,L)}{\partial L} \equiv F_L$$

i.e. the wage is equal to the marginal product of labor. For clarity, write

$$\frac {\partial F(K,L)}{\partial L} \equiv h(K,L)$$

$$\dot w = \frac {d}{dt}\frac {\partial F(K,L)}{\partial L} = \frac {d}{dt}h(K,L)= \frac {\partial h(K,L)}{\partial K}\dot K + \frac {\partial h(K,L)}{\partial L}\dot L$$

$$\implies \dot w = F_{KL}\dot K + F_{LL}\dot L$$

Assume  further

d) complementarity of inputs, $F_{KL}>0$, and

e) diminishing marginal productss (not in the temporal dimension but in the static dimension, due to diminishing rate of returns), $F_{LL}<0, F_{KK}<0$.

Then, if

$$\dot K <0, \dot L\geq 0  \implies \dot w <0$$

The same treatment wil give us

$$\dot r = F_{KK}\dot K + F_{KL}\dot L  >0$$


On income distribution, there is the World Inequality Database. On poverty, the World Bank provides lots of comparable figures, although I believe these are the same data as in gapminder.


Is Keynesian economic theory still considered capitalism?

Capitalism is not well-defined in economics. In most economic textbooks the word capitalism is not even printed.

However, according to dictionary (Merriam-Webster) definition:

  an economic system characterized by private or corporate ownership of capital goods, by investments that are determined by private decision, and by prices, production, and the distribution of goods that are determined mainly by competition in a free market [emphasis added]

The above definition does not seem to exclude the kind of macroeconomic management intervention prescribed by Keynes theory and its newer interpretations. Moreover, I know that political science happens to distinguish between different capitalism such as state capitalism or market capitalism but this is not done in economic theory where the word is scantly used.

Socialism is bit better defined in economics (but it is still term that is not commonly used and avoided as its too value laden and scientists try to avoid value laden terms as much as possible), and it is defined as an economy where means of production are predominantly owned/controlled collectively by the state (see this article on investopedia). Nothing in either original or New Keynesian theory calls for state/collective ownership at all, let alone making that the predominant mode of production, so I dont see any way how the sort of policy prescriptions made by Keynes could be considered 'socialistic' per se in economic meaning of the word.

Furthermore, neither neoclassical or Keynesian theory pertain to any particular economic system in principle. Both schools focus mainly on describing mixed predominantly market economies because those happen to be the kind of economies that are most common in the real world. However, some parts of both neoclassical theory and Keynesian theory would be applicable to centrally  planed 'socialistic'  economies as well.  For example, as @BrianRomanchuk correctly points in his comment the Keynesian aggregate demand management policies are avaiable to any government no matter what economic form of organization/ideology it follows.


What's the opposite of a Pareto improvement called?

I usually use the phrase "Pareto worsening". It is not really widespread, in fact I am not sure I have ever heard anyone else use it. However now I googled it and people seem to use it in connection with Hart's 1975 paper wherein he shows that the opening of some new markets can make every agent worse off. Hart himself did not call this Pareto worsening, but other scholars do. An example is on page 230 of volume II of General Equilibrium, Growth, and Trade. Here is the same phrase used in Information and Securities: A Note on Pareto Dominance and the Second Best.


Name for a slightly-stronger than Nash Equilibrium?


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

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

Now use this in Eq. (3)

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

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


I can get to more technical papers, but it's not a big secret what you have quoted. E.g. The Economist quotes MIT professor John Van Reenen:

  But just because the size of the pie expands [due to free trade], it doesn’t mean that everyone is better off. There are going to be some losers whose slice of the pie is so much smaller that they would have been better off with less trade. However, because the overall size of the pie has got bigger, the government can compensate the losers which can still make everyone better off. [...] But remember: thanks to free trade, you can afford that [better welfare programs], because the overall size of the pie is bigger.

And Harvard prof. Dani Rodrik writes:

  there is one Stolper–Samuelson-like result that is
  extremely general, and which can be stated as
  follows. Under competitive conditions, as long as
  the importable good(s) continue to be produced at
  home – that is, ruling out complete specialization –
  there is always at least one factor of production that
  is rendered worse off by the liberalization of trade.
  In other words, trade generically produces losers.
  The proof of this result is simple enough to be
  stated quickly here. [the proof is still like half a page]

  More recent work in trade theory has emphasized
  heterogeneity among firms and workers. These
  models have additional margins for redistribution,
  between firms and workers that otherwise look
  quite similar. Grossman, Helpman, & Kircher (2017), for example, enrich the Stolper–Samuelson
  framework by considering heterogeneity within
  broad worker categories. ‘‘Managers’’ and ‘‘workers’’
  must combine in teams, and their productivity
  depends on the quality of the match. Trade liberalization induces re-matching and generates distributional effects within occupations and industries,
  in addition to the standard effects across broad
  factors of production and industries.
  Hence in all these models, redistribution is the
  flip side of the gains from trade. No pain, no gain.

My point is not to say that these theoretical models 100% apply to the complex realities of international trade, but rather that economists are aware that under certain conditions some segment of the workforce can be worse-off with free trade... unless something else happens.

Nevertheless, the prevailing opinion among economists, or at least US academic economists surveyed by IGM is that the long term benefits of free trade outweigh the short-term negatives (including [un]employment in some sectors).

As the survey additionally collected fill-in comments/responses, they are an interesting reading, but the first one (alphabetically, from Acemoglu) probably summarizes the critique you inquire about:

  Economists often understate short-term employment costs, which are significant and unequally distributed, but probably less than benefits.

As an example of empirical work evaluating such effects in a concrete context, Caliendo et al. (2015)

  We
  find that China's import competition growth resulted in 0.6 percentage point reduction in the share
  of manufacturing employment, approximately 1 million jobs lost, or about 60% of the change in the
  manufacturing employment share not explained by a secular trend. Overall, China's shock increases
  U.S. welfare by 6.7% in the long-run and by 0.2% in the short-run with very heterogeneous effects
  across labor markets.

Related enough, a more recent IGM survey of a panel of European economists (some of which do work in the US though) shows that they are not blind to the effects of inequality on [liberal] democracy. The latter survey also poses questions on whether higher government spending is justified from this perspective. So compensating or at least caring for losers (not necessarily stemming from free trade alone) is also a topic that economists are not opposed to. (Whether they should talk more about it, is a different issue.)


"Stockholder's equity" is how we label Equity in corporations, so it should be identical to the general concept of "Equity", except if, by a confusing misuse of words, by "Stockholder's equity" the authors meant "Shareholder Capital", which sometimes it is used to mean only a part of Equity (the nominal (par) value of shares issued), the other main parts of Equity being "Paid up capital" (amounts paid "above par"), various "Reserves", Retained Earnings.


Gini coefficients and median / mean income ratio

No, since you can change the Gini coefficient by altering the distribution of incomes in the top half (keeping the total the same) without changing the mean or median income; you can also change the Gini coefficient by altering the distribution of incomes in the bottom half without changing the mean or median income.

Compare the Gini coefficients of {2,2,2,2,2,6,10,10,10,10,10} and of {1,1,1,1,6,6,6,6,6,6,26}: the former will have a Gini index of about 0.33 while the latter will have a Gini index of about 0.46 though the mean and median do not change (6 each)


Effect of population growth on Solow steady state

if the population growth rate grows, why could the capital and income per capita decreases

This is basically asking "why does higher population growth lower the steady state capital per worker"?

Mathematics

Let us assume a Cobb-Douglas production function with constant returns to scale. This is,

$$Y=K^{\alpha}L^{1-\alpha}$$

It can be shown that in the steady state optimal capital per capita is:

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

(for example, see here)

Therefore, an increase in $n$ lowers $k^*$.

Similarly, in the steady state, output per capita is $y^*=k^*{^{\alpha}}$. Thus, a fall in $k^*$ leads to a fall in $y^*$, given that $\alpha \in (0,1)$.

Intuition

To start simple, think of an economy with a fixed level of workers ($n=0$). This economy has an exogenous saving rate $s$. Thus, for an initial level of output $Y$, workers save $s$ percentage of their income $Y$. These savings become investment, which then contributes to expanding capital. Meanwhile, there is a positive depreciation rate $\delta$, which in a given year renders a $\delta$% of the capital stock unusable. These two forces go in the opposite direction, moving capital stock up or down, depending on which force is stronger. Will there be a point in which these forces are in equilibrium? Necessarily there is one. Why? Because $\alpha \in (0,1)$ implies there is decreasing marginal returns to capital, case in which the Inada Conditions hold. In other words, if capital is very low, adding more capital will expand output and investment by very much. Conversely, when capital is very low, an identical increase in capital expands output and investment by very little. In the middle, there is a point where such expansion is equal to the depreciation (which is constant). In the Solow diagram with axes $K$ and $Y$ (in capital letters, not in per capita terms), that point is represented by the intersection between the depreciation function (a straight line) and the $sY$ line (concave, in line with the Inada Conditions).

Now, let us move to the case of positive population growth ($n>0$). Here, employment is increasing every period. Therefore, $Y$ is also increasing. In consequence, savings, investment and therefore capital is also increasing. In this economy, there is no steady state in terms of $K$ (unlike before), because $K$ is growing every period with the expansion of the population size. In terms of the same Solow diagram of above (with axes $K$ and $Y$, in capital letters, not in per capita terms), the function $sY$ is shifting upwards every period, pushing the never-reachable point where $sY$ intersects $\delta K$ further to the right.

Since there is no steady state in terms of $K$, the next question to ask is, is there a steady state in terms of $K/L$? Because of the same logic than before, necessarily there is one. To see this, notice that capital per capita terms has decreasing marginal returns in the production function (see the function above). This is, an increase in $K/L$ by 1% leads to an increase in $Y/L$ by less than 1%. Therefore, for a very low $K/L$, an increase in $K/L$ means a relatively large increase in $Y/L$ and therefore in savings $sY$ and in investment, and therefore in capital. Conversely, for a very high $K/L$, an increase in $K/L$ means a relatively small increase in $Y/L$ and therefore in savings $sY$ and in investment, and therefore in capital. The Inada Conditions ensure there is a middle point by which the forces that lower $K/L$ (in this case, depreciation and population growth) equilibrate the expansion of capital.

Finally, why does an increase in $n$ lowers that optimal $K/L$? On the one hand, the first force in the equilibrium (pushing $K/L$ up) is given by both the savings rate $s$ and the degree of marginal returns ($\alpha$). Neither of these have changed. On the other hand, the second force in the equilibrium (pushing $K/L$ down) is given by both the depreciation rate $\delta$ (which makes a certain proportion of $K$ obsolete) and by the exogenous increase in $L$, which itself depends on $n$. In consequence, an increase in $n$ makes the second force stronger. This pushes the equilibrium to a lower level of $K/L$.

Notice that a way to compensate this is to make the first force stronger, for instance, by increasing the savings rate. This can be easily seen in the Solow diagram, where it is possible to revert to the original $K/L$ steady state by increasing $s$.


What was Milton Friedman's opinion of Supply-side economics?

Friedman's involvement with the Reagan administration was only as an advisor, he was not part of the administration as a cabinet member or on the budget committee (roles he was offered), specifically because he did not want to moderate his writing and public opinion.
On the Reagan administration Friedman supported the Reagan Era tax cuts, but noted that tax cuts must be coupled with government cuts as well. In fact he even said that cutting the size of government must come before tax cuts, and predicted correctly the increase in he deficit. It should also be noted that Reagan himself was strongly in favor of government cuts in areas of education, agriculture, and environment, but he had to pick his battles with the congress controlled by the democrats (this is outlined very well in Steven Hayward's book "The Age of Reagan: The Conservative Counterrevolution").
Friedman also once famously said on Uncommon Knowledge with Peter Robinson "There is no such thing as supply side economics, nor demand side economics, just economics. You do not increase production by taking from one and giving it to another, whether that be from supplier to demander or vise versa". It should be noted this was after the Reagan Administration.
Generally however, Friedman was a strong supporter of the Reagan administration, because he thought that this was the first successful political movement in over a century to embrace the founding principles of America and liberty (he had the same view of Goldwater's 64' campaign which was unsuccessful).


The paper Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error (J. Isaac Miller (2009)) seems to have what you are looking for.

  We consider a cointegrating regression in which the integrated
  regressors are messy in the sense that they contain data that may be
  mismeasured, missing, observed at mixed frequencies, or have other
  irregularities that cause the econo- metrician to observe them with
  mildly nonstationary noise. Least squares esti- mation of the
  cointegrating vector is consistent. Existing prototypical variance-
  based estimation techniques, such as canonical cointegrating
  regression (CCR), are both consistent and asymptotically mixed normal.
  This result is robust to weakly dependent but possibly nonstationary
  disturbances.

Here  is the bit on testing for cointegration:

  In cases where cointegration between ($y_ t$) and ($x_t$) is not
  obvious or expected, 5 testing is desirable. The variance ratio test
  and multivariate trace statistic proposed by Phillips and Ouliaris
  (1990) rely on the estimation of the long-run variance of a different
  residual series. Specifically, ($y_ t, x'_t$ ) is regressed on one lag
  of itself, and the long-run variance of the residual series from that
  regression is estimated. This series is I(0) under the null, so we can
  expect that adding ($z^*_t$) – i.e., using ($y_ t, x^{'*}_t$)  – would
  have a similar effect to adding ($z^*_t$) to the residual series
  below. Specifically, it would inflate the variance of both the
  numerator and denominator of these statistics, so that the limits
  would be preserved. Approaches using more robust variance ratio tests
  (Wright, 2000; Müller and Watson, 2008) hold more promise still.


Expenditure minimization problem in the question is as follows :
\begin{eqnarray*} \min_{x\geq 0, y\geq 0} & \ \ p_Xx + p_Yy \\ \text{s.t.}& \ \ x + 3y \geq U \end{eqnarray*}
where $p_X > 0$, $p_Y > 0$ and $U \geq 0$ are given.
Since prices are positive, the cost minimizing choice will satisfy the condition that $x + 3y = U$. So, we can rewrite the above problem as :
\begin{eqnarray*} \min_{x\geq 0, y\geq 0} & \ \ p_Xx + p_Yy \\ \text{s.t.}& \ \ x + 3y = U \end{eqnarray*}
We can now substitute the value of $y = \frac{U-x}{3}$ in the objective and rewrite the problem as :
\begin{eqnarray*} \min_{0 \leq x \leq U} & \ \ p_Xx + p_Y\left(\dfrac{U-x}{3}\right)  \end{eqnarray*}

Since the objective ${\color{red} {p_Xx + p_Y\left(\frac{U-x}{3}\right) =\frac{p_YU}{3} + \left(p_X- \frac{p_Y}{3}\right)x }}$  is linear in $x$, solution is straight forward :
\begin{eqnarray*} x^h(p_X, p_Y, U)  \begin{cases} = U & \text{if } p_X < \frac{p_Y}{3} \\ \in [0, U] & \text{if } p_X = \frac{p_Y}{3} \\ = 0 & \text{if } p_X > \frac{p_Y}{3}\end{cases} \end{eqnarray*}


Will BRICS countries be the leading innovation countries 20 years from now?

What makes you assume that there is a link between the BRIC(S) countries annd innovation, more than any other country in the world, to make them leaders?

The growth reason in each BRICS country is different. The similarity is partially because of the ratio between labor and capital, economies that invest in industrialization, capital, and get higher growth until they reach their new industrialized potential

There are large differences: Russia's economy is based on energy - oil and gas. China has been subsidizing its industry with a low exchanges rate, a subsidy that is ending now, Brazil has also plenty of energy resources, but alot of unattended poverty and corruption, India faces a lot of structural government issues etc.

An authoritarian doesn't have to lead to lower innovation, Japan in the 19th century became western country in a generation, with Japanese sent to study in Europe.
It is less probable for an authoritarian regime to support innovation, for the simplest reason - it depends on a single authority to understand it, rather than a public agenda oriented regime

What you you should look for as an indicator for innovation is R&D expenditure out of the GDP, patent protection and any "doing business" score you find reliable


Suppose you learn that the richest 10% of people pay 30% of income
  tax. Does it mean that the tax system is progressive?

You are right. It cannot be determined without knowing the income tax of lower-income earners.

  If there are no eligibility restrictions, is this policy likely to be
  progressive or regressive? What might justify this policy?

That is even more uncertain than the previous question because it requires assumptions that are not inherent to --or implied by-- the policy. In fact, giving scholarships to some of the best students contradicts that there are no eligibility restrictions, but that is irrelevant.

First, not all degrees (whether earned at home or abroad) lead to a profitable career. For instance, graduates in graphical design usually earn significantly less than physicians.

Second, the effect of scholarships also depends on whether those students become high-income earners and decide sever ties with their home country. This could lead to a "progressive" scenario of lower inequality notwithstanding that the population that remains in the home country is the poorer sector.

It is just impossible to conjecture about the effects of the policy based on the information given.


Monthly price elasticity and possibility of using daily values

What you're trying to approximate is the quantity

$$
\gamma(t) = \frac{{\rm d}\ln Q(t)}{{\rm d}\ln P(t)}
$$

$\gamma = \gamma(t)$ is a function of time, the better sampling you have of $P$ and $Q$ the better estimation of $\gamma$ you are going to get. Imagine you have one sample every $h$ units of time. From what I can read $h  = 1 ~{\rm month}$, what you can do to measure $\gamma$ at time $t_k$ is calculate

$$
\frac{{\rm d}\ln P(t_k)}{{\rm d}t} \approx \frac{\ln P(t_k) - \ln P(t_k - h)}{h} \tag{1}
$$

with a similar expression for $Q$. But this is really bad in general, here's a better approach

$$
\frac{{\rm d}\ln P(t_k)}{{\rm d}t} \approx \frac{-2\ln P(t_k + 2h) + 8\ln P(t_k + h) - 8\ln P(t_k - h) + \ln P(t_k - 2h)}{12h} \tag{2}
$$

So to give you an idea, if you are measuring the elasticity on ($t_k$ = November 2018) with data measured each month, you will need to know the prices and quantities for ($t_k - 2h = $ September 2018), ($t_k - h = $ October 2018), ($t_k + h = $ December 2018) and ($t_k + 2h = $ January 2019).


Modern Portfolio Theory Vs Marginal Utility Theory

Welcome to EC.SE! Hopefully this will help.

I don't think this characterization is correct. These are not opposing theories. Modern portfolio theory is based on the idea that people choose portfolios to maximize their utility. After that, it depends on the specification of utility. As a simple example, a person with a quadratic utility function will choose a portfolio that is mean-variance efficient. The particular portfolio allocation will depend on the risk-aversion parameter in the utility function.

For examples discussed in other questions on the site, see Calculating the optimal portfolio for an investor with quadratic utility and
Portfolio choice problem of a CARA investor with n risky assets.


What Creates the Price in the First Place

This is indeed a bit confusing. Supply and demand functions depend on potential prices. That is, the agents think "if the price were a given level, what would I want to supply or demand?". So supply and demand depend on a whole range of (hypothetical) prices. However, the equilibrium price (which is a certain price and different from the range of potential prices) is that price where both supply and demand meet. In your example, the equilibrium is where the circular logic stops and finds a resting point, which is also why we refer to it as an equilibrium. This is a concept, which we borrowed from physics and is often used to mean a position where things stop changing/moving.

You are right to ask, however, how this whole process is initialized.

The rigorous way to think about this for economists, is to use what is called a "Walrasian Auctioneer".

You can imagine the process as such. An auctioneer calls out prices. Suppliers report how much they wish to supply, whereas consumers report how much they wish to demand. If these do not meet, the auctioneer calls out other prices. This goes on until demand meets supply and that's when the auctioneer stops.

Of course in reality, there is no walrasian auctioneer. Nevertheless, it is not hard to imagine that a new firm sets some price when it starts and then adjusts it depending on demand. Furthermore, depending on that new suppliers might enter, which changes supply and causes the price to adjust again. This goes on until a stable point is found, which we call the equilibrium.


Does a competitive advantage lead to abnormal profit?

I would say yes. For example, consider a perfect competition scenario, with equilibrium price $p$.
Now say (only) one firm acquires some organizational capital that allows them to have lower their marginal cost from $c(=p)$ to $\tilde c < c$.
This firm can charge price $p^-$ and aquire the whole market now, earning abnormal profits $\pi = (p^- - \tilde c)q$.


For a first look at econometrics, I would recommend Stock and Watson, Introduction to Econometrics. Not only does this book cover the basics well, it gives good, clear treatment of causal inference in econometrics. It covers time series topics, including VARs. For more advanced treatments, I would suggest Fumio Hayashi's Econometrics.

If you feel like you have a grasp on these, you could then look at econometrics books that deal more specifically with macroeconomics. I like the book Structural Macroeconometrics. Others include Methods for Applied Macroeconomic Research and Applied Macroeconometrics.


Mathemtical Economics Question regarding Profit Maximization

Well, it's very straightforward question. You have a cost function, from which you can get a Supply Curve, by taking its first derivative. You'll find competitive price and quantity when the supply curve you got meets the demand curve.

First, our supply curve: $$P = 4Q$$
Then, the demand curve:

$$ P = 32- 2Q$$

Competitive $Q$ is:

$$ 32 - 2Q = 4Q $$
$$Q = \frac{32}{6} \approx 5.333$$

So, competitive price is:
$$ P = 32 - 2 * 5.333 \approx 21.333$$


The actual details of the auction and so on are interesting, but in principle there is no magic. Its just demand and supply:

There is a number of agents that can supply or demand treasury bonds as well as other bonds. There's the government that issues the treasuries, the Fed that sometimes holds them, sometimes sells them, investors of all kinds( brokers, pension funds, individuals, money market funds, etc). All these agents want to sell more if they deem the price high(rates too low) and they want to buy if they deem the price is low (rates too high).

When supply shrinks, then agents that want to buy these assets bid up their prices (bid down the rates). similarly, when supply expands then the price falls (the rate rises) as the buyers bid down the  prices after observing the quantity.

To push up an interest rate, the fed will sell bonds. This will increase supply, until the price falls (i.e. until the rate rises).  To push down an interest rate, the fed will buy bonds. This will decrease supply, until the price increases (i.e. until the rate falls).

  I am curious, though: what if in the case of "raising rates", the Fed wants to sell securities but no bank wants to buy them? And, why wouldn't a bank buy securities anywhere else?

If no bank wants to buy the securities, but the fed is trying to sell them, then their price would go down, down, down, increasing the rate, until somebody wants them. If this rate is too high for the Fed, then it can instead buy these securities, lowering the market rate. In principle, if nobody wants to buy it means they are willing to sell, if nobody wants to sell it means they are willing to buy.

The banks can buy securities wherever they want, but the rates of all securities are closely related to each other. If the fed lowers rates on Treasuries, the rates on corporates, munies, etc, are all going to follow suit, at least to some extent. This is because the securities are all close substitutes of each other, so if you were thinking of buying a treasury, but its price increases, you go and, for example, you try to buy a muni, thereby increasing its price too.


Is there any up-to-date list of hours of work needed to buy a Big Mac?

I could not find any more recent Big Mac Index in terms of hours worked, and I dont think it is avaiable as wage statistics is usually reported with 1-2 year lag in many countries, but the Economist provides the Big Mac Index in USD, EUR, GBP and few other currencies up to January 2020  and it is being kept up to date with about 1 quarter lag. You can find the index here and raw data for all years here.

Based on their index you can calculate how many hours (or in this case mostly minutes) it takes in some selected countries. For example you can find hourly wages by month in the US for 2020 at the U.S. Bureau of Labor Statistics. You will be able to do this for most rich developed countries but not for all countries around the world.


Relationship between the Lagrangian and consumption euler equation?

In this simple problem, using a Lagrangean is an overkill, direct substitution of the constraint is perhaps better.

Anyway, treating the two consumption levels as two distinct decision variables under the budget constraint, the Euler equation emerges from the combination of the two first-order conditions:

$FOC$'s

$$\frac {\partial \mathcal L}{\partial C_1} = 0 \Rightarrow \frac 1{C_1} = \mu$$

$$\frac {\partial \mathcal L}{\partial C_2} = 0 \Rightarrow \frac {\beta}{C_2} = \mu\frac {1}{1+r_1}$$

Substitute the first into the second

$$\frac {\beta}{C_2} = \frac 1{C_1}\frac {1}{1+r_1}$$

re-arrange and you 're done.

I would suggest to also do that with a general utility function, where in the Euler equation the first derivatives of the utility will appear.


Anything written on the process behind "multiplicative" production function?

As I understood from my lectures, a multiplicative function means that the marginal product of one factor increases when another factor increases, and decreases when another factor decreases. The extreme cases (leontieff or additive) don't have this property.

At the moment the teacher explained this, it made sense to me. If one factor increases, it expands the capacity of the other to produce more. I think it makes sense.


Does Russia have higher inflation than US and Canada? If so, why in this particular case does money supply increase doesn't lead to higher prices?

The annual inflation was 5.8% in March 2021 in Russia. There are many reasons for this inflationary pressure such as the weakening of the ruble (Russian Currency) in comparison to the United States dollar. There is another reason for high inflation due to high government spending at the end of 2020 and at the beginning of the year 2021. In comparison to Russia, the inflation rate in the US is 4.16 % as of May 12, 2021. In Canada, the inflation rate is 2.2% in March 2021. Therefore, Russia has more inflation compared to the United States and Canada.
Moreover, your assumptions about deficit financing are reasonable and correct.


What are the effects of abolishing the minimum wage?

So this is a very broad topic. There are arguments pro and against minimum wages and there are many variables to consider.

As for your question, arguments 1-3 are basically argument 1. A higher minimum wage can limit employment / increase unemployment among people whose hourly value of labor to the employer is less than the minimum wage. As a result, those people may also miss out on increasing their value of labor, by missing out on work experience. That much is true. However, it does not mean that there would be zero unemployment without a minimum wage. For example Germany did not have a minimum wage for many years and still had unemployment. This is because there are other reasons for unemployment as well, like skill mismatches, search costs (frictions), reservation wages, etc.

Argument 4 is basically speculation. There is no guarantee that jobs would return to the US without a minimum wage. People will still have reservation wages below which they will not offer their labor and those reservation wages could still be above the current wage in another country. There is also no guarantee that automation would be significantly halted if the minimum wage were to be abolished (although the speed might slow down a bit).

For the sake of fairness, there are reasons economists would favor a minimum wage. One reason could be for example the presence of a monopsony (one dominant employer) and some would argue that is what Walmart has in certain regions.

Suffice to say that there is no clear answer on whether the minimum wage should be abolished or not.


Verifying the constant elasticity of the demand model Q= aP^b

The problem with your calculations is that you have very big changes in price

If you made price increases of $1\%$ in price, you would find the quantity fell by about $2\%$ as shown in the table below leading to an elasticity of about $-2$

If you made the price changes even smaller, the calculated elasticity would get even closer to $2$, and in a sense you are looking for the limit of elasticity as the price change approaches $0$, which will indeed be the constant $b=-2$

 a       b      P       Q=a*P^b pct change Q    pct change P   elasticity

100     -2      1       100.00
100     -2      1.01     98.03      -1.97%          1%          -1.97
100     -2      2        25.00
100     -2      2.02     24.51      -1.97%          1%          -1.97
100     -2      3        11.11
100     -2      3.03     10.89      -1.97%          1%          -1.97
100     -2      4         6.25
100     -2      4.04      6.13      -1.97%          1%          -1.97
100     -2      5         4.00
100     -2      5.05      3.92      -1.97%          1%          -1.97


Why was protectionism considered bad in the great depression?

Net exports aren't in and of themselves a bad thing; they should just be a transitory phenomenon. A prolonged export imbalance should just lead to an exchange rate adjustment which fixes the imbalance.

Protectionism on the whole, in general, leaves all sides worse off. David Ricardo documented it very well; and it wouldn't surprise me if there were proverbs in all the major ancient civilisations to the same effect.

There are exceptions: for example, infant industries typically need protection during their vulnerable early years, so that they can reach sufficient maturity that they can thrive under international competition.

However, that's different to the general protectionism that does get proposed at times of deep slump - the Long Depression, the Great Depression, and the current (2008-now) slump: then, it's one of the (socially and economically) worst options, but does appeal to the masses when they're desperate for an "other" to blame, and for easy answers to complex questions.


Solving a maximization problem by substitution when the constraint is in implicit form

Here are two methods. First method: the substitution can be made by inverting $f$. Since $f$ is strictly increasing and continuous, $f^{-1}$ is well-defined. The constraint can therefore be written
\begin{equation*}
x = f^{-1}\Big(\dfrac{c-(1-P)f(y)}{P}\Big)
\end{equation*}

The objective becomes
\begin{equation*}
\max_{y \geq 0}{P \Big[a-f^{-1}\Big(\dfrac{c-(1-P)f(y)}{P}\Big)\Big]+(1-P) (b-y)}
\end{equation*}

The derivative of this expression with respect to $y$ equals
\begin{align*}
& (1-P) f'(y) (f^{-1})^{'}(\dfrac{c-(1-P)f(y)}{P})-(1-P) \\
= & (1-P) \dfrac{f'(y)}{f^{'} \circ f^{-1}(\dfrac{c-(1-P)f(y)}{P})}-(1-P) \\
& = (1-P) (\dfrac{f'(y)}{f'(x)}-1)
\end{align*}
And thus $f'(y^{*})=f'(x^{*})$ at the optimum.

Second method: since $f$ is invertible, we can do a change in variables and define $w=f(x)$ and $z=f(y)$. The problem then becomes
\begin{equation*}
\max_{w \geq 0, z\geq 0}{P(a-f^{-1}(w))+(1-P)(b-f^{-1}(z))}
\end{equation*}
subject to
\begin{equation*}
P w +(1-P)z=c
\end{equation*}
Substituing $w=(c-(1-P)z)/P$ in the problem delivers
\begin{equation*}
\max_{z\geq 0}{P(a-f^{-1}(\dfrac{c-(1-P)z}{P})+(1-P)(b-f^{-1}(z))}
\end{equation*}
Differentiating with respect to $z$ yields the same solution.


Perhaps you may want to look into Price Discrimination? This however is the concept of companies varying their prices on different consumer markets.

1st degree price discrimination, at it's most optimal, is when companies charges the price of each individual consumer's demand. Those willing to pay the most will pay the most. Your description resembles this procedure, but it is not quite exact. Yours implied bargaining, which may or may not lead to 1st degree price discrimination.

2nd degree price discrimination is setting variable prices depending on the product or the quantity sold, playing off of the consumer's preferences.

3rd degree price discrimination is the segmenting of a market into smaller markets (based on some characteristic), and charging a uniform price in that market. The price between these segmented markets vary.


Is it correct to say that import tariffs are unilateral?

It depends on the importing country or bloc (X), and the country the import is coming from (Y), and the product category (Z).

If X is not a WTO member, and is not party to a trade agreement with Y, then tariffs can be set unilaterally.

If X is a WTO member (and has bound Z) or has signed a preferential trade agreement with Y that covers Z, then the tariff can be set unilaterally within (multilateral, bilateral or regionally agreed) limits.

If X is part of a free-trade agreement (or customs union) with Y that covers Z, then X is constrained to allow duty-free import.


A comment on the number of players in signaling games in general.

Signaling games need not have only two players. In the cheap talk literature, there are papers that study signaling games with multiple informed senders and one uninformed receiver (e.g. Krishna & Morgan, 2001), or one informed sender with multiple uninformed receivers (e.g. Farrel and Gibbons, 1989). There are no theoretical reasons to limit the number of players to two.

Is it possible to have a signaling game in which all players are both informed (about themselves) and uniformed (about other players)?

The answer is yes. For example, auctions with pre-play communication, where each bidder is informed about their own valuations of the object but not about the others'. In the communication stage, they use signals to strategically (mis-)communicate their private information, and to infer about other bidders' types from their signals (e.g. Mathews and Postlewaite, 1988). In general, mechanism design is about signaling privately observed types. But the specific model depends on what you want to do after the signaling stage, whether signals are costly, and what kind of outcome you want the model to deliver, etc.


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

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

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

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


Why is the Fed considering increasing interest rates?

The Fed recently decided not to raise rates because the economy is still recovering.  In theory, as unemployment goes down, it should start to increase inflation.  However, unemployment is low and inflation is also low.  This is probably because people have left the labor force and are no longer counted.  Having low interest rates does stimulate the economy but the Fed wants to raise rates, when possible, for several reasons.  Policy is supposed to be countercyclical so keeping low interest rates indefinitely could lead to inflation.  Also, low interest rates encourage investors to pursue more risky investments for higher yields which can cause bubbles and crashes.  Also, staying at low interest rates limits the Fed's ability to use monetary policy at the zero-lower-bound where they cannot stimulate the economy anymore by using conventional monetary policy.


Demand estimation with a lagged dependent variable

Does it change any interpretation of the elasticity ($β_1$)?

You walk into the firm where you work as an analyst, and the Sales Director calls and asks "I want to raise the price $10\%$ today. How will demand be affected in percentage terms?

Well, you don't expect income to have changed from one day to the next, and what was demanded yesterday -it was yesterday. So the only variable (for today) in the equation is price, and the best you can say is "I expect a $(10 \times \hat \beta_1) \% $ effect".

So it is the short term price elasticity of demand, irrespective of the fact that the level of demand is determined by other factors also, lagged demand included.

  I understand that I could also have some sort of long-run inferred
  elasticity if I set $q_t=q_{t−1}$ after estimating the coefficients of the
  equation.

Yes, either in an old fashioned "deterministic", $q_t=q_{t−1}$ way, or in a stochastic, $E(q_t) = E(q_{t−1})$ "mean-stationary" way.

Assume now that demand is already mean-stationary according to your analysis , and you get the same question from the Sales Director as before. Will your answer change compared to the previous one?

ANSWER

    The answer to the Sales Director should not change, because you can condition on the given and known past, for a more accurate (= focused on the specific situation) answer so you use $\hat E(q_t \mid p_t, I_t, q_{t-1}) = \hat \beta_0+ \hat \beta_1\hat{p_t}+\hat \beta_2I_t+\hat \beta_3q_{t-1}$ and not the unconditional (estimated) relation $\hat E(q_t) = \hat \beta_0+ \hat \beta_1E[\hat{p_t}]+\hat \beta_2E[I_t]+\hat \beta_3E[q_{t-1}]$,which would lead to the long-run (unconditional) elasticity.  But if he was to ask, say, "I want to introduce the product to a new market where the consumers are comparable in income to what we already have. What demand-responsiveness to price should I have in mind?", then the best you could do is provide the long-run elasticity.


What does Leverage ratio mean in context of Banking sector and how is it different from CRAR?

Leverage ratios are typical simple ratios of debt to equity while capital adequacy ratios are usually risk weighted.

  The capital adequacy ratio, or CAR, is a metric applied specifically
  to banks, while a common leverage ratio is used by investors to
  evaluate virtually any type of firm they choose to examine. The CAR is
  used to assess the financial risk a bank is exposed to through its
  existing loans. The ratio is risk-weighted and expressed as a
  percentage of the total exposure. ...

  Not simply a single leverage ratio, but rather several financial
  leverage metrics may be utilized to gauge a business's financial
  health. Two of the most commonly considered leverage ratios are the
  debt-to-equity ratio and the long-term debt-to-capitalization ratio.

What is the difference between the capital adequacy ratio and the leverage ratio?

Source: Investopedia


This is a partial answer, in the sense that it addresses the case for state-sponsored house building, rather than the question of how that should be financed. In general, any means by which the state might finance spending is likely to introduce some kind of distortion into the economy. The question then faced is whether that spending generates benefits sufficient to offset the cost of the distortion.

I agree with the general sentiment of others that if there is a well-functioning, uninhibited market for housing then any intervention in that market (such as an artificial increase in supply) is likely to reduce overall efficiency and, in particular, lead to the misallocation of resources within the economy more broadly. @suriv outlined the intuition for this.

However, if there are distortions that prevent the housing market from functioning efficiently then a state-sponsored increase in housing supply can be efficiency enhancing. This is a simple application of the more general "Theory of the Second Best", which holds that if there is pre-existing distortion in the economy then introducing another distortion can sometimes make things better, not worse.
 There are various reasons why the housing market might not function efficiently. Here are a couple:

Planning laws are sufficiently restrictive so as to reduce the market's ability to supply housing. For example, if planning permission is hard to obtain then developers who have planning permission have a kind of monopoly power over the ability to build houses and are likely to ration supply in order to increase profits. N.B If this is really the problem, then reform of the planning system is likely to be more efficient than a direct housing market intervention. But such reform might also be politically problematic.
Property builders are extremely vulnerable to economic downturns because housing demand is pro-cyclical. They are therefore unwilling to commit to risky, large-scale construction programmes that have long time-horizons.
Speculation on rising property prices induces people to hold undeveloped land or un(der)occupied properties in the hope of selling later when the price is higher.

All of these factors seem to be important considerations in the UK market (which is, I guess, the example that motivated your question). Since we are talking about state-sponsored house building, here is a graph that shows how much of the slack private-sector housebuilders in the UK took-up when the state withdrew from house building in the 1980s:

The answer is "basically none".

But does that mean that the market is now failing to supply enough housing, or just that there was previously an inefficient excess of supply that the market has now corrected? A figure that, I think, is broadly indicative of the fact that the UK housing marketing is currently not functioning well comes from this UK government report. It states that the UK is currently building houses at a rate of 135,000/year, but creating new households at a rate of 240,000/year. The 240,000 figure does not include either backlog from undersupply in past years, or demand for housing from foreign speculators (the FT reports that 75% of new homes in London are bought by foreigners, many of whom are speculators or will otherwise not occupy the property full-time). The UK has never in its history managed to build 240,000 homes per year except at times when the state accounted for close to half of all house building.

As somewhat of an aside, the effects of this long-term failure to meet demand upon the price of UK housing has been significant. Here is a comparison of various national house price indices from The Economist:

If one believes that such price growth is the consequence of a distortion in the market then it has important knock-on consequences for other aspects of economic efficiency: it encourages speculation and high levels of indebtedness, distorts investment decisions, and induces internationally mobile workers to leave the UK. As regional price disparities are magnified by rapid price growth, internal migration is also potentially distorted. If we care about equality then this kind of price growth also implies a growing wealth gap between property owners and non-owners.


Numerical Question on a subsidized monopoly

You probably want to assume that every consumer pays the same bribe. Also, the social surplus depends on the quantity consumed, so it might (spoiler alert: it will) change when the internet is privatized, and when the marginal cost changes.


What are good dataset alternatives to estimate value functions?

As I understand it, you're trying to estimate a demand system for different goods.

Have a look at Aguiar and Bils (forthcoming AER), who use the consumption expenditure survey to do exactly that. The previous link also contains their data and code.

From their abstract:

  We do so by constructing an alternative measure of consumption expenditure, using data from the Consumer Expenditure Survey (CE), that employs a demand system to correct for systematic measurement error. Specifically, we consider trends in the relative expenditure of high-income and low-income households for different goods with different expenditure elasticities.


It sounds like you've basically eyeballed the groups to decide they're similar.  A more advanced way of eyeballing would be to plot the distribution of each characteristic to see how similar they look.

In order to move beyond eyeballing, though, you'd need recourse to statistics.  One common method--that comes up frequently in two-group studies--is to do a statistical test to verify that the groups are similar.

Broadly speaking, you'd look at each characteristic, say height, and assert your hypothesis: average height is the same in both groups.  Then you could do a hypothesis test to see if the average height is actually the same or if it's different.  The specific statistical test you'd use depends on the data in your possession.

For example, see the t-test or the chi-squared test for a difference in means (or just search for "difference in means test").

You'd run the test (statistical software generally has a feature like this) to determine if it shows a significant difference.  If so, you might be comfortable saying the groups are not similar inasmuch as that characteristic (height) is concerned.

Then you'd repeat the procedure for weight and each of the other characteristics.

At the end, many researchers make a little table that shows the $p$-values (which you get from running the test) for each of the characteristics.  This gives your readers the ability to see and decide for themselves whether the groups are similar.


How do you calcualte Yield To Maturity, given only the coupon rate and current required rate of return?

The yield-to-maturity is similar to an internal rate of return, so the calculations need to take into account the timing of cash flows. So your example calculation 10%/.90 = 11.11% does not work. (That is known as a simple interest convention, which I think is sometimes used in the Japanese bond market.)

The calculation form depends upon the coupon frequency of the bond. For an annual coupon, if we denote the yield as y, then the price of the bond equals (convention of \$100 equals par):
$$p = \sum_{i=1}^8 \frac{10}{(1+y)^i} + \frac{100}{(1+y)^8}.$$

However, I do not know what “required return” in the question refers to (a true internal rate of return?). You would need to find the price of the bond using that “required return,” and then work from the price equation to get the yield.


Making predictions with a distributed lag model

So the short answer is yes, you can generate some predictions based on your model. Whether it will generate good predictions is another question. Basically you are only using the spatial variation to estimate your model and no time variation. So your predictions would most likely be very poor unless the relationship is very stable over time. There's also no way of knowing which lagged values of the explanatory variable would be useful in prediction, unless there is some spatial structure that you can use (i.e. some regions are leading indicators for other regions)


loanable funds theory: why is the supply of loanable funds equal to saving (+ dishoarding + new money)?

Does saving increase the supply of credit? Critique of loanable funds theory.
http://wer.worldeconomicsassociation.org/files/WEA-WER-4-Lindner.pdf

In the first step, the concepts of “saving” and “credit” will be clearly distinguished using simple accounting. It will be shown that credit is not limited by anybody’s saving and that no one has to abstain from consumption in order for a credit to be provided. Also, it will be shown that financial saving (an increase in net financial assets) through a reduction in expenditures reduces other economic units’ revenues and thus their ability to spend and save. Using the concept of excess demand and supply, it will be shown that excess saving does not lead to an excess supply of credit − which would lower interest rates − but to an excess supply of goods, services and/or labor which will lower prices and production. How interest rates change is not determined by excess saving: They could increase, stay the same or decrease. Finally, it will be argued that the identification of saving with the  provision  of  credit  is  likely  to  stem  from  the  invalid  application  of neoclassical growth models to a monetary economy.

The  present  paper  shows  that  the  underlying  view  of  the  “saving  finances  investment”  doctrine implies that the amount of loans that can be lent in a period is limited by the amount of saving in the same period and that, consequently,an abstention from consumption (and other spending) is necessary for more credit to be available for investors. This view is the basis of loanable funds theory (Robertson, 1936;Ohlin, 1937a,c,b;Tsiang, 1956). It will be argued that this view is deeply flawed. Using simple accounting rules in the vein of Stützel (1978;1979) and Lavoie and Godley(2012), the paper will first clarify the difference between saving and the provision of credit: saving changes an economic unit’s net worth which the provision of credit does not. The provision  of  a  credit  only  changes  either  the  composition  of a unit’s  financial  assets or the length of its balance sheet, but not its net worth. Second, it will be shown that loanable funds theorists commit a fallacy of composition  when  they claim  that household financial saving  increases aggregate investment  in tangible assets.

In recent history Paul Krugman defends the use of loanable funds model in online debates with other economists. The statistical measures in the United States have two components called national income and product accounts (NIPA) and flow of funds accounts (FFA). These debates seem to revolve around what role the interest rate(s) play in the dynamic increase or decrease of production, income, and financial instruments. There does not seem to be any deterministic role for interest rates and the financial accounts are not directly linked to the NIPA accounts because there are accounting methods to re-value assets, to depreciate assets, to recognize casualty losses, and introduce other discontinuities in the financial sectors. In short there is no simple deterministic mechanism to link financial saving and investment in a complex credit-driven economy.


What are some good books and articles about the principal-agent problem?

In my PhD program everyone was using The Theory of Incentives: The Principal-Agent Model by Jean-Jacques Laffont and David Martimort. It offers a formal and relatively complete treatment without being too technical. I haven't read any other book on the topic, so unfortunately I cannot compare.

If you want to avoid any mathematical formalism, a good introductory article and literature review on the topic is Incentives in Principal-Agent Relationships by David E.M. Sappington, in the Journal of Economic Perspectives (1991).

Finally, I would also recommend that you have a look at the Nobel lectures by Hart and Holmström on contractual relationships inside organizations.


It is quite simple. The engels curve is the change in demand for a good as a function of income, keeping prices fixed

Solve the constrained maximisation problem
$$
\max B^{0.67}Z^{0.33}-\lambda(P_bB+P_zZ-Y) \Leftrightarrow \\
B=\frac{0.67Y}{P_b} \\
Z=\frac{0.33Y}{P_z} \\
\lambda = \frac{0.5303709372}{P_z^{33/100}P_b^{67/100}}
$$

Fix prices at some level. I choose 1 for simplicity. Then the engels is simply
$$
Y=\frac{1}{0.67}B \\
Y=\frac{1}{0.33}Z
$$


In what kind of economic environment would the cliche of "keeping money under the mattress" be warranted?

A fractional-reserve bank typically creates a lot of value by lending out your money to people while you are not using it. If you decide to take out your money on any given day, your dollar might not be there, but if not, someone else’s is! The bank will give you their dollar and wait for yours to come back from a loan.

However, during a bank run, many loans are going to default. So your dollar might not make it back, and if you’re not quick, you can’t take out someone else’s dollar cause they already got it back. Therefore your money could disappear.

No one can come into your house and take your dollar out from under your mattress though...


How to compute elasticity of substitution in labor market of blacks and whites using experience-education groups?

I dont want to be rude but the only equation you copied correctly is the
productivity augmented Cobb-Douglas production function.
Equation 2 is equation 2 from Ottaviano, Peri (2008) (on page 8) it says:
$$L=\left(\sum_{e=1}^{n} \theta_{e}L_{e}^{\frac{\delta - 1}{\delta}}\right)^{\frac{\delta}{\delta - 1}}$$.
In the remaining equations $\theta$ is not under the exponent as well:
$$L_{e}=\left(\sum_{\substack{1 \leq e \leq n\\1 \leq x \leq m}} \theta_{ex} L_{ex} ^{\frac{\eta - 1}{\eta}}\right)^{\frac{\eta}{\eta - 1}}$$
Is the equivalent of Ottaviano, Peri (2008) equation 3 on page 9 and
$$\left(\theta_{exb} L_{exb}^{\frac{\sigma - 1}{\sigma}} + \theta_{exw} L_{exw} ^{\frac{\sigma - 1}{\sigma}}\right)^{\frac{\sigma}{\sigma - 1}}
$$
Is the equivalent of Ottaviano, Peri (2008) equation 4 on page 9 and
the expression for the logarithm of the wage is equation 2 on page 11 of Boustan(2008):
$$ln w_{exr}=ln(A^{\frac{1}{\alpha}}k^{\frac{(1-\alpha)}{\alpha}})+\frac{1}{\delta}\cdot ln(L)+ln\theta_{e}-(\frac{1}{\delta}-\frac{1}{\eta})\cdot ln(L_{e})+ln\theta_{ex}-(\frac{1}{\eta}-\frac{1}{\sigma})\cdot ln(L_{ex})+ln\theta_{e_{exr}}-\frac{1}{\sigma}\cdot ln(L_{exr})$$
Whith the correct expressions its all boring algebra:
Fn. 29 on page 11 says:

Following Ottaviano and Peri (2006), I first express output as a function of the capital-output ratio (κ = K/Y)

Thus we have:
$Y=AK^{1-\alpha}L^{\alpha} \Leftrightarrow Y=A\big(\frac{K}{Y}\big)^{1-\alpha}L^{\alpha}Y^{1-\alpha} \Leftrightarrow \\Y^{\alpha}=Ak^{1-\alpha}L^{\alpha}\Leftrightarrow Y=A^{\frac{1}{\alpha}}k^{\frac{1-\alpha}{\alpha}}L$
Observe that:
$$W = x^{\frac{\zeta}{\zeta-1}} \Leftrightarrow \frac{\partial W}{\partial L_{exr}} = \frac{\zeta}{\zeta-1}x^{\frac{1}{\zeta-1}}\frac{\partial x}{\partial L_{exr}} =\frac{\zeta}{\zeta-1}W^{\frac{1}{\zeta}}\frac{\partial x}{\partial L_{exr}} (*)$$
$\omega_{exr} = \frac{\partial Y}{\partial L_{exr}} = A^{\frac{1}{\alpha}}k^{\frac{1-\alpha}{\alpha}}\big(\sum_{e=1}^n\theta_eL_e^{\frac{\delta-1}{\delta}}\big)^{\frac{1}{\delta-1}}\theta_eL_e^{\frac{-1}{\delta}}\frac{\partial L_e}{\partial L_{exr}} \overset{(*)}= A^{\frac{1}{\alpha}}k^{\frac{1-\alpha}{\alpha}}\theta_e\frac{\partial L_e}{\partial L_{exr}}L^{\frac{1}{\delta}}L_e^{\frac{-1}{\delta}}(1)$
$\frac{\partial L_e}{\partial L_{exr}} \overset{(*)}= \theta_{ex}\frac{\partial L_{ex}}{\partial L_{exr}}L_e^{\frac{1}{\eta}}L_{ex}^{\frac{-1}{\eta}} (2)$
$\frac{\partial L_{ex}}{\partial L_{exr}} \overset{(*)}= \theta_{exr}L_{ex}^{\frac{1}{\sigma}}L_{exr}^{\frac{-1}{\sigma}} (3)$
Plug back (2) and (3) into (1), take logs and you will obtain the result.
NOTE I dont quite understand why the derivative of $k = \frac{K}{Y}$ wrt L is not taken here.


Supply and Demand: Why should lower costs lead to a rise in supply?

You can think about this using the basic theory of the firm that we teach in principles courses, such as this one.  The specifics of the graph will change depending on the assumptions of the market it represents (perfect competition, monopoly, etc), but the story should be the same.

In brief, each individual firm makes a production decision so that marginal cost (MC) equals marginal revenue (MR), where "marginal" means the next unit of production.  Keep in mind that a firm is always trying to maximize its profits.  Therefore, if MC > MR (the cost of the next unit of production exceeds the revenue of the next unit of production), it means the firm could increase those profits by producing one unit less.  If MC < MR, then they could increase profits by producing one unit more.  Only when MC = MR can the firm no longer increase its profits by changing the quantity it produces.

If anything happens in the market to lower production costs, it means the firm's old production decision leaves them with MC < MR, and thus they should produce a higher quantity.  Continuing to produce the same quantity would mean they're earning lower total profit than they could be.

Of course there are a lot of simplifying assumptions in this model, which is why it's one taught in principles classes.  But that's the foundation of the idea you're asking about, I think.


What are the consequences of government spending by imposing tax?

Your professor want probably that you compute the keynesian multiplicator (hint: once you have the general formula, replace dT by dG and see what you get).

Intuition: if you raise G, you will raise your GDP. As Y increases, your consumption increases. But the taxes (T, lump sum) increase also, so the consumption decreases (it depends of the disposable income). The overall effect is a 1 to 1 increase of your GDP.


Equation of exchange and inflation target

It is rather other way around. We want to target about $2\%$ inflation and to do so money supply should expand faster than real growth. Also, the $2%$ target is not commonly interpreted as a target that has to be kept all the time.
For example, as explained in this Brookings blog many central bankers advocate targeting the $2\%$ over business cycle. During recessions it might be prudent to have more 'loose' monetary policy and during expansions more 'tight' one.
Furthermore, relationship given by the quantity theory of money (i.e. the equation of exchange) in more complex models depends not just on the actual realization of the variables but also on their expectations (see Krugman et al 1998). An expansion of money supply that is not expected to last might as well never happen.
Lastly, if an economy happens to be at zero lower bound (ZLB) increasing money supply is no longer helpful in targeting inflation (at least not increasing money supply by usual interest rate targeting). This is because at ZLB peoples preference to hold cash becomes so strong that any increase in money supply will be just offset by drop in velocity as people will just hold on the money (see again Krugman et al 1998).
Thus to sum up, while in order to target $2\%$ inflation often central banks try to expand money supply faster than the real growth, it is not always possible to do so nor it is always desirable to expand money supply so fast across business cycle.


Why is the money supply perfectly inelastic?

The Fed controls the nominal money supply as they are the only ones who can add or remove money from the economy by printing it. Real money supply is only affected by increases or decreases in inflation and is fixed assuming inflation is 0. In the IS-LM model which is what I assume you are referring to it is assumed that inflation is fixed or that the fed will maintain the real money supply at a given point by changing the nominal money supply for given price levels.

Graphically money supply can be shown like so:

The equilibrium between money supply (which is set by the fed) and money demand (which is set by economic factors) generates the interest rate for the economy at a given time. The fed thus has power to affect the interest rate by increase or decrease the real money supply in order to maintain an interest rate. Given that the fed has complete control over the interest rate under this model it is often assumed that LM is horizontal due to the fact that the fed can set whatever rate they choose regardless of economic factors.


GDP versus GNP. Which is a better gauge of a country's economy size and prosperity?

I think the safest answer is “it depends.”

Firstly, the terms “stronger economy” or “enjoy prosperity” are subjective, so I think if you want a stronger answer, you would need to tighten that part of the question up, with more concrete phrasing.

Secondly, we would need to pin down the reasons why GDP and GNP diverge.

Ireland is a well-known example, where GDP is much larger than GNP. This is usually ascribed to multinational corporations funnelling revenue through Ireland to take advantage of low corporate tax rates. In this case, GNP is viewed as being more representative of the state of the Irish economy, since those corporate revenues have very little to do with the Irish economy.

I am unaware of examples where GNP is much larger than GDP, but I believe that it would be easy to create theoretical examples where GNP is telling us very little about domestic economic conditions. (A country with large ownership of foreign assets, where production and income is almost entirely the result of the economic conditions facing those foreign subsidiaries.)

In other words, you need to know exactly what question you want to answer, and see whether GDP or GNP is closer to what answer you need.


Given the supply and demand function what is the difference?

Deriving those functions, you can find $p^*$ and $Q^*$, which, multiplying both, should give you equilibrium profits. Now, if you take that tax rate (20%, I reckon?), you can calculate taxes over profits and the tax-free price.

To find the equilibrium price $p^*$, you need to have those two functions in a system and solve for $p$. Then, just replace it on both functions and you should have equilibrium quantities.

Now, I'm assuming demand absorves all quantities produced by companies, no production restrictions and that this market is one in perfect competition. If this last paragraph changes, then my solution will not be correct.
To answer your question - what is the difference -, well, in this case, it is none because we are not considering production costs. If we did, you can see that both values would change.

Nevertheless, to calculate taxes, you need to work around with the system. That will give you total revenues, cost and tax free. Applying 20% leads to net earnings, because you do not have any production costs associated with the problem - something commonly done in Economics. That or consider a variable $c$ of costs.

This kind of exercises are also good to understand what are the effects of  costs on revenues/profits. There's actually a financial term for that but I cannot recall :)


Measurement for the downstream use of a commodity

If you are looking for certain commodity data from the US.  The USDA Economic Research Service has data on market size of certain commodities.  But I am not sure about firm level data.

https://www.ers.usda.gov/data-products/commodity-costs-and-returns/

There measures include cost and return estimates are reported for the United States and major production regions for corn, soybeans, wheat, cotton, grain sorghum, rice, peanuts, oats, barley, milk, hogs, and cow-calf. The series of commodity cost and return estimates for the U.S. and regions is divided into two categories: Recent and Historical estimates.

I am not sure if this is exactly what you are looking for but this is a good start.  One can also call their office for additional information.


Need help identifying this cognitive bias or fallacy pointed out by Kahneman in Thinking Fast and Slow

When this event occurs it is known as a failure of "transitivity" of preferences.

Transitive preferences are such that for every  X,Y,Z, if X is preferred to Y and Y is preferred to Z then X must be preferred to Z.

Economists define rational preferences as binary relations that are complete and transitive, meaning that we can compare everything and the comparisons are consistent.


Congruence of GDP as calculated by production and by consumption

The GDP expenditure approach is the sum of consumption, private investment, government spending, and the difference between exports and imports. I have not dug into the German Statistisches Bundesamt but unsold goods should be accounted for in the expenditure approach under "change in private inventories" or "inventory investment" (grouped with private investment).


Why is JPY considered a "safe currency"?

Because:

they are a massive exporter, meaning their capital account is negative, and thus they own a lot of assets abroad. Therefore, as this site explains:

When a crisis erupts, the Japanese repatriate that money – they bring it back home. In that process, they’re selling assets in other currencies to buy yen. And at that point it’s a supply/demand issue. The supply of others currencies is rising as the Japanese pull out (those currencies fall in value) and demand for yen rises as the Japanese bring their money back home (the yen rises in value).

they have had and are likely to continue to have among the lowest interest rate in the world (-0.1% now). Therefore, as this site explains:

In what’s known as a carry trade, investors will borrow money in a low-interest rate environment and then invest that money in higher yielding assets from other countries. Japan’s long-standing policy of near-zero interest rates has caused it to become a major source of capital for these types of trades.
When uncertainty subsequently hits global markets, it can cause investors to unwind these trades, which then results in additional demand for the yen.

hoard behaviour + path dependence in financial markets. As the site above explains:

Part of the reason the yen continues to act as a safe-haven currency is simply because everyone acknowledges that it is. Investors around the world have come to embrace the yen as a reliable place to go for safety, and by attempting to take advantage of this, they actually create the intended effect.
If you know that whenever the world panics, the yen is going to rise, then it makes it a no-brainer to buy the yen even if you’re unsure exactly why everyone else is.

Some differ though. An IMF study concedes that:

Safe haven currencies tend to have low interest rates, a strong net foreign asset position, and deep and liquid financial markets. Japan meets all these criteria.

But they find that:

Surprisingly and in contrast to the experience of the Swiss Franc, yen risk-off appreciations appears unrelated to capital inflows (cross-border transactions) [large foreign asset ownership] and do not seem supported by expectations about the relative stance of monetary policies [low interest rate].

They state:

The third possibility is that risk-off appreciations of the yen come about because of portfolio rebalancing transactions that are not fully captured by BoP statistics, such as derivative transactions. For example, when risk perceptions change, exporters or overseas affiliates of Japanese companies may decide to lock in the exchange rate through hedging, or given Japan’s sizeable net foreign asset position, holders of foreign securities may take a long yen position. As such, these derivative transactions may not just reflect short-term speculative behavior, but may just reflect prudent risk management. We find support for this conjecture as risk-off episodes are associated with increases in net non-commercial exposures to the yen in the derivatives market.


Book recommendations on empirical methods in economic research and econometrics?

Firstly, for basic introductory econometrics, the following is quite good:

  "Introduction to Econometrics" by Stock and Watson.

It is light on technical details, and heavy on intuition. This might not appeal to you if you are a math major, but it's the most important thing to get straight if you are interested in applying the empirical methods rather than developing new econometric methods.

Stock and Watson is very basic, so you will probably want to supplement it. Good choices are likely to be

  "Mostly Harmless Econometrics" by Angrist and Pischke

(this is another book that puts intuition first, but now with more formal detail), and for an advanced graduate treatment

  "Econometric Analysis of Cross Section and Panel Data" by Wooldridge.

I don't know Wooldridge very well, but I know that his book is popular and well-loved among econometrics grad students.

These books have a bias in favour of microeconometrics and deal less, if at all, with time series methods. More comprehensive coverage can be found in

  "Econometrics" by Hayashi

or

  "Econometric Analysis" by Greene.

The book by Hayashi is probably better for self-study; Greene is more of a comprehensive reference book.


Is there an economically sound way to decide between buying media or a streaming subscription?

Partly your question relates to more general questions like "buy versus rent a house", or "buy versus lease a machine". Under neoclassical assumptions of  competition, full information, etc, you can imagine that arbitrage would make these options equivalent for the average of the population (or the representative agent). In practice, heterogeneous individuals might prefer one option than the other.
Having said this, I think the study that is more pertinent for your example is "The economics of subscriptions", by Glazer and Hassin (1982). They evaluate whether it is welfare enhancing for a service provider (in their case, a publisher issuing a monthly magazine), to offer both subscriptions and individual sale of issues, rather than one of them alone. Adapting their terminology and notation to the case of music, define:

$\bar p $: average value to a consumer of an album. Might vary among consumers.
$m$: number of albums available with subscription per year.
$t$: price of each album by itself (assume identical). This might include the transaction cost of buying the albums.
$c$: cost of subscription. (Assume no re-selling is allowed, an important disclaimer!).

Subscription
In this setting, the expected value of a consumer's surplus obtained by purchasing a subscription is
$$ m\bar p -c $$
Individual purchases
Here, we assume that you can choose your favorite albums. Hence, for a given population of albums, you will choose the $n$ that give you the most surplus (your favorite artists). For simplicity, I assume you do you know the universe of albums (To add more complexity, you could instead assume you know a section of it, and hence a subscription could surprise you. I leave this example to you.)
The surplus from buying the best $n$ albums (subset denoted $\Theta$) is
$$  \sum_{i \in \Theta} (\hat p + \epsilon_i - t) $$
where $\epsilon_i$ is the value above $\bar p$ of the $i$-th album you choose to buy. The above is equal to:
$$ n(\hat p - t) + \sum_{i \in \Theta}\epsilon_i $$
Hence, the valuation hinges on this comparison:
$$ m\bar p -c \text{  vs } n(\hat p - t) + \sum_{i \in \Theta}\epsilon_i  $$
Analysis
Since you chose the best albums, $\sum_{i \in \Theta}\epsilon_i  $ is large. However, these albums are also included in the subscription. Hence, define the non-negative function $X$ as the combined value of all the albums in the subscription that you would not buy outside of it. This is:
$$ X = (m - n)\bar p - \sum_{i \in \Theta}\epsilon_i $$
Notice that $\lim_{n \rightarrow m} X = 0$.
The comparison is now:
$$ X \text{ vs } c - nt $$
Thus, you prefer the subscription when:

the number of albums available under subscription is high
the albums you would not buy are very valuable
the cost of subscription is low
the cost of individual albums is high
the value of your best albums is low (if some $\epsilon <0$, then such album is below average)
the effect of $n$ depends on the value distribution (the distribution of $\epsilon$). Clearly, at some point you are buying bad albums for the same price, so you rather buy the subscription.
notice that if you do not know all the albums, then there is a stronger case for a subscription as you might discover some very good albums which value might even be higher than those you would buy otherwise. Here, a modelling of such distribution becomes crucial.
the above does not include a risk-loving valuation from risk (i.e. discovering good music!). Such consumer would then more likely favour subscription.


Data Request: Raw housing stock of particular city

There really isn't high-frequency data out there for free, but bi-annual data are available from the Census American Housing Survey. The survey goes back to 1973, though data at the metropolitan area level don't go back that far. Also, the data are extrapolated from a sample, so caveats apply.


Open market purchase of securities and it's effect on balancesheet

When the central bank buys anything, it transfers a deposit (reserves) to the reserves account of the bank of the seller. (The seller could be the bank itself, or a customer of the bank.) This keeps everyone’s balance sheet in balance.

Until the central bank does something to destroy reserves (e.g. sell something), all the bank can do is transfer the reserves to other banks. That is, the reserve increase is “permanent,” even if the initial bank gets rid of them.


Let's consider a simpler example.

You have 10 apples. With that, you can eat $x$ apples and "invest" in the rest $10-x$ apples, plant them, and each would yield two apples tomorrow. Let's say that with some optimization, you decided to eat 4 apples, saving the other 6 apples so that you could have 12 apples tomorrow. GDP would grow by 2.

Is this a result of "interest rate"? No. There's not even a bank here.

Now imagine that there is a bank that ask you to deposit your apples there for a day. What would you demand in return? 2 apples tomorrow for every apple you save today. That's the interest rate. The assumption is that the borrower can do something at least as productive with the money he/she borrowed, and the apples would go to those who can most efficiently use them.


Did (or can) quantitative easing cause an "everything bubble"?

It’s an editorial opinion, and it’s hard to give it a technical meaning.

The distinction being made in the text is between growth in the “real economy” - which would be measured by GDP and/or consumer price inflation - and growth in asset values. For example, there could be no direct job creation because of QE, just equity prices going up.

However, this is an opinion/claim that is hard to evaluate. One argument is that QE would first lower term interest rates (by reducing the stock of debt outstanding and/or signalling that the policy rate would be lower for longer), and this should raise other asset values by decreasing discount rates. (Please note that how QE affected interest rates was the subject of some theoretical controversy; I believe that other questions here discuss this. I am summarising one standard interpretation.)

The idea is that there is a link between rising asset prices and economic activity (known as the wealth effect). Since we do not know how many jobs would have been created in the absence of QE, we cannot be sure how large this effect is.


Distance transported used to price goods in Marxism

Quantities of products are not increased by transportation. Nor, with
  a few exceptions, is the possible alteration of their natural
  qualities, brought about by transportation, an intentional useful
  effect; it is rather an unavoidable evil. But the use-value of things
  is materialised only in their consumption, and their consumption may
  necessitate a change of location of these things, hence may require an
  additional process of production, in the transport industry. The
  productive capital invested in this industry imparts value to the
  transported products, partly by transferring value from the means of
  transportation, partly by adding value through the labour performed in
  transport. This last-named increment of value consists, as it does in
  all capitalist production, of a replacement of wages and of
  surplus-value.

Source: Capital Volume II, Chapter 6: The Costs of Circulation,
I. Genuine Costs of Circulation, III. Costs of Transportation

My understanding of Marx's argument is the following: Transportation does not alter the quantity/quality of products significantly. But, products need to have a use-value in order to also have an exchange value. Thus, an orange for example produced in Spain has an exchange value in UK, only if it arrives in UK, so that it can be bought and consumed. So, transportation adds value to the products, and this is done (as with all products) partly from the labor value (transportation workers) and partly from the means of production (means of transportation: airplanes, ships, cars, trucks...).

Since transportation adds value to the product, and since price is a mirror of value according to Marx, then we can say that transportation tends to increase the price of the product (which is a logical assumption on average).

Regarding distance, I am not sure if that is explicitly mentioned, but again we can deduce from the previous that: bigger distance --> more transportation needed (given constant technological advancement in a period) --> more transportation labor needed + more transportation means of production --> more added value --> tendency for bigger price.


Approximation to a second order partial derivative

I think that this question would be more suitable for math.SE, since it is purely mathematical and not specific to economics.

In your notation, the first derivative would be given by
$$
\partial_A v_i = \frac{v_{i+1} - v_i}{\Delta}.
$$
In order to compute the second derivative, we need to apply this formula with $\partial_A v_i$ itself in place of $v$. This gives
$$
\partial_{AA} v_i = \frac{ \frac{v_{i+2} - v_{i+1}}{\Delta} - \frac{v_{i+1} - v_i}{\Delta}}{\Delta}.
$$
A bit of algebra reveals that this is the same as
$$
\partial_{AA} v_i = \frac{v_{i+2} - 2v_{i+1} + v_i}{\Delta^2}.
$$
Now if your grid is fine enough, you can lower the index $i$ on the right-hand side without changing the result significantly. This gives the equation that you came across. It is generally preferred due to the "symmetry" that it displays between $i-1$ and $i+1$.

For more on this topic, see e.g. Wikipedia at finite difference.


A paper published in 2009 by the Federal Reserve Board gave a brief description

  The BLS surveys about 85,000 items a month in its Commodities and Services Survey. Individual prices are collected at around 20,000 retail outlets across 45 large urban areas. The survey covers all goods and services other than shelter, or about 70 percent of the CPI based on BLS consumer expenditure weights. The CPI Research Database (hereafter CPI-RDB) maintained by the BLS Division of Price and Index Number Research contains all prices in the Commodities and Services Survey since January 1988. We use the CPI-RDB through May 2008, for a sample of "1988-2008".

  The BLS collects consumer prices monthly for food and fuel items in all areas. The BLS also collects prices monthly for all items in the three largest metropolitan areas (New York, Los Angeles, and Chicago). The BLS collects prices for items in other categories and other urban areas only bimonthly.

Details may have changed since then but essentially the database is an detailed dataset of prices for a wide range of selected items charged by a large sample of individual retailers at different points in time

It is not available to the public.  In particular, it contains commercially sensitive information about individual retailers

It is available to some academic researchers who reach an agreement with the Bureau of Labor Statistics putting restrictions on how they handle and how they use the database and on the locations where they access the data; BLS also charges a fee.  BLS provides details on Restricted Data Access on its website


How Does Keynesian Theory Address Supply Shocks, Like the California Drought?

In what follows, I'm going to be very hand wavy - take with a grain of salt.

If you think about it, a demand shock is like a scenario of multiple equilibria (given the fixed levels of wages and prices):

If everyone is employed, everyone has a lot of income, can spend that on goods, and the demand for goods implies a large demand for labor, making everyone employed
If few people are employed, total spending is smaller, so is demand for goods and labor, corresponding to only fewer people employed

The Keynesian solution can be thought of as forcing the first case to happen rather than the second.

If you really have a supply shock, that is, lack of a factor important to production, there is no indeterminacy here. There just isn't that much (oil) available, increasing its price. The RBC spokesperson of your favor would say

  The high price stems from scarcity; both the high price, the low production and high unemployment are efficient.

In the standard problem, rigidity of wages and prices create inefficiency, they can be dealt with. Here, there is no such inefficiency, and no inherent solution to a supply side shock.


Countries don't wage war, Governments do.
GDP is the economic production of a country, which is usually much larger than what the government has as available annual income. Historically government expenditure in the US has amounted to ~20% of GDP since 1940 (and was lower than that previously). (Source)

In general, if a government needs to spend more on a war effort, it has three options: print money, which is going to inflate the money supply and might work for a very short time period but will backfire quickly, raise taxation (which may not be possible once taxes get to a certain point, and the US did do this over the course of WWII) but once you reach a certain point, taxation will slow your production down, at that point you'd have to seize assets from the private sector (which obviously wouldn't go down well in the US). Lastly, the government could go into debt.

To answer the second part of your question, since we know that the US was spending 38% of GDP but was only raising 18% of GDP in taxes (and if you look at the graph it's probably safe to say that it was raising an average of 12-15% over the course of the war) that means there's somewhere in the ballpark of 26-20% of GDP worth of money that has to come from somewhere. Since printing more money isn't going to work, realistically the US government would have had to triple taxes from 1930 levels to pay for the war without going into debt, or it would have had to drop the size of it's military by two-thirds, or some combination thereof, say double taxes and half the size of it's military.
This also leads to some problems: if we had to half the size of the US military, would the allies have been able to win the war? Keeping a balanced budget as a priority over that of winning the war doesn't seem like a wise course of action.

Any increase in taxes would also have a dampening effect on the economy itself, (and would also indirectly increase the costs of some of the purchases that the U.S. government would be making), so while the government might get more revenue this way it might end up with a less cost-effective military.

If the government wanted to avoid that, it could just seize assets from the private sector-- if it just stole from multimillionaires, the rail and coal tycoons etc. it probably would be able to finance the expansion without too many short-term effects, but I doubt it would ever have been a politically viable option. Also, arbitrary seizure of private property is generally a bad thing if you want an economy to run well.

So all of this kind of argues for taking on debt.

Of the three choices going into debt is more palatable for most people. It has the advantage of taking wealth from citizens NOW with the promise of them getting money later, when the government desperately needs money now (to win the war) and couldn't care less about how it will pay the citizens back later.


It might not get you very far, but a start would be Google Trends:


Inflation vs GDP growth as factors driving down the US debt-to-GDP ration post-WW2

Look at the implicit price deflator for GDP. Using the annual series, 1946=11.05, 1956=15.32, so 38.6% increase. (Source: FRED database)

I don’t have time to look at the paper, but that’s possibly what was meant. Not an entirely convincing methodology, but you would have to do something with the deflator as well as nominal GDP to allocate changes.


hint:

Solve for optimal $x^*,y^*$ then substitute the solutions into budget constraint and then solve the budget constraint for $x^*,y^*$ respectively and you will get the demands as a function of the parameters and of course conditional on the optimal consumption of the other variable.

Knowing that we have an interior solution helps because that means we know demand(s) is(are) not zero.


No, all would be the same. Except that its will monetize the android and iOS networks to make money that way.

Like youtube's model, this is how iTunes might operate


What are 'Symmetric Agents' vs. 'Asymmetric Agents'?

“Symmetric agents” generally means that all the agents have the same payoff function and the same information set. In this case, it’s the function you’ve specified. It’s often the case that, because symmetric agents will all respond the same way, they can be replaced with a single representative agent, in contrast to heterogenous agent models.


What causes the "imperialism of economics" and how did it start?

I find the following quotes to be interesting:

  "[Political economy is] a branch of the science of a statesman or legislator [with the objective to provide] a plentiful revenue or subsistence for the people [and] to supply the state or commonwealth with a revenue for the publick services."—Adam Smith, 1776.

  "Economics is a study of man in the ordinary business of life. It enquires how he gets his income and how he uses it. Thus, it is on the one side, the study of wealth and on the other and more important side, a part of the study of man." —Alfred Marshall, 1890.

  "Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses" —Lionel Robbins, 1932.

Together, I think these quotes nicely illustrate the way that economists' perceptions of their own discipline evolved over time. By the 1930s, we have Robbins' startlingly insightful observation that Economics is about choice subject to constraints, which is obviously a very general kind of problem. But even as early as the late 19th century you can already see traces of this kind of thinking in Marshall's words.

This way of thinking about economics is, I think, key to emboldening economists to reach out beyond the confines of market behavior. Indeed, I think one reason why economics has been so imperialistic is that economics is as much a methodology as a body of knowledge. As such, economists have constantly looked for new problems and settings to which they can apply the tools they know.

More recent contributions that have been important are probably:

The work of Gary Becker, whose Nobel citation reads "for having extended the domain of microeconomic analysis to a wide range of human behaviour and interaction, including non-market behavior" Those non-market behaviors include important things such as fertility, marriage, and crime—not traditionally within the domain of economics.
The development of game theory and information economics. These tools equipped people with new ways of modelling social environments. A classical supply/demand type model, or a general equilibrium framework will get you quite far when studying traditional markets, but these tools are much less suitable for studying non-market behaviors that are the preserve of economic imperialism. New modelling frameworks brought about by game theory, the principal-agent model, etc. really opened the way for studying all kinds of new environments.
The Downs model, which was an early application of economic-style (specifically, Hoteling's linear city) modelling to political science—one of the most thoroughly 'colonized' disciplines.


Hint:

These exercises seem to be encouraging you to think about the First Welfare Theorem, and whether it will hold. Recall the theorem which states that if markets are competitive (price takers), markets are complete (full information), and that consumers are locally non-satiated, then every competitive equilibrium should be Pareto optimal.

For each sub-question, there is at least one agent whose preferences are not locally non-satiated. For part (b), you are correct that there will be no trade. That is, you are at a competitive equilibrium. You should discuss if the allocation is Pareto optimal. If the allocation is PO, prove it, and if not, show a counterexample.

For part (c), you do not need to know the utility functions of each agent to do this question. Since we only care about utility up to a monotonic transformation, you can in theory make up a utility function that fits agent A's description. In this case, all three drinks are perfect substitutes, so you can express agent A's utility as

$$u_A(m, j, w) = m + j +w$$

Or any monotonic transformation of that. But this is not necessary. You can solve (c) with just the definition of a Pareto optimal allocation and some intuition. Hope this helps.