Beginner wanting to learn about economics/finance to explore career options?

A great starting point is "Fundamentals of Corporate Finance", Ross, Westerfield & Jordan.

This book will give you a good overview of key concepts in finance. This book is widely used in introductory courses for non-finance majors, to both teach some fundamental ideas, and give a panoramic view of the field.

"Trading" will probably be the topic that is less developed in the book. This is partly because there is no bullet-proof method for trading, to some degree it is an art, and also becuase some of the useful techniques for trading are too advanced for an introductory book. However, after reading this book you should have a good sense of the key idea behind the decisions to buy or sell a financial asset.


When does US Federal Reserve redeem the corporate bonds it bought?

When do the corporates pay back?

These are bonds.  It doesn't matter who owns them.  They get "paid back" -- dividends interest and principal -- according to the terms of the bonds.

What is the impact on economy when they have to payback?

None, because the central bank makes the money disappear.  On the plus side, it slightly reduces the money supply.

where does the Fed get money from for this corporate bond buying?

They "printed money".
A better question (which has also been answered, if you search for it) is why the trillions of printed dollars (aka Quantitative Easing) hasn't produced inflation.


The price and quantity of a scarce resource are determined by supply and demand.  The quantity which would be offered at some imagined price increases with that price.  The quantity which would be purchased at some given price decreases with price.  The actual quantity and price of every transaction will then naturally be the level where the quantity offered equals the quantity demanded.

In the case of savings and investment, the price is the interest rate and the quantity is the amount lent and borrowed.

So there is no fallacy.  The interest rate is the one agreed to when a lender (saver) and a borrower make a deal.  The interest rate isn't the cause, it is the result of the agreement.  The interest rate bid and offered at a given moment are two different numbers.  There is no fallacy because there is no transaction.  At the moment of transaction, there is a single number: the "interest rate" itself. So again, no fallacy.


What is the term for 'forgone cost' as 'opportunity cost' is for 'forgone profit'?

The short answer: we don't need a separate term for "foregone cost", because opportunity cost of doing something = highest (forgone benefit - foregone cost).

I'd like to stress two points about opportunity cost.

First, it doesn't make much sense to say "the opportunity cost in this example"; you need to specify the opportunity cost of doing what? We always explicitly state the opportunity cost of doing something, or opportunity cost of choosing something. In your investment vs bank savings example, the opportunity cost of using the money to invest is \$40, and the opportunity cost of depositing the money in the bank is \$60 (assuming investing and saving are the top 2 most productive use of your money, and assuming no ex-ante risk in investing). In your spreadsheet example, suppose you only have two options to spend 1.5 hours: A - you can spend 1 hour to make the spreadsheet, and use the rest 0.5 hour to do whatever is most productive, or B - you can spend 1.5 hours to program in VBA. The opportunity cost of choosing A is the net benefit of doing B, and the opportunity cost of choosing B is the net benefit of doing A.

Second, I highlighted the net benefit at the end of the previous paragraph. Opportunity cost of doing something is the highest foregone net benefit of the alternatives. Here the foregone net benefit is defined as the (foregone benefit - foregone cost). Let me go back to your spreadsheet example. Suppose finishing the spreadsheet gives you \$50 equivalent of utility, regardless of how you make the spreadsheet. However, let's say, manually making the spreadsheet bores you, incurring \$30 equivalent disutility, and making the spreadsheet via VBA bores your less, incurring \$20 disutility. I also assume the most productive use of your time in that 1.5 hours is taking some rest, which gives you \$40 per hour utility. Now here is the net benefit of option A: \$50 (benefit for finishing the spreadsheet) - \$30 (cost for making the spreadsheet manually) + \$20 (benefit for 0.5 hour rest) = \$40. And the net benefit of option B: \$50 (benefit for finishing the spreadsheet) - \$20 (cost for making the spreadsheet via VBA) = \$30. Therefore the opportunity cost of choosing A is \$30, and the opportunity cost of choosing B is \$40. We don't need a term for "foregone cost".


Dynamic of 10 year UST given supply shock of the bonds that the Fed will buy into

Who will buys bonds; not including the FED

When a government wants to issue bonds, it will usually do so via a bond auction, where the bond will be bought by large banks or financial institutions.

Those institutions will then sell the bonds on, often to pension funds, other banks, and individual investors.  So other banks and individuals also buys bonds.

https://www.ig.com/en/bonds/what-are-government-bonds

other factors/actors pressuring up prices on these bonds.

If the economy is doing poorly (less economy growth) then investors might step back a bit from riskier investment and instead pile into government-backed Treasury’s, which pushes prices higher and yields lower.

https://www.investopedia.com/ask/answers/111414/what-causes-bonds-price-rise.asp

How does the dynamic of all this work with inflation?

When inflationary pressures emerge, Treasury yields move higher as fixed-income products become less desirable. inflation eats into the purchasing power of every dollar you receive from bond interest in the future.

Additionally, inflationary pressures typically force central banks to raise interest rates to shrink the money supply. In inflationary environments, investors are forced to reach for greater yield to compensate for diminished purchasing power in the future.


Would PPP adjustments between countries be irrelevant if all countries had the same relative prices?

That's correct, the PPP adjustments are made to account for the fact that living in some places is more expensive than in others. So if you are comparing two places with equal relative prices, their PPP index should be the same, and so it is irrelevant if you use the adjustment or not.

Note that saying that prices are the same in different countries can be quite tricky, since typically goods that can be found in some countries are not even sold in other countries. But in principle, the PPP is trying to adjust for the fact that the same 100 American dollars have a larger purchasing power in some countries than in others.


Competitive equilibirium of max utility functions

I might be wrong so feel free to point out any mistakes.

Both of them have the same utility function $u(x,y)=max(x,y)$
This means when $Px > Py$ , they'll choose to consume $Y$ instead of $X$ since they get higher satisfaction by selling all units of x and purchasing y.

Take the case of First seller, If he sells all X and purchases Y, His total demand for $Y$ will be $2(Px/Py) + 1$ and since Px/Py >1, total demand will be higher than 3. If he had done the opposite, his total demand will be less than 3.
 Since the utility function is $max(x,y)$ He will choose the former strategy

Hence, the demand for $X$ will be zero but the supply is $a+2$. Also, there is excess demand of $Y$. Hence, this is not a competitive equilibrium.

Similarly, then $Px <Py$, there will be excess demand for $X$ so that isnt a competitive equilibrium either.

The only case we have left is $Px=Py$ where the seller will be indifferent in consuming  either good. Here, each seller consumes all of 1 good each. There will be 2 cases.

Case 1. If seller 1 consumes all $X$, His demand is $2 + (1)Py/Px = 3$ since Px=Py and the supply of X is $a+2$. When we equate this, we get $$a=1$$
Notice that this is the only condition that needs to hold here, B can take any non negative values in this case.

Case 2 is where seller 1 consumes all $Y$ and, His demand is $1+ (2)Px/Py = 3$ and the supply of $Y$ is $b+1$. Since they have to be equal, we get $$b=2$$ And again there's no restriction on $a$ and it can take any non negative values.


Is there an equilibrium between privately owned and publicly listed companies?

I don't know exactly how the numbers would work out, but you would expect an equilibrium but it will depend on many factors.

A complication is that you have public companies taken private and private companies that never go public.  It may be there is some equilibrium between these as they are unlikely to be equivalent. Ex public companies are often highly levered,  while never public are often debt free and cash rich.

Particular important factors would be interest rates and credit spreads.  This is because it boils down to the distribution of capital.  If there is lots of money available to lend then LBOs become attractive and companies can be taken private. If there is strong demand for equity then IPOs become easy.

I think an economy with a shortage of public companies would show overvalued equities and hence IPOs are encouraged (think dot com bubble - shortage of public web companies vs demand). If debt is cheap and there are too many public companies then you will see either take overs or LBOs.

I suspect the effect is most visible within sectors rather than the whole economy.


Proof of nestedness of subgame perfect equilibria

Would this (and why or why not) provide an answer to your question?


What happens to a production possibilities curve whenever there is too much labor?

What should happen? It grows. A production possibilty curve shows that the number of goods that can be produced is limited. If there is "more workforce than needed" (supply of work exceeds demand), prices for work descend, due to competition. That means that you can employ more people with the same capital. So if there are enough of the other limiting production factors (such as soil) available, you can produce more of both products.
Of course the product which is more labour-intensive (in the often used example of butter and guns that would probably be the guns) will profit much more from that.


Why unemployment quantity can be larger than the market employment based on this price ceiling supply/demand chart?

First of all, think about the definition of unemployment as it is used in this example. An unemployed person is someone that wants to work, but who cannot, because he can't find a job - as labor supply is not high enough. The crucial point is that people may want to work in some situations, but in others they may not.

With this in mind, the reason that the equation you postulate is incorrect, is due to the fact that the labor supply in your example is elastic. That means, the higher the wage, the higher is the labor supply. You can see this in the upward shape of the labor supply function. To answer your question: The unemployment quantity under minimum wage becomes larger than the market employment, because after the wage increases more people want to work, and hence the quantity of

  employed people + unemployed  people

increases - as compared to the market equilibrium before where the wage was lower.

It is also interesting to think about a case in which your initial thought would be correct. This would be the case if labor supply was completely inelastic. This situation is reached as the labor supply curve rotates to the left (staying in the initial market equilibrium) until the labor supply curve is a vertical line. In this situation your equation

  quantity demanded at minimum wage + unemployment = market employment

holds. This is how it would look like:


In the long run, would a production-possibility curve expand outward if the country preferred more consumer goods than capital goods?

To keep things simple, let's assume that inputs to production other than capital goods are constant over time, and that production technology is regarded as one of those inputs (ie there is no technical progress).  Let's also assume that the production function is such that output (across the whole range of the production possibility frontier) is an increasing function of capital when other inputs are constant: in symbols $\partial{Y}/\partial{K}>0$.

The question then is whether capital and therefore output can increase given the country's "preference for more consumer goods than capital goods".  If this simply means that its chosen output combination includes a higher proportion of consumer goods than capital goods, then that is certainly possible.  Suppose for example that output consists of $80\%$ consumer goods and $20\%$ capital goods, that the annual capital-output ratio is $2$, and that $5\%$ of capital is lost each year due to wear and tear.  Then the annual loss of capital due to wear and tear is $2 \times 5\% = 10\%$ of output, and capital goods increase each year by $20\% - 10\% = 10\%$.  Thus the production-possibility frontier would expand outwards.

If however the country's preference implies that output contains less than $10\%$ of capital goods, then (on the above assumptions) the production possibility frontier would contract inwards over time.

Note that the above takes no account of the fact that, in practice, capital goods are not infinitely malleable, that is, the production of different goods requires different sorts of capital goods. One might pursue that point by considering how a country's preference for consumer goods might influence its choice of what sort of capital goods to produce (if indeed it produces any).


How exactly does a central bank determine how much to cut/increase interest rates?

They don't know for certain. It's an inexact science. They do the best they can.

Alan Greenspan was known for pouring over all the economic data available for hours while mostly in the bathtub trying to make sense of what was happening in the economy. But ultimately, it came down to making an informed decision based on knowledge, reasoning, experience and intuition.

Policy objectives (which are quasi-political) can also come into play as sometimes desired results can compete. The classic example of this is economic growth vs. inflation.

Critics of government monopolized central banks argue that it is impossible for any single individual or group of policy makers to choose rates correctly and overnight interbank lending rates should be allowed to float freely and be determined by the market vis-a-vis supply-demand equilibrium. Hence the popularity of LIBOR and to a lessor extent EURIBOR as these are closer to market pricing than, say, the Fed Funds Rate. However, these are still only averages of central bank policy decision and, therefore, are not purely market-driven.


I wish I could leave this as a comment, but the first formulation is a solution to a maximisation problem of the form
$$
\max_{C_t} \sum_{t} \beta^{t} u(C_t) \\
\text{s.t. } \quad C_t +K_{t+1} \leq (1-\delta)K_{t} + w_{t} + r_tK_t \quad \forall t
$$

The second formulation is a solution to a maximisation problem of the form
$$
\max_{C_t} \sum_{t} \beta^{t} u(C_t) \\
\text{s.t. } \quad \sum_{t} C_t \leq \sum_{t} (A_0 +Y_t)
$$

In a way, the first is a sequential problem, while the second is a time zero problem. In some instances the approaches are equivalent, but I'm not an expert on this.


Can an irrational function be a utility function?

I don't particularly understand the question.
Start with any function $f:X \rightarrow \mathbb{R}$.
Define $x \succeq y$ if $f(x) \geq f(y)$.
We get a rational preference over $X$.
By the way $\sin(x) + 1$ is a perfectly valid utility representation.


Is Cobb-Douglas the only output function corresponding to a competitive economy?

Let $a+b<1,\;\; a,b>0$.  Pay the factors of production their marginal product:

$$rK = \frac {aQ}{K} K= aQ,\;\;\ wL=\frac {bQ}{L} L=bQ$$

So total payments to factors of production will be

$$rK +wL = aQ + bQ = (a+b)Q < Q$$

And the question is: who gets the rest of the output that has been produced?


Negative expected value; risk neutral choice

There are three type of individuals : risk averse, risk neutral and risk loving.

Individuals evaluate risky prospects such as to maximize the expected level of their utility. So, an agent is risk averse if, at any wealth level $w$, he or she dislikes every lottery $Z$ with an expected payoff of zero, $EZ = 0$, so that : $Eu(w + Z) =< u(w)$

Risk neutrality : $Eu(w + Z) = u(w)$
Risk love : $Eu(w + Z) = u(w)$

Assuming that $Eu(w + Z) = EZ$ (expected value of the lottery $Z$) => Risk neutral agent.

$Eu(w+ Z) = EZ = - 5$

$Eu(w) = 0$

An risk averse agent won't take the gamble. A risk neutral agent won't take the gamble. We don't know for the risk loving agent, depends on his utility function.


The difference between signaling and screening stems from the fundamental difference in bargaining power- who offers the contract for which her utility is the highest. While in screening the uniformed party proposes the contracts, in signaling it is the informed party.

For your general conjecture, I refer to Stiglitz and Weiss (1990): "Sorting Out the Differences Between Signaling and Screening Models":

  However, if the indifference carves of the informed agents satisfy what roughly would amount to a single crossing property in two dimensions, and some technical conditions hold, then all contacts in the screening game break even, and the set of outcomes of the screening game is a subset of the outcomes of the corresponding signaling game.

It has nothing to do with refinements such as the intuitive criterion, divinity and so on. These refinements are useful to "refine away unreasonable equilibria". Here, the issue is that the set of PBE is potentially quite rich while some equilibria rely on "unreasonable beliefs". The refinements formalize which of those beliefs are "unreasonable".

If you are interested, you can also look at settings that combine signaling and screening. This is the literature on informed principals, initiated by Myerson and Maskin & Tirole (1990, 1992). The informed principal first offers a contract to screen the agent while the contract proposal itself may reveal private information of the principal.


Oligopolistic producers and retail price wars

A producer won't always want the retail outlets to compete on price. This is the reason for minimum resale price maintenance. By competing on price, it may be that the retailers competition amounts to something closer to a zero-sum game. Supposing there are some consumers who value something like service, it might be better for joint profits to provide good service and thus bring in new consumers. You might imagine two stores selling electronics. The stores might find it best to cut price to pull the customers away from the other. The producer would rather there be good service, display models, helpful employees, etc to bring in new customers.

Reference: Winter (1993)


Are there economic studies surrounding the efficacy of gun control?

To answer the headline question directly: yes, there are.

While economists are among the central participants, this is really an interdisciplinary policy-oriented question. The Science of Gun Policy is a fairly recent and comprehensive review of the research overall, published by the Rand Corporation. It's over 400 pages long and I haven't read it. But if you glance through it you will get a sense of the many complex angles that this question has been examined from. Relevant outcomes are not limited to violent crime per se.

Table 21.1 on pages 332-333 summarize the evidence for which policy measures may affect which outcomes, according to the current evidence. Regarding violent crime specifically, there is moderate evidence ("two or more studies—at least one of which was not compromised by serious methodological weaknesses... and contradictory evidence was not found in other studies with equivalent or stronger methods.") to show:

waiting periods reduce total homicides
background checks by dealers reduce firearm homicides (evidence for private-seller background checks is less conclusive)
firearm prohibitions for individuals subject to restraining orders decrease intimate partner homicides.

I have not looked through the relevant studies for these particular findings to see which ones are specifically by economists, but in any event, these are probably the most conclusive findings you will find. Someone else might be able to give you a more in-depth look at the economics research per se.


The book probably intends you to think like this

so you have a downward-sloping demand curve (lower prices lead to higher demand), but if demand increases for a reason not related to price (a shift from the Demand 1 curve to the Demand 2 curve) then the new equilibrium on the upward-sloping supply curve will be at a higher price and quantity

There are a lot of implicit assumptions here, especially

the direction of the slope of the supply curve
whatever changed the demand curve did not affect the supply curve


Block pricing vs Perfect price discrimination

In a nutshell, it is because people talk.

Information asymmetry happens at the firm/consumer level. The consumer does not know exactly how much it costs the firm to produce a given product, nor are they able to discern the actual quality of the product without expert knowledge. But what they do know is the price of the product, and whether or not individuals within their network have purchased the product (think reviews on amazon).

In a perfect discrimination situation, each individual will get their individual price for the product. If I buy a widget at $20, and learn that it cost my friend 10, I wouldn't buy the widget. I'd ask my friend to buy that widget for me. Hence the blocks. An analogy would be cars, why there are different 'trim' levels for at its core, the same car. Some people want alloy wheels, others want tinted windows. Different combinations of trim constitute different classes (blocks) and as a result, the firm can sell these seemingly similar products under different price ranges (Basic < Limited Edition)

At the same time, from a production perspective, the marginal cost for each product differs when you scale up or down. Your 100th widget will cost less on average than your 1st widget and vice versa. As a result, even if the monopolist wanted to, perfect price discrimination would be impractical given the varying production costs.

This might not capture the your question in full, but other people are free to chime in and I'll revise as needed.


Buy a company with credit or bonds. Does this happen?

I have a question. A company is worth 1 million dollars, in terms of present value of revenues, discounted at rate R. Can I borrow 1 million dollars from a bank and buy the company?

Yes.  It is done all of the time.

  Can I borrow 1 million dollars from a bank and buy the company? If the bank charges me R, I am indifferent?

No, you are not indifferent unless there is a mandatory repayment schedule.  This is a riskless contract to you otherwise.  If there is no better rate of return for you, then you begin to repay the loan, but if a new opportunity develops at $R'>R$ then you stop repaying the loan.  If there is no mandatory repayment schedule then you would always opt for the loan as you can require the bank to keep a bad opportunity and you can keep any good opportunity.

In periods where $R$ is the superior opportunity, you repay the loan until it is fully repaid.  In periods where $R'$ dominates the original opportunity, you send the cash flow into the new opportunity.  The loan is acting as if it were a free option contract.

There is an implicit cost to not taking the loan.

None of this necessarily holds if there is a repayment schedule or if there is a loan rate of return which does not equal $R$.

As to bonds, again it is the terms and conditions that matter.  In the real world bonds are costly to issue.  It appears here that bonds and bank loans are identical so you would be indifferent to using a bond or a loan, but not indifferent to buying the firm on credit since the bank or bondholders will accept taking all of the risk for the return $R$.

If the return $R$ were risky and there were cash repayment obligations, then it is difficult to determine if you would be indifferent or prefer to borrow because the option requires exercise making it a forward contract and not an options contract unless there is also the capacity to prepay.  You would be strictly indifferent if and only if there existed a mandatory principal repayment scheme.  Otherwise, assuming that at the moment, no opportunity $R'>R$ existed, then you would take the loan and buy the firm.

This entirely depends upon the bank accepting the profit of the firm as the interest payment.  This would never happen in the real world.


Why do yield spikes reflect badly on tech stocks

You are referring to recent market events where the yield of US Treasury bonds has risen and some tech stocks have been falling?   My interpretation of this situation is that the rise in yields reflects growing optimism in the broader economy , as we overcome Covid and head back to work.  In the stock market, this leads to a preference for traditional stocks that do well in a ‘normal’ economy, and a rotation away from the tech stocks that did especially well in the pandemic.  This we have a correlation rather than a causation.


How does an elastic Money Demand affects the effectiveness of fiscal policy?

a small rise in interest elasticity shifts the equilibrium position of IS-LM CURVES to the right


More of a comment:

There should be an expectation operator in the statement of the problem, otherwise problem doesn't make sense.

That "...the deterministic and stochastic value function must be the same..." is not quite right. The value of $\sigma^2$ is crucial in the restriction

\begin{align}
\rho = \left(-n + \sigma^2\left(1 - \frac{\alpha\gamma}{2}\right)\right)(1-\alpha\gamma).
\end{align}

If $\sigma^2 = 0$, then presumably $\rho < 0$ for economically reasonable $\alpha$ and $\gamma$, in which case the deterministic problem may be ill-posed. What is true is that the stochastic value function takes the given form only if the parameter restriction holds.

Factoring out the Ito term $\frac{1}{2} \sigma^2$ from the right hand side

$$
\sigma^2\left(1 - \frac{\alpha\gamma}{2}\right) (1-\alpha\gamma),
$$

the restriction can be written as

$$
\rho + n (1-\alpha\gamma) = \frac{1}{2} \sigma^2 [ (1-\alpha\gamma) - (-\left(1 - \alpha\gamma\right)^2)].
$$

On the right hand side, we have a elasticity of intertemporal substitution term $(1-\alpha\gamma)$ and a risk aversion term $-\left(1 - \alpha\gamma\right)^2$. What the restriction says is that, with a particular choice of $\sigma$, they offset each other, up to time preference $\rho$ and the drift $n(1 - \alpha\gamma)$. Therefore the value function is independent of $\sigma$.

That the value function is independent of $\sigma$ is an artifact of the restriction, and choice of CRRA $u$. Not true in general.


Fixed effects model is estimated as:
$$   y_{i t} − \bar{y_i} = ( X_{i t} − \bar{X_i} ) \beta + ( \alpha_i − \bar{\alpha_i} ) + ( u_{it} − \bar{u_i} )$$
So the country fixed effect is always relative to the average fixed effect.
If a country has negative fixed effect that means it is less productive than average country in your sample. If you choose different sample results might change.


how to calculate the average annualized return?

Annualized return simply means average amount of money that a investment earns each year over a given amount of time.

If the compounding rates are the gains you've earned on your investment, The annualized return is:

$$AR = (1+totalreturn)^{\left({1\over{n}} \right)}-1$$

This equation shows the return each year over a full span of time.  Total return is the total change in the variable over all periods.


Are tariffs ever levied on services and does MFN apply?

GATS doesn't apply tariffs, but

  The GATS comes in two parts; firstly a framework of rules, principles and concepts which underlie
  obligations regarding measures affecting international trade in services; and, secondly, the specific
  negotiated commitments listed in countries' schedules for service sectors. The GATS covers four
  modes of supply: (1) cross-border supply; (2) supply through the movement of consumers to the
  location of the supplier; (3) supply though the establishment in a country of the commercial presence
  of legal entities from another country; and (4) the supply through natural persons of one country in the
  territory of another.

  The key articles in the GATS regarding the scheduling of commitments are Article XVI (on market
  access) and Article XVII (on national treatment). Market access as such is not defined in the GATS.
  Rather the approach of the GATS is to list six categories of measure which are prohibited unless
  specified in a countryís schedule (for each of the four modes delivery). The categories cover the
  following: (a) limitations on the number of service suppliers: (b) limitations on the value of service
  transactions or assets; (c) limitations on the number of service operations or on the quantity of service
  output: (d) limitations on the number of natural persons who may be employed; (e) limitations on the
  type legal entity through which a service is supplied; and (f) limitations on the permissible size of the
  participation of foreign capital either in terms of a maximum percentage limit on foreign shareholdings
  or in terms of the total value of an individual entityís or of aggregate foreign investment. National
  treatment is defined as treatment no less favourable than that accorded to like domestic services and
  service suppliers. Under Article XVII measures entailing deviations from national treatment are also to
  be included in a country's schedule.

Basically limitations (a)-(f) allow various forms of quotas for services from other countries.

As for MFN, GATS has its own version/definition of it. Basically:

  Article II of the GATS constitutes a general obligation which is, in principle, applicable across the board by all Members to all services sectors. Article II:1 of GATS states:

    "With respect to any measure covered by this Agreement, each Member shall accord immediately and unconditionally to services and service suppliers of any other Member treatment no less favourable than that it accords to like services and service suppliers of any other country".

And as with similar WTO agreements, there were exceptions allowed

  Article II:2 states:

    "A Member may maintain a measure inconsistent with paragraph 1 provided that such a measure is listed in, and meets the conditions of, the Annex on Article II Exemptions". The liberalizing content of the GATS depends to a large extent on the nature of these specific commitments.

  The annex makes it clear that no new exemptions can be granted, at least by this route: any future requests to give non-MFN treatment can only be met through the WTO waiver procedures. [...]

  While Article II applies across the board, Article XVI on market access and Article XVII on national treatment only apply to sectors included by a Member in its schedule of specific commitments.

  [... T]he "Scheduling of Initial Commitments in Trade in Services: Explanatory Note" states that "where an MFN exemption has been granted for a measure, a Member is free to deviate from its Article II obligations, but not from its Article XVI and XVII commitments. Therefore, in such cases, a Member may accord treatment more favourable than the minimum standard to some Members, as long as all Members receive at least the that minimum standard of market access and national treatment appearing in its schedule."

  It follows that an MFN exemption would give a Member who had made no commitments in a sector considerable freedom to discriminate. However, an MFN exemption which coexists with fully liberal market access and national treatment commitments would have little meaning - unless a Member wished to provide more favourable treatment to certain foreign suppliers than it does to its own.


Re: "You could say this is 'creating' money" - no you couldn't. This would be conflating money and wealth. Wealth can be created without new money being created - indeed wealth was created before money even existed. Conversely money can be created without creating wealth. So they are entirely separate things. A crude analogy: wealth is to money as apples are to numbers. You can count apples using numbers, but growing new apples does not create new numbers.

With regard "In the end logically, this money becomes concentrated in a few people." - not true. People don't earn money in order to collect big piles of it and spend all day counting it. Instead they use it to buy stuff which means that the money circulates through the rest of the economy.

With regard "How is it the United States can still grow, despite sending more money out than it takes in?"... it doesn't send out more money than in takes in (at least not to any great extent). Foreigners do not accumulate great piles of dollars that they earned from selling American's stuff - instead they use their dollars to buy American assets, like US government bonds.

With regard how money is created, please be aware that this is a controversial area and there is a huge amount of misinformation on this subject. The best document to read that I know of on the subject of money creation is this one published in the Bank of England Quarterly bulletin in 2014.


What at all justifies income taxes (as opposed to sales taxes only)?

There's a fair amount to unpack in the question, so it might be useful to take it step by step, and consider everything from a more abstract, economic theory perspective.

  ...those who are more hardworking (or, at least, those who are more skilled) are essentially punished....

We should be careful making statements like this for a couple of reasons. First, the assumption may or may not be true, depending on what model of wages you think applies. For example, if wages are largely determined by bargaining, then it isn't clear that wages necessarily directly (or perfectly) correlate with how hard an individual works, or their skill level. Even if we use a non-bargaining wage model, plenty of "unskilled" jobs (for example, auto workers or welders) make more than "skilled" jobs (for example, many teachers). Second, it isn't clear that progressive taxation should be considered "punishing" high income earners. Given that tax brackets are all applied at the margin, earning more only means that (all else equal) your last dollar will be taxed more than your first dollar.

  because we tax low-income citizens less, we are making their life quality nearly the same as everyone else, which encourages unemployment.

While we're flattening the differences between the highest and lowest income earners a bit, I'd hesitate to claim that "we're making the quality of life [of low income earners] nearly the same as high income earners." Given that income still has substantial impacts on quality and duration of life, I'd be hard pressed to agree that we've equalized quality of life.

Beyond that, of course, there's the larger Social Choice problem of "why is somewhat equalizing quality of life a bad thing?" Given that employment and income potential aren't entirely defined by an individual's own effort, but are correlated with many factors that are determined by one's "luck of birth," creating a society that doesn't at least attempt to account for this exogenous "luck" factor seems arbitrary and somewhat cruel.

  ...we would be punishing those who spend a lot - essentially, those who abuse their wealth more.

Again, I'm a bit intrigued by your choice of wording there- why do you consider someone spending income "abusing" it, particularly if we accept your earlier premise that income is tied closely with effort? Isn't spending one's income merely realizing the actual utility potential they earn from doing a job? And if that's the case, why should we discourage spending one's income by substantially raising sales taxes?

  This, therefore, would encourage philanthropy (and otherwise spending money on things other than buying.)

There already exist commonly used mechanisms to encourage philanthropy through taxation: deductions. This method provides a much larger potential incentive to encourage philanthropy, since it effectively makes giving to charity "cheaper" than both spending and holding earned income (since money given isn't counted against your income), as opposed to merely spent income under your proposal. In other words, with an income tax of $\tau$, every dollar I give to charity only costs me $(1-\tau)$, which is the amount I would keep if I took the dollar as opposed to donate it. If there's only a sales tax, then the cost is the full dollar.

So, getting to the crux of the question- there are several reasons the world currently has income taxes. First, there's a distributional concern: the sales tax that would be required to offset income taxes would be quite high, and would cause significant hardship for poorer families. Moreover, only having a sales tax can lead to incentives for wealthier individuals to horde wealth as opposed to spend it, which actually leads to significant economic distortions, and adverse economic outcomes (for example, a fair amount of recent research suggests that too high levels of wealth inequality can lead to slower overall economic growth). As to whether there are fairness implications, I'd point out that the regressive nature of sales taxes are important on this point. Given that a comparatively larger burden of the tax would fall on poorer individuals (since they spend higher proportions of their income), eliminating the income tax in favor of a consumption tax would have distributional consequences.

I don't mean to sound nit-picky or like I'm dismissing your question out of hand, for the record. There is an important debate to be had for any society regarding how its citizens should shoulder the combined tax load. However, I think most of the debate occurs "inside" of your assumptions made in the question, and only by closely examining those can the debate be meaningful.


Given

$$\max_{x_2^h} \quad U^h(\phi(\bar z + y^h - x_2^h), x_2^h)$$

You have to find FOCs by taking the chain rule twice for the first argument. Denote the argument for function $\phi$ as $(\cdot)$.

$$\frac{\partial U^h}{\partial x_2^h} = \frac{\partial U^h}{\partial \phi} \cdot \frac{\partial \phi}{\partial x_2^h}$$
$$\frac{\partial \phi}{\partial x_2^h} = \frac{\partial \phi}{\partial (\cdot)} \cdot \frac{\partial (\cdot)}{\partial x_2^h}$$
$$\implies \frac{\partial U^h}{\partial x_2^h} = \frac{\partial U^h}{\partial \phi} \cdot \frac{\partial \phi}{\partial (\cdot)} \cdot \frac{\partial (\cdot)}{\partial x_2^h}$$

Thus, letting $U^h_{1,2}$ represent the partial derivative with respect to the first and second arguments of $U^h$ respectively:

$$\begin{align}
\frac{\partial U^h}{\partial x_2^h} & = U_1^h(\phi(\bar z + y^h - x_2^h), x_2^h) \cdot \phi_z(\bar z + y^h - x_2^h) \cdot -1 \\
& + U_2^h(\phi(\bar z + y^h - x_2^h), x_2^h) \cdot 1
\end{align}$$

The second argument in $U$ has no $\phi$, so only chain rule should be applied there.


Deriving the golden-rule savings rate in a Solow Model

The "golden rule" is the level at which steady-state consumption is at a maximum, given the parameters of the model. Steady state consumption is

$$c^* = (1-s^*)\cdot f[k^*(s^*)] = f[k^*(s^*)]  - s^*f[k^*(s^*)] \tag{1}$$

where $0<s^*<1$

We also have that, at the steady state (for constant capital)

$$s^*f[k^*(s^*)] = \delta k^*(s^*) \tag{2}$$

Inserting $(2)$ in $(1)$,

$$c^* =  f[k^*(s^*)]  - \delta k^*(s^*) \tag{3}$$

We want to maximize steady-state consumption, so we take the first derivative and set it equal to zero,

$$\frac {\partial c^*}{\partial s^*} = f'[k^*(s^*)]\cdot \frac {{\rm d}k^*}{{\rm d}s^*} - \delta \frac {{\rm d}k^*}{{\rm d}s^*} =0 $$

$$\implies \big(f'[k^*(s^*)]\ - \delta \big)\frac {{\rm d}k^*}{{\rm d}s^*} =0 \implies f'[k^*(s^*)] = \delta \tag{4} $$

From the production function we have

$$f'(k) = \frac 1{\sqrt {k}} = \delta \implies k^* = \frac 1 {\delta^2}$$

The rest are evident.


Empirical Evidence on rational inattention:

-Title: Attention Discrimination: Theory and Field Experiments with Monitoring Information Acquisition,
Authors: Vojtěch Bartoš, Michal Bauer, Julie Chytilová, and Filip Matějka.
Source: IZA Discussion Paper No. 8058.

Link: Attention Discrimination: Theory and Field Experiments with Monitoring Information Acquisition

-Title: What Can Survey Forecasts Tell Us about Information Rigidities?
Authors: Olivier Coibion and Yuriy Gorodnichenko.
Source: Journal of Political Economy, Vol. 120, No. 1 (February 2012), pp. 116-159

Link: What Can Survey Forecasts Tell Us about Information Rigidities?

-Title: A Rational Theory of Mutual Funds’ Attention Allocation,
Authors: Marcin Kacperczyk, Stijn Van Nieuwerburgh, Laura Veldkamp.
Source: NYU Working Paper No. 2451/28347 June 5, 2014

Link: A Rational Theory of Mutual Funds’ Attention Allocation


Why is $\Delta p \Delta q$ in this diagram infinitely small?

It says "for small values of delta p and delta q". So something small times something small is something very small. Basically we are taking a limit and as delta p and delta q go towards zero, the product goes to zero faster.


Increase in the number of jobs in an economy: Central Bank raises interest rates?

When people find jobs, they start receiving salaries and their consumption increases. Increased demand for goods and services leads to increase in prices, or inflation. Fed is expected to respond with a rate hike to keep inflation in check.


Basic microeconomics: supply, demand and substitutes in production

Sounds pretty good to me. I think it would be more coherent to change the way you say this:

  As demand for ice cream rises, the demand curve for it shifts to the right, and assuming the supply curve for it remains still, this shift will increase both the price and quantity of ice cream. In turn, as ice cream prices rise, producers make more of it, and thus more skim milk.

I would change it to say this:

  As demand for ice cream rises, the demand curve for it shifts to the right, and assuming the supply curve for it remains still, this shift will increase both the price and quantity of ice cream. In turn, the increase in production will cause a upward shift in the supply of skim milk because skim milk and ice cream are "complements in production."

I make this change because you when you say that "this shift will increase both the price and quantity of ice cream" you have already said that the production of ice cream has increased (it increased along the supply curve).


How many Nash equilibria are there in the above game?

There can't be an equilibrium in which no one tells the police. In that case, it is a profitable deviation to tell since $v-c>0$.
There can't be an equilibrium in which more than one player tells the police. In that case, it is a profitable deviation for one of them to remain silent since $v>v-c$.
There are five pure strategy Nash equilibria in which only one player talks. This one player would be worse off by remaining silent, $0<v-c$, and the silent players would be worse off by telling, $v-c<v$.
Next, you consider mixed strategies. For the same reason as above, there is no equilibrium in which one or more players alway talk and others mix between talking and silence as pure silence is better given someone talks to the police for sure. Similarly, there is no equilibrium in which only one player randomizes and all others remain silent, as this one player would not be indifferent between both actions, talking is always better given the others don't.
There are equilibria in which two players randomize and the others are silent. Wlog, suppose player 1 and 2 talk with probabilities $p$ and $q$, respectively. For each player, talking always gives payoff $v-c$. Both players must be indifferent (otherwise they would not want to randomize). Hence,
$v-c = p v + (1-p)0 = q v + (1-q)0$ which we can solve for $p=q=\frac{v-c}{v}$. Given this indifference condition, it must also be a best response for player 3,4,5 to remain silent. This is true as $v-c\leq p^2 v + 2p(1-p)v$, because $v-c=pv<(p^2+2p(1-p))v$ and $p<(p^2+2p(1-p))$ for any $p\in(0,1)$. There are $\binom{5}{2}=10$ such equilibria.
Similarly, there should be $\binom{5}{3}=10$ and $\binom{5}{4}=5$ equilibria in which 3 and 4 players talk and the others are silent, and one equilibrium in which all five players randomize over both options with some probability $z$ solving $v-c=(1-(1-z)^4)v$.
All in all, there should be $5+10+10+5+1=31$ Nash equilibia.


Isn't recession is when there's an actual decrease and not just a less rapid growth?

NOTE: the question has been modified to refer to a global recession (or I missed the global qualifier). This answer is for a national recession. The answer by @Fizz discusses the global case. I will leave my answer unchanged.

There is no international standard for a recession definition. Definitions are country-specific. For example, in the United States, the National Bureau of Economic Research (NBER) has a committee that makes recession date determination decisions, based on a number of criteria.

The NBER has a FAQ, which probably covers everything you want to know: link.

(Other countries have similar committees.)

Otherwise, people use two consecutive quarters of declining real GDP as the definition of recession. The advantage is that this is uniform across countries. Some people call this a “technical recession” in countries that have a recession-dating body (like the NBER).

Note that we need to look at quarterly GDP, annual GDP could still rise (as in the question), yet there is a recession.

For countries that grow very rapidly in real terms, some people will call a reduction in the growth rate a “a growth recession”. The developed countries no longer grow that fast (in recent decades, only some Asian economies like China grew that fast on a sustained basis), and so it does not come up very often. As such, the term is not very well defined, since it is not used much.


Hint: how does a positive monotone transformation of the utility function affect the consumer's maximization problem?

Edit,

Suppose the optimal bundle for some agent with some utility function $u$ is given by $x^{*} = (x_{1}^{*},x_{2}^{*})$. Suppose then that I take the transformation of $u$ by some strictly monotone function $f$. I claim that $x^{*} = (x_{1}^{*},x_{2}^{*})$ is the optimal bundle for the new utility function $v = f \circ u$.

Suppose not, suppose that there is another bundle $\hat{x} = (\hat{x}_{1},\hat{x}_{2})$ such that $v(\hat{x}) > v(x^{*})$. But by the definition of $v$, we have $$\tag{In}\label{In} f(u(\hat{x})) > f(u(x^{*}))$$ Then, since $f$ is strictly monotone, it is invertible and so from \ref{In} we must have $u(\hat{x}) > u(x^{*})$, which contradicts optimality of $x^{*}$.

The $\ln$ function is one such strictly monotone function on domain $\Re_{+}$.


Why does the United States' national debt matter?

Government debt generally (not just for US) matters (but is not necessary a problem) for country's economy for several reasons:

The most obvious one, generally speaking, debt is not just free money. You have to pay interest rate on debt which costs money that could be otherwise put to other uses. For example according to the US. Treasury the interest costs of US debt in 2019 were almost 600 billion dollars. Now thats not much compared to the size of US economy, but it is not trivial amount as well. Also, this cost would increase with the size of government debt, so even though at current level the debt costs for US are not that large (relative to economy size), if US government debt would continue to increase its debt at rate that outpaces economic growth then eventually this would became a problem.
Having large government debt limits government ability to stimulate economy during recession. There are limits on how much government can borrow as pointed out by @Giskard in his comments. In recession it usually is optimal for government to run deficit to stimulate the economy, but that can be only done if there are people willing to borrow it enough money. Maybe borrowing from other countries could be affected by US soft power (that is question for political scientists) but most of the US debt is own by private people/investors (see here). Generally if people will think that likelihood of US to monetize or default on its debt is high they will be reluctant to lend more money.
Connected to the previous points, if debt to GDP is so high government cant raise enough revenue to pay for interest and nobody is willing to borrow US more, it has to either monetize its debt or default on it. Monetizing debt (creating new US dollars to pay for it) could potentially lead to high inflation, and while little bit of inflation is good for an economy high inflation rates can be disastrous. If US would potentially default on debt it would restrict the US ability borrow in future (however, note that at current level of debt to GDP US is nowhere near a point where this would be a concern. US bonds have still very high rating meaning markets think the probability of US default is incredibly small - in fact US bonds are still often used as an example of risk-free asset).
Governments and businesses are essentially competing for borrowing up peoples savings. Large government borrowing might decrease the amount that private business and individuals can borrow to fund their projects. Even when government debt is sustainable in the sense that debt to GDP ratio is stable, from social welfare perspective having large government debt can be bad, especially if you think that private sector could invest the money more efficiently (See Blanchard et al Macroeconomics, an European perspective for more discussion of this). This does not seem to be huge problem in the present for US because low interest rates indicate excess of savings, but it could be problem in future or at higher levels of debt to GDP.

Note that this list is not necessary exclusive, but I think it provides overview of main points that could cause economists to worry.

Also note, none of the above implies that gov. debt is necessary a bad thing. Depending on situation there is always some optimal level of public debt to GDP ratio (and this optimum in most cases is above 0). However, it is also not sustainable to have debt that is not on a stable path (debt that grows faster than the economy), and even sustainable levels of debt put drain on the economy unless the debt is used on projects that objectively have the highest marginal rate of return which is probably true for some of the gov. spending but its very unlikely to hold for all of it.

Furthermore, I don’t know many economists who would say that current level of debt to GDP in US is huge problem, rather many economists are worried that even when US economy is as strong as it is now, US gov keeps the debt to GDP more or less constant instead of trying to reduce it now so there is more fiscal space for dealing with next crisis. Most of those economists that worry about US debt do so not because of its size now but because of worry that it will increase to more unsustainable levels in the future if US gov. debt to GDP continues to increase.


Would GDP for a pure endowment economy be equal to zero?

GDP would not be zero in endowment economy in general. There are still prices and also interest rates, savings and investment in endowment economy. First, lets ignore other countries because foreign aid complicates GDP calculations (as Art pointed out if the endowment is foreign aid GDP would be zero). So lets suppose there is only one country, lets call it Arstotzka, which has an endowment economy (i.e. production is fully exogenously given).

A simple macro endowment model of economy would be the following.

There is one representative individual with following utility

$$u = \sum^T_{t=1} u(C_t)$$

where $U$ is the utility, and $C_t$ is a consumption at time $t$. Standard assumptions apply $U'(C_t)> 0, U''(C_t)< 0 $, that is utility is increasing but at decreasing rate.

Now this will be an endowment economy so lets assume initial endowment of $A_0$ and additional per period endowment $Y_t$.

Logically consumption must be equal or less the endowment, but rational consumers will always use up their whole resources (in this model there is no inheritance) so I can set it as an equality (this just simplifies the math):

$$\sum^T_{t=1} C_t= A_0 + \sum^T_{t=1} Y_t$$

This problem gives us the following lagrangian:

$$\mathcal{L} =  \sum^T_{t=1} u(C_t) + \lambda \left( A_0 + \sum^T_{t=1} Y_t - \sum^T_{t=1} C_t\right) $$

First order conditions are given by:

$$u'(C_t) = \lambda \implies C_1 = C_2 = C_3 =... =C_T $$

This means that the consumption will be same in each period because marginal utility of consumption is constant.

Hence we know consumption will be $C_t = \frac{1}{T}\left( A_0 + \sum^T_{t=1} Y_t \right) $

Furthermore, assuming no government and hence no public saving the saving is by definition just difference between endowment income and consumption at time $t$ $S_t = Y_t- C_t$

Now lets parametrize our model.

Lets suppose we only have two years $t=1,2$. Next the initial endowment is set to 0\$ (to simplify calculations) and the per period endowments are $Y_1 = 60\$ $ and $Y_2= 40\$ $

Hence consumption based on the above solution will be $C_1 = 50\$, C_2=50\$$ so in period 1 there is 10 dollars of savings and in period 2 10 dollars of dis-saving $S_1=10\$ $  $S_2=-10\$ $.

Now GDP using consumption approach would be in period 1 $Y = C + I + G = 50 + 10 + 0 = 60 $ (since $I=S$  which is the same which you would get through the income approach as by our set up the endowment in $Y_t = 60\$ $.

To sum it up GDP wont be zero because endowmends are income. In real life on a tax return it would be some windfall profit but regardless thats just semantics. In real life pure endowments dont exist so we dont really have a name for them in accounting formulas but the point of income approach is to add whole income of a nation regardless of how you call the source of income as long as it was produced withing borders of a country for GDP. For expenditure, approach you again just add all spending in an economy again regardless of the fact that spending was based on purchasing some some endowment output $Y_t$ or actually produced through some inputs.


How does a positive capital shock cause an increase in land price?

You might want to assume a Cobb-Douglas production function for the sake of simplicity.

$Y=A L^{\alpha_1} N^{\alpha_2} K^{1-\alpha_1-\alpha_2}$

Hint: Look at to the cross derivatives.


There are two ways I can think of interpreting this question.

My first thought is that a single bank doesn't lend out more money than it has, but the banking system does. So let's say someone deposits 100 dollars in Bank A and the reserve requirement is 10%. Then Bank A can lend out 90 dollars. Let's say that money is deposited in Bank B eventually. That bank can then lend out 81 dollars. This money then gets deposited in Bank C eventually, and it can lend out 72.9 dollars. This process continues, and if you take the sum of all this lending, you get that the money supply is now:

$$\sum_{n=0}^\infty 0.9^n(100) = \frac{100}{0.1} = 1000$$

So the banking system can lend out 1000 dollars without being considered unstable under this 10% reserve requirement. Notice how it kind of looks like we are double counting the money that is in the economy, and that's the point of fractional reserve banking. There isn't actually 1000 dollars, but there is credit worth that much floating around in the system.

The second way you could argue though is that individual banks in fact can lend more money than they have in their account. It creates an electronic record crediting the borrower's deposit with the sum of credit. So here, the limitation is still the reserve requirement. Say Bank A gets a deposit of 100 dollars. It can then lend out 1000 dollars at a 10% reserve requirement. Since it doesn't have 1000 in cash, it gives out credit.

I think that the real economy will use a combination of these two methods to get its lending out, but regardless, the result is the same. A simple money multiplier.

Edit: To reiterate (read: copy-pasted) from the comments below, how can a bank lend out credit that isn't backed up by paper/physical money?

FDIC insurance from the central bank, but more to the point,
The bank isn't going to back up all the credit at the same time. Say in our above scenario (100 dollars, 10% req.) the bank lends out "air money" of 5 dollars to someone, who then spends the credit purchasing from a business. The business then claims on that credit, and the bank still had some reserve (10 dollars in cash) to pay the business. Meanwhile, the bank, because it lent out so much credit, is also collecting a lotttt of interest, and borrowers pay back that interest...in cash. That replenishes the reserve. So in an equilibrium money market, hopefully the rate at which the bank gets cash in interest is the same as the rate which they pay back the "air money" with that actual cash.

Take the car example from in the comments. That is, say you "promise both your friends a car, but you only have one car and both friends know this". Well, the analogy is a little stilted, not quite parallel to what a bank is like. If you were a bank, you would only lend (not give away forever) out the car if you were promised to get it back with some interest, (maybe more gas or something). Problems only happen if both friends want the car the same time.


What's an example of a resource, raw material that has become scarce?

Some examples you might consider:

Fine art when the artist dies (this doesn't reduce the number of works by that artist, but does reduce the number of works that can be expected to exist in the future)
The electromagnetic spectrum - there are a bunch of interesting resources concerning auctions for space on the spectrum
Short .com domain names


What's the use of '% to GDP' type of variables?

Imagine that I am trying to determine whether eating corn has any effect on your height. I see that in the US, total corn consumption is 20 million tons per year (made up number, all others will be made up as well) and adding up the heights of the 300 million citizens we get 500 million meters. Similar statistics for France are 4 million tons per year and 100 million meters.

Total American corn consumption was higher, as well as total American height.
Is this because corn has an effect on height? Or is it that both statistics are likely to be proportional to the size of the country (measured here by population)?

Depending on what your exact hypothesis is, you may want to filter out size effects by measuring these statistics of the national accounts as % of GDP.


How to describe a utility function in words?

The best way to go about it is to examine the marginal rate of substitution.

Take
$$
x^\alpha y^\beta = C
$$
and use the implicit function theorem to derive the slope of the indifference curve:
$$
x^\alpha y(x)^\beta = C
$$
$$
\alpha x^{\alpha-1} y(x)^{\beta} + x^\alpha \beta y(x)^{\beta-1} y'(x) = 0
$$
$$
MRS(x) = y'(x) = -\dfrac{\alpha y(x)}{\beta x} = -\dfrac{y}{4x}.
$$
This gives the rate at which the consumer is willing to give up $x$ for $y$ and stay on the same indifference curve. In words, "If the consumer currently has the bundle $(3,4)$, he is willing to give up $4/12$ of a unit of the $x$ good for a bit of the $y$ good."

You might worry that the MRS does not full capture the Cobb-Douglas utility function, but you can recover Cobb-Douglas preferences by "solving" the differential equation $y'(x) = -\alpha y(x)/\beta x$, since it can be rewritten
$$
\dfrac{y'(x)}{y(x)} = - \dfrac{\alpha}{\beta x}
$$
and the left-hand side is the derivative of $\log(y(x))$ and the right-hand side is the derivative of $\log(x)$, implying that
$$
\log(y(x)) = - \dfrac{\alpha}{\beta}\log(x) + v
$$
so that
$$
\log(y(x)^\beta x^\alpha) = v
$$
and
$$
y^\beta x^\alpha = e^v = u(x,y)
$$
so that the MRS fully characterizes the Cobb-Douglas utility function.


How to find the cost function for perfect complements

Hint: Think how many units of $x_1$ and $x_2$ are needed to produce $q=1$ in order to minimize the cost. What about producing $q=2$? Can you generalize it?
In order to minimize the total cost, you want to use as few units of either input as possible. Imagine you wanted to produce $q$ units. You would need at least $x_1=q$ and $x_2=q$ (otherwise you wouldn't be able to produce $q$). Therefore, to produce $q$, you choose precisely $x_1(q)=q$ and $x_2(q)=q$. These are the derived factor demand functions. You only need to plug them in the cost identity
\begin{align}
TC(q)&=w_1 x_1(q)+w_1 x_2(q)\\
&=w_1 q +w_2 q\\
&=(w_1+w_2)q
\end{align}


Differentiating a conditional expectation: RBC models with uncertainty

As I noted in a comment, to consider non-trivially a derivative, we must have a non-constant function in the first place. So, in generic terms, we are looking at the conditional expectation function $E(X\mid Z)$ and not at the conditional expected value of $X$ given a specific value $Z=  z$.

Then, $E(X\mid Z)=g(Z)$, i.e. it is a function of $Z$ only, not of $X$, so it appears that its derivative with respect to $X$ should be zero.

But: the way the problem is formulated, we treat the $X$, ($A_{t+1}$ in the OP's example), as a decision variable. Namely as a variable for which we can choose the value that it takes. But this conflicts with the fundamental characteristic of a random variable, i.e. that it is not under our control and its actual realization is unknown.  By treating it as a decision/command variable, we effectively neutralize any aspect related to a random variable, the conditional expectation aspect in our case. And it is in that sense that we can consider the derivative "ignoring" the existence of the conditional expectation operator.

Note that, for the problem laid out at the end of OP's question, if income $Y_t$ is known at the time of the decision for current consumption, then $A_{t+1}$ is also completely determined, there is nothing random/unknown/uncertain about it. This then allows, in a Lagrangian formulation, to treat $A_{t+1}$ also as a decision variable and consider derivatives with respect to it.


How constant returns to scale leads to zero economic profit?

The argument is that if there are constant returns to scale then the marginal product of each factor of production is constant as total quantity changes. This makes the production function homogeneous in the first degree and it will look something like
$$Q=\dfrac{\partial Q}{\partial A}A +\dfrac{\partial Q}{\partial B}B +\dfrac{\partial Q}{\partial C}C$$

Then if each factor of production is paid at a rate equal to its marginal product, the complete value of the production will be distributed to the factors of production, since

$$PQ-\left(P\dfrac{\partial Q}{\partial A}A +P\dfrac{\partial Q}{\partial B}B +P\dfrac{\partial Q}{\partial C}C\right)=0$$

so there will be no economic rent or profit

The practical problem with this is that constant returns to scale is a very strong assumption.  The theoretical problem (at least for marginalist theories) is that there is no natural equilibrium for the level of production


Log of a Negative Market-Book Ratio in a Regression Model

Well the problem can be dodged by the use of some simple solution of just adding a constant to all values which circumvent issues of taking logarithms of negative numbers. Usually the mean is used as a centering point. If the mean is negative though some other number must be chosen.

Interpretation of such a transformed variable would be different from its regular logged counter part.

These are just some hunches on what could have been done. Its odd that methods aren't mentioned for this case.


How much physical currency does the Fed transfer to banks per year?

The amount of currency in circulation (bills and coins) is published by the Federal Reserve. (Available at the FRED web site.) The annual change in this time series is the amount created.

This is the amount outstanding, it does not tell us how much currency is being destroyed and replaced. Also, there is seasonal demand for currency, and some cash is shipped back and forth.

The creation of currency is not really a "transfer" (gift). The banks need to buy the currency by exchanging reserves (settlement balance at the Fed) for the notes.

Finally, the Federal Reserve does not single out how much it deals with any particular banks by name under normal circumstances. (During some of the special operations undertaken after the Financial Crisis, the Fed published some information about their counterparties.) The most you would get would be on the basis of the category of bank.


Does anyone recognize the shape of this residuals vs. fitted plot?

If you watch closely, you will find out that the slope of the lines is -1. I.e. the values of y along every one of the lines are exactly equal. That is you get this lines only because you have great many cases for which the left hand side variable is equal. The lines are visible because relative to the number of observations there are not that many different values of y.


The tangent lines are drawn because they are trying to get you to think about the magnitude of the slope at each point on the production function. The marginal product of labour is the derivative of the production function, and will look like a decreasing function when drawn graphically, starting off with high values for low levels of labour, then decreasing to low values for high levels of labour. This corresponds to how the slope of the production function starts off steep and then gets flatter. Because the gradient decreases, this is called 'diminishing' returns.

We assume capital is constant when looking at this graph.


Are cryptocurrencies a ponzi scheme or a bubble?

In general, "Ponzi schemes" in the context of asset pricing refer to "rational bubbles", or a failure of the transversality condition you need when passing from a flow identity to a present value identity. They are not "fraudulent schemes". For instance, there can be a rational bubble on a "fundamentally" worthless asset in a perfect foresight world if its price grows at the real interest rate available in the broader economy. (This is actually what you're talking about, in case it's not clear to you - each investor assumes they can offload the asset at a higher price to another investor, and you push the problem of the "greatest fool" to infinity, which makes the assumption a rational one ex post.)

Is there any evidence for the existence of such rational bubbles? Cochrane (2002) points out that rational bubble theory does not account for the association of "bubbles" with high trading volume. In a rational bubble, it is rational to hold the asset in every period: there's no reason to observe high turnover along with high prices. They are also silent on the association of high prices with high volatility - in a rational bubble context, volatility (induced by shifting from one equilibrium to another) is always present, and the choice of equilibrium (the fact that we're on an explosive price path) does not produce more volatility than usual. Rational bubbles appear to be a poor explanation of events that people have historically described as "bubbles" (and of the price behavior of cryptocurrencies).

In contrast, the convenience yield theory outlined in Cochrane (2002) and also in this blog post seems to fit the data much better. If "overvaluation" is driven by a liquidity premium induced by shorting constraints and a short-term constraint on supply, then we would expect to see the standard prediction of monetary economics that high prices should be associated with high turnover. In that case, overvaluation relative to "fundamentals" should also require shorting constraints - in the case of dollars vs treasuries, for instance, it's illegal to print banknotes or close substitutes to money to finance a purchase of bonds, which is a kind of shorting constraint. Indeed, shorting constraints are what we see in the cryptocurrency market: BTC futures have only recently started trading on stock exchanges, and even then the "electronic paper" that you hold when you take the long side of a BTC futures contract is not the same thing as holding BTC directly, so what appears like a possibility to short BTC through these contracts is in fact not so. (It satisfies "speculative demand", so it's possible to "bet on cryptocurrencies" without having to hold any, but it's not possible to use these contracts in the place of cryptocurrencies in transactions.)

If you want to ask whether cryptocurrencies are a bubble, then you have to define what "bubble" means. If it is "overvaluation relative to fundamentals", then is USD a bubble? After all, it's trading at a premium relative to T-bills. If you include any convenience yield the asset may have in your definition of "bubble" so that USD is not one, then it's likely that cryptocurrencies are not "bubbles" either. It's very difficult to say anything about whether cryptocurrency valuations are "justified" or not by this explanation, since the convenience demand of cryptocurrencies, like of cash, has components which are not transparent. We're mostly in the dark, and I wouldn't try to outguess the market price of an asset in a circumstance where we know next to nothing about the factors which are driving the convenience demand for it.


What are estimates of the elasticity of demand for credit with respect to interest rates?

These papers look relevant, to one degree or the other:

Karlan, D., & Zinman, J. (2009). Observing unobservables: Identifying information asymmetries with a consumer credit field experiment. Econometrica, 77(6), 1993-2008.
The authors write:"We estimate the presence and importance of hidden information and hidden action problems in a consumer credit market using a new field experiment methodology. We randomized 58,000 direct mail offers to former clients of a major South African lender along three dimensions (...) These three randomizations, combined with complete knowledge of the lender's information set, permit identification of specific types of private information problems. (...) We find strong evidence of moral hazard and weaker evidence of hidden information problems."

Mandell, L. (1971). Consumer Perception of Incurred Interest Rates: An Empirical test of the efficacy of the Truth-In-Lending Law. The Journal of Finance, 26(5), 1143-1153. "The purpose of this article is to use national sample survey data to measure
the effect of the Truth-in-Lending Law (enacted in 1969) on the consumer’s knowledge of interest rates that he is actually paying on an installment loan.(...)
Aside from measuring the overall effect of the law on all persons, analysis
of various population subgroups will be made to see whether the law has had
differential effects upon the interest rate perception of persons based upon
personal characteristics such as age, income, amount borrowed, total debt and
education."

Calem, P. S., & Mester, L. J. (1995). Consumer behavior and the stickiness of credit-card interest rates. The American Economic Review, 1327-1336.
The authors present empirical evidence (from a 1989 Survey) that supports the "stickiness" of credit card interest rates, attributing it, as they write, to "(i) consumers facing search costs; (ii) consumers facing switch costs; and (iii) firms facing an adverse-selection problem if they were to unilaterally reduce their interest rates."

Ausubel, L. M. (1991). The failure of competition in the credit card market. The American Economic Review, 50-81. The original paper to which the previous one provided additional support. It contains both theoretical discussion and empirical evidence, as well as counterfactual calculation (what "would" the interest rates be if perfect competition held in this market).


Why do so many models assume homothetic preferences?

Here a short answer: Homothetic, identical preferences have the modelling advantage that the distribution of income across individuals does not matter for aggregate demand. That is, if you want to study, let's say, monetary policy where you do not expect changes in the distribution of income to affect your policy recommendations, then this is a reasonable assumption to make. If you want to study questions where changes in the distribution of income have large impact on policy recommendation (e.g., optimal taxation) this may be a bad assumption.


Do free-trade economies typically offer any protection for domestic markets?

I think the (or at least, a) relevant concept is that of non-tariff barriers to trade. Wikipedia has a nice summary.

Let me quote a couple of sections from the article:

  Non-tariff barriers to trade (NTBs) or sometimes called "Non-Tariff Measures (NTMs)" are trade barriers that restrict imports or exports of goods or services through mechanisms other than the simple imposition of tariffs. The SADC says, "a Non-Tariff Barrier is any obstacle to international trade that is not an import or export duty. They may take the form of import quotas, subsidies, customs delays, technical barriers, or other systems preventing or impeding trade." According to the World Trade Organisation, non-tariff barriers to trade include import licensing, rules for valuation of goods at customs, pre-shipment inspections, rules of origin ('made in'), and trade prepared investment measures.

-

  According to statements made at United Nations Conference on Trade and Development (UNCTAD, 2005), the use of NTBs, based on the amount and control of price levels has decreased significantly from 45% in 1994 to 15% in 2004, while use of other NTBs increased from 55% in 1994 to 85% in 2004. [...] The need to protect sensitive to import industries, as well as a wide range of trade restrictions, available to the governments of industrialized countries, forcing them to resort to use the NTB, and putting serious obstacles to international trade and world economic growth. Thus, NTBs can be referred as a new of protection which has replaced tariffs as an old form of protection.

So regulatory and similar barriers to trade have become widespread—often as a way to circumvent restrictions on protectionism.


What is the relationship between the disciplines of Economics and Economic Geography?

I see both Economic Geography and Ecological Economics as different.
Economic Geography is the study of the determinants and effects of the spatial distribution of economic activity. Economic Geography is considered as a sub-field of economics, so it's applying standard economic thinking to the geography. In particular, Paul Krugman studied the location of economic activity across space, using agglomeration economies to explain why industries cluster within particular countries and regions.
According to Robert Costanza, Ecological Economics is a transdisciplinary field. It studies the interdependence and coevolution of human economies and natural ecosystems. It's true that this coevolution is studied both intertemporally and ... spatially, but not as a sub-field of economics. It's an attempt to look at humans embedded in their ecological life-support system, not separate from the environment.


advanced mathematical treatement of revealed preference and utility theory?

Here is a good, thorough book on revealed preference theory. I copied the bibliographic information from my Kindle copy.
Title: Revealed preference theory / Christopher P. Chambers, Federico Echenique. Description: New York : Cambridge University Press, [2016]

Chambers, Christopher P.; Echenique, Federico. Revealed Preference Theory (Econometric Society Monographs) . Cambridge University Press. Kindle Edition.

There is also the 1988 classic by David M. Kreps, Notes on the Theory of Choice (Westview publishers) and the 2013 Microeconomic Foundations I, also by Kreps (Princeton University Press) has quite a thorough discussion.


What are the economic after effects of a 10% pay cut to all state employees?

From a simple and purely theoretical point of view:
Option (A) would give you a lower level of consumption and income state-wide and generally is a budget-balancing method, not an economic equilibrium-producing method. Option A is surely on the opposite side of the "policy target" spectrum, compared to B and C.
Option (B) is considered best when prices are not "sticky" - that is they drop quickly on a recession. Current data shows ( https://fred.stlouisfed.org/series/CP0000USM086NEST , https://ycharts.com/indicators/us_monthly_gdp ) that prices in the US have dropped but at a very lower speed than GDP, so I'm inclined to call them sticky.
(To put it bluntly: When that happens, people lower their food and medicine consumption, they get sick and die. Not the best idea. )
When that doesn't happen, and prices adjust quickly for the amount of income lost, equilibrium ensues. I'm inclined to say that this has never happened in the history of the human race, apart from closed experiments. At the very least, I know of no such case in modern economic history (that is, after the Renaissance till now).
Option (C) is the approach that is thought of as most successful when sticky prices occur, because a stimulus bill will put money in people's hands and consumption and production will return to their "equilibrium" level faster.
Critics of option (C) -which seems to be the most fitting at the time- cite concerns over inflation rates higher than those prior to the crisis, and also, there are problems concerning the distribution of money, that is, if no one pulls strings over the system. We wouldn't want to be ignorant over political matters.


Cointegration in stock market between different market places

Your question is not particularly clear - but let me try to give some elements that may help:

Think about why do you want to convert prices into the same currency? Pure stock market performance is usually evaluated using Local currencies. You can compute daily, weekly or monthly returns (that is % price increases) for each stock index and then do whatever analysis you wish to do: correlations, cointegrations ... you name it.
If you really need to convert indices into the same currency, you should take the close price in local currency and then convert that price into the currency of your choice (Bloomberg does this for you if have an acces, otherwise you will find exchange rates on the IMF website). Then you compute the returns as in 1.


What is the ideal way to update an old value to today's currency value?

I think this question stems from misunderstanding from what inflation is. My best guess is that this happened because most macro books will say that inflation is a monetary phenomenon as in mainstream economics it is accepted that inflation over long periods of time is affected mainly by money supply. This is illustrated by equation of exchange (see Blanchard et al Macroeconomics an European Perspective) which is given by:
$$P= MV/Y$$
This is the same equation that Brian also mentioned in his comment just solved for prices. Here $P$ are the average prices, $M$ money supply, $V$ velocity, and $Y$ real output. The standard textbook argument for inflation being monetary phenomenon goes like this. Velocity is assumed to change over business cycle but not really over long run and hence it cannot be responsible for all inflation and we can hold it constant. Moreover, real output tends to increase over time which should be deflationary. Hence the argument goes that over long run inflation should be caused by $M$.
However, this does not mean that inflation is defined in terms of $M$. The definition of inflation is simply the change in average prices for example:
$$\pi_t= \frac{P_t-P_{t-1}}{P_{t-1}}$$
This is what inflation is. Moreover, inflation also is measure of how money looses value. The issue is that money especially in short run might not loose value just because there is more of it (i.e. by $M$ increasing) but also because velocity changing or real output dropping. Furthermore, $M$ and $V$ are not always independent. At zero lower bound any increase in $M$ will be offset by changes in $V$ because at zero lower bound peoples preference for holding (but not necessary spending) cash will be infinite (abstracting from issues such as storage costs for large sums of cash). What even more, models that are above simple undergraduate textbooks rely not just on actual values of $M$, $V$ and $Y$ but also on peoples expectations of these (see Krugman 1998).
Hence you simply cannot calculate how money looses its value from $M$. At minimum to calculate change in $P$ using $M$  you would need to know and control for not just what $M$ is but also what real output is and velocity is but here you will run into problem that real output is usually calculated by deflating nominal output by CPI - so you introduce the same problem you wanted to avoid. What even worse velocity itself is usually not directly observed but imputed from data. And this is all before we start factoring in all the expectations we should that are extremely difficult to measure. Compared to such convoluted way using CPI directly is far more sensible even if it may be imperfect measure.


Intuition for the CES consumption index in New-Keynesian DSGE models

Heuristically, you can think of the integral as just a sum:

$$ \bar{C} = \left( \sum_{i=1}^n C_i^{1-\frac{1}{\epsilon}} \right)^{\frac{\epsilon}{\epsilon - 1}} $$

where $\bar{C}$ is an index of aggregate consumption, and utility is given by $u \left( \bar{C} \right)$.

It's easy to check that the marginal rate of substitution between goods $j$ and $k$ is given by

$$ \text{MRS}_{jk} = \left( \frac{C_j}{C_k} \right)^{-\frac{1}{\epsilon}} $$

which means that the (absolute value of the) elasticity of substitution is $\epsilon$.

With a continuum of goods, the analogue of summation is integration, and you can (loosely) think of the MRS between goods $j$ and $k$ as

$$ \left( \frac{C_t (j)}{C_t (k)} \right)^{- \frac{1}{\epsilon}} $$


You cannot empirically calculate the demand function in your current setting. Finding a demand function is indeed very difficult in general.

What we can observe, i.e. the data you have, is the market equilibrium over time, i.e. the equilibrium price and quantity levels. These are determined by the interplay of supply and demand. So when you observe a price and quantity you are not observing demand, but rather a combination of demand and supply.

To find the demand curve, you would need, for example, an instrument variable, i.e a variable that is correlated with demand, but independent of supply.


a question on the endogenous growth model

"Endogenous Growth" is actually the short version of saying "Endogenous Technology Growth"

Exogenous (Technology) Growth Models

The rate technological progress $g$ is Exogenously given.

In both Solow and RCK, we can find $A_t = (1 + g)^t A_0 \ \ $(or $A(t) = A(0) e^{gt}$ if in continuous time). $Y$ increases over time because $A$ increases over time. This assumption of growth rate is very strong.

Endogenous (Technology) Growth Models

The rate of technological progress is Endogenously determined.

For example in Two-Sector Growth Model (Rebelo), we have

production $Y = C + I_K =  A \ (vK)^\alpha \ (uH)^{1-\alpha}$ and education $I_H = B \ ((1-v)K)^\alpha \ ((1-u)H)^{1-\alpha}$

Now $v$ and $u$ are endogenously determined, and thus $H$ is endogenously determined. $A$ doesn't change, but $Y$ will increase over time due to increase in $H$.

Another example will be the Learning-by-Doing Model.

Recall in Exogenous Models $A_t$ is exogenously given by $A_t = (1+g)^t A_0$

But now we want $A_t$ to be determined endogenously. Thus we assume technological progress is due to knowledge creation, and knowledge is a side-production of investment. And thus we let $A_t \equiv \sum_{i=0}^N K_{it}$ (there are N identical firms)


Why does savings equal investment (scenario)?

To clarify the first scenario: you assume Joe can buy this car. However, Joe has to either earn an income (and therefore, produce something himself) or he has to dissave. In the first case, Joe has produced 500 output and earned an income of 500. He spends his income on a car, but Amanda saves the money. As is clarified in other answers, Joe's output goes to inventories (because not purchased by Amanda), which are counted as (unplanned) investments. S = I = 500, C = 500, Y = S + C = 1000. You mention in a comment that most consumers do not produce something. In fact, they do. At work, when earning their income (with which they buy the car), they created added value (this is the production (500) that goes to the inventory when Amanda does not buy it). Think of the income they earn at work as their part in the created added value, their contribution to real production. Consider the second case when Joe does not work.

In the case Joe dissaves to buy the car instead of working and using his income (he just drives around, without producing), 500 savings have to be deducted from your final result for the first scenario, so that S = I = 0, C = 500, Y = S + C = 500.

In the second scenario, forget about Joe's 500 for a while. Assume Amanda invests 250 (one car) in inventory, which means she has produced 250 (one car) first (and sold nothing), so that I = Y - C = 250, C = 0. Consumption is zero because Amanda sold nothing and Joe bought nothing.

An income can only be earned when value added was produced. Therefore, the  500 Joe has received cannot be seen as an income, and since only income can lead to consumption or saving, Joe had neither consumed nor saved. The 500 Joe received is an expansion of money supply (and has no real interpretation) and will increase prices proportionally (assume V and Y to be constant in the fisher equation (MV=PY)). The 250 that Amanda produced has now increased in value, but in real terms her investment in inventory will still refer to the 250 (one car).

This actually illustrates the importance of distinguishing nominal and real variables in the economy. The macro-economic identity you refer to is only about real variables.


How does the Federal Reserve reduce "excess reserves"?

As you point out excess reserves have indeed been going down since around 2014.

The Federal Reserve doesn't force member banks to withdraw excess reserves, although the Fed can provide incentives to do so by lowering interest rates on those reserves. In other words, excess reserves have been going down because member banks have chosen to withdraw reserves to, for example, purchase financial assets.


Under the gold standard, how did the redemption of gold work in practice?

It depended on the year and if a banking suspension was in effect in the town.  In 1834 it was absolutely true that you could walk up to a bank and demand one ounce of gold or in some time periods silver for \$20.67.  Of course, you would have to accumulate \$20.67 which was a lot of money.  The Treasury would demand upon receipt of a banknote any and all gold represented by those notes at all times during this period.

You should double check the amount because I thought it was pegged at $20 over that time period.

  Temin, Peter.  The Jacksonian economy  Norton New York  1969

EDIT

The converse was not true unless it was a minted coin.  The period was known as the free banking era.  I hadn't noticed the converse question.  You should read Temin's book.  There are also other books on the free banking era.  Paper money was not printed by the United States until Lincoln authorized the creation of demand notes under an 1861 Act.  See

  Statutes at Large.  37th Congress, 1st Session. Chapter XLVI.


Why don't governments mandate a wage decrease in recessions?

I will only attempt to give a partial answer, since the full answer is very large. You could possibly create new questions that are narrower to follow up. (My feeling is that this website works best on narrower questions.)

One possibility is that New Keynesian theory is just plain wrong. As a disclaimer, that is my view. However, that is a controversial view.
The next issue are practical problems that standard New Keynesian models ignore.

I am not going to discuss (1) in great length. I think the standard critique of sticky prices (which goes back to Keynes) is that you are cutting nominal demand at the same time. The economy will not return to full employment, partly for reasons I cover in (2).

The problems with trying to cut wages and prices are as follows.

Legal. Does the government have the authority to do so?
Practical. How do we know whether a firm has complied, without having a ministry in charge of price administration? It’s not as if workers will voluntarily run to the government to say that their wages were not cut. We cannot put in place such a ministry during a recession, which typically lasts months.
Ignores the effect of debt. Most people and firms have mortgages and other fixed obligations. Broad-based income cuts would result in a mass default event, which will cause a recession to turn into a full-fledged financial crisis.
The government has just seized control of price setting (which was historically done in the 1970s to control inflation). How does it set prices in order to achieve its objective? How does the government exit?


The following information comes from this report, which was published by the British Government.

I'm not going to summarise the whole thing, but go over the major points. However if you are interested in the topic I suggest you read the whole thing, or even take a look at the more technical version which can be found here.

The report breaks down the higher costs into three issues:

Policy and systemic issues
Funder/client issues
Supply chain delivery issues

Policy and Systemic Issues:

Urban Density: The report indicates that high urban density coupled with high land costs has driven up the price of infrastructure in the UK, however it says that it does not adequately explain the whole problem.
Planning and consultation process: Inconsistency between how planning works with different areas of the country as well as general constrains placed on the early planning process has been marked as a key driver of higher costs in the UK than Europe.
Regulatory Compliance: The report indicates that high environmental and safety regulation has led to what some contractors call "not cost effective". However the report also mentions that the UK has the best safety record in Europe. So it would be a tradeoff to lose such regulations.
Wider construction market issues: The UK has the smallest construction market of the big five countries in Europe which has seen a shift from fixed to variable resources. This means there are less firms investing in construction which leads to higher levels of subcontracting and supply chain specialisation. The report argues that this leads to higher transaction costs along the supply chains.

Funder and Client Issues:

Stop and start investment: The report makes a very interesting argument here whereby it says that the UK's short term investment plan compared to Germany and Frances long term investment plans, allows the latter countries to reduce costs. This is because it allows for opportunity for innovation and the ability to plan work more efficiently. As well as the fact that it generates investor certainty as the projects are more long term.
Poor governance and ineffective incentivisation of cost control: The report argues that the tender process is not focused on cost minimization and there are not enough ways to incentivise it. As most projects work through a quoted budget as opposed to aiming for the lowest cost for a required peformance.
Poor asset information and cost data: The report argues that lack of information about infrustructure costs makes for poor descion making.
Commercial issues and procurement processes: The UK relies heavily on bespoke specifications and contracts, where out of the box solutions would often suffice. Many western european countries have the nature of these contracts codified in law, whereas the UK doesn't.
Insurance: More expensive in the UK

Supply chain delivery issues

There is poor supply chain integration in the UK
There is high fragmentation among construction industries in the UK leading to inefficincies
Large skills gap
Lower productivity

tl;dr

  "There is no single overriding factor driving higher costs. However,
  the investigation has identified that higher costs are mainly
  generated in the early project formulation and pre-construction phase"


Is cash(currency) a security and a debt instrument?

I don't think cash could be described as a security... one of the characteristics of securities is that they have imperfect (if very high) liquidity and provide a return (be it fixed or variable). Cash is the definition of liquid and inherently provides no return - you could earn interest on cash by depositing it in a bank but then you are creating a debt obligation in effect - the cash inherently, as in cash in a physical safe, generates zero return nominal by definition. You could think of cash as a debt security where a debt is theoretically placed on the issuer. But: in practice the debt is impossible to pay. You cannot bring a bill into the fed and demand they honour it. So I suppose it would be a debt security in the theoretical sense but it lacks almost all properties of debt securities:
cannot be repaid in practice, never intended to be repaid, perfectly liquid etc, and it has a value that cannot be expressed in terms of anything but itself.


Indifference curve - Does $dU = 0$ hold in higher dimensions? / Problem of integrability

Seems to me $dU = 0$ is true by definition unless $dU$ is not defined

because the function $U$ is not differentiable in some variable.
E.g. $$U(x,y) = |x| + y$$
because there are a countably infinite number of dimensions but the partial differentials are not always absolute convergent and hence cannot be summed up. E.g.: $$U(x_1,x_2,x_3,x_4...) = x_1 - x_2 + x_3 -x_4...$$
because the dimensions have a larger than countably infinite cardinality. I have never seen this in micro but it is theoretically possible. E.g. expected utility over continuum states.

Edit:
This seems to offer an extremely thorough walkthrough of the integrability problem in $n$ dimensions.


What are alternatives to lottery that would create same economic impact?

Municipal bonds are a method of local funding. The bonds could be funded through borrowing money or tolls. The bonds will probably yield better returns than the lottery for money givers. This means that municipal bonds could be an effective way of generating revenue in a short period of time. On the other hand, one key difference between bonds and the lottery is that at some point, additional funding is needed for bonds, whether through tolls or borrowing.


Yield curve and cash rate (multiple choice)

D)

A can be eliminated because the yield curve includes expectations of future rates (forward rates).

B is true but incomplete because it doesn't include monetary policy or current long term rates.

C is mostly true, but incomplete because it doesn't mention the expectations for future short term rates.  You could also make an argument that the curve does not include expectations for long term rates.  For example, if the curve goes out to 30 years, it does not give you the 6 month forward 30 year rate.  Therefore if your definition of "long term rates" is the 30 year rate, the curve does not provide expectations for


Is market failure the same allocative inefficiency?

In this context 'market' usually means some allocation mechanism. For example free market, or a market where someone has monopoly power. Allocation of goods and resources can be done in other ways: e.g. you can divide all resources evenly among production processes and all goods evenly between consumers. This will generally result in allocative inefficiency (were all production processes equally important and efficient?). But it is not market failure because there was no market, just an allocator/social planner.


Why doesn't Barnes and Noble just lower its prices?

Kling's maxim: Price Discrimination Explains Everything
Who are the sorts of people that purchase at Barnes & Noble? Less price elastic buyers, like those that are purchasing a gift, those less comfortable with buying online, those that value in store recommendations and assistance, and those that just like the in store experience. Barnes & Noble wants to maximize profits, not maximize revenue. Selling to more price sensitive buyers like you means also lowering prices for less price sensitive buyers.
Say the cookbook costs Barnes & Noble \$15 to buy. If they set the price at \$20 they make \$10 of profit selling one copy to you and one copy to the price inelastic buyer. If they set the price at \$40 they make \$25 in profit selling just one copy to the price inelastic buyer.
In summary: Barnes & Noble targets buyers willing to pay high prices and lowering prices means making so much less per unit sold that they cannot make up the lost profits on higher quantities