Buy-or-sell deal when there is cash shortage

Let's assume $A$ stated that the company is worth $P$.

I propose the following mechanism:

$B$ has to choose one of two alternatives:

Sell his share for $bP$.
Pay an amount of his choice, $x\leq aP$, and then with probability $\frac{bP+x}{P}$ get $A$'s share and with probability $1-\frac{bP+x}{P}=\frac{aP-x}{P}$ lose his own share (in addition to paying $x$).

If $B$ thinks that the company is worth less than $P$, he should go with the first option, just like in the original scheme.

Otherwise he should pick the second alternative, paying as much as he can to maximize his profit expectation. Should $B$ have enough money, he would pay $aP$ and get $A$'s share w.p. 1, if not, there is no way of allowing $B$ to get the company without ripping $A$, unless this is done randomly..


Imagine you're Player 2. What different "scenarios" could you find yourself in?

If Player 1 chooses Right, then Player 2 could observe if Nature played Up or Down. So you have 2 information sets there.
If Player 1 chooses Left, then Player 2 couldn't differentiate between (Up, Left) and (Down, Left). How many information sets should there be here?

So in total, you should have how many information sets? You currently have 4. Which one should you "combine"?


Does GDP typically refer to Real GDP or Nominal GDP?

The dataset states "Annual percentage growth rate of GDP per capita based on constant local currency" so it real GDP growth in this case.
GDP can refer to both nominal and real GDP, there is no preferred meaning. You have to read what is written in text/dataset.


In many models, we assume that firms simply want to maximize profits, and there are no externalities. If these assumptions are true, then a free market will be racism-free, gender-blind etc, etc. However, this is not the case in the real world. People that own and operate firms not only want to maximize profits, often they also have all kinds of biases, including social biases like racism, sexism, etc; as well as cognitive biases, for example when they want to make the firm as big as possible even if that is not profitable. In all cases, this biases necessarily mean forgoing profits. For example the paper you cite. Ross Levine has other papers on the topic.

However, the question of segregation is broader than this. For some type of relationships, "segregation" can make economic sense. For example, if you have a common resource, like a lake that provides some fishes, limiting who has access to such lake to only people who take care of the lake and does not overfish it, can have clear advantages, and be socially efficient.

In short, segregation can be the result of a friction, like cognitive or social biases. This is not a market failure, properly speaking, but it entails some inefficiencies, so in that sense, it does not make "economic sense". But you can also have segregation, being the optimal response to a situation that involves externalities (like in the example of the lake). This segregation can make "economic sense" in that it is individually rational, and it may or may not be socially efficient.

Consider an example where it is likely not socially efficient. Suppose there is a big proportion of people who are racist, and you own a restaurant. Let's assume you are not racist and you only care about maximizing profits. It is perfectly reasonable to think that you will deny service to people based on race if that will make your racist costumers more likely to visit your restaurant. This segregation makes "economic sense" even though it might not be socially efficient in some way or desirable (the social welfare can be measured in many ways). Notice that I needed to assume that your other customers somehow have negative externalities from you selling to racial minorities.


Find all of the Pure and Mixed Strategy Nash Equilibria

I assume that you are calculating a mixed strategy for the row player so that the column player is indifferent between choosing $A$ and $B$.  And the reason why you get a negative probability is that the row player cannot make the column player indifferent by choosing, say strategy $C$, with a positive probability $\in [0,1]$.  This is because the column player (always) strictly prefers $B$.

  Side-note: To avoid such confusion in the future, try to see whether you can apply math to calculate a mixed strategy to a game.  Here you clearly cannot (because of the above argument), and that is why math is giving you a ''weird'' answer.  Namely, math yields an answer to a question: What would be a hypothetical probability with which the row player chooses, say, strategy $C$ to make the column player indifferent?


Specifying a Diff-In-Diff with multiple treated groups over multiple years

Firstly, the diff-in-diff already is a fixed effects estimation. If you run a regression with FE and your time variant terms ($S_i*T_t$ and $T_t$) as in the plain and simple diff-in-diff setup, as such:

$$ Y_{it}=B_0+B_1T_t+B_2S_i+B_3S_i*T_t+e_{it} (1)$$

You should obtain similar results. Secondly, your specification -- since it will be on a multiple treatment setup -- should consider if your treated groups in different periods of time are disjoint, that is, if a unit of observation might receive the treatment multiple times. Considering that adding a fixed effects in time might be convenient for your estimation, as you were considering, I would work with the following specification if the the treated groups are disjoint:

$$ Y_{it}=\alpha_0+\alpha_1S_i*T_t+\alpha_2S2_i*T2_t+v_t+u_i+e_{it} (2)$$

And if they are not disjoint, I would consider a interaction between the treatment effects:

$$ Y_{it}=\beta_0+\beta_1S_i*T_t+\beta_2S2_i*T2_t+\beta_3(S_i*T_t)*(S2_i*T2_t)+v_t+u_i+e_{it} (3)$$

You should also consider testing the common trend hypothesis, since you still need an adequate control group.


Can government and people spend money foolishly be a main cause of inflation?

No, it cannot cause inflation. Inflation is a general rise in the price level, a decrease in the purchasing power of money. While military spending, for example, could cause inflation if paid for through seigniorage (essentially, devaluing a currency by printing more of it), there's neither any reason in theory nor any empirical evidence to support the idea that inflation would result from military spending per se.

Intuitively, if spending were shifted toward military expenditures and away from consumer expenditures, the price of consumer goods would likely fall, not rise. Similarly, the effect on producer prices would be ambiguous, as the price of consumer goods would likely fall, while the price of military goods would likely rise. If prices aren't rising, you don't have inflation.


How does Marx economics get evaluated in modern economics?

Here are some comments on Marx from people who can certainly not be called marxists.

  If Karl Marx and V. I. Lenin were alive today, they would be leading
  contenders for the Nobel Prize in economics. Marx predicted the
  growing misery of working people, and Lenin foresaw the subordination
  of the production of goods to financial capital’s accumulation of
  profits based on the purchase and sale of paper instruments. Their
  predictions are far superior to the “risk models” for which the Nobel
  Prize has been given and are closer to the money than the predictions
  of Federal Reserve chairmen, US Treasury secretaries, and Nobel
  economists, such as Paul Krugman, who believe that more credit and
  more debt are the solution to the economic crisis.

Paul Craig Roberts,  United States Assistant Secretary of the Treasury for Economic Policy under President Reagan in 1981, Source

  The American economy is still, by most measures, deeply depressed. But
  corporate profits are at a record high. How is that possible? It’s
  simple: profits have surged as a share of national income, while wages
  and other labor compensation are down. The pie isn’t growing the way
  it should — but capital is doing fine by grabbing an ever-larger
  slice, at labor’s expense.

  Wait — are we really back to talking about capital versus labor? Isn’t
  that an old-fashioned, almost Marxist sort of discussion, out of date
  in our modern information economy? Well, that’s what many people
  thought;

Paul Krugman, Nobel Prize in Economic Sciences 2008, Source

  extraordinary that 100 years after Das Kapital ... so little else
  should have emerged

Sir John Hicks, Nobel Prize-winning British economist, Source


Note that the fixed effects estimates use only within-firms differences, essentially discarding any information about differences between firms. If predictor variables vary greatly across firms but have little variation over time for each firm, then fixed effects estimates will be imprecise and have large standard errors. So, if there is not enough variation or change in gender ownership, I may expect a non significant estimate in fixed effects compared to a cross-sectional model.


Credit Frictions as the source of Business Cycles

Yes credit frictions do have an amplifying effect on supply shocks while they often attenuate demand shocks and they also give increased persistent to the effects of the supply shocks in many models.

Once you have a specified DSGE model you can choose exactly where the shock originates from and the strength of the shock. See for instance Gerali et. al. 2010. Credit and Banking in a DSGE model of the Euro Area. They incorporate a banking sector into a traditional DSGE model. Their variance decomposition shows that it is mostly shocks originating in the banking sector which explain the fall in GDP during the financial crisis. However that is empirical estimation.

What you can do and what they do is to shock bank capital so as to simulate a loss. They show that this loss in bank capital has effects on output, consumption, inflation, investment and so on. So by incorporating financial and/or credit frictions you can simulate shocks to these which in turn should have real effects in your model.

The paper can be found here: http://www.bancaditalia.it/pubblicazioni/econo/temidi/td10/td740_10/td_740_10/en_tema_740.pdf

EDIT:
There are actually papers that are examining the question at hand in even more details than the Gerali et. al paper mentioned above. Two of these are Iacoviello, M. 2014. "Financial Business Cycles" where he examines a recession whcih is initiated by losses suffered from banks. Another paper is Jensen et. al. 2013. "Changing Credit Limits Changing Business Cycles" where they examine financial liberalization in a DSGE model. They find that financial liberalization leads to higher macroeconomic volatility.


Beliefs about equilibrium paths with overlapping strategies

In signaling games, beliefs as well as strategies constitute an equilibrium. In other words, beliefs are a part of the equilibrium object. By deciding which equilibrium to focus on, you also (partially) determines the beliefs consistent with that equilibrium. The key restriction is that beliefs be derived from Bayes' rule using sender's strategy and the prior.

Consider the following game, where P1 is the sender and the common prior is Type I realizes with probability $p$.

Separating equilibrium

In a separating equilibrium, different types choose different actions (Type I chooses $A$ and Type II chooses $B$). Then, upon seeing action $A$, P2 (the receiver) updates her belief using Bayes' rule:
$$
\mu(\text{Type I}|A)=\frac{\Pr(A|\text{Type I})p}{\Pr(A|\text{Type I})p+\Pr(A|\text{Type II})(1-p)}=\frac{(1)p}{(1)p+(0)(1-p)}=1
$$
Therefore P2's conditional belief at node $x$ is $1$. Similarly for her belief at the information set $\{x',y'\}$

Pooling equilibrium

Now, consider a pooling equilibrium, where both types choose $A$. Then, upon seeing action $A$, P2's belief is calculated as
$$
\mu(\text{Type I}|A)=\frac{\Pr(A|\text{Type I})p}{\Pr(A|\text{Type I})p+\Pr(A|\text{Type II})(1-p)}=\frac{(1)p}{(1)p+(1)(1-p)}=p
$$
which is the same as her prior. This makes sense because P1's action provides no additional information in a pooling equilibrium. (P2's off-equilibrium belief can be arbitrary, unless you want to apply refinements such as consistency of the sequential equilibrium).

The bottom line is: you cannot talk about an equilibrium separately from the beliefs. By talking about a particular equilibrium, you also implicitly restrict the set of beliefs consistent with the said equilibrium.


Any study on performance gap between optimal mechanism and linear mechanism?

Robustness and linear contracts by Carroll says that linear is optimal (in his class of environments). Tim Roughgarden from Stanford also studies `the price of anarchy' related to using simple but suboptimal mechanisms.


Monetary policy and potential output growth

Can monetary policy affect potential output growth?

Yes. Otherwise, central banks would be indifferent to quantitative easing and other measures.

  how is this consistent with the neoclassical thesis's of money neutrality in the long run?

It is not. The premise that "new money neither creates nor destroys machines" sounds accurate only in isolation. But in the real world, companies bind themselves to financial (as well as fiscal) obligations which are in terms of nominal variables.

Certain monetary policies may render those companies cash-strapped, thereby triggering liquidity crises, bankruptcies, higher cost of financing, emigration of skilled workforce, and other effects. Altogether, this may result in structural changes in the economy.

Thus, while the thesis assumes that the aggregate supply curve is vertical, it misses the logical notion that this curve may shift to the left or to the right in the long run.


Why does state-owned company so aggressive in making profit?

You have to distinguish between state owned public service companies and state owned for-profit companies, the for-profit companies are really commercial companies with governments being major shareholders. I would not use the term "state owned" in case of the latter form. Governments can form joint-ventures with private and multinational companies. Governments in this instance would have a special investment management agency or just a fund that are formed to attract investments from abroad. And, in every new joint venture, the government is the main shareholder. So, in CNPC's case, government is a proper shareholder just like institutional shareholders. Since Chinese government is the main shareholder it has the majority of voting rights and would certainly want a good return on investment and they are "aggressive in making profit" as you suggest.

In the former case where the companies, if it can be called a company, are formed to provide public services (think of nationalised train companies), they are not there to make profit, but provide low cost high quality services.


How does the Contract Law definition of 'consumer surplus' relate to the Microeconomics definition?

O'Sullivan & Hilliard write: Consumer surplus is a "type of non-financial loss" and

  can be defined as the amount by which the particular plaintiff values performance of a particular obligation over and above its market value.

This is identical to the economist's definition of consumer surplus.

Using Pindyck and Rubinfeld's example: If a student was willing to pay as much as $\$13$ for a rock concert ticket (this is the value she places on the "performance of a particular obligation") but only had to pay $\$12$ (this is the price or the market value of the ticket), then her consumer surplus is $$\$13-\$12=\$1.$$


Is monetary expansion the same as quantitative easing

It is not. Monetary expansion is increasing the money supply (through whatever method).

Quantitative easing increases the money supply / injects liquidity, but  also reduces privately hold stocks (and hence can reduce risks from the banks' balance sheets).


How to interpret "desired significance level"?

I am not sure what you mean by "appropriate significance level."

Basically how sure you want to be is your choice. A frequently used analogy is the presumption of innocence. You are considered guilty only if this is proven beyond reasonable doubt. But what exactly is reasonable?
This is for you to decide. If you require very strong evidence then the probability of making a false positive conclusion (Type I error) decreases. But this will increase the probability of making a false negative conclusion (Type II error).
In the presumption of innocence analogy: If you change the law in a way that will require more evidence for a conviction, you will send fewer innocent people to jail (Type I), but you will also let more guilty ones go (Type II).

The significance level is the probability of a Type I error occuring.

In some situations you can perform a cost benefit analysis. In quality control you may be able to determine the cost of the damage caused by a malfunctioning part and then compare this to the cost of throwing away a properly functioning part. Using these you can actually calculate a cost minimizing significance level. However in other situations this is not feasible, or sometimes not even desirable. Then you have to make your own decision about the significance level.

In econometrics the most frequently used significance levels are 0.1%, 1% and 5%. My understanding is that this is a rule of thumb and there is actually no calculation behind it. (I could be wrong.)
Given some data you might say that "the findings are significant on the 5% level but not on the 1% level," or you can simply give the p-value, this is what is usually done.


How to create a Budget line in excel or R

Another R code that does it...

m <- 100
p <- c(1, 2)
curve(m/p[2] - p[1]/p[2]*x, from = 0, to = m/p[1], lwd = 2,
      xlab = expression(x[1]),
      ylab = expression(x[2]))


Mathematically

To calculate the total demand curve (aggregate demand has a different meaning), you just need to ask yourself that for each price, how many units will be demanded.

You have three groups:

A. 20 people, perfectly elastic at $p = 2$. This group will buy 20 units as long as $p \leq 2$.
B. 40 people, perfectly elastic at $p = 4$. This group will buy 40 units as long as $p \leq 4$.
C. 50 people, perfectly inelastic. This group will buy 50 units no matter what.

Mathematically,

$$A(p) = \begin{cases} 20 & \text{if $p \leq 2$} \\ 0 & \text{otherwise}\end{cases},\quad
B(p) = \begin{cases} 40 & \text{if $p \leq 4$} \\ 0 & \text{otherwise}\end{cases},\quad
C(p) = 50$$

Total demand is just a function of $p$: $Q(p) = A(p) + B(p) + C(p)$.
If we start at $p = 1$, what's $A(1) + B(1) + C(1)$? Do this for all prices, and you'll get the total demand curve.

Graphically

You could also do this graphically... draw up the demand curve (would look like a rectangle) for each group. The total demand curve will just be the horizontal stack of these rectangles.


Marginal productivity, wages, and profits in neoclassical economics

Recall the profit function.

$$\pi=pf(x)-wx$$

where $x$ is a set of inputs, and $w$ is a set of input prices.

A firm is profit maximizing when $MC=MR$ or in a competitive case where $MC=p$. If a worker is paid his marginal product (where $MPL=w$) we only pay what he produces.

If  marginal cost is constant and marginal revenues are constant across all production sets, then the firms profits will be zero.

However if there are diminishing returns from the inputs then every worker is paid less, thus allowing for profits to exist in the short run.

Bottom line: In the short run, through the diminishing returns from labor that profit for the firm comes into existence.

In the long run however, new firms enter capturing more and more of the profits until they are reduced to zero.


What is the Thomson Reuters tool that is used in universities?

It is a huge financial database which consents you to export data easily via the datastream tool for excel. There you can find common data (such as those available via online databases, e.g. yahoo finance or investing) but also intra-day data, indexes, analysis and the platform consent you to apply directly some statistical techniques. It is a great source, useful especially when you cannot get data from free sources.


There are more and more free database available. Here are a few that I like:

Quandl: this platform gathers data from many providers. Not all database are free, but there are enough data to play around with. One of the best things about Quandl is the APIs and the Excel macro, which allow you to easly send requests and download data.
Yahoo Finance: one of the most popular I guess. It is also possible to use some excel macros to download the data, see for example this macro from InvestExcel
GOOGLEFINANCE: If you like Google Sheets, then the function GOOGLEFINANCE is very handy and works quite well. It allows you to get real time data as well as historical data.


When should one use Lagrange Multipliers as opposed to calculating the ratio of Marginal Utilities for MRS?

Lagrange multipliers not only incorporate constraints on a maximization/minimization problem, but the multiplier itself can have a meaningful interpretation. For example, say we have the problem:

$$\max_{x, m}: U(x, m) = m + \phi(x) \quad s.t. m + px = y$$

Where $m$ is a numeiare good, $p$ is the price of good $x$, and $y$ is income.

Now you could just rewrite the constraint as

$$m = y - px$$

and substitute that into the original maximization problem. But you can't always do this easily. So you can also solve with a Lagrangian.

$$\mathcal{L} = m + \phi{x} - \lambda(m + px - y)$$

Solving for $\lambda$ will give you the shadow price of income, or the marginal price of income. That is, it represents the rate of increase in maximized utility as income is increased. You also need to find $\lambda$ to get a nice full Marshallian demand, or to relate indirect utility to Marshallian demand in Roy's identity.

Even for problems that aren't utility maximization, $\lambda$ is still representing the rate of change of the quantity being optimized as a function of the constraint variable.

Here's a useful example with the firm maximization problem and bribing problem.


Is the consumer surplus on a Giffen/Veblen good negative?

Actually, neither demand for Veblen good nor for Giffen good is strictly increasing in price.

In case of Giffen good the demand actually looks as shown below in picture 1. The reason for this is that you can only increase demand for the Giffen good up until you consume your entire budget. Once the price gets higher then that you still get normal downward sloping demand.

Consequently if you would apply the definition of CS as the area below the demand and above equilibrium price (excluding the corner solution when Q=0) you would still get positive consumer surplus, as no matter what the equilibrium price is there still will be some finite positive area under the demand and above equilibrium price.

In case of Veblen good the demand actually looks like at the picture below. The reason for it looking like this is that the Veblen demand cannot start already at zero price, as for example if diamonds would cost 1 euro they could not be considered status symbol. Only at a certain equilibrium price when the good is not accessible to 'ordinary' people does the demand become upward sloping above the 'snob'line.

Hence, in this case as well the CS defined as area below demand curve and above equilibrium price will be positive.

This being said, I actually looked at all microeconomic textbooks I own, and I do own a lot of them both at undergraduate and graduate level, and none actually shows calculation of CS, or mentions how CS behaves for either of these cases even when they mention them. So to be honest I am not 100% confident that the CS idea would extend to these cases, but in principle blind application of CS definition to the above cases would still give you positive CS.


What are the assumptions of real business cycle theory and Keynesian theory?

The distinction is between "nominal" and "real" recessions and booms.

Real business cycle theory was developed to point out the fact that variations in employment and hours could occur even in an economy where markets were working competitively and there were no pricing frictions. In the RBC world, recessions and booms are driven by "real" factors: variation in technology, variation in the supply of commodities used as input in the production process, etc. A consequence is that in the RBC world while increased government spending on consumption goods indeed raises output and employment (the fiscal multiplier in RBC models is between 0 and 1), following such a policy during a recession is socially suboptimal. (You force people to work more and consume less.) To justify government spending during a recession is no easier and no harder than to justify it during "normal times", and then the argument becomes one about market failure, public finance, etc.

In contrast, Keynesian theory (and its modern cousins) say that while "real recessions" in the above sense may indeed exist, there are also "nominal recessions": these are recessions caused by "less spending" (for instance, if you're working with MV = PY, they are recessions caused by a fall in V). The reason this creates a recession is because there are nominal rigidities in the economy - workers are unwilling to accept nominal wage cuts, producers face "menu costs" which make price changes infrequent, etc. Because of these rigidities, a fall in "aggregate spending" manifests itself not only in the form of lower prices, but also in the form of lower output.

So far, everything I said is also consistent with monetarism, for instance. However, this is not all there is to Keynesian theory: Keynesians go further and claim that the solution to a shortfall in spending is for the government to increase spending and "make up the lost demand". In other words, if you think of the AD-AS model, Keynesians think that government spending can raise AD. This idea has been discredited in academia for decades because it ignores budget constraints - there's only so much money available in the economy, if the government borrows money from you and spends it, that's money someone else did not spend. It's not clear how government spending boosts "money velocity", and in fact there are New Keynesian models where increased government spending is deflationary and makes a nominal recession worse by creating more demand for real money balances.

Keynesian ideas have made a resurgence in the past 10 years thanks to the zero lower bound. The argument above about budget constraints is no longer true when nominal interest rates are stuck at zero, because now people will actually start hoarding cash instead of spending it. Therefore, increasing government spending does not "crowd out" private spending, because households and firms are just sitting on the cash they have anyway. Monetary stimulus is ineffective because any additional money is just held by the public. This is the "liquidity trap" a nutshell. Critics point out that permanent monetary stimulus as opposed to a temporary one can still work in a liquidity trap (as pointed out in Krugman (1998)) and that monetary models (say, with cash-in-advance constraints) are indeterminate at the zero lower bound: without anchoring consumption and prices in the future to some level chosen arbitrarily, it's not possible to pin down a unique equilibrium of the economy today.

There's more to be said on this subject, but this should be enough for an answer.


On the previous page (introducing equation 2.2) the authors state that "consumption asset" means "wealth portfolio", so $R_{c,t+1}$ is the return to the wealth portfolio, which makes sense from the equation you quote.

  the log return to the consumption asset (wealth portfolio), $r_{c,t+1}$.


Why solving the model for a benevolent social planner gives an efficient allocation?

I think the general proof is in this paper.

Thinking in a simple exchange Edgeworth Box, a competitive economy involves prices, which mediate the relationship between consumers relative valuation of goods - the marginal rate of substitution. A (benevolent) social planner does not need those prices, as goods will not be traded in the market, but simply allocated to whom it "corresponds", based on the same optimality conditions. Such equilibrium is simply found by equalising consumers marginal rate of substitution.

In other words:

equilibrium in competitive economy through exchange/markets:

$$ MRS^1_{X,Y} = \frac{P_x}{P_y} = MRS^2_{X,Y} $$

equilibrium via allocation from benevolent social planner:

$$ MRS^1_{X,Y} = MRS^2_{X,Y} $$

(the formulas above can be trivially extended to $n$ consumers and goods)


Generally, and surprisingly, yes, lotteries are similar to auctions. What do I mean by that?

In an auction, you increase the likelihood of winning by increasing your bid. In many auctions, if you increase the bid sufficiently much, that probability will go to one.

A similar thing is true for lotteries: the more tickets you buy, the higher is the likelihood of success. It is not a one-for-one correspondence, but it holds. And again, by predicting other people's actions (are they more likely to bid/gamble on week days or week ends), you can increase your chances of winning the lottery.

However, this means that you can increase your chances of winning, not that you will make a net surplus ("get a lot of money"). In the same way as sometimes, you can bid "too high" and make a net loss in an auction, you can pay a too high price for the (expected) win. In a lottery, this is quite often the case.


I got the answer from the professor after the assignment was graded during review. I am posting it here as it may help someone else in the future. Apparently, (vintage) data in trapezoid form for GDP are provided at Philadelphia Fed.
They have a trapezoid form because when they are plotted on a contour graph they have a trapezoid shape (the graph is from a correct review sample assignment from our professor):


How could Pablo Escobar earn so much money?

Not sure an economist can answer this particular question about Escobar's wealth and not only because all the given estimates are uncertain. A more interesting question for an economist (or at least for me) would be: What is Escobar's (a drug firm) mark-up? Or what is the economic size of the international market for cocaine?

The most serious source of information I was able to find is the 2012 World Drug Report of the United Nations Office on Drugs and Crime (UNDOC). UNODC estimates suggest that

The total retail market for cocaine amounts to some US $85 billion in 2009 (p.70).
Columbian production proxied in terms of hectares is around 89% (based on 2009's estimates (68,000+73,000)/158,800 - Table 12).

So, if you assume that all Columbian production is produced by Escobar's cartel his total benefit is about USD $75 billion for the year 2009.

Edit: However, we cannot assume that Escobar's cartel got 89% of the retail value (thanks to @Alecos Papadopoulos for this point). The USD 75 billion is the equivalent of the "box office" for a movie - but the producers of the movie (i.e. Escobar's cartel) do not get all the box office.

Then, the question is what is the proportion retained by the Escobar's cartel? I have no clue! However, Levitt and Vetakesh QJE paper document that "earnings within the (drug) gang are enormously skewed (..) with high-level gang members earning far more than their legitimate market alternative." So, by extrapolating from this result and assuming that the drug market is vertically integrated and controlled by the Escobar's cartel, we may speculate that the latter (and Escobar himself) may get a big part of the box office.

In this report, you may also find more reliable estimates about

The total number of cocaine users: 16 million (Table 7)
and the estimates per region.
Purity-adjusted prices per gram in those regions

So if you find some data on consumer's average consumption and Escobar's production you may get a better estimate of his wealth.


Net exports term in aggregate expenditure

Seems like what you are adding up is not the Gross Domestic Product, rather something like the Gross Domestic Expenditure.
$$
C+I+G+X-M = Y = C+I+G+M-X
$$
could only possibly hold if $M - X = 0$, that is if the trade balance was zero. If this is not true, e.g., if $M - X > 0$ than a country's gross expenditure is larger than its production, so counting these things will not both sum up to $Y$.


Typical duration of bonds purchased in QE

This paper is a few years old. You might want to look at page 6.
Briefly, it varies by government and across time.
https://www.treasury.gov/resource-center/data-chart-center/quarterly-refunding/Documents/February2015TBACCharge1.pdf


Ranking products according to Price Elasticity Of Demand

The question is not subjective if you accept the assumption that similar products are likely to be substitutes, i.e. if you wanted chocolate ice cream but none was available you are more likely to get vanilla ice cream than pork chops.

The trick is that the groups can be ordered from smaller to larger, e.g. all ice creams are frozen desserts but not all frozen desserts are ice creams. If the price of a whole product group increases it is more difficult to find a cheap substitute than if only one product's price had increased. In this case all other products in the product group would be available as substitutes at their original prices.

Using this assumption you should be able to finish the assignment.


a) Increase in the size and frequency of AD shocks to the economy.>

More inclined would encourage more demand from other regional countries, which in turn supports the shortage of domestics demand

  b) Increase in the size and frequency of money demand shocks to the economy.>

Less inclined would be better since independent currency regime provides local goverment (ie. the central/state bank) more flexibility in controling supply and demand money in order to deal with money demand shocks

  c) Increase in the cultural similarities between the country and the country or region it is joining.>

More inclined should be a great idea in this case as countries in that region could exchange labor and goods at lower relative cost compared to remain local currency regime

  d) Decrease in capital mobility restrictions combined with an increase in immigration restrictions.>

More inclined to common currency is my answer. Common currency is not the same as establishing an OCA (Optimal Currency Area) so immigration is a less-crucial criteria than capital mobility in considering a decision of commmon currency.


The literature on optimal income taxation kicked off with Diamond, Mirrlees (1971). In their model, people differ only by ability, i.e. the highest earning person is the most productive one. As a consequence, any marginal tax rate on this person will be detrimental to production and hence to social welfare (in this model). Therefore, the optimal top marginal tax rate is zero!

The main innovation was initiated by Emmanuel Saez (Saez (2001) and Piketty, Saez (2012)). The basic idea is that the social planner maximizes a social welfare function (SWF) that captures the fact that individuals are to some degree inequality averse. Plus, they allow the introduction of welfare weights, i.e. a normative decision on whose well-being matters for the society as a whole. The innovation of this literature is the formulation, that allows to calculate an optimal tax rate based on observable (or, rather, estimatable) figures. This is referred to as the sufficient statistic approach. See e.g. Eq.7 in Piketty, Saez (2012) for the optimal top tax rate $\tau$:

$$\tau = \frac{1-g}{1-g+a *e} $$

This depends only on three parameters: $e$ is the extent to which top income earners are able to dodge the tax. In the basic model, this is only labor supply, but later contributions (incuding the one you cite, but also Saez et al. (2012), [yes, Saez again]) acknowledge that there are many other avoidance strategies. $g$ is the social welfare weight of the top-income earners and $a$ is an indicator of the income distribution.

The optimal top marginal tax rates above 70% stems basically from the assumption that $g$ is zero, i.e. society as a whole does not really care about the richest. Another key factor is the magnitude of $e$. If I argue that with a sufficiently high top tax rate, all millionaires will leave the country, I assume a high $e$, which drives down $\tau$. There are also researchers that came up with different values for $a$. One quite well-known criticism is from Mankiw et al. (2009). They back up their arguments however, e.g. on less reliable data, which is why I don't find it very substantiated at least on the top tax rate issue.

For a general discussion on optimal taxation beyond the top tax rate, see also Diamond and Saez (2011).

Summing up, the Saez literature is a great tool to link data and economic theory and has been heavily used. Empirically, estimating the various margins of $e$ is very difficult and has been tried numerous times. The top tax rate of 70% or higher is debatable as it has some normative settings. But overall, this literature has made compelling arguments in favor of progressive taxation and higher taxation of inheritances. It might be my personal bias, but I'm not aware of any fundamental, substantiated criticism to the Saez approach.


U.S. Bureau of Economic Analysis, when was that created?

Bureaucratic history time! Yes, this agency (and its predecessors) have always been responsible for GDP; GDP was created a couple decades after the Department of Commerce and the Department of Labor split up.

The full answer is that the Bureau of Economic Analysis (BEA) was created in 1972 as a bureau in the Social and Economic Statistics Administration (SESA), then made an autonomous bureau within the Department of Commerce in 1975, with the abolishment of the SESA.

When the BEA was created in 1972, it was created out of the Office of Business Economics (itself an autonomous unit) in the Department of Commerce. In turn, the Office of Business Economics was established in 1945 inside another autonomous unit, that parent unit being the Bureau of Foreign and Domestic Commerce.

It was during the period of the Bureau of Domestic and Foreign Commerce (housed in the Department of Commerce) that GDP was created (in part by the work of Simon Kuznets on a measure of national income), but the agency preceded this by many years.

The Bureau of Foreign and Domestic Commerce, for its part, was transferred to the the Department of Commerce when the DoC was created in 1913 (by splitting up the Department of Commerce and Labor into two separate cabinet departments). It had previously been within the Department of Commerce and Labor, and was known as the Bureau of Statistics prior to 1912.

The Bureau of Statistics in the Department of Commerce and Labor was created out of the Bureau of Foreign Commerce (housed in the Department of State), and the Bureau of Statistics (housed in the Department of the Treasury). Each of those bureaus also had other names during the 19th century, but we've probably already gone way further back than you had intended.

This history thanks to the National Archives.


A vacant job is an asset if we consider that the firm can match with a worker and get a positive expected profit. Firms post vacancies up to a point where $V=0$. If $V$ were positive, more firms would enter, would post additional vacancies, and would get a `rent' (by matching with worker).


What is the economic meaning of a differentiated variable cost function

HINT

What is the difference between variable and fixed cost? Try separating your total cost into fixed and variable cost. To do this, think about what costs the firm faces even when they have no output (let quantity produced be zero.) For a bit of intuition, think of these costs perhaps as rents paid by a firm during the initial setup stage (time spent fitting a factory with production equipment). They have a certain amount of bills to pay even though they produce nothing.

After doing this it should be a straight forward thing to differentiate and interpret.

MEANING

Let's take your example. We can see that we have a cost of 75 (let's assume American dollars) regardless of how much output we produce. So Q=0 still incurs a cost of $75. Then by definition, this is the fixed cost portion of your total cost function.

Then since any cost function is the sum of fixed and variable costs, we have that your variable cost function is $$C(Q)=Q^3-5Q^2+12Q$$

differentiating with respect to $Q$ yields: $$3Q^2-10Q+12$$

This is your marginal variable cost. Notice this is the same function achieved by simply differentiating the total cost function. This is because fixed costs are constants (and not functions of Q) and therefore disappear when C is differentiated with respect to Q.

Then we can just refer to the equation above as marginal cost

Marginal cost equations tell you how much your total cost rises when you decide to produce an additional unit of output. Notice here that making the production decision incurs a new sort of "fixed" cost.

So let's examine what happens when Q increases:

$$Q=1 \implies MC=5$$
$$Q=2 \implies MC=2$$
$$Q=3 \implies MC=9$$

and this is enough for us to tease out another important part of this function! Notice that marginal costs decrease as production increases over our initial range and then, at a certain point, marginal costs begin to increase as production continues to increase. This is a example of increasing marginal returns and decreasing marginal returns (respectively)

In general, you can picture a marginal cost curve as a differentiable nike symbol or a U where the right side of the U is drawn much higher than the left side(and where it is a bit slanted to the right This would tend to infinity as Q tends to infinity).

Alright - hope that cleared some things up. And to top it off, you can do a bit of reading about marginal cost.


The effect of inflation differentials on the relative prices of goods across countries

During an inflationary period the value of the US Dollar has not increased, but decreased. From within the US, goods are becoming more expensive because each US Dollar is worth less.

Inflation is believed to be caused by an oversupply of money; if there is an oversupply of US Dollars, it will lead to a decrease in its value. If inflation is increasing at a higher rate in the US than in South Africa, the Dollar will be relatively cheaper, making it more desirable. Thus, an increase in the demand for the US Dollar, and a decrease in its supply.


Prove relation between expected utility and utility of the mean

The conclusion you want to prove is not always true. I will give you a graphical and mathematical answer.

Graphical analysis

Consider the example in the image below:

There is one lottery, with expected payoffs $z_1$ and $z_2$, and average $E(z)$. The expected value of this lottery in terms of utility is $U[E(z)]$.

Now, assume a second lottery, with higher $z_1$ and smaller $z_2$, such that the expected value is the same, i.e. $E(z)$. The expected value of this lottery is the same, $U[E(z)]$. Yet, because of lower variance in the second lottery, the point E in the second lottery is closer to D. (In the extreme case of no uncertainty, D and E coincide). In other words, $E[u(z)]$ in lottery one is lower than $E[u(z)]$ in lottery two, even if they pay the same on average.

The contradiction of your statement follows immediately. Take the second lottery just introduced, and decrease $z_1$ by a small $\epsilon$. Now, the expected income of the lottery is marginally lower than $E(z)$, which is the opposite relation to the one in your question. There clearly is a small $\epsilon$ such that the relation between $E[u(z)]$ in the two lotteries remains as before.

The proof follows the same logic for the case of risk loving individuals (where uncertainty is preferred to certainty and the utility function is convex).

Actually, the only case where your statement does hold is for risk neutrality. This can trivially be seen in the graph too.

Mathematical analysis

First, we know that $\dfrac{d U(x)}{d x}>0$. Then, it is true that:

$$ U(x_p + \pi)=E[U(x_p)] $$

$$ U(x_q + \phi)=E[U(x_q)] $$

where the term inside the parenthesis in the left-hand side are the certainty equivalent. The sign of $\pi$ and $\phi$ depend on the nature of the utility function. There are three cases:

Risk aversion

If utility is concave (i.e. agent is risk averse), $\pi$ and $\rho$ are positive. Therefore:

$$ U(x_p) < U(x_p + \pi) = E[U(x_p)] $$

$$ U(x_q) < U(x_q + \phi) = E[U(x_q)] $$

Assuming that $U(x_p) > U(x_q)$:

$$E[U(x_p)] = U(x_p + \pi) > U(x_p) > U(x_q) $$

However, $E[U(x_q)] > U(x_q)$. It is evident that nothing more can be said regarding the relation between $E[U(x_p)]$ and $E[U(x_q)]$. The result you want to prove does not necessarily hold in this case.

Risk acceptance

The proof is exactly the same, but reversing the signs.

Risk neutrality

$\pi$ and $\phi$ are zero.

$$ U(x_p) = E[U(x_p)] $$

$$ U(x_q) = E[U(x_q)] $$

Assuming $U(x_p) > U(x_q)$ implies that:

$$ E[U(x_p)] > E[U(x_q)] $$

Thus, in this case the conclusion you want to prove is true.


What is low unemployment and low gdp growth symptomatic of?

One simple explanation can just be that unemployment is artificially low. Perhaps many people went out of the labor force (i.e. stopped looking for a job) after a long period of not being able to find one, and now they don't count as unemployed in the data. Similarly, maybe the economy is not growing enough to create good jobs, but many people are partially employed so that the unemployment rate looks artificially low again because even though people have jobs, they might want to work more hours, but can't.

There might be other more interesting causes, but I think that exploring them will require to zoom in a particular country and take into account the institutional details, etc.


What is the difference between preferences lacking "completeness" and being indifferent?

As alluded to in the comments the distinction is roughly:

Indifference: The decision maker knows she will receive the same utility from the consumption of $x$ or $y$.
Incompleteness: The DM does not know her preference between $x$ and $y$. (Note, this could stem from a lack of information, or because no preference exists)

So, from a conceptual vantage, the difference is that indifference is the existence of knowledge, whereas incompleteness is a lack of knowledge. While interesting in a foundational/philosophical sense, the distinction is subtle and likely not the reason economists have spent so much thought on the subject. However, the difference has behavioral implications! and this is important for economics.

For example, imagine various choices between "pizza", "hot dog", or "hot dog and $\$0.05$". Perhaps, the decision maker has never had pizza or hot dogs and therefore finds them incomparable. As such, from the choice set $\{p,h\}$ she would choose either (since neither option is known to be inferior[1]). So $C(\{p,h\}) = \{p,h\}$.  Now, the decision maker also likes money, so although she does not know her preference for a hot dog, she will always choose more money to less, all else equal: $C(\{h, h+5\}) = \{h+5\}$. But her indecisiveness regarding the two foods might not be resolvable for 5 cents, so, it is reasonable that $C(\{p, h, h+5\}) = \{p, h+5\}$. But this violates the weak axiom of revealed preference. Such a choice function cannot be rationalized by a complete and transitive relation.

Notice if the decision maker was actually indifference between $h$ and $p$ then, $C(\{p, h, h+5\}) = \{h+5\}$. In summary: incompleteness can cause "thick" indifference curves, and this can violate the basic tenets of rational choice theory.

[1] There are other interpretations of choice under incompleteness, for example, allowing the choice function to return an empty set.


How to find the variance co-variance matrix for 4 assets and market returns using the CAPM?

Sharpe says you can always do a linear approximation to the returns of a family of assets and use that approximation to calculate a covariance matrix. For such an approximation to have economic content, one typically assumes that 1) residuals are uncorrelated with factors and 2) each asset's residuals are uncorrelated with that of any other. The second one has more bite and in particular, is likely not to hold in a one factor model.

It is worth mentioning that in your equation above, the diagonal entries are not exactly what you write. Instead it is:
$Var(R_{i,t}) = \beta_{i,m}^2 \cdot \sigma^2_m +\sigma^2_\epsilon $
where $\sigma^2_\epsilon $ is the variance of the residual of the linear approximation equation.


How would you draw a MSB,MSC,MPB,MPC graph for this?

First of, you would not be able to infer actual data on marginal measures of social benefit or social cost from this prompt alone, as they do not indicate any such information (if they are constant or variable). You'd instead have to conjecture the explicit effects of the saving of water. In doing so, we can, more safely than not, assume that conserving water is a positive externality of this subsidy, and this marginal benefit is ..clears throat.. constant.

The subsidy being imposed, we notice that Supply (MPC) curve moves to the right; that is, for every same level of price, producers now supply more to the market.
Furthermore, we notice that the Demand (MPB) curve remains constant, as no measure that takes place should change the needs of the consumers for agricultural products.
On this we will add a constant Marginal Social Benefit; that is the positive externality of rationing on water usage. Mechanisms at work, classical economic theory suggests, would imply that the consumption of these subsidized products, saves more water; so people naturally want to purchase more of them. This being the case, the Marginal Social Benefit curve is established further to the right than the Demand curve.

One final point of equilibrium is that where $Q=Q_2$, and producers receive price $P_0$ as part of their subsidy, while costumers pay an actual price of $P_2$.
The cost of this subsidy is $Q_2 * (P_0-P_2)$.


I think that potentially your teacher made a mistake (unless this is some tricky 'gotcha' problem) or if the problem involved actually creating the total cost function from some piece of text there might have been mistake in creating the total cost function. If you dont think that applies then read on.
1. Shut down point is at q=0
The first possibility is that indeed shut down point is simply zero. The shut down point is the point at which average variable cost ($AVC$) reaches its minimum - the minimum point can be either found by calculus (by minimizing the $AVC$ function) or indeed by equating $AVC$ to marginal costs MC $AVC=MC$.
The intuition for this is that normally the average cost curve will always decline when $AVC>MC$ and starts increasing only when $AVC<MC$ because marginal cost is the cost for the last product and intuitively if the last added variable to the sample is higher than average of sample then addition of that new variable increases the whole average and vice versa. As a consequence the minimum of average cost curve will be reached when $MC=AVC$ See the example below from Mankiw principles of economics:

However, in your case marginal cost is always above average variable cost ($MC>AVC$) except when $q=0$ when they are actually equal. You have a special total cost function which has average cost function and marginal cost function that looks nothing like the one in textbook. In fact I decided to model your cost function in R in order to drive the point. This is how your marginal cost (in blue) and average cost (red) look like:

As you can see in your case the marginal cost (blue line) is always above average variable costs (red line) except for when $q=0$.
2. Could your teacher possibly mean firm exit (long-run shutdown)?
It is not uncommon for teachers to call exit from the market long-run shut down (see one example here from Texas tech university lecture notes). In the case your teacher meant exit as a long-run shut down then long run shut down point would be given at an intersection of average total cost and marginal costs (see below example from Mankiw's principles of economics).

In this case $ATC=MC$ would equate at some non-zero $q$
3. The above only gives you $q$ coordinate of shut down or exit point
Note that in both examples provided above for firm to actually shut down or exit the price needs to be below the minimum AVC (shut down) or ATC (exit) respectively. The shut down quantity $q_{\text{shut down}}$ only tells you the $x$ coordinate at which AVC reaches its minimum. To see how firm will actually behave you need to always check whether the price (which will be on $y$ axis) that correspond to the shut down coordinate is actually lower than either minimum point on AVC (in case of shut down) or ATC (in case of exit) as shown in the pictures from the Mankiw's textbook.


Volume of trade covered by regional trade agreements

What you're looking for is called "utilization rate" and I believe a government agency in most countries should have this information. Here's one example: https://english.bdi.eu/article/news/the-preference-utilization-rate-of-eu-free-trade-agreements/


Financial Economics and Corporate Finance

This is referring to a general principle in finance. What matters most is the assets you have and the things you invest on, not really the way you finance these investments.  In the balance sheet, the asset side has the information about the assets you have, while the liability side has information about how you financed them.

This general principle comes from a very powerful idea called "the efficient markets hypothesis". Miller and Modigliani showed that if the financial market is perfect (basically if it has no private information, transaction costs, taxes, etc), the overall profitability of an investment does not depend on how it is financed!

Of course, markets are not perfect. However, many many studies have documented that most of the time, the financial market is pretty close to being perfect, especially in developed economies like the  US. So financing decisions do matter, but investment decisions matter a lot more.


I'm not sure what exactly in plain English means, but here is a try:
Think about it as consuming water.
Look at condition 1. If you have no water, you would die, making you extremely unhappy.
If someone came up to you and offered one bottle of water, it would make you infinitely happier than having no water, as you would live! (You would pay any amount of money to get that single bottle!)
The second condition states that eventually giving you extra water gives you less and less extra happiness. That first bottle was life saving, the second helps a lot,... but after the thousandth bottle, having extra water is nice, but having a thousand bottles versus a thousand and one does not increase your happiness too much.
The implication of the assumptions ensure that if I asked a consumer how much water she would like (for some price usually), she would pick a number between 0 and $\infty$.
She wouldnt pick 0, as we argued before, and eventually she cares less and less, so she would not buy $\infty$ bottles.
A famous example is $U(c) = \log(c)$.


What are some good repositories for economic data

Be more specific on what you need.
Quandl would be a pretty general source which hasn't been mentioned yet.
For macro data the St. Louis Fed is pretty good and thorough. Eurostat for European data. historicalstatistics.org for historical data.


Does a stock market crash "undo” the multiplier effect's money creation?

All price changes in the stock or commodities markets impact the money supply to the extent it results in a change in margin credit. Do note that the amount of credit itself must change and not the price alone.  A crash only has an impact if it results in net changes in the amount of credit.

This is a second order effect of a crash and not a first order effect.  It also usually has no material impact on the money supply.  Although a crash may have a large impact on notional concepts of wealth, the effect on the supply of money itself is usually neutralized by the banking system.  It is normal, even in the 1929 crash, to see bankers announce they will keep open the brokerages' lines of credit and stand ready to purchase safe assets such as Treasuries in unlimited quantities from these brokers to hold the money supply roughly constant.  If brokers sold enough treasuries, it could even expand the money supply.

The size of the money stock (M2) is 13.4 trillion dollars.  The total size of all margin credit from all sources is 554 billion dollars.  Although this is four percent of the money supply, which is a lot, you are also forgetting that in a crash margin purchases will begin happening too.  Just as brokerages will be issuing margin calls, other investors smelling blood in the water will be purchasing on margin, though this will be a smaller effect.

The Fed normally drops the interest rate to expand the money supply after a crash to compensate for the loss of money created by the reduction in margin credit.  Remember that 554 billion would not be wiped out in a crash, it would just be reduced, at least initially, as brokers required repayment.


In order to understand this its important to understand how actually commercial banks contribute to money creation. It is true that commercial banks are part of money creating process but I think that you misunderstand the way in which they are part of it. When you go to commercial bank to get a loan commercial bank neither domestic or foreign is allowed to just create the money for that loan out of thin air. Only central bank can do that.
Rather the money creation process works in a way that central bank creates base money and in addition also allows commercial banks to borrow from it newly created reserves. Afterwards, the commercial banks help to multiply the base money due to fractional reserve system. For example, if fractional reserve requirement is $10\%$ that means that if a person deposits $\\\$100$ into the commercial bank they are allowed to lend out $\\\$90$ and keep $\\\$10$ as a reserve. Afterwards when the person who borrowed $\\\$90$ deposits them (or spends them and someone else deposits them), bank will again be allowed to keep only $\\\$9$ as reserve and lent out $\\\$81$. In this way eventually up to $\\\$1000$ of new money can be created. This process is reversed once the loan is being paid back. The point is that commercial banks cannot simply create the money out of nothing so their domestic/foreign status does not matter that much.
Foreign commercial banks can make loans in dollars by simply first entering the forex market, buying some amount $X$ of dollars and then lending that amount to its customers. Alternatively foreign bank can also borrow dollars from other bank that has them and then lend them further.  When we talk about dollars in particular foreign banks have even access to federal funds market (see this Fed Cleveland explainer) so they can borrow from there as well.


Omited Variable Bias and descriptive statements

This is not about causality. Causality is a statement that $x$ causes $y$ but it is not the value of the coefficient ($a$ in your model). Even if you care just about coefficient estimates you will get wrong answer. This is because the formula for estimate of the coefficient $a$, that is $\hat{a}$, in simple OLS can be expressed as:

$$\hat{a} = a + \beta \frac{\text{COV}(x,z) }{VAR(x)} $$

That is the estimate of $a$ you get from OLS is the true estimate $a$ + the true value of $\beta$ which would be the coefficient of $z$ if you would actually include it in a model by estimating $y=c+ax+\beta z + error$ multiplied by the covariance of $x$ and $z$ and divided by variance of $x$. Now variance of $x$ must be non-zero just to be able to estimate OLS in the first place and variance is always positive so the over or underestimation will be given by the sign of the covariance and the $\beta$.

Now whether you care about causality or no this bias is still important consider the following example. You want to estimate the effect of education of parents on number of children they have. You dont care about causality you just want to calculate whats the coefficient inside your sample i.e. you only care about whats the average number of children for a couple with average years of education, and in addition suppose that education is also correlated with income. Also to make calculations easy lets assume that VAR$(x)=0.5$ and COV$(x,z)=0.5$ and that average years of education of parents are 10 years. Now lets suppose the true model looks like this (I already replaced $c,a,\beta$ with actual numbers):

$$y_i= 10 -0.3x_i-0.2z_i + u_i$$

In this true model a family with average education of 10 would have on average 3 less kids compared to family with no education. Note I am not saying anything about causation this is just purely caring about descriptively describing the household with average education.

However, note what happens if we now omit $z$ from the regression model and calculate $a$ using the formula above:

$$y_i= 5 - 0.42x_i+ u_i$$

now the estimate suggest that family with average education has 4 less kids which is plain wrong - this estimate underestimates the number of kids for average family by $25\%$. In this case the sign stayed the same but thats just due to the numbers I chose in real life bias could easily change the sign of the coefficient altogether.

Hence, even if you dont care about causality and you just want to use regression for some description of dataset you care about omitted variable bias.

PS: Also in my answer I left out $by$ from your example: $ y=c+ax+by+error$ since there must be some typo you cant regress $y$ on itself, yet your formula includes $y$ on both sides. Or to be specific you could do that but mathematically coefficient is always set to $1$ when you regress dep variable on itself so there is never a reason to do that.


It depends on what you mean by generically. The Prisoner's Dilemma has exactly one equilibrium. If you generate the payoffs in your $2 \times 2$ game by drawing payoffs from continuous i.i.d.'s then there is a non-zero probability (seems to me that the exact number is 25%) that you will get a game similar to the Prisoner's Dilemma, i.e. a game with strictly dominant strategies for both players.

There is also a 'smaller' class of games with even number of equilibria, you can read about them here:

http://mindyourdecisions.com/blog/2014/10/07/game-theory-tuesdays-why-most-games-have-an-odd-number-of-nash-equilibria/

  The Oddness Theorem (Wilson 1971) states that nearly all finite games have an odd number of Nash equilibria. In this post, we’ll explain what the theorem means in practical terms.

You can also have a game with an infinite number of equilibria. (E.g. a $2 \times 2$ game with all zeros.)

However if the number of equilibria is finite you cannot have more than three in a $2 \times 2$ game.


Insignificant Interaction effect in applied econometrics (multinomial logit regression)

It is not 100% clear what procedure you used to do the subgroup tests, so I will cover a few bases. Below, I suggest exploratory tests to better understand the results. The logic in this response is the same as you would follow in a linear model.

If you are taking the results from the single model and doing post hoc tests of the coefficents, be sure that you are interpreting the model correctly. Because men are the implicit reference category, the constant represents the men's average (ceteris paribus) and the constant plus b1 is the women's average. Similarly, b2 is men's "slope" with respect to x2, while b2 + b3 is women's "slope" with respect to x2. So, to test whether x2 matters at all for women, you would have to test b2 AND b3 together.

That said, it sounds to me like, after running the full model, you ran the model separately for men and women (minus the sex-related terms) to investigate further. Here's a few things to investigate:

How different are the other parameters for men and women in the separate models from the main model?

Are there similar point estimates?
Are the same variables significant?
Do the models have comparable model fit?

What kind of variation do you have in your data? You can do descriptive and exploratory analyses to understand this.

Present a descriptive table of the frequencies by sex, x2, and j. If every "cell" created in this way had exactly the same count, you would be rather unlikely to get a disparity between the subgroup models and the full model (unless the data generating processes for men and women are entirely different, and/or there is heteroskedasticity by sex).

That is, my hunch is that you have "micronumerosity" for some of the women in certain outcomes, and thus you cannot get a small enough standard error to distinguish the interaction term.
Another way of looking at this is figuring out the realm of common support for your model.

Run descriptive statistics (mean, SD) on the other variables separately for men and women and look for discrepancies. If there are substantial differences, it could mean something other than sex is driving the difference, and/or that collinearity between that other variable and sex is complicating the estimation.

If the covariates are normally distributed, you could run a series of t-tests in addition to eyeballing the means. (If you wanted to be more formal about this and take into account multiple hypothesis testing, you could do various kinds of balance checks, essentially using the x variables to predict sex.)

Graphs of the area of common support or distributions of other variables conditional on sex can help show what you find.

To write up the results, I'd suggest presenting a table with the coefficients for the full model without the interaction, the full model with the interaction (showing the interaction is not significant), and the models by gender.

For the discussion section, you can mention that you looked into the role of the interaction term. You can show your results about micronumerosity and covariate balance by sex (whether or not they seem to explain the problem). All of these are exploratory analyses, and so they can't stand on their own as definitive explanations. But they help you address what should be done in future analyses (e.g. that a larger N overall is needed or that oversampling people in small cells would help, or finding other ways to increase the precision of the model).


Let the set of alternatives be $A = \left\{a_1,a_2,...,a_k\right\}$. Let the number of players be $n$. Let the set of preference orderings over $A$ be $\mathcal{P}$. Then the set of preference profiles is the Cartesian product
$$
\mathcal{P}^n = \times_{i=1}^{n} \mathcal{P}.
$$
Let us denote the preference ordering
$$
a_1 \succ a_2 \succ ... \succ a_k
$$
by $p^*$. Define the Social Choice Function $F$ by
$$
\forall p \in \mathcal{P}^n: F(p) = p^*.
$$
This SCF $F$ clearly has universal domain, is not a dictatorship, and is also independent of irrelevant alternatives. (Or any alternatives for that matter.)


What are the household holdings of financial products in China?

I do not think there is some dataset that has such an detailed breakdown that you want. However, one of the most widely used datasets on financial assets held by households are the various national surveys including the Survey of Chinese Consumer Finance and Investor Education (SCCFIE), China Household Finance Survey (CHFS), or Chinese Survey of Consumer Finance (CSCF). These datasets might not be directly freely avaiable but if you message the authors in the studies cited below they should provide them for replication purposes unless they happen to be confidential.
All three of the above are widely used in academic literature (just few examples include: Liao, Huang, & Yao (2010), Xie & Jin,(2015) or Chu, Wang, Xiao, & Zhang, (2017)).
These surveys are typically highly detailed but unfortunately won't have everything you cite you would like to see. For example, Liao, Huang, & Yao (2010) based on SCCFIE showed that the financial and non-financial assets were in 2008 distributed in China thusly:


Disposable Income $Y_D$ as a function of $Y_G$ and $Y_E$ is:
$$Y_D = Y_G + (1-\alpha) Y_E$$
Given wage rate $w$, and $Y_E = wH$, the budget equation can be written as:
$$Y_D = Y_G + (1-\alpha)wH$$
Preferences of the individual over $Y_D$ and $H$ are represented by the utility function
$$U(Y_D, H) = \dfrac{Y_D}{(1+H)^2}$$
So the utility maximization problem is :
\begin{eqnarray*}\max_{Y_D, H} && \ \ \dfrac{Y_D}{(1+H)^2} \\ \text{s.t} &&  \ \ Y_D = Y_G + (1-\alpha)wH \\ &&  \ \ H\geq 0 \end{eqnarray*}
Here is the picture to demonstrate optimal solution :

Solving the above problem we get the optimal labor supply as
\begin{eqnarray*} H^*(w, \alpha, Y_G) = \begin{cases} 1-\dfrac{2Y_G}{(1-\alpha)w} & \text{if } (1-\alpha)w - 2Y_G > 0  \\ 0 & \text{if } (1-\alpha)w - 2Y_G \leq 0 \end{cases}  \end{eqnarray*}
So the optimal utility as a function of $w, \alpha, Y_G$ is as follows:
\begin{eqnarray*} U^*(w, \alpha, Y_G) = \begin{cases}  \dfrac{((1-\alpha)w)^2}{4((1-\alpha)w - Y_G)} & \text{if } (1-\alpha)w - 2Y_G > 0  \\ Y_G & \text{if } (1-\alpha)w - 2Y_G \leq 0 \end{cases}  \end{eqnarray*}

Now the Govt. chooses $(Y_G, \alpha)$ by solving :
\begin{eqnarray*}\max_{Y_G, \alpha} && \ \ U^*(w, \alpha, Y_G) \\ \text{s.t} &&  \ \ Y_G = \alpha wH^*(w, \alpha, Y_G)  \end{eqnarray*}

Solving it we get
$\alpha^* = 0$ and $Y_G^* = 0$


Why Turkey's president thinks that by cutting interest rate it will lower inflation?

I'm gonna start this off by saying this is speculative, so take this answer with a grain of salt.

In order for a counter intuitive measure like this to work, there must be something else going on that over-shadows it. (Inflation topics tend to be riddled with things like this). I admit I don't know what the economic climate in Turkey is like currently; but I can think of a way that it would make sense to lower rates and expect lower inflation.

In light of recent events, Turkey has been the focus of some very negative media coverage as of late, and some of it for good reason. The last couple years for Turkey have been rough to say the least; but that's not the macro-trend of Turkey.
Turkey is an emerging market economy, they have urbanized dramatically from 2000-2015, maintained strong macroeconomic and fiscal policy frameworks, opened up to foreign trade and finance, harmonized many laws and regulations with European Union (EU) standards, and greatly expanded access to public services. It also recovered well from the global crisis of 2008/09.

Tying this back to your question now, it could be the case that Turkey's government spends too much money and is the biggest factor in the inflation numbers. If President Erdogan can better enable the people of Turkey to replace the effect of government spending organically (enable the people via lowering interest rates), then he can purposely scale back government spending (which would lower inflation b/c it's the bigger factor).

In summary: Erdogan may be trying to stabilize Turkey's economic climate via lower government spending which will reduce aggregate demand, leading to lower growth and less demand pull inflation. The macro trend of Turkey and forecasted growth expectancy is very high, and probably over heated, despite the recent negative issues in the micro economic climate.


What happened to the money multiplier after QE?

You may want to look at the following paper by Cukierman (2017). The author compares inflation for a period of identical base expansion in post Lehman US and hyper-inflationary Germany in the 1920s. They mention exactly what you said, that banks have increased their reserves at the Fed. In the US this has not translated into a heightened demand for goods and services as was the case in Germany. Furthermore the author cites fundamental differences in the economical and institutional circumstances as a reason for the difference in transmission. I suggest reading the paper for a more in depth explanation.


Why a new startup should ask a big investment company to value them as low as possible?

Each startup typically attracts multiple investors, each having its own evaluation of the company. Investors participate in funding series, when equity is sold at the same per-share price. Otherwise, it's difficult to explain an investor why he paid more for the startup than others did.

When a startup finds investors who buy their stakes at high evaluation, the startup cuts off more reasonable investors. And reputable VC funds don't like overpaying.

So, the startup ends with some silly investors holding their equity, while unable to find more money at comparable prices.

In the end, founders are better off while targeting realistic evaluation, not milking a single naive investor.


How can the GDP's growth rate be positive, when the GDP decreases?

Your first link is "GDP (current US$)".
Your second link "GDP growth (annual %)" is "based on constant local currency" (from "Details").
For figures that correctly correspond to your second link, see instead this third link: "GDP (constant LCU)" (LCU = local currency unit).
The discrepancy between the first and third links is explained by the great fall in the Mozambican metical (against the USD) in 2015 and 2016:


In Barro's (2009) Rare Disaster Model in AER: How to derive equation (5)

There is probably an error in your formula for $\sum_0^s v_i$.
You can use a trick to directly compute $E_0 e^{(1-\gamma)v_i}$ using
\begin{align}
E_0 e^{(1-\gamma)v_i}& = \Pi_0^s E_0e^{(1-\gamma)v_i}.
\end{align}
Notice $e^{(1-\gamma)v_i}$ is a random variable equal to 1 with probability $1-p$ and $(1-b)^{1-\gamma}$ with probability $p$. Therefore,
\begin{align}
E_0 e^{(1-\gamma)v_i}& = \Pi_0^s (1-p+pE_0(1-b)^{1-\gamma}),\\
& = (1-p+pE_0(1-b)^{1-\gamma})^s.
\end{align}
The term $E(1-b)^{1-\gamma}$ now appears your expression.


What is the advantage and disadvantage of fiscal illusion policy in terms for the financial market?

Too long, didn't read: the market does not care.

Colombia's Pension Reform: Fiscal and Macroeconomic Effects, by Klaus Schmidt-Hebbel, states black on white (p 22) that

  issuing explicit domestic debt for paying off implicit government debt does not have first-round macroeconomic and financial effects

on the condition that the financial markets see through the debt swap. Fiscal illusion aimed at tax payers does not have any impact on tax payers, but the same Schmidt-Hebbel notes that the market could be fooled too.

Peek and Wilkox looked into it and conclude that there is no data showing that fiscal illusion ever had an impact on interest rates, which leads me to conclude that, despite KSH's prudence, there is no (first hand) effect of fiscal illusion on the financial market. Of course, it can have secondary advantages such as leading the market to assume more political stability by raising popularity, or leading the market to distrust you, but these are corollaries of the effects of fiscal illusion on the people rather than pros and cons of fiscal illusion to the market.


Maybe this helps: The interest rate is the price of money. If the supply of something goes down, while the demand stays the same, the price moves up. So if the supply of money were to go down, the interest rate would go up, if the demand for money stays the same.

Now, to reduce the money supply and with that to keep an economy from overheating, the central bank could just collect dollar bills and keep them in a vault for later use. Less money, means higher interest rates, means less investment, means less heat in the economy. However, it is easier for the central bank to simply change the price it charges banks borrowing from it overnight. This is just one of three policy tools that the bank uses, the other two being open market operations and reserve requirements. By increasing the price of money, the effect is similar to a change in the money supply, so that the central bank effectively reduces the money supply.

Hope this helps. Have fun studying this! I really enjoy the topic, even though I still know way too little about it!


performance as utility function / price?

There is a long tradition in economics (some 50 years worth of research) called "Hedonic Price Analysis".

It consists of "allocating" (through regression estimation) the price of a product to its various qualitative features ("characteristics") quantified, that presumably are valued by the consumers, i.e. those that are utility-enhancing. These characteristics are either quantified (e.g. Computer RAM measured in GB), or "1/0" dummy variables (the characteristic exists/it doesn't). Note that in the related empirical studies actual transacted prices are used, i.e. prices that the consumers have accepted to pay.

The estimated coefficients from the regression provide the monetized "willingness to pay" per unit of characteristic (or per existence of it). Once you have them, you can extrapolate outside the sample to find the total "willingness to pay" for a product $i$, say $W_i$, by multiplying its characteristics by the marginal willingness to pay for each characteristic.

In essence, in this way you transformed something that is considered ordinal and un-measurable (utility) into a monetized equivalent (using the "revealed preference" approach, since you used prices that the consumers actually paid).

If you then compare this magnitude to some advertised price of this product, $P_{ai}$, then a ratio like

$$\text{Prf}_i = \frac {W_i}{P_{ai}}$$

could be your "Performance" index. If for example it is higher than unity, it means that the product "is a good bargain" for the consumers, because the monetary value of the utility they will get out of it, is higher than the money they will have to pay to acquire it.

NOTE: Hedonic Price Analysis is not just something that academic economists do. In many nations, official Price Indexes are for several years now adjusted for quality, using the methods developed by economists throughout the years.


How to show the production function is concave in K and L but not strictly so?

So we want the Hessian to be NSD, so we need the PMs to alternate weakly.

$H=\begin{bmatrix} F_{kk} & F_{kl} \\
F_{kl} & F_{ll}
\end{bmatrix}~~NSD \iff~~~F_{kk},F_{ll}\leq0~~~\&~~F_{kk}F_{ll}-F_{kl}^2\geq0$

We are given that $F_{kk},F_{ll}<0$ so we need to figure out the cross partials.

Constant returns to scale implies that we have a homogeneous of degree 1 function:

$F(K,L)=KF_k+LF_l \implies  F_l=KF_{kl}+LF_{ll}+F_l~~ \&~~  F_k=LF_{kl}+KF_{kk}+F_k$

Now we can substitute these equations into the expression for the 2nd PM:

$\big(-\frac{L}{K}F_{kl}\big)\big(-\frac{K}{L}F_{kl}\big)-F_{kl}^2=0~~~~~$
 and we're done.


Socialism doesn't work because an elite does not like to give up their privileges easily. After it took a wave of bourgeous revolution over a number of centuries to force the aristocracy to give up their powers and to enter a power-sharing agreement with the bourgeois which led to the decline of feudalism.

Marx suggested that this movement would not stop with the bourgeois, but would then go on to animate the so called third estate.  This indeed did occur over the 20C, but in the final analysis, not successfully and this has led to some people to say that Socialism does not work. The other side of this thesis is that it was simply strangled at birth, and this is what the Trumans policy of containment amounted to.


Measuring "Intangible Utility" (reference request/methodological discussion)

This is just a follow-up on denesp's comment. In economics, the utility is a tool used to represent choices, and therefore the right way of measuring the individual's utility from listening to the song is to elicit his willingness to pay for it. This can be done by a Becker-DeGroot-Marschak mechanism that eliminates moral hazard. Note that this refers to ex-ante anticipated utility.

The only way to look at actual experienced utility is to rely on other means of investigation, like neuro-imaging or survey questions, in the spirit of happiness research. But this is quite controversial, since the concept of experienced utility is itself poorly defined. Most economists would not agree to base welfare analysis on such measurements. You can have a look at happiness research (e.g. Deaton, Kimball, Benjamin, ...) if you want to learn more on this.


What is the difference between Q4/Q4 and Y/Y GDP growth?

If you could include the source(s) you were talking about that would be great. Without further info, my initial guess is that the Q4/Q4 means you compare GDP in 2018Q4 to GDP in 2017Q4. Y/Y means you compare GDP in the whole year of 2018 to that of 2017.

Upon further inspection, if you take a look at the US's real GDP, you'd get the following:

Growth in 2018Q4 compared to 2017Q4: 2.52%
Growth in 2018Q3 compared to 2017Q3: 3.13% [Link]
Growth in 2018 compared to 2017: 2.93% [Link]

So I think your Y/Y number is right... but the number for "2018Q4/Q4" might have been growth in Q3?

Update

It seems like the number reported was the initial estimate (which gives YoY growth of 2018Q4 to be 3.1% and 2018 to be 2.9%) in February 2019. The third estimate (which is what FRED uses) was released in December 2019 and yields YoY growth as calculated above.


Insurance Company's Role after Natural Distaster

Is anything special expected of insurance companies after a natural disaster?

Insurance providers in high-risk areas tend to increase the premiums, particularly for re-insurance (Froot, 2001). Some insurers will also leave the market, with others coming in (Grace, Klein & Liu 2005)

Semi-related: One paper with a 1970-2002 analysis of disasters and financial flows suggests that in poorer countries the migrant's remittances increase after the hurricanes covering $\frac 45$ of the damages, but in richer countries it only stimulates lending, not fully offsetting the losses (Yang 2008).

  Are there ever concerns about insurance shortages? The insurance companies typically try to create a "healthy" risk pool, but if several natural disasters hit, are they still expected to function as normal?

According to the news there wasn't shortage or bankruptcy concerns in the Hurrican Irma. The straight answer for that question is it depends on the impact of the damages.

About functioning as normal: they will probably increase the premiums, as stated above, and might implement lower compensation limits for future losses, or exemptions for certain kinds of damage (e.g. most insurances stopped covering terrorist attacks after the 9/11, or priced it extremely high).

  Many different sectors have to cooperate to put affected urban communities back together. Recently there are reports of labor shortages that has stunted the rebuilding of some of the cities affected by the hurricane season of 2017.

This is not the insurer's problem. If you suffered damages, you receive the previously agreed compensation. It is up to you to rebuild or not with the compensation you received, with whatever conditions the market has at the moment.


Yes, you are correct. That solution implies a utility of $0$, while any other solution necessarily will give you negative utility.

It is an odd problem for its violation of local nonsatiation: It is indeed optimal for the household to throw away the rest of his income.

Update

Let's add the either a or b and see what happens:

$$max(-[(10-a)^2+(10-b)^2])$$ $$s.t.\ a+b \le 40,\ a\ge 0,\  b\ge 0,\ ab=0.$$

The optimal solution set now contains $\{(10, 0), (0, 10)\}$. The preferences between this one are still globally satiated at $(10,10)$, but as the point is not feasible, we set one of the coordinates to that value and keep the other one at $0$.


Is there an economic interpretation of the production transformation function?

It is, as you say, a mathematical device to define the production set in a way that is analytically tractable

I have seen one description as thinking of it as a measure of the amount of technical progress now required to make the combination $y$ a feasible one, so

if $F(y)=0$ then that combination is just feasible with current technology,
if $F(y)\lt 0$ that combination is feasible with less than current technology,
if $F(y)\gt 0$ that combination requires more than current technology enables and so is currently not feasible

though this looks more like handwaving and rationalisation rather than something actually meaningful


How to calculate the minimun of Average Fixed Cost knowing the Average Fixed Cost

As the quantity of output of a good increases, fixed cost (by definition) remains the same and therefore average fixed cost per unit of output continuously decreases.  Therefore the average fixed cost curve does not have a minimum, except in the sense that it is asymptotic to zero.
A much more important concept than average fixed cost is average total cost, that is, the average of the sum of fixed and variable costs.  This often has a minimum, but can be continuously decreasing when there are significant economies of scale.


GMM Estimation of a parameter from Intratemporal Euler of capital constraints

To elaborate on what has been said in the comments already, using GMM based on Euler Equations generally involves uncertainty that motivates some sort of expected orthogonality between a moment equation and some instruments. Here is a common example of a "Consumption-Based Asset-Pricing Model" (see, for example, Campbell, 1993, 1996) posted by Dave Giles:

A representative agent chooses a consumption time-path to maximize expected discounted utility

$E\left[\sum_{i=0}^\infty\beta^i U(c_{t+i})|\Omega_t\right]$,

where $\Omega_t$ is the information set at time $t$, subject to the inter-temporal budget constraint,

$c_t + p_tq_t = r_tq_{t-1} + w_t$, for all $t$.

The optimal consumption path satisfies:

$p_tU'(c_t) = \beta E[r_{t+1}U'(c_{t+1})|\Omega_t]$, for all $t$

Which gives the Euler equation:

$E[\beta(r_{t+1}/p_t)[U'(c_{t+1}) / U'(c_t)]|\Omega_t] - 1 = 0$.

He then imposes the CRRA utility function $U(c_t) = c_t^{1-\gamma}/(1-\gamma)$, making the Euler equation become

$E[\beta(r_{t+1}/p_t)(c_{t+1}/c_t)^{-\gamma}|\Omega_t] - 1 = 0$.

This yields the moment equations:

$E[\{\beta(r_{t+1} / p_t)(c_{t+1} / c_t)^{-\gamma} - 1\}z_t] =
 E[E[\beta(r_{t+1} / p_t)(c_{t+1} / c_t)^{-\gamma} - 1|\Omega_t]z_t] = 0$

with $z_t$ a vector of instruments belonging to $\Omega_t$.

In this scenario, the uncertainty referred to is captured in the expectation operator over the information set $\Omega$. Notice that the interpretation of $\Omega$ motivates which instruments to use in the estimation.

Takeaway: if you want to use Euler equations to motivate GMM, you need some kind of uncertainty. Use uncertainty structure to decide instruments.

Sources

Campbell, J. Y., 1993. Intertemporal asset pricing without consumption data. American Economic Review, 83, 487-512.

Campbell, J. Y., 1996. Understanding risk and return. Journal of Political Economy, 104, 298-345.


Can futures buying/selling distort price discovery?

Yes, that is plausible although will not necessarily be the case. I will focus on put & call options.

Consider the put-call parity, which I rewrite as

$$S+P=C+K*exp(-rt)$$

where S denotes the stock [price], P put, C call, and K the strike price.

Buying enough call options will increase C. If that were the only change in the market (regarding this stock), that would "break" the put-call parity and therefore an arbitrage opportunity would ensue.

Since K is fixed, the only possible changes to offset C's increase are an increase of P and/or of S. An agent who notices C going up is likely to interpret that someone else has information in the sense that S will go up.

Unless that agent also has information in the opposite direction, it would be irrational for him to buy P in his attempt to take advantage of the arbitrage opportunity. Thus, he is likelier to buy S instead of P at least while the put-call parity is restored. Buying S tends increase its price (as is the case with any financial instrument).

Similarly, in the event of C's increase, the agent might set up a strategy that consists of taking a short position on C and hedge it by taking a long position on S (he might have to borrow because C<S, but that is irrelevant to the point). Opening that long position tends to increase S.


Are there more historical examples of big change in prices thanks to demand/supply changes like the tulip mania?

Every price change of a good is due to a change in supply/demand. Based on your example are you maybe thinking of sudden price changes due to a bubble? For example with the tullip mania the price of the tullips was completey detached from the utility that anyone actually got from owning tullips. In a nutshell people were willing to pay exorbitant prices for these tullips because they expected to be able to sell them for an even higher price in the future.

Another example would be the dotcom bubble where there was a sudden drop in the value of internet based companies. I want to mention that the people spending a years salary on a tullip bulb weren't necessarily stupid or naive. Think about it like a time bomb where you don't know when it is going to explode. Holding the bomb(owning the asset) allows you to make money and you can hand off the bomb anytime you want. If you are however holding it when it explodes you lose all of your money.

Another example would be the cryptocurrency market.


Question about misperception in IS-MP model

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

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

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

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

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

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


Measure combining growth and distribution of income

One concept fairly established in economics is the idea of generalized Lorenz dominance.

The Lorenz curve (https://en.wikipedia.org/wiki/Lorenz_curve) plots percentiles of the population on the x axis and the cumulative percentiles of income on the Y axis. If the point (30,10) is on the curve, then this means that the bottom 30% of the population have 10% of the income of the population.

This allows us to compare the inequality of two countries by comparing how low or high their Lorenz curve is. If curve A is everywhere above or equal to curve B, then A is weakly less unequal than B. However, even the poorest person in B may still earn more than A.

The generalized curve multiplies the Y axis with the average income of society. Now we can not only compare A and B in terms of inequality, but also by how well individuals are off in these societies. Curve A being everywhere above or equal to curve B means that every percentile of society A is weakly better off than every matching percentile in society B.

Shorrocks showed that under certain conditions a parameterized family of social welfare functions is higher in society A relative to society B for all parameters if and only if the generalized Lorenz curve of A is higher than B at all points.

Shorrocks, Anthony F. "Ranking income distributions." Economica (1983): 3-17.


No, this question is based on fundamentally flawed premises.  There is a plenty that you can criticize about UBI and generally literature does not consider UBI efficient redistribution policy, but none of what is mentioned in the question holds for UBI.
Addressing UBI

Lets start by correcting misconceptions:

Theory of tragedy of commons has nothing to do with what you describe. The theory of tragedy of commons is:
a) A theory about situation where private property rights are non-existent. Unless you want to make claim that property rights are missing in the market for ice cream, barber services or entire market generally suffers from lack of property rights - which is empirically absurd assertion outside few specific markets or countries like North Korea - tragedy of the commons simply does not apply here as for tragedy of the commons you first have to have some commons to begin with.
b) the tragedy of the commons is not about increases in prices. In fact, under tragedy of the commons prices will tend to be lower, or in some cases even impossible to exist without further government intervention (e.g. clean air is an example of resource suffering from tragedy of commons) than they would be in presence of property rights. Furthermore, the tragedy of the commons will generally cause prices to be undesirably low (from societal perspective) which will result in overexploitation of common resource.

UBI Should not Cause Significant Inflation:

First, it is important to understand that profit maximizing firms can't just set prices in arbitrary fashion. They are limited by the parameters of the market such as the level of competition or market structure we are talking about. Inflation, is generally unaffected by redistribution.
Inflation is macroeconomic phenomenon and depends on the equilibrium price level set on the money market. The money market equilibrium can be in it's simples form described by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY$$
Where M is the money supply, V velocity of money, P price level and Y output.
Solving for price level and log-linearizing we get:
$$\ln P=\ln M+\ln V−\ln Y$$
Thanks to everything being in logs we can directly interpret any change in $P$ (i.e. inflation if change is positive or deflation if negative) in response to right hand side variables as percentage changes. So if money supply would expand by $1\%$ we would expect inflation to increase by $1\%$ ceteris paribus.
However, UBI does not directly affect the right hand side variables.
a) Provided that UBI is funded by taxes not high powered money it does not affect money stock of economy at all. So it does not affect $M$ at all.
b) Velocity of money is quite constant in a long-run, in short-run it depends mainly on the business cycle and interest rates. There is no reason to suspect UBI would have any effect.
c) UBI is a redistribution measure so it transfers output from one part of economy into another. To the extent this is funded by distortionary taxation it reduces economic efficiency and output in an economy which has no market imperfections. However, real life economies contain externalities, missing markets and other issues that can create efficiency cause for redistribution (see discussion of this in Atkinson (2015) Inequality). Generally, empirical literature shows that too large levels of redistribution can lead to lower growth of output, but modest redistribution seems to have little to none impact on it (see Jonathan, Ostry and Berg: Redistribution, Inequality, and Growth). Consequently, unless the UBI would be set to some extremely large value it should have no significant effect on $Y$ and thus again no effect on inflation.
UBI could distort relative prices because while everyone receives the UBI only some people pay for it. To the extent that the spending patterns of people who receive net transfer and those who on net pay into the system relative prices could change in a way that would hurt poor even if inflation remains overall constant. This would happen because it would lead to increase in demand for goods that low-income people consume while simultaneously decreasing demand for items that high income people consume. However, this effect would happen with any redistributive measure, and in addition there is no reason to believe this effect would be large enough to offset real increase in welfare of the poor thanks to the redistribution.
Literature on UBI
For overview of literature on this you can see Hoynes and Rothstein (2019) or Martinelli (2017) and sources cited therein. As mentioned, at the beginning, literature is generally negative towards UBI but that is because research shows it is less efficient and more wasteful than traditional redistribution systems, not because it would lead to inflation.


Why labour, capital, and output levels cannot be pinned down in perfect competition?

Thus, the furthest we can go in terms of characterising the equilibrium in this economy/firm relates to the optimal capital-labour ratio. In effect, nothing can be said about the level of inputs and outputs, $L^*$, $K^*$, or $Y^*$.

I don't think this is true. You combined two equations into one, and thereby lost information. The optimization problem is

\begin{equation}
 \max_{K,L} p\cdot AL^{\alpha}K^{\beta} - w \cdot L - r \cdot K
\end{equation}
Taking derivatives w.r.t. $L$ and $K$ yields two first order conditions and the only two unknowns are $L$ and $K$.
$$
\alpha \cdot p\cdot AL^{\alpha-1}K^{\beta} = w
$$
$$
\beta \cdot p\cdot AL^{\alpha}K^{\beta-1} = r.
$$
As you noted this implies the cost minimization equation of
$$
\frac{L^*}{K^*} = \frac{\alpha}{\beta}\frac{r}{w},
$$
but why go that way? You could get
$$
L = \left(\frac{r}{\beta \cdot p\cdot A K^{\beta-1}}\right)^{\frac{1}{\alpha}}
$$
and plug this into the first equation, yielding
$$
\alpha \cdot p\cdot A\left(\frac{r}{\beta \cdot p\cdot A K^{\beta-1}}\right)^{\frac{\alpha-1}{\alpha}}K^{\beta} = w.
$$
And then
$$
K^{\frac{\alpha\beta - (\alpha-1)(\beta-1)}{\alpha}} =
K^{\frac{\alpha + \beta - 1}{\alpha}}
= \frac{w}{\alpha \cdot p\cdot A\left(\frac{r}{\beta \cdot p\cdot A}\right)^{\frac{\alpha-1}{\alpha}}}.
$$
Clearly this is not very pretty but it is very solvable.

Note: I did not go into second order conditions but this is only a maximum if $\alpha + \beta < 1$.