How does the notion of utility differ from that of value?

This turns out to be a surprisingly complicated issue. On one hand

  ‘value depends entirely upon utility’ (Jevons, 1970, pp. 139 and 77, respectively). [...]

  For the marginalists of the first generation, a marginal utility curve incorporated the relation between a commodity and human wants; total utility was a derived concept and corresponded geometrically to the area beneath the curve (the integral, in mathematical terms).

  Gradually, it became more natural to consider utility, right from the beginning, as a a property of consumption bundle, rather than individual consumption goods. An important step in this direction was made by Edgeworth (1881). [...] Utility of a consumption basket, rather than marginal utility of individual goods, thus became the ‘primary’ concept.

On the other hand the more commonly used notion (nowadays) of von Neumann-Morgenstern (cardinal) utility isn't the same thing as the neoclassical one, but is close enough:

  What is controversial is whether the utility function derived by the N-M method can
  be taken to reflect the true subjective utility of the individual in the sense of the
  neoclassical economists such as Edgeworth. A firm negative answer has been given:

    "what relationship, if any, does the N-M cardinal utility theory have to that of the
    neoclassical utility theorists? It is generally (though not universally) agreed that
    there is none - the two utility measures have nothing in common insofar as their
    cardinality is concerned" (Baumol 1977, p. 431; see also Banmol 1951, 1958).

  [...]

  Baumol is right, at least formally. The N-M hypothesis does not show that the
  utility function derived, though predictive of the objective choice of the individual,
  actually reflects his subjective utility in the sense of the neoclassical. On the other hand,
  most practising economists are also right, at least effectively, in accepting the N-M
  utility indices as subjective. This is so since, as is shown below, using the same set of
  axioms as the N-M hypothesis, with only the recognition of finite sensibility (that
  human beings are not infinitely sensitive or perfectly discriminative), it can be shown
  that the utility function derived from the N-M method is in fact a subjective utility
  function in the sense of Edgeworth.

Also, the step (back) from cardinal to ordinal utility is due to Pareto

  Pareto inverted, so to speak, Edgeworth’s problem: rather than deriving the indifference curves from a prior knowledge of a utility function, he did it the other way round – his ‘primary’ concept was a series of indifference curves (later to be called ‘preference ordering’) and from them an analytical description of utility (ofelimità, in his terminology) was derived. What mattered now was the index of the indifference curves, a higher index corresponding to a higher utility.

  He (correctly) remarked that a surface having I as ordinate was not univocally determined: in so doing he discovered what came to be known as ‘ordinal utility’: a result that first-generation marginalists would perhaps have much appreciated!


Repositories for working papers in economics and finance

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


What exactly is the difference between the PPP ("purchasing power parity") and LOOP ("law of one price")?

PPP uses the price level, the price of the consumer basket. The price level can be identical without all prices being identical. An example:

Consider a consumer basket with just two goods and assume the weight of both goods in the basket is one half. If $p_1 = p_2 = 4$ then the price of the consumer basket is
$$
P = \frac{1}{2} \cdot p_1 + \frac{1}{2} \cdot p_2 = 4.
$$
However you get the same price level if you have $p_1 = 3,  p_2 = 5$.

So you can have two countries with identical price levels but differing prices. The converse of course is not possible. Thus LOOP implies PPP but PPP does not imply LOOP.


How does any government "create" the currency in the first place?
Do the central banks just print some notes and offer it as a service? Say, Use our notes as an exchange medium

Currency in economics is just the notes and coins in circulation. These are minted and printed by government. In every country the institutional arrangement will be bit different. In some places central banks do the printing/minting of the currency in some others its done by mints or treasury departments. In US the printing of paper money is done by The Bureau of Engraving and Printing (BEP) and minting is done by the US Mint (see explainer in Investopedia). These agencies are nominally under the treasury department but in practice they create new currency when Fed orders it.
If you are interested in money more general not just currency (i.e. notes and coins) then in general money is created by Fed with help of private banks. The money is created whenever bank makes a loan as whenever a loan is issued a matching deposit is created with the money in it. This is done for a most part all electronically. The amount of loans private banks can issue depends on monetary policy of Fed, its regulations and how much reserves/base money it creates (if you are interesting in reading more on this you can have look at this BoE paper McLeay,  Radia, and Thomas; 2014). Money is also created when Fed directly purchases some assets, for example when Fed purchases treasuries it is done with newly created money.
It is not enough to just say: "Use our notes as an exchange medium" in fact there are many examples of countries where people decided simply not to use official government issued money but decided to switch to some other money (this is known as currency substitution). For example, in Zimbabwe people substituted their local currency for dollar (such currency substitution is called dollarization) and in fact between years 2009-2015 even government of Zimbabwe decided to give up and declare dollar official legal tender.
In order for money to be used there must be some demand for it. The demand for money can be created by government requiring that all taxes be payed with its issued currency. Furthermore, in order for people to keep using the issued money they must also be able to perform the function of money reasonably well (i.e. be medium of exchange, unit of account and store of value). In Zimbabwe the problem was that due to hyperinflation money completely lost its store of value function and hence people decided to use dollar - but that's just one example.

Or, is it something like we own the land and other assets, we put it at a value of some X amount

Not anymore. Modern fiat money are not backed by anything of intrinsic value. In the past under gold standard money was backed by gold and ever further in past money was literary some commodity (it could be gold or other precious metals, but also shells, stones, coca, cigarettes, livestock etc.). In such systems money derived their value also from the intrinsic value of the asset (or more precisely commodity).
If you want to know about history of money then a good non-technical account is provided by Ferguson in Ascent of Money and more technical account can be found in Davies (2010). History of money.


How exactly does a stock price gap overnight?

A stock price is the price where two entities are willing to transact. The prices are often affected by new information. If a company has a major announcement to make during the day, trading is often halted, and then the price can be radically different after trading resumes, since investors may have revised their valuations.


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

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

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

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


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

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

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

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


Leontief Tableau Économique (produit net)

In this transaction table, farmers produce 5 as a producing industry and consumes 2 (out of 5) as a purchasing industry. This means that they retain 2 as food for themselves and sell the remaining.

A hint: The physiocratic "net product" is equivalent to agricultural rent payment.


What is the relationship between economic growth and equality?

More often than not economic growth will increase wealth and income inequality. This is because wealth is not uniformly distributed across the population, with a small percentage controlling a large share of the worlds wealth.
This small percentage of people tend to hold wealth in income-generating assets such as shares in top companies. This means that when the economy is during well and experience high economic growth, companies will be making a lot of profit. This profit is then paid out to their shareholders. This can increase inequality.
However, it's possible for government policies to break the link between economic growth and rising inequality. One way governments do this is with progressive taxes, where people with a higher income also face a higher tax rate. Another policy is inheritance tax rich limits the ability of rich parents passing on their wealth onto their children


Doubt in understanding the advantages of Fixed Exchange Rate

Basically, if you are the government, its a way that you are telling everybody that they should believe your commitment to low inflation. They should believe you, because you'll hurt yourself a lot if you allow inflation.

More generally, economists sometimes talk about agent's ability to commit to a policy: say, governments might promise something, but its hard for investors to believe that they'll follow through. SO one way to solve this problem is that the government builds creates an institution, where breaking the promises hurts a lot.

The classical reference is Odysseus getting his crew to tie him to a mast so he would not throw himself at the sirens in the sea.  He is in effect choosing to bind his future self, curtailing his own freedom. The value of this is that it gives him freedom to do other things (travel along the siren infested waters and listen to their song).

A fixed exchange rate can serve such a purpose: The idea is that a country fixes the exchange rate. This fixed rate makes it very obvious and very costly to behave badly, say by printing money or increasing government borrowing. The fixed rate constrains the government from bad behaviour.

Of course, this decision is not free. In the case that you set a fixed rate and then you end up behaving badly, then the result is worse than if you had never fixed the exchange rate in the first place. (Imagine Odysseus drowning if he is tied and the boat sinks and he is unable to swim away.)


A sunspot is just a publicly observed random variable upon which players can condition their actions (formally it's part of the history of the game).

It's helpful because it is a nice easy way to convexify the set of equilibrium payoff vectors. In many papers (in my experience) it is a convenient assumption that simplifies things, yet may not be necessary--that is the effect of sunspots can be accomplished without their use, it's just more of a hassle.


as you see that is a Cobb Douglas function(Monotonous transformation), I will assume you already know how to get the X* and Y* Marshallian . "w" is the wealth of the consumer. In case you dont know how to get the marshallians you have to maximize the utility ( "U = log(x) + log (y)") subject to the constrain budget (w = Xpx+Ypy)

$ X(*) = w/2px $

$ Y(*) = w/2py $

So let's start with the income elasticity, we want to know how the consumption of X will change when the income//price of x (own-price) //   (cross price )price of y changes, but we want it in terms of percentage/relative ( that's why we want elasticities ) .

So the income elasticity is :

$(\frac{\partial X}{\partial w})*(\frac{w}{X}) =(\frac{1}{2px} )(\frac{w}{\frac{w}{2px}})\ = 1 $

cross price elasticity:

$(\frac{\partial X}{\partial py})*(\frac{py}{X}) =(0)(\frac{py}{\frac{w}{2px}}) = 0 $

own price elasticity :

$ (\frac{\partial X}{\partial px})*(\frac{px}{X}) =(\frac{-w}{2px^{2}} )(\frac{px}{\frac{w}{2px}}) = -1 $

I will let you search what means that numbers! :D

Hope this helps you!


Why would creditors accept a comfort letter that can't be legally enforced, from borrowers that refuses to guarantee?

It's not as much a matter of reputation as much as it is a question of signaling. not paying one of your debts could signal to other suppliers that you are NOT ABLE to pay which will prompt them to stop any on-going deliveries and require much stricter payables conditions. These kind of things happen more often in companies facing difficulties. The apparent (real or fake) inability to pay could materialize into a number of headaches with other counter-parties and render you unable to follow up with any business if you just used this "excuse" to gain more time. There is an example where we recently saw this with TESLA in their relationship with Panasonic, turned out they just wanted to delay payments as much as possible but it raised a number of questions on their cash flow situation and ended up causing a lot of volatility (albeit temporary) in their listed liabilities (equities and bonds).


Is there a general name for the setup in which payoffs are not known exactly but players try to influence each other's perception of the payoffs?

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

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


Existence of pure strategy Nash equilibrium

The most simple example is the example of unlimited periods and Bertrand pricing, in any given period the "pure strategy" (with 2 firms) is to produce 1/2 of monopolist quantity and sell at monopolist price and recieve profits = π(1-d)^t
Where d is discount value
t is period
Any deviation will result in 0 profits every period following the deviation, thus in an infinite period model is not worth it.


eBay economics - total revenue impact from expanding ecosystem by 1 seller

eBay seems to think that additional sellers increase its profit (not just revenue), because it advertises the option to sell on its website and tries to recruit more sellers. That's the empirical answer.

Theoretically, eBay could refuse to list the additional seller's product and not charge the seller any fees, so by revealed preference, eBay cannot be worse off with an additional seller. If eBay was forced to list every seller who comes along, then the revealed preference reasoning would fail, so then eBay may or may not be better off with an extra seller.


Why the GDP does not decrease even when we are saving from our income?

"GDP" stands for "Gross Domestic Product". It measures the income generated, prior to any consumption-saving allocation. In other words, to be able to save you must first generate product/income and then decide to save. So savings does not affect the level of the already created income, since it is a part of it. The archetypal closed economy with no borrowing is characteriazed by the identity

$$Y = GDP = C + I = C + S$$

When we look the matter from an expenditure approach, we essentially consider the different uses of income (and in that sense the use of the term "expenditure" may be a bit misleading). And savings is also a way to use your income (where "use" has a broader meanign than "spend").


Flat Term Structure and Immunized Portfolio Strategy

Note: This answer is preliminary, as I am unsure about some components of the question. I will note that it is a very long time since I studied portfolio immunization, and so I am describing how this would be looked at in the industry.

The simplest strategy for immunization in this case is to purchase five zero coupon bonds, each with a principal value of \$500,000. This means that your portfolio generates cash flows that exactly match the liability.

(That part of the question is unclear to me. One could attempt to duration match the liability, which would make the answer more complicated.)

The price for \$1 for the i-th zero coupon is: $\frac{1}{(1.02)^i}$, (the zero coupon price formula, using a simple interest rate convention).

The cost for the immunization is the sum of the five costs.

The market value weight of each bond is its market value divided by the sum.


Does the Samuelson condition assume all the prices for the private goods are the same?

I thought it might be helpful to discuss the LS condition in general as it pertains to the LS equilibrium:

A Lind./Sam. equilibrium allows for a unique equilibrium price $q_i, \forall i \in {1,...,n} \equiv N$, the set of agents, for the public good. The clearing condition for the public good price vector, given by $\sum MRS=MRTS$  (as stated in another answer here) is an aggregate condition. Individuals value public goods differently, which is reflected by vector $q$.

To make it a bit more intuitive: If it were necessary that each individual contribute equally to a public good, then our idiosyncratic valuations would prevent some (or maybe many) of us from contributing to a public goods project (because the fixed contribution exceeds our individual, unique valuation for that public goods project). This could cause us to scrap projects that are actually socially desirable. And in easily conceivable circumstances, it can cause us to scrap projects that would be beneficial to every person in our society.

The price vector $q$ does not necessarily comprise distinct prices. However, the question is can it? The answer to that question is, clearly, yes.


Does consumption decrease directly lead to a shift in Aggregate Demand curve to the left?

You mention here a crucial point that falls nowadays more and more in oblivion, that is the well-known aggregation issue across consumers. The described behavior of the individual and aggregate demand curve can only be expected to be observed when the essential properties of the individual demand functions can be bequeathed to the aggregated demand function. For this case one needs a particular type of utility function, it must be of Gorman form, that is, the utility functions of consumers must be quasi-linear, or to put it differently, they must be linear in the numeraire good to get an aggregate demand function that inherits their properties from the individual demand functions (cf. Varian Microeconomic Analysis 1992, third edition, pp.152-154).


How the presence of increasing returns to scale lead to market failure

Perfect competition in the economy leads to the theoretical presumption that with firms entering the market when prices are above their average total costs and leaving when they are below average total costs, the equilibrium point comes when prices are equal to average total costs, which in turn is equal to each continuing firm's marginal cost at a point where these marginal costs are increasing.  For each firm, their marginal revenue will be equal to the price set by the market. Consumers will see no firm whose marginal cost is below the market price, and so should regard the result as efficient.

With increasing returns to scale, marginal costs are never increasing for an individual firm.  The effect is to encourage the emergence of a single firm taking the entire market and having pricing power.  This natural monopoly will lead to that firm seeing that its marginal revenue is below its price (if it lowers prices then it may gain new customers at that new price but it will lose money on existing customers) and when it maximises profits by setting prices at the point where its marginal revenue is equal to its marginal cost, that price will be higher than its marginal cost, and so be seen as economically inefficient from the perspective of consumers.


CRRA utility function with a scale parameter

As it is well-known, preferences (even under risk) are invariant to affine transformations of the utility function. Therefore, adding a 'scale' parameter adds nothing in terms of fundamental preferences (i.e. in terms of comparing streams of consumption). I cannot even imagine what kind of 'numerical results' would be sensitive to it.


Sum of residuals in multiple regression equals 0

Completing the notation with the indices
$$
\forall j: \sum_{i=1}^{n} X_{i,j}\hat{u}_{i} = 0.
$$
As you say, if $X_0$ is the constant then
$$
\forall i: X_{i,0} = 1.
$$
Inputing $j = 0$ into the first equation
$$
\begin{align*}
\sum_{i=1}^{n} X_{i,0}\hat{u}_{i} & = 0 \\
\\
\sum_{i=1}^{n} 1\hat{u}_{i} & = 0 \\
\\
\sum_{i=1}^{n} \hat{u}_{i} & = 0.
\end{align*}
$$


Sunk costs - Book value and Market value

Sunk cost "is a cost that has already been incurred and cannot be recovered." For example, paying people to dig a hole in the ground. If you can sell the asset then the money you get can't be part of the sunk cost because that portion of the cost was recoverable.


Quasiconvexity of the indirect utility function

The functions and their variables are different, so there is no "inflection" or flipping.

The utility function $u$ which maps from the space of goods $X$ to $\mathbb{R}$ is convex and quasiconcave.

The indirect utility function $v$ which maps from the space of prices to $\mathbb{R}$ is quasiconvex.

Intuitively:
$u$: If you average two consumption bundles your utility is not lower than the average of the utility of the two bundles. Rather than eating just meat one day and just vegetables the other day you prefer to mix these everyday.

$v$: If the price vector is $p$ one day and $p'$ the other day you may be better off than if it was $\frac{p + p'}{2}$ every day. It is easy to check that anything you can buy under the second price regime you can also buy under the first. However there might be consumption bundles that you can only buy under the first price regime.


There have been several changes to the way the CPI is calculated over the years. A significant change occurred with respect to weights and hedonic adjustments in 1998 (I believe the pre-1998 series is what ShadowStats, without having any of the underlying data, attempts to replicate), and one in 1983 that, among other things, changed the way that housing services were calculated from an "asset price" approach to a "rental equivalence" approach.

The 1983 change was made to more accurately reflect changes in consumer prices, rather than reflecting changes in asset prices, which is not the point of the CPI. The 1998 change was made in part to more accurately reflect changes in the quality of goods produced, because it had been apparent for some time, particularly in the tech sector, that a computer sold one year for $500 was much more "computer" than the one sold a year or so earlier for the same price, and was therefore actually cheaper in real terms once you accounted for the change in the quality of the goods.

None of the old measures are still tracked, for two reasons:

The old measures were targeted for these changes because they were not believed to accurately reflect economic realities.
Economic statistics agencies like the BLS have limited budgets, and calculating multiple versions of a series is more costly than calculating one version.

So the series you want doesn't exist basically because it'd be a waste of money to have the government calculating numbers that economists believe are wrong.

Old series are dropped all the time for these reasons; for example, around the time of the 1998 change to inflation calculations, the BEA adopted the NAICS industry classification and dropped the SIC system, because the NAICS system was believed to more accurately reflect the structure of industries at the time. For example, before NAICS, computers were in a category called "Industrial And Commercial Machinery And Computer Equipment" right between the pump/compressor/industrial oven category and the industrial refrigerator category. At the same time, guided missiles were lumped into the same category as space vehicles (under transportation), so that we didn't tell the Russians exactly how much we were spending on our intercontinental ballistic missiles (or so I've heard).

However, if you want an independent check on the BLS-calculated CPI numbers, you can check out MIT's Billion Prices Project (a similar project, the "Google Price Index", is no longer publicly available, to my knowledge). You will find that they generally come to the same conclusions as the CPI.


M * V = P * Y is not in a form of growth rate, so it needs to be changed into

ΔM + ΔV = ΔP + ΔY
Because V is constant, then

14 + 0 = ΔP + 5

ΔP = 9%

ΔP = Change in price = inflation


"Normal" vs "actual" variables in empirical work

"Normal" in this context means "trend" (usually a simple linear trend, but in principle could be a non-linear trend by using for example the Hodrick-Prescott filter device).

Decompose output $Y_t = T_t+Y_{c,t}$, where $T_t$ is the trend component and $Y_{c,t}$ is the cyclical component (note that the cyclical component can be positive or negative). Then

$$OMH_t = \frac {Y_t}{L_t} = \frac {T_t+Y_{c,t}}{L_t}$$

while

$$NOMH_t = \frac {T_t}{L_t}$$

Then the ratio of actual to normal is

$$\frac{OMH_t}{NOMH_t} = 1+ \frac{Y_{c,t}}{T_t}$$

This gives a "mark-up" (or "mark-down" if $Y_{c,t}<0$), on "normal costs" and it is in this sense that it "represents the cyclical component of costs". Namely, this ratio is the gross mark-up or mark-down we need in order to go from "normal" costs to actual costs.


Timeline of comprehensive NIPA revisions

You can read what looks like the entire collection of back issues of Survey of Current Business on the BEA website but the old issues seem to be PDFs that are not indexed by the site's search engine. You can see the 1995 revision discussed there. This seems to be the 1965 and 1980 revisions. The seem to have changed the termenology on the major revisions at one point. In 1980 the called it The National Income and Product Accounts of the United States: An Introduction to the Revised Estimates for 1929-80 instead of Preview of the Comprehensive Revision
of the National Income and Product Accounts which they called in since at least 1995.

That still leaves five more still to discover. I set my DownThemAll to download the whole archive and then I'll see if can get anywhere with searching the pdfs.


Does the FDIC's insurance of your money in your bank account cause inflation of the bank were to go under?

No, for three reasons. First, FDIC bailouts are funded via the guarantee fund, which is a pre-funded insurance fund that has never required an injection of cash. Second, if such an injection were to occur, it would happen through an appropriation from Congress, which would be implemented via a debt issuance from the Treasury— the Fed has zero authority to bail out the FDIC guarantee fund. Third, bank failures actually tend to involve a net contraction of the money supply, as distressed banks are less able to engage in new credit extension.


Value representation theorem for countable set

I use the usual notation $(\succeq,\succ,\sim)$ instead of $R$. I assume that $X_{\sim}$ in your question is the set of equivalence classes of $\sim$ on $X$.

Suppose that the cardinality of $X_{\sim}$ is equal to $n \geq 1$. There exist $x_1\cdots,x_n$ such that $x_1 \prec \cdots \prec x_n$. Define $v(x_1)=1,v(x_2)=2,\cdots,v (x_n)=n$.

Since $\sim$ has $n$ equivalence classes, for any $y \notin \{x_1,\cdots,x_n\}$ there exists a unique $x \in \{x_1,\cdots,x_n\}$ such that $y \sim x$. Define $v (y)=v(x)$.

The function $v$ defined on $X$ takes values in $\mathbb{N}$. I leave it to you to check that $v$ is a utility representation of $\succeq $.


When it is said that currencies are 'fixed' against each other, they are maintained fixed. The exchange rate will still keep fluctuating, as there is obviously still a supply of and demand for the currency. The goal of the central bank is just to keep it within a certain range. In the case of a gold standard, the central bank basically guarantees gold as accepted currency. That makes that, if the U.S. dollar depreciates against the French dollar, U.S. producers will prefer to pay in gold, as your excerpt states. This basically reduces the supply of dollars, and the demand for French francs (how old is that textbook?!). So you can see that by guaranteeing the use of gold as a currency, the exchange rate automatically readjusts to a fixed level.
But the key is that is still fluctuates! This point is easier to appreciate in case a currency is pegged against another one. In that case, the central bank will actively intervene in the market for the foreign currency to keep the domestic currency within a certain band, by selling its foreign reserves. In the case of a gold standard, there is a sort of decentralized intervention: the central bank's guarantee incentivizes producers and consumers to use the form of currency (gold or cash) that is cheapest to them, and that way, both forms' prices continually readjust wrt each other.


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

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

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

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

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

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

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

Good luck!


If rent control "doesn't work" and supply induces demand, how can cities improve affordability?

Disclaimer: this answer was significantly rewritten to spell out explicitly how it answers OPs question and to add some sources (thanks to @Fizz). The gist remains the same.

The only case I know where housing policy seems to work the way you envision is Vienna (the Austrien capital). They use a combination of several of the policies on OPs list, they have been doing this for a long time and they seem to be very good at implementing them in productive ways.

First, the city owns a significant proportian of all apartments, enough to have pricing power in the market (about 60% according to source). Additionally there are rent control laws on the privately owned housing (see for example here for some housing policies). Nevertheless private housing is more expensive than public housing (source).

Second, the city is engaged in long term planning for housing and they do that wholesale. So they are not just building houses on existing ground attached to existing infrastructure but they are creating entire new suburbs including attachment to public transportation, schools and all the other infrastructure needed for a successful city. The sources above also talk about that in more detail.

This is hard to pull of because it takes much longer to bear fruit that a typical election cycle. Doing things that cost money now and are very useful in 20 years is difficult for elected politicians. So even if politicians or people in general in other cities like to copy the Vienna model, it is not just a few simple policy changes.


Are there plausible scenarios for the U.S. dollar to fall out of use as the world's reserve currency?

There are many plausible scenarios in which the dollar ceases to be the de-facto currency. They all have a few things in common. For people to stop using dollars for international trade, there would need to be two circumstances:

A reduction in trust in the USD (not just in US politicians)
A good (better than the USD) alternative currency

While political emotions run strong, both in the US and abroad, these emotions do not normally have a large effect on the economy.  There has been no significant change in American business practices, law, monetary policy, or productivity as a result of the change in leadership.  This has been very clear.  You can easily argue that American reputation abroad has been harmed, but that doesn't translate to negative economic repercussions.  Remember, the Soviet Union was using the dollar for international trade during the cold war.  A reduction in trust in the USD would come about if there was significant inflation of the dollar or if the US stopped producing things that people want to buy.  Neither of those appear to be on the horizon.  As the result, there has been no change in the attitude toward the dollar.

At the same time, the best candidate by far for an alternative currency, the Euro, has had significant problems recently.  It doesn't matter if the world thinks very highly of European politicians and dislikes American politicians; they aren't going to switch from dollars to Euros unless they perceive Euros to be a safer and more liquid currency.

Similarly, foreign investors will not withdraw from American investments wholesale unless they perceive a real risk to the investment potential. These types of decisions (on a large scale) are made in a cold, calculating way.  Until something happens that might actually affect the potential of US-based investments, there won't be a large change in demand for them.

Interestingly, when there are shakeups in the US economy (like when treasury securities were downgraded) the result is often the opposite of what you might expect.  There's a general concern about the worldwide economy and then a flight to quality, causing an increase in demand for relatively safe US securities, including the ones that were the apparent cause of the panic.


Why do banks keep vault cash instead of depositing all reserves at the central bank?

"Vault cash" is the money that a bank will keep on premises (which is usually kept in their vault) to deal with their day-to-day cash needs.

The bank must have a certain amount of cash on hand in order to deal with these types of every day transactions.  "vault cash" is considered to be part of a bank's reserves, and banks will usually be required to have a certain amount of "vault cash" on hand.

Bank reserves are essentially an antidote to panic. The Federal Reserve obliges banks to hold a certain amount of cash in reserve so that they never run short and have to refuse a customer's withdrawal, possibly triggering a bank run.

The required bank reserve follows a formula set by the Federal Reserve Board's regulations that are based on the amount deposited in net transaction accounts. These include demand deposits, automatic transfer accounts, and share draft accounts.


Yes, it is possible. In the long run, firms enter until they break even. Suppose firms are symmetric. Then for each firm the break even condition is that the average costs equal the price. This is because the price is equal to the average revenue. The average revenue is given by $px/x=p$ where $p$ is price and $x$ is quantity. If revenue equals costs on average, then there are no profits left to be made and this is the equilibrium number of firms.

Further, in a competitive market, price equals marginal costs. Hence, the break even condition there is also price equals marginal costs. Alternatively, in this case the condition is Average Costs equal Marginal Costs. From this condition you can find the break even quantity. From there find the break even price, by setting price=marginal costs. Then plug in the break even price and quantity into the demand function to determine how many firms must enter until the market equilibrium price and quantity are equal to the break even price and quantity. The result is the long run equilibrium number of firms.

Note that the question is only reasonable in the presence of fixed costs. If there are no fixed costs, the long run number of firms is infinite and we have a trivial answer. However, the treatment of this topic in textbooks as well as academic papers alwa assumes the presence of fixed costs.


Optimal decision for perfect substitutes utility function ?

Utility maximization problem is:

$\max\limits_{(x_1, x_2)\in\mathbb{R}^2_+} 4x_1 + 14x_2 \\ \text{s.t.} \ \ m = \frac{1}{2}x_1 + \frac{3}{2}x_2$

This problem can be converted into an optimization problem involving just one variable $x_1$:

$\max\limits_{x_1} 4x_1 + 14\left[\frac{2}{3}\left(m - \frac{1}{2}x_1\right)\right] \\ \text{s.t.} \ \ 0 \leq x_1 \leq 2m$

Differentiating the objective $4x_1 + 14\left[\frac{2}{3}\left(m - \frac{1}{2}x_1\right)\right]$ with respect to $x_1$, we get $\left(4- \frac{14}{3}\right) = \frac{-2}{3} < 0$. So we observe that the objective is decreasing in $x_1$. Therefore optimal choice must be the smallest $x_1$ we can have i.e. $x_1 = 0$ and hence $x_2 = \frac{2m}{3}$.


Kroft and Pope (working paper, published in JoLE 2014) ask exactly this question, and their tentative answer is "no".

They view Craigslist as a unique opportunity to study the benefits of online job sites, since it grew rapidly and somewhat idiosyncratically while other popular sites grew steadily (leaving few opportunities for identification). That said, they don't have a great identification strategy - they just treat the rise of Craigslist starting in 2005 as an event study and compare MSAs where it grew quickly to MSAs where it grew sluggishly, making the case via various alternative specifications and falsification tests that there isn't any substantial bias.

Interestingly, they find that Craigslist does seem to have crowded out traditional newspaper classified ads, but had no discernible effect on unemployment. (This doesn't surprise me too much, since Craigslist seems like a pretty minor advance over traditional classifieds for job search, and if anything you'd expect a contribution from other sites that are more specialized or make more efforts to facilitate matching.)

On the other hand, they find that Craigslist does seem to have some effect on rental vacancy rates. Perhaps simple, searchable Craigslist-style classified ads facilitate rental search (I know they have for me) but are too crude to do much for employment.


Can data from discrete choice experiments be used to predict models be used to predict willingnes to pay by specific individuals?

In principle it would be possible to do so. In fact this is exactly what we do if we convert a marginal effect at the mean to a willingness to pay. We calculate it for the average person in the dataset.

One can also distinguish the average WTP by subgroups and socio-economic characteristics such as gender. The reason why academic papers do not often go beyond that (I guess) is that the predictions become so specific that they are hardly interesting anymore. Who would be interested in the willingness to pay of say "a 27 year old male with 12 years of education, an annual income of 24000€, voting republican and an interest in violent video games"? What about when he is 28 years old? Given that these models are typically non-linear their WTPs are going to be different.

Moving to a practical point of view price discrimination at such detailed level is impossible at the moment and for a number of products it may even be illegal (insurance is an exception).

Finally, a problem with any contingent valuation problem is that is willingness to say rather than willingness to pay. This is less of a problem in markets for goods with which the participants have experience with the good in question, but there will always be a bit of hypothetical bias.


Why does a tariff have no effect to an exporter?

A distinction should be made between two different types of tariffs.

Let's define good imports as goods that enter into a country, across its border, for commercial purposes. Those imports could be subject to a tax on trade, called an import tariff. Thus, the Isoland country only taxes goods that enter. If no one imports the goods, this tax is irrelevant.

Let's define good exports as goods that move outward across a country's border for commercial purposes. Export tariffs would be a tax that a country imposes on its exports, which makes them more expensive. Isoland does not want to tax these goods because it would be a burden on its own businesses.

Note, however, that these export tariffs can be put in place to encourage domestic consumption of domestically produced goods instead of exports. This could be the case in the context of a food or health crisis if a country wants to discourage exports. This is not the cas in your example.


Is there really a Nash equilibrium in this example?

The Nash equilibrium is indeed (down, right).
Note that your chart has helpfully underlined the max value among all possible strategies each player can play, conditional on what the other player plays. The steps on the graph  are useful as well: If no numbers are underlined in a cell, that strategy set is strictly dominated by something else. If one number is underlined, one player will want to unilaterally deviate.
Assume the players play (down, right):

P1 will not want to play up or center as their return will be 1 in those cases
P2 will not want to play left or middle as their return will be 1 in those cases

You can try this for any other cell with underlined values and see one player will be better off deviating. For example, in (up, middle) P2 would prefer to deviate to (up, left), then P1 would deviate to (center, left), P2 to (center, middle), P1 to (middle, up), etc.
FYI: the equilibrium should be referred to by its strategy rather than its values.


what is the marginal cost divided by the average cost

$MC/AC$ is not a quantity, it is a function. More precisely it would be written as $MC(y)/AC(y)$.

It is true that in a competitive setting in the long-run equilibrium $MC(y^*) = AC(y^*)$.

However, this can also be true in a monopoly setting. For example in the special case when $C(y) = c y$ where $c \in \mathbb{R}_+$, you have
$$
\forall y: \ MC(y) = c = AC(y).
$$
Also the monopolist's profit-maximizing $y^*$ is independent of any fixed costs $F$, but $AC(y^*)$ is not. For example if the inverse demand function is $p(y) = 1 - y$ and the cost function is $C(y) = y^2 + F$ then
\begin{align*}
y^* & = \arg\max_y (1 - y)y - y^2 - F = 1/4 \\
MC(y^*) & = 2y^* = 1/2 \\
AC(y^*) & = y^* + F/y^* = 1/4 + 4F.
\end{align*}
In this case
$$
\begin{array}{lcl}
MC(y^*)/AC(y^*) < 1 & \mbox{ if } & F > 1/8 \\
MC(y^*)/AC(y^*) = 1 & \mbox{ if } & F = 1/8 \\
MC(y^*)/AC(y^*) > 1 & \mbox{ if } & F < 1/8.
\end{array}
$$
Yet there is exactly one firm in the market, so there is no competition in the classical sense. Nor is it the case that the firm is a natural monopoly at $F = 1/8$. This could mean that this is the 'efficient level of competition', but it is not the case, because when  $F = 1/8$ we have
\begin{align*}
y^* & = 1/4 \\
p(y^*) & = 3/4 \\
AC(y^*) & = 1/2 \\
\text{Profits} & = 1/16 > 0.
\end{align*}


Isn't buying currency with high interest rates a double whammy?

Yes, it’s the uncertainty. If you tried hedging the currency, the hedge would be generally such that there would be a loss that offsets the interest advantage. (This is known as covered interest rate parity. In oractice, there is a spread that causes behaviour to deviate from that -the currency basis. So you can lock in a small spread, but it is typically on the order of 10 basis points or less. During a financial crisis, the basis can get relatively large.)

If you do not hedge, the volatility in the currency rates over one year is normally greater than the interest rate differential. Buying a high interest rate currency is known as a carry trade. It is profitable until it isn’t. For an example, look at the Japanese yen in the early to mid-2000s. In that period, Japanese interest rates were the lowest in the developed world. It was thus a popular currency to short. It would then have periodic bursts where its value would shoot up, forcing shorts to cover.


How do I solve the Envelope Theorem condition in Microeconomics?

I'm guessing your inquiry is concerning the chain rule of total derivatives.
In the special case that $B(q-r)$ is for some reason omitted out of the expression, the derivation sequence would be this.
$$\frac{\partial{u}}{{\partial\theta}}= \frac{\partial{u}}{{\partial{C}}}\frac{\partial{C}}{{\partial\theta}} = -1*\frac{\partial{C}}{{\partial\theta}}=-\frac{\partial{\frac{q(\theta)}{\theta}}}{{\partial\theta}}C′(\frac{q(θ)}{θ})=-(-\frac{q(θ)}{θ^2})C′(\frac{q(θ)}{θ})$$
If your problem is with the latter part of the expression above, I'd suggest you read through derivation rule of composite functions.
As @Giskard has pointed out, it is unclear from the question why the term $B(q-r)$ would be omitted and perhaps you'd like to provide additional information on that.


If a GDP deflator is continually greater than 100%, does that mean inflation is still occuring?

No, a deflator greater than 100 means that the price level is higher than in the base year. It doesn't mean that inflation is still occurring. In fact, you could be experiencing deflation after a period of inflation and if prices today are still higher than the base year, have the deflator be above 100. A growing deflator is an indication of inflation. To detect inflation acceleration you'd need to see changes in the log(deflator) growing over time.


Will the third Heathrow runway fill up within 25 years?

It is difficult for anyone here to know exactly what Warnock-Smith had in mind with his comment or whether he has conducted some analysis prior to his comment.

Nevertheless, he may be referring to the research on congestion in general, which has largely focused on road travel.

It is well-known that, contrary to popular belief, increased capacity can make congestion worse. The reason for this is so-called "induced demand". Once there is a larger capacity, a demand increase will typically follow, thereby keeping congestion at the same rate or making it even worse. One mechanism behind this increased demand is that there could be a latent demand already underlying. This means that there are consumers who want to take trips, but don't due to congestion issues. However, after the capacity increase, the realized demand increases.

This phenomenon has been observed for example with increased highway capacity, as noted in this news piece. For a literaure review on highways, see Susan Handy's 2015 article "Increasing Highway Capacity Unlikely to Relieve Traffic Congestion".


Deriving equation for income offer curve

What I have derived here is more appropriately called Engel curve.


Strictly increasing function transformation

This is a strictly increasing monotonic transformation simply because the preferences in the previous function are the same in the transformed function as well.


Your FOC is correct. They took the FOC a step further and concluded that $\lambda_t=0$ for $t<T$. I quote from page 11:

  To obtain these conditions note that since $f(0)=0$ and $U'(0)=\infty$, it is clear that the inequality constraints in (4) do not bind and it is clear that $k_{T+1}=0$

The intuition is that the inequality constraints will only bind when you consume all capital today ($k_{t+1}=0$) or you invest all your capital and consume nothing today ($k_{t+1}=f(k_t))$. Both of these cases (save the former when $t=T$) imply that you will be consuming nothing for at least one period. Combining this with the MU being infinite at zero, obviously this cannot be optimal.


Signaling games (games in which an informed "sender" moves first and an uninformed "receiver" second) typically have a plethora of Perfect Bayesian Equilibria which is not really appealing in terms of predictive power.
However, as you already said, some equilibria may be "unreasonable". Refinements serve the purpose to formalize which of these equilibria are unreasonable.

Sequential Equilibrium is not really helpful in eliminating the equilibrium multiplicity, because the multiplicity of equilibria stems from the fact that PBE allows off-path beliefs to be "crazy". That is, we can support many equilibria by assigning "crazy" beliefs when a signal is sent that was not supposed to be sent on equilibrium path.

I take the fact that you ask about divinity as a signal that you dug deeper into signaling so that you know the Spence model and the Beer-Quiche game. Otherwise, look up these examples as they are helpful to illustrate the issue. I provide references below. Back to said issue: For example, we can support a no-education pooling equilibrium in a standard two-type unproductive-costly-education Spence model by imposing that a receiver does not update her beliefs when she observes education - we can even say that education signals a low type, because positive education is an off-path message. As another example, in the Beer-Quiche game, you can support a quiche pooling (sequential) equilibrium where the off-path message (drinking beer) is interpreted as wimpy.

To understand why divinity is helpful, you should understand another refinement first.
Perhaps the most widely used refinement is Cho & Kreps (1987) "Intuitive Criterion"(IC). In a standard two-type Spence signaling model, IC eliminates all but one equilibrium, the least-cost separating one (Riley outcome). Very sloppily saying, IC labels off-path beliefs as "unreasonable" if one type can say:

  "I am going to send this out-of equilibrium message $m$ for which you
  may have a weird belief. I do this to signal that my type is $x$
  although you may believe I am some type $y$. However, notice that if I
  were such a type $y$, I would be better off by staying on equilibrium
  path regardless of what you infer from $m$. Also notice that as a type $x$ I am better off by sending $m$
  IF this speech convinces you that I am really $x$."

Now this is a relatively simple idea to eliminate weird beliefs. Thing is that it does not always work. For example, we can add a third type to the standard Spence model. Now IC does not solve our multiplicity problem. You can verify (or read in one of the references) that IC does not eliminate hybrid equilibria in which the high types send a separating signal while for some education levels low types and medium types are pooled.
The issue here is that possibly more than just one type may benefit from credibly announcing a speech as above. A belief that all such types are equally likely to do this deviation satisfies the IC. However, it might be that some types are more likely to deviate to this off-path message.
Now, enter divinity, an even more powerful refinement.

"More powerful" refinement means that it has even stricter restrictions on off-path beliefs. The D1-criterion restricts the off-path belief upon observing an out-of-equilibrium message to be a point belief with all mass on the type who is most likely to make this deviation: Intuitively, after receiving
message $m$, there are more best responses of the receiver that improve the equilibrium utility of type $x_1$ compared to $x_2$. D1 says Receiver should infer that she deals with a type $x_1$ and put weight zero on type $x_2$. Note that in the two-types Spence model, both criteria coincide. In contrast, in the three-types model D1 eliminates all but the least-cost-separating equilibrium.

D2 is even stricter than D1: It requires the posterior to put weight zero
on a type $x$ upon observing $m$ if for every best response of the Receiver that causes type $x$ to deviate there is some other type $x'$ that strictly benefits from the deviation. Divinity and Universal divinity (after Banks&Sobel 1988) are based on D1 and D2. Divinity weakens D1: Receiver does not have to put belief mass zero on type $x_2$, but his posterior must not increase the likelihood ratio of $x_2$ to $x_1$. Universal divinity is stronger than D2 in that it applies D2 iteratively.

For a more formal treatment, read the original papers. A good summary is provided by Peter Camton. He also discusses the Beer-Quiche-game and in addition covers cheap talk games and the corresponding refinement, neologism-proofness. This guide on refinements may also help (they discuss the 3-types Spence model I refer to).
To stay within the community, see the answers to this well-received question.


Why are imported Chinese products in India cheaper than those locally produced?

Consider an exact same product, say an umbrella, which is both imported from China in India and locally produced. The reason why the Chinese product is cheaper compared to the local one could be related to differences in productivity or total factor productivity. The Chinese product could be relatively cheaper because Chinese firms use better production techniques,
higher-quality general labor and capital input, better managerial practice/talent, or better information technology. See the JEL survey about What Determines Productivity?

The recent paper by Rodrik and co-authors documents that labor productivity is higher in China than in India (see Table 1). This could be a first reason why prices of the same product differ.


You are correct, that it is taxes less subsidies = taxes - subsidies or in another word net tax for some particular product. For example, following OECD:

Taxes Less Subsidies On Products:
Net taxes on products (net indirect taxes) are the sum of product taxes less subsidies. Product taxes are those taxes payable by producers that relate to the production, sale, purchase or use of the goods and services. Subsidies are grants on the current account made by general government to private enterprises and unincorporated public enterprises. The grants may take the form of payments to ensure a guaranteed price or to enable maintenance of prices of goods and services below costs of production, and other forms of assistance to producers.

Of course, you can extend the definition outside taxes for just products I just wanted to showcase an example of more detailed definition.
As to its grammatical correctness, English is my 2nd language and this is economics site not site on English language - but you will commonly see 'taxes less subsidies' used all across academic literature. It might appear grammatically incorrect as it is part of the jargon, so of course this is not the way how laymen might discuss taxes.


Road to equilibrium in a basic economic model

If you want to focus on the real world, we need to realise that the savings equal investment (S=I) is an accounting identity. That is, it always holds, no matter what.

Importantly, it holds on any time frame, which means that every single transaction will obey it. (You would need to imagine an extremely short-term national accounts that reflects just one transaction.) Therefore, there is no conceivable set of transactions that break the accounting identity, assuming that the accounting is done correctly.

The supply/demand relationships in the real world are trickier. Production of goods could exceed "demand", as the excess ends up in inventories. However, we could pretend that the increase in inventories was planned, and so once again production equals demand. The money supply/demand relationship just tells us that the private sector allocates between "money" and "bonds", but that appears to be another accounting identity. (I am unsure about that statement, and it may take a few steps to get to that point. Since all financial instruments end up being held by some entity, presumably supply and demand have to match.)

In other words, accounting identies always hold, and that is independent of what any particular model says.

If we return the model, "equilibrium" is an assumption/solution technique to find a solution to the systems of equations. That is, within the IS/LM model, the market balance conditions determine the solution. If we change the model, we might get difference conditions to determine the solution.

Since a mathematical model is not the same thing as the real world, we should not say that real world behaviour is directly related to the mathematics. That is, it is unclear if it makes sense to ask whether the real world reaches "equilibrium", without defining what real-world phenemona define "equilibrium." Instead, the test is whether the mathematical model (whose solution is defined by "equilibrium") offers useful insight to real world behaviour.


This website will be helpful.
Ask that in here.
http://www.urch.com/forums/phd-economics


Single Peaked Preferences and Condorcet Cycles

Single-peakedness of preferences is not enough to guarantee the existence of a Condorcet winner, a position that cannot be defeated in majority voting (hence preventing cycling). You would also need that the set of alternatives to admit a linear order (and single-peakedness is with respect to this order).

With a linear order on alternatives and a profile of single-peaked preferences, it is easy to argue that the "median voter", a position that divides the set of voters into two subsets of equal size based on whether their bliss points are on the left or right of the median position, is always a Condorcet winner. For a more rigorous presentation, I'd refer you to Proposition 21.D.1 and its proof in the MWG textbook.

To see why the linear order on alternatives is necessary, consider the following figure (taken from Wikipedia):

Here, the space of alternatives is 2-dimensional, and there is no natural way to define a linear order on $\mathbb R^2$. Voters' preferences are still single-peaked in the sense that each voter has only one bliss point. As a result, we cannot rule out cycling (non-existence of Condorcet winner) as is shown in the example.


How did the silver standard "insulate" China from the beginning of the Great Depression (1929-1931)

As argued by Ho (2014) the silver standard helped China because downward trending silver prices were producing mild inflation during the period 1929-31 and also helped to devalue exchange rate between gold and silver.
First, as already discussed in this Economics.SE answer, mild inflation is important for an economy to avoid excessive unemployment due to nominal rigidity of wages especially in the recession. In fact this is one of the many reasons why the conventional wisdom of combating recession is expansionary monetary policy (see Blanchard et al. Macroeconomics a European Perspective).
Furthermore, it is worth noting that Great Depression was so severe in US because US monetary policy went in exactly  opposite direction to the above mentioned conventional wisdom. As famously argued by Friedman and Schwartz in the monetary history of  the United States the Great Depression would arguably be only mild recession if Fed would not decide to pursue disastrous contractionary monetary policy.
Second, as discussed by you and also in the article you linked increasing gold prices and decreasing silver prices allowed the exchange rate depreciate vis-à-vis gold standard currencies   and currency depreciation is another conventional way of countries fighting recessions (again see Blanchard et al mentioned above). Normally, this policy can be risky because other countries could also competitively devalue their currency leading to potential currency wars, but in this case as their currency depreciated gold standard currencies appreciated.
Also, I disagree with your assessment here:

But after looking at historical prices of both metals leading up to and following the Great Depression, I saw divergence, but not dramatic divergence. So my intuition has been depleted.

According to data from macrotrends the price of gold rose between Jan1929-Dec1931 from approximately ${\\\$}315.38$ to ${\\\$}402.71$ (growth rate of $\approx +27\%$), while  price of silver decreased from ${\\\$}8.07$ to ${\\\$}5.17$ (change of $\approx -35\%$) in the same period. Or in another terms the ratio of prices $Gold/Silver$ changed from approximately $39$ to $78$ (approximately doubled) - that is quite a large change in exchange rate. I would be surprised if such appreciation of Gold vis-à-vis Silver would not result in some non-trivial boost for Chinese exports.


What the book calls the "Weierstrass Theorem" is more commonly known as the Extreme Value Theorem, which states that a continuous function defined on a compact domain attains a maximum and a minimum.

A common proof of this theorem involves the use of the Bolzano–Weierstrass theorem, which you learned in your math course, and which says every bounded sequence has a convergent subsequence.

So the two theorems are actually different, albeit related, statements.


What are the most common methods of determining valuation used by economists that claim Bit-Coin is on the verge of being a bubble

There are two ways to look at the value of a financial instrument. One is the underlying asset base, the other is the yield.

Bitcoin has no underlying asset base and no yield.

Therefore, its only value is whatever people imagine it to be.

In other words, it's completely overvalued. But that does not mean it is on the verge of massive corrections. There is an old saying (attributed, as they often are, to Keynes) that the market can remain irrational for longer than you or I can remain solvent.


How come the CBO reported the Federal Deficit for FY2014 was \$483 Billion when debt went up by \$1.1 trillion?

First off, you are looking at the wrong column to compare like with like.

Total debt went from \$16.7tr to \$17.8tr but that includes intragovernmental debt.  Changes in this number will net out in the deficit calculation (this is one part of the government lending money to another part).

Secondly, you are starting on the wrong date.  You need to go full year, so start from 30-Sep-2013 and go to 30-Sep-2014 (you would think 1 day wouldn't matter, but a lot happens on that last day of the fiscal year!), so your link should be: Treasury Direct FY 2014

So the real number you expect to see change in line with deficit is the "held by public".

This changed from \$11.976tr to \$12.784tr, an increase of $808bn over the period.

So that leaves a gap of $325bn to be explained.

This can be explained by the fact that various things are considered "off budget" for purposes of calculating the deficit, a small example I can remember is the U.S. Postal Service.  Prior to Obama the Iraq and Afghanistan war were considered "off budget".  I think various overseas aid payments are also off-budget.  Also any loans or asset purchases or financial gains and losses will impact the debt value, but will be treated "off budget".

This "off-budget" idea may seem a little dodgy but it should probably be seen in comparison to corporate accounting.  For corporate accounts you would not expect the income statement and cash flow statement to exactly match.

Doing the Math for 2013

Ok, so this is the best I can find, I'm afraid it is projected for 2014 but it gives you the idea.  We can do the calculation for 2013.

The Budget for Fiscal Year 2015

Go to page 207, then there is a table showing the bits that contribute to the debt change.

If we re-ask your question for 2013 (where we have data), then your links are:
Monthly Budget Review: Summary for Fiscal Year 2014
and
Treasury Direct FY2013

Then we see that the deficit was \$680bn and the public debt changed from \$11,269,585,800,039.32   to \$11,976,279,236,073.83 = \$706.7bn

Now according to the budget tables, we see that Unified Deficit is \$680bn but that there is an additional 22bn of changes in financial assets and liabilities, bringing us up to $702bn.

Not bang on, but probably as close as you are going to get - rounding and different sample dates probably makes the difference.  You can see from the projections for 2014 that there is a much bigger value of \$271bn, which is only (!) \$54bn short of the actual number we are seeing.


Editing formula for finding Marshallian Demand with Cobb-Douglas utility function

$u=cx_1^adx_2^b$ is equivalent to $u=(cd)x_1^ax_2^b$
the values of $c$ and $d$ do not impact the optimal bundles. I'll provide complete working on your other question (Marshallian Demand for Cobb-Douglas).


Usually, when people use non-equidistant axis, it is because they want to emphasize some variation more than others. For example, if most of your data is between 0 and 1, but you have one outlier on 100, then an equidistant axis would make it hard to analyze most the variation, because it emphasizes the wrong parts.

In this case you have a log-scale, which is a simple nonlinear axis that (in general) emphasizes small values over larger ones. Whether that makes sense with oil prices, is - to me - unclear.


How do you use a Log-linear model when you have negative Xs?

The elasticity of Y with respect to X is often estimated by running a regression like this:
$$ \ln Y = \alpha + \beta \ln X + error$$

However, this isn't always applicable because it is perfectly fine to ask what is the percent change in Y to a percent change in X even if X or Y are negative. There are other issues too, like the fact that the elasticity may not be constant over X.

Let's go back to the textbook (Varian (1992), p. 235) for the definition of the elasticity of $Y$ with respect to $X$:
$$ \epsilon(Y,X) =\frac{\partial Y}{\partial X} \cdot \frac{X}{Y} $$
Which equals another common definition of the elasticity:
$$=\frac{\partial \ln Y}{\partial \ln X}$$
which we often use when estimating the elasticity with linear regressions.

However, the advantage of the first form is that you don't have to use the log function to evaluate it. All you need is a local estimate of the derivative, X, and Y.
One strategy would be just to do that.

However, what you are doing could well be nonsensical because percentage changes are weird when working with negative values. For example, consider X going from -11 to -10. This is a 9.1 percent decrease in X ((-10-11)/-11). However, this is is an increase in X! Going from 11 to 10 is also a 9.1 percent decrease in X. What would be the economic conditions where we think going from -11 to -10 and +11 to +10 would have the same effect on demand?


Is belief in future dividends the only long term value of stock?

Disclaimer: There are a lot of interesting aspects to this question. Shareholder voting rights, control over the company, etc. are all interesting things to consider. Here, I only focus on a few parts of the question.
Excess Volatility
Claim: Are actual stock prices much too volatile to be explained by dividends? Is this evidence that the price of a stock depends on more than just future dividends?
It's perhaps not much of an exaggeration to state that the paper that won Robert Shiller his Nobel prize in economics is the paper "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?" In this paper, Shiller looks at historical prices and dividend payments and asks the question, suppose market expectations of future dividends were on average correct? What should the prices of a stock been historically if those expectations were on average correct? He argues that we can do this by looking at the dividend payments and prices and constructing and "ex-post rational price" at each point in time, called $p^*$. He then compares that price to the actual historical prices, $p$. This is shown if Figure 1 below for the S&P Composite Stock Price index from 1871 to 1979, after detrending both series. The result is that $p^*$ appears to be far too smooth relative to $p$. He argues that this is a problem because it implies that actual stock prices are too volatile to be explained just by movements in future dividends.

References and other resources:

Shiller, Robert J. "Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends?" The American Economic Review 71, no. 3 (1981): 421-36. Accessed March 12, 2021. http://www.jstor.org/stable/1802789.
You can view the following online lectures here. This is from "Asset Pricing with Prof. John H. Cochrane. PART II. Module 3. Time Series Predictability, Volatility, and Bubbles" https://youtu.be/mhGQeJyKVvU?t=275

Important Note: In the current asset pricing literature, there is a strong belief that this "excess volatility" puzzle is not a puzzle at all. Empirical and theoretical investigation seems to indicate that this "excess volatility" arises from variation in discount rates. Shiller constructed this ex post ration prices by assuming that the discount rate was constant over time. Empirically, this seems to be far from the truth. For a good discussion of this, see the following:

Cochrane, John H. "Presidential address: Discount rates." The Journal of finance 66, no. 4 (2011): 1047-1108.

For a video of a presentation of this paper, see here: https://www.youtube.com/watch?v=ZDsOiftolUI

Class lectures of this can be seen here:

3.2 One-Period Identities
3.3 Campbell-Shiller Present Value Formula
3.4 Volatility

Rational Bubbles
Claim: Perhaps stock prices can be explained by a belief that prices will continue to grow in the future, even if dividends do not? That is, suppose the price of a stock is not derived from a belief in future dividends but in the belief that prices will continue to growth without bound.
There is a literature that investigates the possible effect of "rational bubbles" on the price of a stock. This is summarized nicely in the "Discount Rates" paper cited about. One way to investigate this question, as described in the Discount Rates paper is to use the Campbell-Shiller (1988) present value identity,
$$
dp_t \approx \sum_{j=1}^k \rho^{j-1} r_{t+j} - \sum_{j=1}^k \rho^{j-1} \Delta d_{t+j} + \rho^k dp_{t+k},
$$
where $\Delta d_{t+j} = d_{t+j} - d_{t+j-1}$, $dp_t := d_t - p_t = \log(D_t/P_t)$, $D_t$ is the dividend, $P_t$ is the price, $r_{t+1} = \log R_{t+1}$ is the log return of the asset, and $\rho \approx 0.96$ is a constant of approximation. This is an identity based on the definition of returns $R_{t+1} = (D_{t+1} + P_{t+1})/P_t$. This says that the normalized prices of an asset ($dp_t$) is derived from three possible terms:

Future returns on the asset (discount rates)
Future dividend growth paid by the asset (cash flows)
The future price of the asset (bubble term)

Investigation of the contribution of each of these terms to the volatility of normalized prices indicates the nearly all of the volatility comes from variation in the discount rates term and essentially none comes from the dividend growth and rational bubble terms. This also explains the above "excess volatility" puzzle. Note that this still means that dividend explain the value of a stock. It just rules out that changes in the price-dividend ratio of a stock are not explained by changes in future dividends nor by belief in rational bubble growth in prices.
You can view more of the details of the empirical investigation in the paper or the same videos linked in the previous two section.
Conclusion
The attack against the present discounted value model of stock prices embodied in the "excess volatility" puzzle seem to have an explanation in the fact that discount rates vary over time. An investigation of the contribution of future dividend growth, discount rates, and "rational bubbles" to dividend-price ratios indicates that "rational bubbles" do not seem to explain prices. Rather, dividend yields seem to be entirely explained by discount rate variation. Further investigation seems to indicate that prices and dividends seem to be cointegrated. All of this combined is consistent with the theory that prices reflect the present value of expected future dividends.
However, as noted in my disclaimer above, this leaves open many interesting questions. There is still much to do and learn in this literature.


Long-,short-term interest rates and inflation

Does the logic go as follows?

  short term rate + expected inflation= long term rates?

Not exactly. There is some confusion. Inflation distinguishes between real and nominal interest rates, whereas the discrepancy between short- and long-term interest rates is derived from the preclusion of arbitrage opportunities. It is neither actual nor expected inflation, but the forward rate, what explains the discrepancy between short- and long-term interest rates.

By way of example, suppose the short- and long-term rates currently are 3% and 5%, with short- and long-term referring to 1 and 2 years, respectively. The interest rate $r_{f}$ for the 2nd year should be such that $(1+0.03)(1+r_{f})=(1+0.05)^2$. Any other rate $r_{f}$ would allow either the borrower or the lender to make profit with no risk (or somewhat equivalently, to make profit without having to invest his own funds).

It is true that a lender requires higher return for long-term loans than for short-term ones because a longer term entails greater exposure to risk. But the inflation is just one of multiple risks that the lender factors in when determining at what rate (of return) he is willing to lend money.

Edited on 7/22/2018 (at 3:29PM EDT) to supplement as per 2nd-to-last comment

There is no robust or widely-adopted method for calculation of long-term rates based on estimated future inflation (and/or short-term rates). Nor is there a mathematical expression describing how --or even whether-- market forces use the estimated future inflation for determining the rate at which lenders are willing to commit funds for a long-term period. I personally doubt that such method or expression could ever exist.

One can only resort to qualitative reasoning to sketch the generic effect that some information tends to have on long-term rates. In the case of expected/estimated future inflation, it might be implicitly (at most, but perhaps not at all) reflected in other factors and preferences that influence those market forces. Uncertainty --as you rightly point out in one of your comments--, risk aversion, and cost of opportunity are three of many other factors and preferences that influence how much a long-term rate would differ from the short-term rate.

Although it is reasonable to conjecture that these estimates, factors, and preferences are positively correlated with the duration of a long-term period, it would be very hard (or I would say futile as well as impossible) to reliably model by how much they cause a long-term rate to differ from the short-term rate.


Monopolistic Competition- productive efficiency

Let $q$ denote the output of the firm, and let $\varepsilon_p(q)$ denote the elasticity of price w.r.t. quantity sold. We know that when profit is maximized
$$
|\varepsilon_p(q)| = \frac{p(q)-MC(q)}{p(q)}.
$$
We also know that in the long-run equilibrium firms have zero economic profit, i.e.
$$
AC(q) = p(q).
$$
Productive efficiency is achieved when $AC(q)$ is minimized, and at that point
$$
AC(q) = MC(q)
$$
holds as well. Combining these we get
$$
|\varepsilon_p(q)| = \frac{p(q)-MC(q)}{p(q)} = \frac{AC(q)-AC(q)}{p(q)} = 0.
$$
So the only case when all these properties coincide is when the quantity sold has no effect on the market price, i.e. when demand is perfectly elastic.

An explanation without the elasticity part:
From the other two properties (long-run equilibrium and productive efficiency) we have
$$
MC(q) = AC(q) = p(q).
$$
Together with profit maximization this implies that firms are price takers, $MR(q) = p(q)$, but since
$$
MR(q) = \frac{\text{d} \ p(q)q}{\text{d} \ q} = p(q) + p'(q)q
$$
this is only possible if $p'(q) = 0$, which again means that demand is perfectly elastic.

All the above assumed that the demand and inverse demand functions are continuously differentiable. You could have a situation with not perfectly elastic but kinked demand, where profit maximization occurs exactly at the kink. In this case $MR(q)$ does not exist at the point of profit maximization.


If bidders have quasilinear preferences and monetary transfers are possible, then the two notions are equivalent: If $x$ is an allocation of the object and $t$ is a vector of monetary transfers with a balanced budget (so the sum of all transfers is 0), then the pair $(x,t)$ is Pareto efficient if and only if $x$ is the utilitarian allocation (object goes to the bidder with the highest valuation).

If monetary transfers are not possible, every allocation of the object to some bidder is Pareto efficient.


Different values for US Public Debt, why?

The OECD number includes intragovernmental debt, which is debt not held by the public, while the Wikipedia number does not. One of the largest of these debts (several trillion dollars) is related to Social Security, which is a debt owed by the federal government to the Social Security Trust Fund. A review of the history of this debt and its implications is available from the Social Security Administration.


Difficulty in an economics' optimization problem using Kuhn-Tucker conditions (interpretation difficulty)

The OP clarified in a comment that a) "income" here means "revenues" and not "profit" (it is not always the case), and b) that Karush-Kuhn-Tucker multipliers work just fine if we define them to be non-positive instead of non-negative (they do, but it is not a widely known fact).

The other bad terminology in the statement of the problem is the "unit cost" one -it is really meant "marginal cost". So we have to obtain the Total Cost function from its partial derivatives. This is easy to do since we see that the cross-partial is zero.

So if

$$\frac {\partial TC}{\partial x_1} = x_1,\;\;  \frac {\partial TC}{\partial x_2} = 2x_2$$

it follows that

$$TC = \frac 12 x_1^2 + x_2^2 + FC,\;\;\;FC\geq 0$$

and we want to minimize it subject to the constraint $p_1x_1 + p_2x_2 \geq \bar R$.

PS: It appears that the revenue floor is $3$?


The Central Bank of Russia (CBR) gives tons of statistics. Take a look at "Net Inflows/Outflows of Capital by Private Sector" and “Balance of Payment” in different representations. I warn you ahead that it’s not that clear from the data what moves where.

There are several reasons for capital flight:

Dollarization and flight to safety. That is related to high inflation and bank runs over the past 25 years, after the collapse of the USSR. Russians do not fully trust the ruble or the local financial system. A lot of Russians hold foreign cash, mainly dollars and euros.
Sanctions. Because of the Ukraine issues, the West put sanctions and effectively closed its financial markets. So, Russian banks and enterprises cannot refinance and have no way but to pay debts. Paying debts is like capital flight.
NX = S – I. Russia has chronic CA surplus, which means capital outflow. It lasted for years. See this. If you have insufficient investment demand inside country for its savings that means capital outflow. That is related to point 1 also.


Given the very general description of the problem, I can think of the following (also very general) way of formulating it mathematically.

Let $v_n$ be the buyer's value from owning $n$ plots of land, with $v_3>v_2>v_1$.
Let $c_i$ be seller $i$'s private valuation of the plot she owns. Let $b_i$ be seller $i$'s bid, and we assume the buyer will purchase $n$ plots of land whenever $v_n$ is greater than or equal to the sum of the $n$ smallest $b_i$'s, and each seller gets the amount she asks for in the bid.

Seller 1's objective is to choose $b_1$ to maximize the following:
\begin{align}
&\Pr(b_1+b_2+b_3\le v_3)b_1
\\&\qquad+\Pr(b_1\le\max\{b_1,b_2,b_3\}\text{ and }b_1+\min\{b_2,b_3\}\le v_2\text{ and }b_1+b_2+b_3> v_3)b_1
\\&\qquad+\Pr(b_1=\min\{b_1,b_2,b_3\}\text{ and }b_1\le v_1\text{ and }b_1+\min\{b_2,b_3\}> v_2)b_1
\end{align}
The problems for the other two sellers would be symmetric.

If you assume that $c_i$'s are i.i.d. draws from a distribution $F$, then it seems plausible to solve for a symmetric Bayesian Nash equilibrium, where every seller bids according to the same bidding function, $b_i=\beta(c_i)$ for each $i$.

Using $b_i=\beta(c_i)$, and perhaps with the assumption that it is strictly increasing, you should be able simplify the $\Pr(\cdot)$'s in the objective function. The rest is just to solve for the bidding function. I will leave you to finish the remaining steps.


There are a couple of imprecisions. First, there are 3 subgames: two that start with player 2 moving, and the complete game is also a subgame.

Second I think that A is a best response for player 1 iff $r\geq \frac{z-y}{x-y}$ otherwise, B is the best response (perhaps this was just a typo).

Third, note that the fraction is guaranteed to be positive and smaller than 1 given the restrictions on the parameters,  but it is not necessarily equal to $0.5$, For example, let $x=5$, $z=3$ and $y=2$, then the fraction is equal to 1/3.

Fourth, you are missing other equilibria, when $r=\frac{z-y}{x-y}$, then player 1 is indifferent between A and B, and any randomization of A and B also constitutes an equilibrium.

Lastly, when writing the equilibria, you must specify what player 2 does in each information set (or node in this game)

Thus: $$NE=\{(A, (ra+(1-r)b)b)|r\geq \frac{z-y}{x-y}\}\cup\{(B, (ra+(1-r)b)b)|r\leq \frac{z-y}{x-y}\}$$
$$\cup \{((pA+(1-p)B), (ra+(1-r)b)b)|r=\frac{z-y}{x-y}, 0\leq p\leq 1\}$$

Where $(ra+(1-r)b)b$ specifies that player 2 randomizes in the first node and chooses b in the second node.


In principle it's a plane for 2 independent variables or a hyperplane for more. An exception is when your independent variables are a continous and a dummy variable. In that case the dummy basically changes to the intercept only so you could show two lines with different intercepts.

A work around if you have 2 continuous independent variables is to show the relation between the dependent and one independent for several values of the other independent.


Difference between 'surplus' and 'welfare'

Surplus and welfare are different concepts, but not for the reasons you state, although there are elements of validity in both (1) and (2).  They may, however, be used interchangeably in certain contexts and where certain conditions are met.

Both “surplus” and “welfare” are terms from ordinary language that in economics are used in more precise senses.  "Surplus" has several senses in economics, and is commonly clarified by the words accompanying it: (in microeconomics) "consumer surplus", "producer surplus" and their sum "total surplus", (in macroeconomics) "budget surplus (of a government)" and (in Marxian economics) "surplus value".  Where it is used alone, the context will usually make clear which of these is meant: the question appears to be concerned with the microeconomic senses.

Consumer surplus and producer surplus are normally defined in terms of supply and demand curves in a single market.  Such curves can in principle be estimated from observations of supplier and consumer behaviour, without reference to utility.  So although consumer surplus can be related to utility via marginal utility theory, utility is not needed in its definition and, as Steven Landsburg points out, surplus should be measured in monetary units, not units of utility.  Welfare, equally, is often related to utility at a theoretical level, but in applied work is often estimated without reference to utility and measured in monetary units.

“Welfare” in economics is used both in macroeconomics, where there have been various attempts to identify an appropriate set of adjustments to GDP to provide a suitable measure of overall welfare in an economy, and in microeconomics, where the focus is on welfare in a single market or a few related markets.   But these are not entirely different senses of the term.  They both retain from ordinary language the essential idea that welfare is good - something policy should aim to increase - and in this respect there is an important difference, even in microeconomics, between surplus and welfare.  “Surplus” is a purely descriptive concept (a term of positive economics), whereas “welfare” is – to borrow a little from philosophy – a thick concept, one that is both descriptive and evaluative.  Let’s consider three situations which can help to clarify our understanding of these concepts.

Firstly, consider a standard supply-demand diagram for a single product, and suppose supply increases (the whole supply curve moves to the right).  Normally, we would say that both surplus and welfare have increased.  Now suppose that the product is one which is harmful to those consuming it.  Would we still say that surplus has increased?  Yes, because “surplus” is a purely descriptive term, so we can quite consistently say that surplus has increased while thinking it might have been better if this had not occurred.  Would we still say that welfare has increased?  Quite possibly not.  Points we might want to consider before drawing a conclusion are whether consumers are aware of the harm and acting rationally, and if not whether their pleasure from consumption outweighs the harm.  This distinction between surplus and welfare can be found in debate on the regulation of smoking (here is an example).

Secondly, consider the effect of a tariff on an imported good.  The tariff raises the domestic price of the good, with resulting changes in the consumer surplus and producer surplus relating to that good. Would we say that the change in welfare is the sum of those changes?  No, because (even if we ignore effects on related markets and on exporting countries) the revenue raised by the tax is also relevant to welfare.  In a simple partial equilibrium analysis, therefore:

Welfare loss  =  Reduction in CS – Gain in PS – Increase in government revenue

This distinction between surplus and welfare can be found in (A) and (B).

Thirdly, consider a change in a market for a good subject to a production externality, say air pollution.  Here we would say that the change in welfare is not just the change in producer and consumer surplus in the particular market, but should also take account of the externality.  However, to draw a distinction between surplus and welfare on this basis would be an oversimplification since, in the economics of environmental valuation, the concept of consumer surplus is routinely applied to non-market goods.  For example (although the details are complex and the results unlikely to be very accurate) a demand curve for air quality (suitably measured) in a region might be estimated using the hedonic pricing method which uses the housing market as a surrogate for a market in air quality.  Once a demand curve has been estimated, it is possible to calculate the change in consumer surplus due to a change in air quality and include this in a measure of change in welfare. Having said that, it is questionable whether methods are available to estimate consumer surpluses for all non-market goods, so to that extent there is validity in (2).

The conditions that would be needed for a change in total surplus in the market for one product to be an accurate measure of the change in welfare resulting from a policy change would therefore be quite stringent, including at least the following:

•  No direct effects of the policy change on other markets;

•  No effects of change in the market on other markets;

•  No harmful effects of the product on those consuming it;

•  No externalities in production or consumption of the product.

Sometimes these conditions will be met, to a reasonable approximation, and then it might be appropriate to use the terms “surplus” and “welfare” interchangeably.

Finally, a brief consideration of the idea that surplus relates to one market while welfare relates to many markets. Because “welfare” is an evaluative term, it makes sense to apply it to situations involving either one or many markets, even if in some cases it is hard to find suitable criteria to determine whether a change is an increase in welfare.  “Consumer surplus”, on the other hand is normally defined for a single market, and the path-dependency problem (see (C)) is a complication in aggregation across markets, except in special cases (this is where, if the connection is made with utility theory, quasi-linear utility is relevant).  To overcome the path-dependency problem, either compensating variation or equivalent variation are sometimes used as alternatives to (ordinary Marshallian) consumer surplus, but then there is the further problem that the theoretical income-compensated demand curves underlying these measures cannot be estimated from observations of consumer behaviour.  To that extent there is validity in (1).

References

A. Koo W W & Kennedy P L (2005) International Trade and Agriculture Blackwell Publishing p 104

B. Mankiw B G & Taylor M P (2006) Economics Thomson Learning pp 172-3 (a European version of the well-known textbook)

C. Johansson P-O (1991) An Introduction to Modern Welfare Economics  Cambridge University Press pp 42-52


Non-constant returns to scale and competitive factor markets

Frankel examines the use of the Cobb-Douglas formulation in aggregate data, where as a matter of macroeconomic(and essentially logical) identity output is exhausted in paying the factors of production.

So the macroeconomic identity states, for any aggregate production function

$$Q=F(K,L) \equiv rK + wL$$

where $r,w$ are ex post average unit rewards for the factors of production (hence the identity character).

The only way to equate $r$ and $w$ with marginal product is to have a function homogeneous of degree one ("constant returns to scale") because it is only then that we have

$$F(K,L) = F_K\cdot K + F_L\cdot L$$

and we can map $r=F_K,\; w=F_L$.

If the function is homogeneous but not of degree one but of a degree $k\neq 1$, then we have

$$F(K,L) = \frac 1k(F_K\cdot K + F_L\cdot L)$$

which leads to $r=(1/k)F_K,\;\; w=(1/k)F_L$

If $k>1$ we have Increasing returns to scale and factors are paid less than their marginal product (again, on average and on aggregate), while if $k<1$ we have Decreasing returns to scale and factors are paid more than their marginal product.

We then run into trouble regarding the behavior and structure assumptions at the micro level that lead to such a result at the macro-level.


Weierstrass Thm: Continuous Fn Attaining Extrema on Compact Domain $u:\mathbb{R^L}\rightarrow\mathbb{R}$

The Weierstrass Extreme Value Theorem guarantees this. However, it's used so frequently that economists take it for granted or omit it in graduate courses and research papers. MWG is a maturity book. Part of mathematical maturity is being able to fill in the details for a proof.


what is the difference between microeconomics and microfinance?

Kind of a good question, but it's to do with etymology, nitpicking or something. While economics is the allocation of scarce resources and finance is the allocation of scarce resources over time, microeconomics is a study while microfinance is a provision of financial services.

Thus, the 'micro' in microeconomics refers to the scope of study namely that microeconomics studies the behaviors of individuals and firms instead of state issues of growth, inflation, and unemployment.

However, the 'micro' in microfinance refers to the scope of recipients of financial services.


What sort of impact would one expect on investment as a result of an approaching election?

There are many ideas to look into and some research:

IDEAS

Elections are presumably a time where the future becomes uncertain in the sense that there is a likelihood the new leader will change the course of a nation. From that point of view its about increased uncertainty.
Elections are often about corruption. The current political party will use corruption to remain in power. Often this means an increase in public expenditure or a loosening of monetary reins.
Potentially, some elections change the mood of a country because they absorb lots of people's energy, make them fight each other, as the candidates sometimes expose the least likable instincts in order to try and win.

EMPIRICS

Some of the work of Nick Bloom consists of structural estimation of a model of a firm that adjusts to changes in the amount of uncertainty in the environment. This kind of work suggests that for a fixed productivity level, investment (and disinvestment) rates fall in response to increases in uncertainty. The intuition is that of the threshold for exercising stock options: you are more likely to wait to exercise a call option if volatility is greater. Under the assumption that there is more uncertainty about future policy during elections, these models will tell you that investment will be lower during these periods.
Canes-Wrone and Park describe survey results in terms of people delaying purchases during election times.
Julio and Yook stuy cross- border capital flows in response to policy uncertainty, which is often the result of election periods.

SUGGESTIONS

Maybe, a way to go about this empirically is simply to look at the responsiveness of investment to q, as a function of how far elections are. If the coefficient of q in investment regressions is lower in the quarters right before presidential elections, you would have a reasonable and yet interesting result.


Maybe someone can get into more details, but generally speaking

  The range of estimates is large, from a loss of GDP of nearly ten percentage points (in the least
  attractive trade and inward investment scenarios modelled by the Treasury, NIESR and the Centre
  for Economic Performance at LSE)
  1
  to a gain of four points (Minford, for Economists for Brexit
  – a
  clear outlier) – see figure 1.

  The main reason for the differences lies in the assumptions made about shifting from the
  current access that the UK has to the EU single market to a new regime in which the UK
  faces restrictions.

Those were from 2016 estimates/papers.

Also, economists were not terribly good at predicting Brexit-related effects insofar, at least short term; see https://economics.stackexchange.com/a/27492/6210 While the gloom and doom may have been overstated, some effects are apparent already, in some analyses:

Apparently the chilling effect of Brexit on investments may have been a real thing (but that assumes the counterfactual dotted trend was a sure thing).

As a sort of an update, some days ago (Sep 3, 2019) UNCTAD has posted an article on the narrower issue of potential UK losses in a "no deal" scenario due to continuity trade agreements with other countries not yet agreed.

  In relation to exports to countries with which the UK has not yet secured the continuation of preferential access, the UK could face substantially higher MFN tariffs, especially on agricultural products. For example, processed food products could face an average increase in tariffs of about 17 percent. Similarly, apparel, textiles and motor vehicles would also face substantially higher tariffs. In value, most of the losses would be concentrated in motor vehicles (about USD\$750 million) and in chemicals (USD\$200 million).

  [...]

  Among the countries which currently grant preferences to the EU but for which the UK has not yet reached an agreement to grant continued preferential market access, Turkey, South Africa, Canada,  Mexico, Japan, Egypt and Morocco are the markets where the UK is expected to have larger export losses. In particular, the UK is expected to lose about USD\$500 million  of exports in the Turkey market, about 5 percent of its exports to Turkey. In South Africa, the UK is expected to lose about USD\$240 million, equivalent to about 9 percent of its exports to South Africa.

There's an update to the update as well. On Sep 11, the UK has announced an "agreement in principle" with South Africa and with a few other, smaller countries from Africa.


Which measure of total loans is more relevant to Financial Stability?

Measuring the total loans by their utilization rate is more effective in determining the financial stability of the banking sector. These 'utilized' loans are IN EFFECT, aka, in use and simultaneously have a risk factor. Un-drawn data is not that useful because it might never be drawn and therefore pointless when determining stability measures.

My reason for saying this stems from the hard data perspective. You have hard, real data when measuring the total loans by their utilization rate. You have theoretical(not hard data, and there-fore theoretical risk factor) utilization rates when it comes to "spoken" credit lines available but not necessarily drawn.

Hope this helps.