Reliable US yearly population and netmigration estimates by state from 1970 up to today I am looking for US data on population and net migration by state and year from 1970 up to recent years (2015, 2016, 2017)?

Is there a reliable, clean and integrated/compatible source?

For 2010 to 2017 I found this US Census State Population Totals and Components of Change: 2010-2017 website. Is there anything similar for previous periods?

Other sources I considered that are not adequate:

Net Migration   Patterns for US Counties: only decennial
Census::CPS Historical Migration/Geographic Mobility Tables: does not disaggregate by state

Census State to State Migration Flows are available from 2004 - 2016. Census's State Intercensal Tables: 2000-2010 has annual state population data over the 2000-2010 period. Combining this with Census's State Population Totals and Components of Change: 2010-2017 gives population series for back to 2004.


How did the Bail-In in Cyprus Work? I've seen some articles online about the Cyprus-style bail-ins

When the bail-in actually happened there, they took money from people's accounts, but from where did they take the money?

For example, if someone had a CD there or a brokerage account with the bank, were those included as targets for bail-ins? Or was it limited to savings and checking accounts?

Apparently it's deposit accounts, which I think means both savings and checking accounts.

No, brokerage accounts are definitely not it, as they do not represent a liability for the bank. The issue is that the 'bail-in" is a reduction in the debt the bank has towards its depositors. When you own 100 of deposits, it's the bank that owes you, but when you owe a brokerage account that owns 100 of stocks, the bank owes you nothing. So, you received a statement from the bank saying you had 200000 euros in your account, then they impose a 40% levy on the uninsured part (100000). So next month you receive a bank statement that says you have now have 160000 in your account...


How does a liquidity guarantee for Asset-Backed Commercial Paper used to finance a Conduit work ? A liquidity guarantee was what a lot of banks used to insure outside investors payments if an asset in a Conduit defaulted. The way they were doing it was not really dispersing the risk evenly throughout the economy to outside money markets.

Can someone explain a liquidity guarantee and the process of how it works economically in more simpler terms ?

Unlike what is often assumed the in the realms of theoretical macroeconomics there is not always an infinitely deep market with constant buying and selling. In fact, one of the reasons Investment banks are so important is in the role they play in making markets for buyers and sellers of stocks and financial products of many kinds.

Lets think about liquidity in the current context - the liquidity of a, say, firm's shares is determined by the available quantity, indications of interest &C. We could construct a working difenition of liquidity as the difference between bid price and selling price (in the context of a firm's shares although the intuition holds).

In practice, the liquidity guarantee means that an entity involved in the exchange acts as the guarantor for there being bid prices and selling prices, a guaranteed quantity of shares available, and especially ensuring that the discrepancy does not become too great between bid price and selling price. This is of importance for, say, investors, since a smaller spread significantly affects the transaction costs, risks etc.

It is essentially someone (post-financial crisis it has often been the government) guaranteeing that a market will be made (with buying and selling prices in good faith) for a given time period (or indefinitely). It is a form of prevention of stocks becoming illiquid, almost like a form of insurance.

The application of a liquidity guarantee is far from limited to buying/selling shares in a firm of course (although I believe the intuition is the same) - a notable example has been the US government's temporary liquidity guarantee programme which was constructed in the aftermath of the 2008 financial crisis with the purpose of getting banks to begin lending to each other again - the purpose of the programme was "to decrease the cost of bank funding so that bank lending to consumers and businesses will normalize."  and "to strengthen confidence and encourage liquidity in the banking system by guaranteeing newly issued senior unsecured debt of banks, thrifts, and certain holding company, and by providing full coverage of non-interest bearing deposit transaction accounts, regardless of dollar amount."

Banks who made out liquidity guarantees are essentially insurance salesman and hence are exposed to the downside if things catastrophize. Often this insurance money was being kept in markets that would also be affected by market forces that made the liquidity guarantee they were insuring catastrophize in the first place! (These problems were exacerbated by many other factors including very high effective leverage rates).


Question about the Law of Supply I have a contention with the Law of Supply's dictum "if the price of a good falls, then the quantity supplied of that good falls, ceteris paribus."
Imagine a market for widgets produced by multiple factories with colossal machinery; the average cost differs among the factories.
If the price of the good decreases, then, according to the Law of Supply, quantity supplied decreases. The explanation I'm supposed to give in examinations goes along the lines of "the profit margin decreases, hence producers are incentivized to produce less".
Yet I would argue that, provided the drop in price is not drastic, every factory should produce the same amount as before, even those for which the price has dropped below the average cost, as this scenario would leave their owners better off compared to paying the fixed costs without revenue. Thus, the same quantity of widgets would be produced after the price drop.
The holes in my contention that are obvious to me are:

If the decrease in price was drastic, then some owners would be obliged to shut down their factories.
If the same machinery could be used to produce bananas instead of widgets, then the factories would switch to banana production if it yields more profit, thereby reducing the quantity of widgets supplied.

I also think that my argument is only valid in the short run: then, the marginal costs of individual firms would be more or less constant, and negligible changes in it would probably be brought about by small-scale laying off of employees. In the long run, owners could sell machinery and buildings and the marginal cost would be more variable.
So, taking account of all assumptions so far, i.e. the decrease in price is not drastic, the machinery is not good for anything other than producing widgets, and we are only considering the short run, then decreases in price should effect only slight changes in the quantity produced: this would be represented by a very inelastic supply curve. But, if interpreted as a marginal cost curve, this curve also says that for tiny nudges in the quantity produced, the marginal cost varies significantly, which is contrary to my earlier understanding that the marginal cost is approximately constant because factories cannot dump machinery easily in the short run.
What am I missing?

The law of supply holds under fairly general conditions. Essentially, it states that "quantities respond in the same direction as price changes." Formally,
$$(p-p')(q-q')\geq 0,$$
where $p$ is price, $q$ is quantity and primed and unprimed reflect two different states. You see that the inequality is weak such that a constant range is not excluded. However, a decreasing supply curve would violate the law of supply.
Moreover, your argument appears to be a bit fuzzy. Sure enough, it implies that for a given price-quantity pair $(p,q)$ that $S(p) = S(p-\epsilon)=q$, when $\epsilon$ price changes are not drastic. However, then consider price-quantity pair $(p-\epsilon,q)$ and another non-drastic price drop. Your argument appears to imply $S(p-\epsilon)=S(p-2\epsilon)=q$ and so on culminating in a constant demand function, which --it seems-- you do not want to apply.
It seems more reasonable to suggest that a marginal price drop also has a marginal effect on supply such that $S(p)=q$ and $S(p-\epsilon) = q - \varepsilon$, where both $\epsilon$ and $\varepsilon$ are tiny such that a "non-drastic price drop" implies a "non-drastic quantity reduction."


Basic question on calculating unemployment rates I would like to know if I have interpreted the following statement correctly and would be grateful of any help at all.

"The unemployment rate for 16-24 year olds not in full-time education was 12.2%"

I read this as the proportion of economically active 16-24 year olds that are not in full-time education and unemployed is 12.2%.

To clarify I believe it says $$12.2\%=\frac{\text{economically active (full time education and unemployed)}}{\text {economically active (FTE unemployed + FTE employed)}}$$

Is this correct?  I have looked online and have only seen the term unemployment rate in terms of the general population.

I am not an economist but a maths teacher and require the information to understand material for an upcoming context based exam.  I have no trouble with percentages but need to make sure I have interpreted the economics correctly.

Thanks in advance for any clarifications.

No, it's not correct. You are supposed to exclude people in FTE from labour force. Unemployment rate is a proportion of labour force which is unemployed. Labour force is defined as a sum of those employed and those looking for jobs (so it also excludes pensioners, parents on parental leave etc.). In your example the labour force should consist of only the people 16-24 years old.

I.e. $$12.2\% = \frac{\text{unemployed who are 16-24 years old}}{\text{labour force who are 16-24 years old (employed + unemployed)}}$$

Edit: I added that in this example labour force is restricted to specified age group.


Why if the economy will produces too much there will be an increase of prices in nearly all goods and services? I am taking an online Economics course and not understanding why if the economy will produces too much there will be an increase of prices in nearly all goods and services?
If for example there will be produced twice as much hats then needed, the price per hat will fall?

An economy that produces too little will suffer from high
unemployment, since the low rate of employment opportunities will be
inversely proportional to the high number of able-bodied workers. An
economy that produces too much will see widespread increases in the
prices of nearly all goods and services as the demand for them
outpaces production capabilities. This general increase in prices is
known as inflation.

From Teaches Economics & Society (MASTERCLASS) by PAUL KRUGMAN

The passage from Krugman is quite confusingly written. What Krugman has in mind is not increase in production per se but increase in aggregate demand which is associated with more production.
The short run relationship between real output and price level (change in which gives you inflation) can be visualized on aggregate supply-aggregate demand (AS-AD) diagram (see Blanchard et al Macroeconomics or Mankiw Macroeconomics for more detail).
If production (Y) expands because economy is able to produce more and firms expand their production that will lead to decrease in prices (P) - and hence deflation.  As the picture I below drew shows, when economy produces more because firms on the whole supply more to the market (AS shifts to the right), the price level would be expected to fall ceteris paribus:

However, what Krugman has in mind is change in aggregate consumer preferences that shift demand more (i.e. AD shifts to the right), this will lead to higher prices and more production (in the short run) because this higher demand and prices motivate firms to supply more. However, Krugman makes it sound in the passage above as if there was increase in supply by firms (where the chains of events starts with more production rather than with more demand as in this second case).
In this case aggregate prices increase because people demand too many goods and services and firms can only satisfy that extra demand at higher cost (since production capability of economy given by AS did not change). Consequently, firms will only be willing to supply extra goods and services if they are motivated by higher prices.


How do I distinguish price-taking in perfect competition from monopsony? I'm working on a practice problem where I'm giving the following:

Suppose a firm is a price-taker and can sell the good it produces at price $p$.

There is more to the problem, but it is not relevant for my question.

I am not given any more information about the market other than the firm is a price-taker. So it is therefore not a price-setter meaning the market is setting the price.

I can imagine two scenarios under which a firm would not be a price-setter.

(1) if there were perfect competition between sellers, the firm could not set a price.

(2) Also, if there were only one buyer, the firm would not be able to set a price either since the buyer could refuse to buy until the price went low enough.

My Question:

Is there something that distinguishes price-taking due to competition between sellers from price-taking due to monopsony? How do I tell which one it is?

You may notice that the price would almost surely vary with the quantity the firm wants to sell if it were operating on a monopsonic market. (Exotic cases when this is not true may be ignored as then competitive and monopsonic markets are indistinguishable). As you are given price and not price schedule, it is a sure indication that market can be considered competitive for any practical purpose.


GDP to employed people ration - solow swan model Two countries A and B have identical production function $Y=AK^{1/3}N^{2/3}$, they are identical when it comes to all other factors with the exception that savings rate is $s_A>s_B$.
a) What is the GDP to number of people employed ratio in those countries?

Question is about Solow  - swan model. How to apply this model in this particular case, because i am completely lost.

GDP per worker is the ratio of GDP (Y) to the number of people employed (N), it is Y divided by N. Some books denote it as little Y (y). Divide both sides of the production function by N (remember to use the rules of dividing exponents for N on the left hand side i.e. subtract the exponents, for N it will be 2/3-1 = 1/3).

Simplify the equation, so on the left hand side you should have (K/N) raised to the power of 1/3. You can replace this fraction with little k (k), raised to the power of 1/3. The little k represents capital per worker then.

1) $$ Y = A K^{1/3} N^{2/3} $$

2) Divide by N

3) $$ Y/N = A K^{1/3} N^{2/3-1} $$

4) $$ Y/N = A K^{1/3} N^{-1/3} $$

5) $$ Y/N = A (K/N)^{1/3} $$

6) $$ y = A (k)^{1/3} $$


What exactly is on the Fed balance sheet? All the rage these days is how crazily big the Fed's balance sheet has grown. Looking on federalreserve.gov, I can see its value topped up ~6,573,136 millions USD (~6 trillion USD).

Fine, but is there an exhaustive list of all the assets on this balance sheet? Loans? Bonds? Cash? Equities?

See this federal Reserve webpage that provides links.

Note that these are aggregates; there are specialised reports on various components of their balance sheets.

The FRED website has these series in an interactive database.


The effect of future increase in production on current market equilibrium I am going through the microeconomics course of the MRUniversity and in the end of the chapter on supply and demand there is a question that I don't get. Here is the question:

  If oil executives read in the newspaper that massive new oil supplies
  have been discovered under the Pacific Ocean but will likely only be
  useful in 10 years, what is likely to happen to the supply of oil
  today?

  a. The supply of oil will rise today
  b. The supply of oil will fall today
  c. There will be no change in the supply of oil

Now my analysis is that this means there would be more competition between the oil suppliers in the future and as a result some oil suppliers may decide to leave the market sooner and as a result the supply of oil will decrease. But according to the site the correct answer is that the supply of oil will rise. What is wrong with my analysis?

A key distinction is whether the good is storable.

Example 1: Milk (non-storable)

Q: Imagine that there is new technology being developed that will increase the supply of milk ten years from now. What will happen to the supply of milk today?

A: Nothing. Each supply and demand curve is specific to the time period.

Example 2: Oil (storable)

Let's assume oil producers currently have access to oil reserves that they are voluntarily leaving in the ground. That is, firms are effectively storing oil (by leaving it in the ground).

In such a case, increasing the supply of oil in the future is similar to increasing the supply of oil today. You can draw from future supply by storing less today.

Some intuition:

Imagine you have 10 cookies and were planning on eating 5 today and storing 5 to eat tomorrow.

Q: What happens to your cookie supply today if I tell you that I'll give you another 4 cookies tomorrow? Will eat 5 cookies today and 9 tomorrow?

A: No. You'll store fewer cookies for tomorrow.

If you're storing a good for the future, an increase in future supply will increase supply today.


Should the control variables in an econometric regression be correlated with both the dependent and the primary independent variables? If, for instance, my dependent variable is some happiness index, and my independent variable is a dummy for whether they experienced some randomly occurred natural disaster. I am trying to analyze the effect of having experienced that disaster on the happiness index.

I am using a fixed effects model.

I have basically two interrelated questions:

What I read so far is that in regressions, control variables need to be correlated with both (primary) x and y variables. If that is the case I do not see a lot of variables that are correlated with both the disaster and happiness, besides:

Wealth (the poor are affected more by the disaster; wealth is also correlated to happiness)
Some disaster-induced variable like dummies for whether the disaster affected their water source, whether they had to live in a temporary shelter (tents), whether their livestock was killed, etc., which are all correlated with happiness.
However, I also think that if I control for both of these factors, then I am controlling for the mechanism in which an individual's happiness could be affected by the disaster, i.e. taking away the effect of the earthquake-induced factors in the second point above. Am I thinking correctly?

Is it plausible to control for factors like age, education, etc.? These factors influence happiness (may even influence post-disaster happiness), but these variables like age are not directly correlated with whether they experienced disaster or not. Am I thinking correctly?

First of all, you mentioned that the disasters you are dealing with are "randomly" occurring.  So I want to provide the following as food for thought:

There is an important question here about what your "disaster" variable actually measures and at what level it was "randomized" (if at all).  If it is measured in spatial terms (was an individual at this particular place when disaster occurred), it is hard to imagine that this would be a binary variable (you experienced a disaster or not) and not something measured on a scale (how much damage you area experienced), unless treatment and control groups are far away from each other.  But in that case, it is hard to imagine that this variable would be random (both groups having equal probability of experiencing the same or similar type of disaster).  If it is measured in temporal terms (was there a disaster on day x) and there is no spatial variation in the data, then it is also not clear whether this variable is random because a lot of places experience the same disaster year after year and changes can be made over time in the same location based on previous experiences to better plan for future events.

But if the variable is, in fact, random, then by the beauty of randomized treatment you don't need to worry about control variables because the treatment variable is exogenous.

Question 1:

In answering your questions, I am going to assume that your "disaster" variable is not random, which seems like a more reasonable assumption.  I am also thinking of "experiencing a disaster" not just as whether you were in that place or time when the disaster occurred, but as something that had a physical/physiological/mental affect on you.  If it meant just being in that place or time then it is hard to think of anything affecting someone being in that place or time without specific context.

So we have to think about possible confounding variables.  Do any variables exist that affect whether someone "experiences" a disaster and that also independently affect someone's happiness level?  Yes, wealth fits that criteria, as a wealthier individual may have better safeguards in place (like earthquake or flood insurance) to allow them to deal with the impact of a disaster.  Other possible variables are age and health level.  Health affects happiness and during times of disasters those living in nursing homes or having chronic conditions like kidney failure or COPD are more affected by loss of power, for example.  Similarly, whether someone lives alone can be a confounder.  Occupation can be possibly, as emergency workers may be more impacted by disasters or some other professionals may be better trained to deal with the consequences of disasters.

Your thinking about not controlling for disaster-induced variables is correct.  You should not control for variables that are themselves not fixed at the time of "treatment".  They should be allowed to change when your "treatment" variable changes.

Question 2:

Like I said above, I would think of age as a confounding variable in the relationship between experiencing a disaster and happiness.  But if you have variables that you believe do not directly affect "experience" of a disaster but that do affect happiness, then it is still recommended to include them in the model because this reduces the error variance in the model (i.e., standard errors of coefficient estimates will be reduced).


Effect of Promotional Sales on a Demand Curve If there is news that shops are having a sale on dress shoes (beginning right now), will it shift the demand curve for this good?

I initially said yes, as a sale should increase the quantity demanded of dress shoes (resulting in a shift in the demand curve).

However, the answer in my textbook says no. I do not understand.

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

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

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

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

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

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


What is the subgame perfect pricing policy for seller? Suppose there is a seller S who is selling to 3 different potential customers H, M, L

The good is a durable good and it's utility in terms of dollar equivalent is as in the picture below:

So if H buys in period 1 it's total payoff will be 1500+700-p1 where p1 is the price paid to seller in period 1.

If any buyer buys in 1st period they will be out of the game for the second period.

So if H buys in period 2 it's total payoff will be 700-p2 where p2 is the price paid to seller in period 2.

If any customer does not buy they get a payoff of 0.

The game starts with S announcing the price p1 the H, M and L simultaneously and independently decide whether to buy or not. Whoever buys in period 1 is left out in period 2 and all the players are observable to everyone involved.
Then S announce price in p2.

Given this what will be the subgame perfect pricing policy for seller S and strategies for all players involved.

My attempt:

Below image shows the possible pay off matrix for each period.

From all three possibilites we can see that H will always buy in period 1. Given that H will always buy in period 1 the best possible case is Case 2 for S which maximizes the payoff of S to 2697.
Therefore the subgame perfect pricing policy is set p1 = 1199 and p2 = 299

To find the SPNE you want to consider all possible scenarios that the seller might face in the second period, and what his best strategy would be. This will help you study the seller's actions in the first period since they will lead to different scenarios in the second one. In fact, saying "the subgame perfect pricing policy is set p1 = 1199 and p2 = 299" is not a valid statement, the subgame perfect policy should be of the form: " the seller chooses p1=number in the first period and p2= a function of which players remain in the market"

Let me be more clear with what I mean:

The seller might find in t=2 that no one has bought the good, and must decide between choosing p2=300 and selling three units (revenue of 900), choosing p2=400 and selling 2 units (revenue of 800) or choosing p2=700  and selling one unit (revenue of 700). Clearly, in this case, the best pricing policy is 300.

Similarly, the seller might find himself in the situation that one player has bought the good in the first period. Say player M bought the good in period 1. In that case, it is better to set p2=700 and sell 1 unit than p2=300 and sell 2 units.
(Notice that this case is not very relevant because if M finds it profitable to buy in period 1 so will H, but it is a possibility you must consider.)

It is not hard to see that unless buyers L and H are the only ones in the market in period 2,  the seller will find optimal to choose p2 to be equal to the smallest valuation among the players still in the market, and every player that has not bought the good, buys it.

Given this strategy, you can now study the choice of p1. For example: If the seller sets p1=2200 no one will buy in period 1.  This is because buyer M will rather wait to period 2, anticipating that no one will buy in period 1, thus the seller will drop the price to 300. Therefore, she will be able to make a surplus of 700-300=400. We learn that for buyer H to be willing to buy in the first period, she must get a surplus of at least 400.  Therefore, the maximum that the seller can charge buyer H for the good in period 1 is 2200-400=1800. To sum up, if p1=1800, H buys in t=1 and the other two buy at t=2 at p2=300, giving a total revenue of 1800+600=2400.

Through a similar argument, you can find that if the seller wants buyer M to also buy at t=1, the largest price he could charge this buyer is p1=1500 (otherwise, buyer M would prefer to wait and have a surplus of 100 at t=2). Now let's compare the total revenue of p1=1800 vs p1=1500. If p1=1500, M and H buy at t=1 and L buys at t=2. The total revenues are 1500+1500+300=3,300, which is better than 2,400.

Lastly, would it make sense to try to sell to buyer L? in that case, the biggest price you can charge in t=1 so that L buys is  p1=900. Since anyway L cannot guarantee himself any surplus. However if p1=900, all buyers buy at t=1 and you make a total revenue of 2,700.

We conclude that the subgame perfect pricing policy is to set p1=1500, and p2 equal to the smallest valuation among the buyers still in the market, except if only buyers L and H are in the market. In that case,  choose p2=700. (Note that expressing the equilibrium strategy of the buyers will also be a bit wordy, but I think the question is interested only in the seller's pricing policy, so this is sufficient).

It might sound redundant to express p2 the way I did, but it is crucial in order to show that no player will have an incentive to deviate.


Nobel prize for empirical work Did any recipients of the economics Nobel prize receive their prize for work that was primarily or substantially empirical (rather than theoretical) in nature?

In 2011, Tom Sargent and Chris Sims were jointly awarded the Nobel Memorial prize for empirical work.

  The Royal Swedish Academy of Sciences has decided to award The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for 2011 to Thomas J. Sargent and Christopher A. Sims "for their empirical research on cause and effect in the macroeconomy."

Dr. Sargent's contribution was related to the use of structural macroeconometrics in policy and analysis and Dr. Sims' contribution was to the use of vector autoregressions (VAR) to analyze temporary changes in policy and other factors.

Source: Nobel Prize Website


Best history of macro book? I'd like to know if you know some book that summarize the history of macro ? I'm in Master (after undergrad) so I don't ask for beginner's book. I've begun to read "a history of macroeconomics from keynes to lucas and beyond" from Michel De Vroey but he is not very clear in his explanations.

Beyond Michel De Vroey's book, I know of no other book on the history of macroeconomics, as it is praised by macroeconomists. See for example this review.

De Vroey has a true vision of macroeconomics, he shares it with his reader and gives clear guidelines to understand the developments in the field.

Anyway, you will find below some nice references that could be useful:

The State of Macro, by Olivier Blanchard of MIT.
What do we know about Macroeconomics that Fisher and Wicksell did not? , by Olivier Blanchard of MIT.
The Macroeconomist as Scientist and Engineer, by Gregory Mankiw of Harvard.
Slideshares on a Brief History of Macroeconomics by Markus Brunnermeier and Delwin Olivan of Princeton.


Find Indifference curve/s and Marginal Rate/s of Substitution given only one point Arka likes fries. She wants to consume as much as possible. She consumes either regular (1 oz) or large sizes (5 oz).

Draw her indifference curve through $(x_R, x_L) = (10,0)$ and her indifference curve through the bundle $(x_R, x_L) = (10,2)$.

Determine her $MRS_{R,L}$ at $(x_R, x_L) = (10,2)$

Give an example of a utility function that captures her preferences.

What I tried:

$(10,0)$: Corner solution?

$(10,2)$: I'm thinking some indifference curve that does not intersect the indifference curve passing through $(10,0)$. Is that unique?

How can I do this without prices, utility or marginal utility? The formula from Wiki:

$$MRS_{R,L}(10,2) = \frac{MU_R(10,2)}{MU_L(10,2)} = -\frac{p_R(10,2)}{p_L(10,2)}$$
or in some strange books
$$MRS_{R,L}(10,2) = \color{red}{-}\frac{MU_R(10,2)}{MU_L(10,2)} = \color{red}{+}\frac{p_R(10,2)}{p_L(10,2)}$$
Well if we are at a point of tangency then (following Wiki)
$$MRS_{R,L}(10,2) = \frac{MU_R(10,2)}{MU_L(10,2)} = -\frac{p_R(10,2)}{p_L(10,2)} = -\frac{dR(10,2)}{dL}$$
I got nothing.

Some $U(x_R, x_L)$

s.t.

Domain includes $(10,0)$ and $(10,2)$

$$U(10,0) < U(10,2)$$

$$x_R' + 5x_L' < x_R' + 5x_L'' \to U(x_R',x_L') < U(x_R',x_L'') \ \text{(thus making #2 redundant?)}$$

$$x_R' + 5x_L' < x_R'' + 5x_L' \to U(x_R',x_L') < U(x_R'',x_L')$$

Domain is all pairs of nonnegative numbers (thus making #1 redundant?)

Is that right?

In general, you are right to be mystified: specifying a point (consumption bundle) isn't enough to compute MRS and indifference curves.

However, in this problem, I would suggest you take the first sentence seriously as a description of her preferences.  She likes fries.  (She doesn't care about what box they come in!)

Let $v(f)$ represent her utility as function of $f$, the quantity of fries she consumes (in oz).

Mechanically, $f = 1R + \frac{1}{5} L$, where $R$ and $L$ are the quantities of regular and large orders of fries she consumes.  So, her utility as a function of these is:

$$u(R,L) = v(1R + \frac{1}{5} L).$$

Now you can compute marginal utilities $u_R \equiv \frac{du}{dR}$ and $u_L \equiv \frac{du}{dL}$ and the marginal rate of substitution $MRS_{L,R} \equiv \frac{u_L}{u_R}$.    You will see that in MRS, the $v'(\cdot)$ terms cancel out, and you are left with an MRS of $5$, at every bundle $(R,L)$.  These are linear preferences over bundles, and the indifference curves are straight lines with slope $-1/5$ (if you put $R$ on the horizontal axis).

This makes intuitive sense in two ways.

First, the canceling tells us that preferences are independent of the specific functional form of $v(\cdot)$, so long as it is an increasing function.  This is because utility functions only encode ordinal preferences.

Second, the MRS gives the rate at which she would be indifferent to  trading those two goods.  If you offered her five 1 oz boxes for one 5 oz  box, she wouldn't mind, since it's all the same to her.  (If you offered her a penny more, she would gladly make the trade, and if you offered a penny less, she would refuse.)

As an aside, we could say that the relationship $f = 1R + \frac{1}{5}L$ encodes the household production function: how she transforms things she can buy (boxes of various sizes) into the thing she really likes (fries).  This approach is associated with the work of Gary Becker and is commonly used in family and health economics.


What is the prime sign that a country is transitioning from a developing to a developed economy? Developed Economy = low human capital flight, good infrastructure, low corruption, high per-capita income, dominated by hi-tech industry, high expenditure in R&D, high-quality higher education, high-quality health care, and so on.

Developing Economy = high human capital flight, bad infrastructure, high corruption, mediocre per-capita income, dominated by agriculture or service sector, not enough expenditure in R&D, low quality higher education, low life expectancy, and so on.

What is the first sign that a country is transitioning from a developing to a developed economy?

If we want to point to 'only one sign', what would that be?

And, Why?

I don't know what the 'first sign that a country is transitioning from a developing to a developed economy', but I would look at the rates of output growth and study its acceleration.

In a layman's words, a transition from low to high income regime requires convergence to a high income teady state. This is only possible if the growth rate of aggregate output, underpinned by improvements in all aspects of the economy, has been consistently higher than that observed in high income (which you call developed) economies. Transition is complete (or the country achieves a 'developed' status) when the economy's growth rate reaches its long run steady state rate (typically low (<2% p.a.) positive growth rate).


Question on profit maximization with government taxation (I) A monopolist has a cost function $c(q)=q$. It faces the following demand function $ q(p)=100/p$ for $p\le 20$ and $q(p)=0$ for $p\ge 20$. What are the profit maximizing price and output.

(ii) a monopolist has a cost function $c(q)=\alpha q$ where alpha is fixed marginal cost. It’s demand function has a constant price elasticity of demand whose value is $-3$. The government imposes a tax of 6 dollar per unit of output. By how much will the monopolist price rise?

My solutions are as follows:

I am not sure whether it is correct or not. Please tell me and show me my mistakes.

ii.

I don't think the demand function in (i.) applies for this question. Here's what I did:

By Lerner Index, $\displaystyle{\frac{P - MC}{P} = \frac{-1}{E_d}}$

Since $E_d = -3$, we get $P = \frac{3}{2} MC$

We know before tax MC is $c'(q) = \alpha$, and after tax MC is $\alpha + 6$

In this sense, MC increased by 6, so P will probably increase by 9


Why wouldn't an arbitrageur who shorts an overpriced security, and longs a substitute company, break even? A Random Walk Down Wall Street (2015 11 ed, but an 2019 ed. is upcoming). p. 249 Top.

  Suppose irrational investors cause an oil company security to become overpriced relative to both its fundamental value and its peer oil companies. Arbitrageurs can simply sell the overpriced security short and buy a similar substitute oil company security. Thus, the arbitrageur is hedged in the sense that favorable or unfavorable events affecting the oil industry will influence both companies. A rise in the price of oil that makes the shorted security rise will make the arbitrageur’s long position rise as well.

Why wouldn’t this arbitrageur just break even, especially after transaction costs?
Case 1 of 2: The oil industry improves.
Then as written overhead, the substitute oil company's and shorted security's price rise. The former causes the arbitrageur  to gain money, and the latter  to lose money.
Case 2 of 2: It tumbles.
Then the substitute oil company's and shorted security's price drop. The former causes the arbitrageur  to lose money, and the latter  to gain  money.

Yes, you've understood half the reason for taking the joint position: if sector-wide movements occur, then the position stays neutral: i.e. it is insulated from those movements.

It's not sector-wide movements that this position is trying to profit from. So it's wise to insulate the position from those movements.

What this position is trying to profit from, is the relative over-pricing of the shorted-security, and the relative under-pricing of its competitor. If the arbitrageurs are correct, and can stay solvent long enough, then each of their two positions will make a profit when the shorted security drops in price, and the held security rises in price.


Fehr & Schmidt, ultimatum game, inequaltiy aversion, perfect subgame Nash equilibrium I am preparing for an exam. I have found an old exam but I have no solutions for it, so I tried to solve it, but I dont know if I did it correctly and need therefore your help.

The problem looks as follows:

Ultimatum game, proposer (Player 1) and responder (Player 2) bargain about the
 distribution of 80 Euro. The proposer offers an amount$\ [0; 80]$ to the responder
who may accept or reject this offer. If responder accepts, he gets$\ z_2$ and the proposer gets$\ z_1=80-z_2$. In case of rejection, both get nothing.

I am looking for the subgame perfect Nash equilibrium.

$\ U_i=z_i-0,4max(z_i-z_j,0)-0,8max(z_j-z_i,0) , i\neq j , \epsilon (1,2)  $

First of all, I am confused since usually the assumption is $ \underline{\beta>\alpha}$. This, does not apply here in my opinion. Since the term $\ 0,4max(z_i-z_j,0)$ expresses envy, where the$\ 0,4$ is generally expressed as an $\alpha$, but given here as a number. On the other side, the term$\ 0,8max(z_j-z_i,0)$ expresses fariness, generally given by the preference paramter $\beta$.

Anyway,  I tried to solve it via backwardinduction as follows:

2nd Stage:

i) Responder accepts if $\ z_2>z_1$ and it holds that

$\ U_2=z_2-0,4(z_2-z_1)>0$

$\ z_2>0,4(z_2-z_1)$

I think, this condition will never be satisfied, because the propeser will never offer more than half of the amount in question, the 80 Euro here in this example? For me that is the reason why the term  $\ 0,4max(z_i-z_j,0)$ in the utility function just gets zero.

ii) Responder accepts if $\ z_1\geq z_2$

$\ U_2=z_2-0,8(z_1-z_2)>0$

$\ z_2>0,4(z_1-z_2)$  with $\ z_1=80-z_2$

$\ z_2>0,4(80-2z_2)$

$\ z_2>\frac{320}{13} $

I think, I dont need the 1. Stage anymore since I already calculated the optimal share of the 80?

That is: $ z_2*= \frac{320}{13}+\varepsilon $ , where $\varepsilon $ is the smallest possible amount to add.

$ z_1*= 80-\frac{320}{13}-\varepsilon $

Questions:

Is my categorization regarding envy and fairness correct?
Is it of any importance for calcutlations that $\beta>\alpha$?
Is it correct that$\ z_2>z_1$ will never be fullfilled?
Is my subgame Nash equilibrium correct?
Did I miss something?
Is there a more easy approach, if preferences towards envy and fairness are given?

I would be very greatful for some help on this problem.

Many thanks in advance.

There are a couple of things here. First of all, envy is when your own payoff is smaller than the other player's payoff, which is the case when $z_i<z_j$. So the coefficients here are $0.8$ for envy and $0.4$ for compassion (envy looms larger).

Solving the game using backward induction, we need to first find the minimum value that player 2 is willing to accept. A purely self-regarding player will accept any positive offer from player 1. But with fairness preferences, player 2 will actually decline low positive offers as unfair. To find the threshold, we first note that player 2 gets a utility of $0$ if she declines the offer (in which case both receive 0 payoff). Suppose player 1 offers player 2 an amount $z_2$. Player 1 would keep the remainder, $80-z_2$. The utility is piece-wise linear, with a kink at 40 (equal split), like this:

We need to find the value for $z_2$ where player 2's utility crosses the x-axis (red dot). Since this happens below 40, the relevant part of the utility function is the envy case. Thus, we solve $z_2-0.8(80-z_2-z_2)=0$, which turns out to be $z_2^0=\frac{320}{13}\approx 24.6$.

Knowing the acceptance threshold we can now turn to player 1. Player 1 has the same Fehr-Schmidt preferences as player 2. Since the utility function is strictly increasing in own payoff, player 1 wants to keep as much of the pie as possible. Anticipating player 2's acceptance threshold, player 1 will offer $z_2^0=\frac{320}{13}$, maybe adding a small $\varepsilon$ to resolve player 2's indifference.


Are these two derivatives the same with regards to TR? Given that Marginal Revenue is change in Total Revenue:

TR = P*Q
P = f(Q)
TR = f(Q) * Q
MR = dTR/ dQ

Or

TR = P*Q
Q = f(P)
TR = f(P) * P
MR = dTR/dP

Which of these approach is right? My end goal is to relate revenue to elasticity. Does it matter how I arrive to it?

Both of these approaches are correct and valid approaches, in the first approach you calculate the derivative of total revenue with respect to quantity in second with respect to price.

If you are interested in seeing how total revenue varies with quantity you can use the first one if you want to see how the total revenue varies with price then the second one.

Also, you can have multiple different elasticities. Elasticity for single variable function is just by definition $EL=\frac{f’(x)x}{f(x)}$. Depending on what types of elasticity you want to relate the total revenue and what  exactly is your ultimate goal of your study either of the formulas could be used.


Understanding the law of supply In high school, I've never really questioned the law of supply, taking it as a given.

As I begin an introductory economics course in university, "relearning" the fundamentals of Economics, I realise I'm coming up against some difficulties trying to genuinely understand a fundamental concept: the law of supply. I have searched for similar questions here that concern this but none address the specific nature of my question.

I was initially confused at the direct link between price and quantity supplied, given by my textbook, which states that at higher prices, producers will find it more profitable to produce more and will thus do so. At this point in the text, concepts of MC, MR, cost curves etc are a few chapters away, and I am somewhat clueless about them at the moment, but do feel free to use that in your explanation if needed - I know that ultimately, marginal cost has something to do with this but I'm not sure what (I've forgotten most of my high school stuff).

I guess a key concern is this: if more is produced, then total cost of producing also increases right and it may not always be more profitable to have more quantity supplied, unlike what my textbook says. So does the supply curve already account for this? I.e. at every point, the revenue earned will definitely be more than the cost? How can we just assume this?

The interesting thing is, I'm actually able to sort of understand it by reading values off the supply curve by looking at the x-axis (quantity) first (which is a valid approach) then y-axis (price), which is that if producers are to supply more, they will need greater revenue to cover greater costs of production to allow sustained profits (preferably increased profits, maybe same amount - but less important at this point).

In fact, this "inverted" law of supply is what I'd prefer. When I then try to "re-invert" this to try and understand the actual law of supply whereby price change is the cause and quantity supplied is the effect, I'm confused once more. Was hoping somebody could explain how exactly this works, preferably in relation to the explanation for the "inverted" law of supply.

Was wondering also if there's a "mathematical proof" for this - that'd be great, though the intuition behind it should preferably still be explained in plain simple words.

As you noted correctly, it has something to do with the costs.  An important point here is a cost of producing an additional unit, and not average cost.

Let me give the following example.  Suppose that you are an owner of a bakery, and you have a single employee who works $8$ hours and produces $8$ breads a day ($1$ bread an hour). Assume you have to pay your employee $\$1$ an hour for the first $8$ hours and $\$1.50$ (overtime) for each additional hour (after $8$ hours), and you sell each bread at $\$1.20$.

One day you think to yourself: why not to produce and sell $9$ breads (you come to this thought by the same reasoning as in your question)?  Then, you realize that in order to produce the $9$th bread, you need to keep your employee working for an additional hour and have to pay overtime, namely $\$1.5$ for the $9$th hour.  However, you will still sell the $9$th bread for $\$1.20$, which means you will lose $\$0.30$ from producing and selling the $9$th bread.

Suppose that the price of bread has increased to $\$1.60$.  Now, you surely want to keep your employee for the $9$th hour (or even more), since for each additional bread produced (after $8$ breads), you will make $\$0.10$ profit per bread.  So, you can see that an increase in price induced you to supply more.


How to compute the utility function when risk aversion is equal to 1? How to compute the utility function when risk aversion is equal to 1?
If the utility function of consumption is set as,

$\frac{C^{1-\sigma} - 1}{1-\sigma}$.
Is it meaningful as $\sigma$ is equal to 1?
How to prove it if so? Thanks a lot!

Take the limit as $\sigma \rightarrow 1$,
\begin{align*}
\lim_{\sigma \rightarrow 1} \frac{C^{1-\sigma}}{1-\sigma}.
\end{align*}
This will then results in log utility. Calculating the limit goes as follows.
Since plugging in $\sigma = 0$ would give $\frac 0 0$, we use L'Hopital's rule.
This gives us
\begin{align*}
\lim_{\sigma \rightarrow 1} \frac{C^{1-\sigma}}{1-\sigma}
  &= \lim_{\sigma \rightarrow 1} \frac{- C^{1-\sigma} \log C}{-1} \\
  &= \log C.
\end{align*}


What would be the shape of the Indifference curve with slope 1/xy? Let the utility function be: $U(x,y) = \log x +y^2$.
In this case, the MRS is coming out to be $\frac{1}{2xy}$. Thus, how will the shape look like?

Wolfram Alpha might come with some help. Try entering $\log x+y^2=n$ for different n's (levels of utility). You will get the idea of how the indifference curve looks like.

e.g.
https://www.wolframalpha.com/input/?i=logx%2By%5E2+%3D+1.4


Why are there infinitely many indifference curves? If an indifference curve shows quantities where a consumer's utility from consuming two goods are equal, then why are there infinitely many indifference curves? From the diagram, you can have Q1,Q2 on IC1, but then you'd have Q1,Q3 on the other indifference curve, wouldn't that mean the consumer would receive the same utility from consuming Q1 and Q2 as well as if he had consumed Q1 and Q3, i.e. for a given Q1, the consumption of Q2 gives the same amount of utility as Q3? Shouldn't this mean that the indifference curve should be unique?

Utility is constant for all points $(q_B,q_A)$ on an indifference curve. So there is a number $u_1$ such that
$$
\forall (q_B,q_A) \in IC_1: \ U(q_B,q_A) = u_1.
$$
Similarly there is a number $u_2$, such that
$$
\forall (q_B,q_A) \in IC_2: \ U(q_B,q_A) = u_2.
$$
If $IC_1 \neq IC_2$ then $u_1 \neq u_2$.


How can I represent players with different information given continuous choice ranges? I must represent in extended (tree) form the following Game Theory problem:

A committee of experts must recommend a policy $a_1\in \mathbb R$ to Congress. Congress will then choose a policy $a_2\in \mathbb R$. The result of this policy is uncertain, determined by $x = a_2 + w$, where $w$ is random variable uniformly distributed between $[0,1]$, chosen by the "nature" player. The experts know the value of $w$, but the Congressmen are only aware that $w\sim U[0,1]$. The benefits to the congressmen and the experts are given by $-x^2$ and $-(x - 0.5)^2$, respectively.
So, the sequence of the game is the following: the nature player "chooses" $w$, then the experts choose an $a_1$ to recommend, and finally the congressmen choose $a_2$, the acutal policy.

My problem is the following: I can't figure out a way to represent the fact that the experts know the value of the continuous $w$, but the congressmen don't.

One way to represent the game tree (assuming that the congressman observes the expert's choice):

The game tree is drawn using LaTeX with istgame package.

\documentclass{standalone}

\usepackage{amsmath}
\usepackage{istgame}

\begin{document}

\NewDocumentCommand\vpay{m}
{ \begin{matrix} #1 \end{matrix} }

\begin{istgame}[scale=2,font=\scriptsize]
\cntmdistance{20mm}{70mm}{50mm}
\istrootcntm(0)[chance node]{Nature}
  \istb{w}[r]  \istb{w'}[r]         \endist
\cntmdistance{20mm}{40mm}{25mm}
\istrootcntm(1)(0-1)<-170>{Expert}
  \istb{a_1}[r]  \istb{a_1'}[r]     \endist
\istrootcntm(2)(0-2)<-10>{Expert}
  \istb{a_1}[r]  \istb{a_1'}[r]     \endist
\cntmdistance{15mm}{20mm}
\istrootcntm(3)(1-1)
  \istb*{a_2}[r]{\vpay{-(x-0.5)^2\\-x^2}}   \endist
\istrootcntm(4)(1-2)
  \istb*{a_2'}[r]{\vpay{-(x-0.5)^2\\-x^2}}  \endist
\istrootcntm(5)(2-1)
  \istb*{a_2}[r]{\vpay{-(x-0.5)^2\\-x^2}}   \endist
\istrootcntm(6)(2-2)
  \istb*{a_2'}[r]{\vpay{-(x-0.5)^2\\-x^2}}  \endist
\xtCInfoset(3)!.55!(5){Congressman}
\xtCInfoset[dashed](4)!.45!(6){Congressman}
\xtCommentTo[draw=none]($(0)!.5!(2)$)(1.5,0)
  {$w\sim U[0,1]$}[r]
\xtCommentTo[draw=none](3-1)(-1,-1)
  {where $x=a_2+w$ and similrarly for other cases}[r]
\end{istgame}

\end{document}

If you want an arc type continuum of actions:

\documentclass{standalone}

\usepackage{amsmath}
\usepackage{istgame}

\begin{document}

\NewDocumentCommand\vpay{m}
{ \begin{matrix} #1 \end{matrix} }

\begin{istgame}[scale=2]%,font=\scriptsize]
\cntmdistance{20mm}{70mm}{50mm}
\istrootcntmA(0)[chance node]{Nature}
  \istbA(.865){w}[r] \istbA(.865){w'}[r]     \endist
\cntmdistance{20mm}{40mm}{25mm}
\istrootcntmA(1)(0-1)<-170>{Expert}
  \istbA(.915){a_1}[r] \istbA(.915){a_1'}[r] \endist
\istrootcntmA(2)(0-2)<-10>{Expert}
  \istbA(.915){a_1}[r] \istbA(.915){a_1'}[r] \endist
\cntmdistance{15mm}{20mm}
\istrootcntmA(3)(1-1)
  \istbA*{a_2}[r]{\vpay{-(x-0.5)^2\\-x^2}}   \endist
\istrootcntmA(4)(1-2)
  \istbA*{a_2'}[r]{\vpay{-(x-0.5)^2\\-x^2}}  \endist
\istrootcntmA(5)(2-1)
  \istbA*{a_2}[r]{\vpay{-(x-0.5)^2\\-x^2}}   \endist
\istrootcntmA(6)(2-2)
  \istbA*{a_2'}[r]{\vpay{-(x-0.5)^2\\-x^2}}  \endist
\xtCInfosetO(3)(5){Congressman}
\xtCInfosetO[dashed](4)(6){Congressman}
\xtCommentTo[draw=none]($(0)!.5!(2)$)(1.5,0)
  {$w\sim U[0,1]$}[r]
\xtCommentTo[draw=none](3-1)(-1,-1)
  {where $x=a_2+w$ and similrarly for other cases}[r]
\end{istgame}

\end{document}


Why does equity have historically poor performance after rate cuts? I am struggling to understand why equity markets seem to suffer shortly after fed rate cuts. Here is a rather telling chart:

Question

Assuming not some kind of spurious relationship, what's the intuition behind the  connection between rate cuts and equity dropping?

Maybe the rate cuts draws investors attention to the weakness of the macro conditions and makes them more risk-adverse?

If this trend holds for a longer series, my guess is that this is due to the correlation between the federal funds rate and general economic conditions. The federal funds rate is usually cut in anticipation of a weakening economy or during a period of low growth.
It is well known that the expected returns on financial assets, including stocks and many other kinds of assets, vary with the business cycle. For example, see Fama and French (1989), "Business Conditions and Expected Returns on Stocks and Bonds." The most common explanation for this is that effective risk aversion is higher in bad times than in good times (e.g., as measured by GDP or aggregate consumption). This phenomenon is discussed more generally in the paper, "Discount Rates", by John Cochrane (2011). (Ungated access here.) For example, on p.1052, we read

  There is a strong common element and a strong business cycle
  association to all these forecasts. Low prices and high expected
  returns hold in “bad times,” when consumption, output, and investment
  are low, unemployment is high, and businesses are failing, and vice
  versa.


Interest rate and yield curve in a mild recession I came across this statement in a fairly official document, the phrase in bold does not seem consistent. I cannot contact the authors of the said document, so I am posing my question here. Here is the statement.

"Under a mild recession followed by a sluggish recovery and inflationary pressure,
interest rates rapidly increase and yield curve flattens."

Why would interest rates rapidly increase? Is it understood that the interest rates here refer to the rates the Federal Reserve sets?

Because interest rates have been at abnormally low levels for quite some time and the Federal Reserve bank is required to pay stockholders' dividends at 6 percent, the Federal Reserve must either issue or collect more money.

Both of these choices negatively impact the value of the US dollar as they both hurt the American economy one way or another.

A mild recession followed by a sluggish recovery may well lead to a politically initiated response that pressures the Federal Reserve to increase the money supply and inflation.

The reason the Federal Reserve concludes that interest rates rapidly increase is because they need the borrowers of this newly created money to pay back their loans sooner (to get their stockholders' 6 percent dividends).

Source:
http://www.federalreserve.gov/aboutthefed/section7.htm


What does "r" represent in the total cost function? I know that the total cost function of a firm in the short run is:

TC  = wL + rK,

where rK is essentially a constant. I understand the variables w, L and K, but I still don't get what r is. I mean, what  do I input as "r" when I'm trying to draw up a total cost function?

Thank you.

r is the user cost of capital.
User cost refers to the expenses borne by the owner or renter of a capital asset resulting from the use of the asset for a given period of time.
A standard metaphor is that of a machine being worn down over time as it is being used. During the time of use it creates a flow of goods through a production process. The capital gets it value from this flow of goods it can create. Simplify this metaphor to a machine that during three months can produce three pieces of bread - one each month - each sold for 1 dollar. The total value of the machine 3 dollars (ignoring discounting) so if you were to buy the machine you would pay 3 dollars. However if you just want to used it for a month it will only produce 1 piece of bread the value of 1 dollar so one month of machine is just worth 1 dollar.
Things are offcourse very much more complicated but you can google how the user cost of capital is derived.


what are the categorization by industry in economics? I wanted to know what industries are there from an economics point of view, and how each industry branches into different parts. Just categories and names will do , or if you can point to a resource please do.

Several countries have it defined in their tax code, or by the national statistics institute, or the central bank. Stock exchhanges also define industry categories.

For general purposes or international comparisons you can use the categories defined by the world bank (see also in word version), or from the United Nations.


Can lower working hours beat unemployment? The common sense reasoning is downright simple: if X hours of works are needed per month, and Y people are available to work, give each person X/Y hours of work each month.

I understand that there are generic frictions that prevent this:

people not being qualified to do some jobs
people not wanting to do some jobs

And also specific frictions:

people not wanting to get a lower salary because of lower working hours.

Without being as extreme as in the introductory example: In a given sector, where there is a surplus of qualified people willing to do a specific job, and whose average salary is higher than the minimal salary necessary to live above the poverty threshold: It makes sense to reduce at the same time salaries and working hours, in order to allow more people to get a salary.

However, except from France which has reduced working time from 39 to 35 hours per months, such measures are not widespread, and seem scarcely considered.

Therefore one wonders whether such measures can actually work. If they do, why are they not more widespread? If they don't, what is the issue preventing them from being effective?

In Germany in crisis times working shorter hours (short-time work, Kurzarbeit) can be used by firms to prevent layoffs. There are legal regulations how labor unions need to be consulted on how this is done. It has been argued that this has helped to overcome the 2008 crisis better than some other countries, e.g.: "What Explains the German Labor Market Miracle in the Great Recession? The Evolution of Inflation Dynamics and the Great Recession", Brookings Papers in Economic Activity, Spring 2011, Michael C. Burda & Jennifer Hunt; "Explaining the German Employment Miracle in the Great Recession – The
Crucial Role of Temporary Working Time Reductions", Alexander Herzog-Stein, Fabian Lindner, Simon Sturn, June 2013


What are some good advanced level textbooks on public economics? I'm taking a public policy course and the textbooks that were recommended for the course are way out of sync with the course material. These are:

Gruber, Public Finance and Public Policy

Stiglitz, Economics of the Public Sector

Which are all well and good, except they are too basic.

For example, in class we've derived the Samuelson condition using Lagrange multipliers and analyzed how it differs from the equilibrium with voluntary contributions. But there's nothing of the sort on these textbooks.

Our course outline is as follows:

1.    State intervention in the economy

a.  Efficency

b.  Fundamental Welfare Theorems

2.    Market failures

a.  Absence of competition

b.  Externalities

c.  Public Goods

d.  Information issues

e.  Incomplete markets

3.     Public Goods and the Public provision of Private Goods

a.  Public goods: efficiency conditions

b.  Public provision of Private Goods. Rationing systems

4.    Externalities

a.  Theory of externalities

b.  Private and public sector solutions

c.  Distinction between the use of prices and quantities in solving externality issues

5.    Social Choice

a.  Issues with preference aggregation. Arrow’s Theorem

b.  Different voting systems. Median voter theorem

c.  Social welfare functions: utilitarianism, Rawlsian criteria and intermediate
cases

6.    Taxes

a.  Introduction to taxes

b.  Fiscal incidence

c.  Inefficiencies derived from imposition and their consequences for optimal
taxes

d.  Taxes and labor supply, saving and decision making

e.  Fiscal reform

I would appreciate immensely any sort of guidance on this front.

The best book in my opinion for your case is definitely Intermediate Public Economics by Jean Hindriks and Gareth D. Myles. It is often used as a standard text for public finance at your level and covers most of the material you need in an interesting and accessible way.


Second Price Auction - adjusting PDF for reservation price The situation:

There is a second price auction with 2 players. Consider a second-price auction with 2 players.  Their valuations of the object at auction
are and are independently and identically distributed with pdf $f$ and cdf $F$.
over $[0,\hat v]$. Assume $f$ is continuous and positive over $[0,\hat v]$.

Now here comes the question: a reservation bid $r$ is now implemented - the winner pays the second of the highest bids including the reservation price, or if both bid lower no-one wins. I want to find the pdf that both bids are above $r$ and above some $x$, and add this to an equation calculating expected revenue for the auctioneer.

I have already found the pdf for both bids being above some value of $x$: $2f(x)(1-F(x))$. The pdf for both being above $r$ is $(1-F(r))^2$.

I've had a look at an answer for the problem, and it suggests that the combined pdf is $\frac{2f(x)(1-F(x))}{(1-F(r))^2}$. Could someone explain to me how this is so?

Then, when calculating expected revenue for the auctioneer, we have for the case where both bids are above $r$: $(1-F(r))^2\int_r^\hat v{\frac{2f(x)(1-F(x))}{(1-F(r))^2}}dx$. I'm also quite confused why we multiply by $(1-F(r))^2$.

To find expected revenue of the seller in a second price auction with reserved price consisting of two bidders who bid their valuations in equilibrium, we do the following :

Given that valuations are i.i.d with pdf $f$ and CDF $F$ over $[0, \hat{v}]$, the revenue that the seller gets for different realizations of players' valuations are as indicated in the graph below:

Therefore, expected revenue of the seller is :
\begin{eqnarray*}  &&\int_r^\hat{v}\int_r^{v_2} v_1 f(v_1)f(v_2)dv_1dv_2 + \int_r^\hat{v}\int_{v_2}^\hat{v} v_2 f(v_1)f(v_2)dv_1dv_2  \\ &&+\int_0^r\int_r^\hat{v} r f(v_1)f(v_2)dv_1dv_2  + \int_r^\hat{v}\int_0^r r f(v_1)f(v_2)dv_1dv_2 \\ &=&  \int_r^\hat{v}v_1 (1-F(v_1))f(v_1)dv_1 + \int_r^\hat{v} v_2 (1-F(v_2))f(v_2)dv_2 + 2rF(r)(1-F(r)) \\ &=& 2\int_r^\hat{v} v_2 (1-F(v_2))f(v_2)dv_2 + 2rF(r)(1-F(r))\end{eqnarray*}


How inflation affects exchange rates? I have a question regarding the impact of inflation on exchange rate between trading countries.

Let's assume a hypothetical situation where the UK and the USA trade with each other. The USA import goods from the UK and the UK exports goods to the USA.

Assume the exchange rate £1=$5 at the beginning. The UK is selling one widget to the USA for £10. Now let's imagine an inflation of 100% happened so that the UK prices this widget £20.

Now, my reasoning is that £ should weaken against dollar so that £1 = \$2.5.
So inflation weakens country's currency.
My reasoning is that this is logical that this should happen because now £1 is worth less than it was before the inflation (with the same amount of pounds you could buy twice as much before the inflation than you can now) so £1 should cost \$2.5 instead of \$5. Is my reasoning correct?

Consider two standard relations that tend to hold:

$$i_t = r_t + \pi^e_{t+1} \tag{1}$$

where $i_t$ is domestic nominal interest rate, $r_t$ is domestic real interest rate, and $\pi^e_{t+1}$ is expected domestic inflation. The expression is known as the Fisher equation.

Also, we have the uncovered interest rate parity

$$ i_t  = i^*_t - [s^e_{t+1} - s_t] \tag{2}$$

where $i^*_t$ is "foreign" nominal interest rate, and $[s^e_{t+1} - s_t]$ is expected appreciation of domestic currency in percentage terms ($s$ is the natural logarithm of "foreign currency per unit of domestic currency" exchange rate).
Combining the two and re-arranging we have

$$[s^e_{t+1} - s_t] = i^*_t - r_t - \pi^e_{t+1} \tag{3}$$

Assume that inflation is monetary, and keep  $i^*_t,r_t$ constant. Then expectations for domestic inflation will tend to reduce expected appreciation of domestic currency, and may even turn it into an expected depreciation, especially if expected domestic inflation is high. Shortening the length of the time periods, this tendency becomes more of "actual" inflation and "actual" exchange rate.

The fundamental reason is of course what the OP was thinking: if we think of USD as another good (which it is since it is a store of value and can be exchanged for goods), then, if English pound loses value due to inflation and can buy less goods, why should it be still able to buy the same amount of the good "USD"?


Intrinsic value of non-voting shares which don't pay dividends What is the intrinsic value of a company's non-voting stock shares which don't pay dividends?

My understanding is stock ownership has value in the form of controlling the company or receiving a portion of the profits.  Where does value derive from when neither of these is present?

Just because a share doesn't presently pay dividends, doesn't mean it never will. The gamble is that eventually, it will pay dividends. So the share's value is the market's estimate of the net present value of a future cashflow discounted by two factors: one, the discount rate to reflect that this is a future cashflow not a present one; and two, the probability the cashflow will start later, or never.


Price ratio determined by endowments only? Am I right to say in an Exchange Economy with two consumers with identical preferences, the equilibrium price (WEA) of the two goods would be determined by availability of two goods, i.e, total endowment?
Whereas if their preferences are not identical, this is not true, the equilibrium(WEA) would be determined by utility functions and endowments together?

No you are not. Preferences determine the equilibrium, even if they are identical, because they determine the value of the endowments.

Consider two agents, one ("A") having ice cream only, and one ("B") having lava only.

Case 1: Both hate lava

Assume lava burns tongues and is useless (typical Economist). Then, the initial endowments of B have zero value, as no one wants them. The equilibrium allocation equals the initial allocation.

Case 2: Both find lava useful

Now, imagine lava being useful for lava lamps (whatever). They still have identical preferences, but now they attach some positive value to lava. The value of B's initial endowment has changed, and hence he can trade at least some of it for ice cream. The equilibrium allocation no longer equals the initial allocation.


How does Marginal rate of substitution change? If you are at a point $(x,y)$ where your $MRS(x,y)=3z$, and you later exchange goods to be at point $(x-a,y+b)$, where your $MRS(x-a,y+b)=z$, can you conclude that you are one the same indifference cure, different one, or is there no conclusion possible?

I don't think any conclusion is possible without more detail, but if we make a few assumptions we can see where they lead us.

Assume $a,b > 0$ and $z < 0$

Assume the consumer in question has well-behaved preferences and therefore their indifference curves must be monotonic and convex

Given these assumptions (which I think are fairly reasonable, although I'd want to see them explicitly stated if this was a formal question) then the answer should be that the post-exchange indifference curve is different from the earlier one.

Given that $a$ and $b$ are greater than zero, we know that the consumer has lost some of the first good and gained some of the second. Examining all possibilities they could be in one of three positions relative to their original indifference curve:

Above the original curve
On the original curve at a different point
Below the original curve

Neither Case 2 nor Case 3 are plausible. We know that the slope of the new curve at $(x-a, y+b)$ is three times shallower than the that of the original curve at $(x, y)$. The assumptions of convexity and monotonicity require that the original indifference curve become steeper as it approaches the y-axis. See below for a colourfully-amateurish representation.

Note that in the example pictured above the resulting indifference curve is impossible as it crosses the original indifference curve - a situation that can never arise.

That leaves us with Case 1 as the sole possibility, which means that $(x-a, y+b)$ must be on a new indifference curve as per the illustration below.


Macroeconomics v Microeconomics Microeconomics concepts greatly help us to understand the broad aggregates which are used in Macroeconomics to understand the overall functioning of an economy  but are there any ways in which Macroeconomics help us to understand the behavior of individual units?

[...] are there any ways in which Macroeconomics help us to understand the behavior of individual units?

Putting aside the totological cases in which a utility would directly integrate macroeconomic signals such as, e.g. key-rates, AFAIK, no there are not.

As you mention, Macroeconomics is about aggregate level considerations and/or identities That being said, you will find theoretical frameworks, such as  General Equilibrium Theory that imply/represent microfounded behaviours with the intention of adding them up instead of directly dealing with accounting-like macro aggregates.


RDD, wages, and day of birth What I am doing: I use the regression discontinuity design (henceforth RDD) to study differences in wages received by people born at the end of the year and by those people born at the beginning of the year. I have a panel dataset with observations on 5 years in a row and use Stata. My running variable is the amount of days between the date of birth and the end of the calendar year. The cut-off date is January 1st.

The problem: I pool observations across years, but in doing so now the running variable presents no value on its left.

My proposed solution to this problem: I move the time window of interest from Jan-Dec to July-June. This implies the creation of a new running variable where 0 is assigned to people born on July 1st,..., 30 is assigned to people born on July 31st,...,and 364 is assigned to people born on June 30th. Now the cut-off value is 183, which still corresponds to January 1st. Finally, I also center this new variable as recommended by the literature on RDD, so that July 1st is now -183, January 1st is now 0, and December 31st is +183. Now I have observations both on the left and the right of the cut-off value of the running variable; this new variable also allows me to run the RDD with different bandwidths.

My questions:

What do you think about this new re-scaled variables? Could this
solution be considered data manipulation in bad sense? (like, am I
inventing data and get results that do not reflect reality?)
I am using the sharp RDD, is this appropriate?
If sharp RDD is appropriate, should I use also the fuzzy RDD as
robustness check? (As robustness checks I already use different
tools, as proposed here)

This question is present also in "Cross Validated."

(1) Since the RD design identifies an effect only at the cutoff (in your case, at precisely 12am on the last day of the year), I don't think it's an issue of data manipulation for you to be removing the tails. Your estimates really shouldn't be sensitive to observations far away from the cutoff, but this depends somewhat on how granular your data is and how many observations you have (a lot of birth data is quarterly, which may make this strategy difficult).

(2) Sharp vs. fuzzy design refers to the assignment of the treatment. If your treatment of interest is being born December 31st vs. being born January 1st, then this is a sharp design because the running variable deterministically assigns treatment. If there is noncompliance with treatment, (i.e you were born December 30 but you somehow end up getting "treated" as though you were born in January the following year) this is when you would use the fuzzy design.

(3) Sharp RD is just a special case of fuzzy RD. Say $Y$ is your outcome of interest (in this case, wages), $X$ is your running variable (day of the year), $D$ is a dummy variable for treatment assignment where $D=1$ if $X>c$ and $D=0$ if $X\leq c$, and $c$ is the cutoff (December 31). Then the treatment effect for the fuzzy design is (from Lee and Lemieux 2010):

$$
\tau_{fuzzy} = \dfrac{\lim_{\varepsilon\downarrow0} \mathbb{E} \left[ Y | X = c + \varepsilon \right] - \lim_{\varepsilon\uparrow0} \mathbb{E} \left[ Y | X = c + \varepsilon  \right]}{\lim_{\varepsilon\downarrow0} \mathbb{E} \left[ D | X = c + \varepsilon  \right] - \lim_{\varepsilon\uparrow0} \mathbb{E} \left[ D | X = c + \varepsilon  \right]}
$$

Because $X>c$ means by definition $D=1$, the denominator reduces to $1$, leaving us with the sharp treatment effect.


Could leisure be considered a Giffen good? One of my microeconomics fellow students asked this and it got me thinking. The leisure demand curve is a mirror of the labour supply curve. In the section where the Income Effect is greater than the Substitution Effect, would leisure be considered a Giffen good as well as an inferior good? Because the price of undertaking leisure is your wage.

I have two sources here:

Argument by David Friedman: http://www.daviddfriedman.com/Academic/Price_Theory/PThy_Chapter_5/PThy_Chapter_5.html

EDIT:
From the link:

An increase in wages (say, from \$10/hour to \$11/hour) has two effects. It makes leisure more costly--each hour not worked means \$11 less income instead of \$10. That is an argument for working more hours at the higher salary. But at the same time, the increased wage means that the producer is wealthier--and is therefore inclined to consume more leisure. It is possible for the second effect to outweigh the first, in which case the increased wage causes a decrease in hours worked, as shown in Figure 5-4. This is called a backward-bending supply curve for labor; the backward-bending portion is from F to G (and presumably above G). The result, in the case of a single producer, would be a supply curve for goods that sloped in the wrong direction; for some range of goods, higher prices would generate less output instead of more.

This is not the first time we have seen a conflict between income and substitution effects. In Chapter 3, the same situation generated a Giffen good--a good whose demand curve sloped in the wrong direction. I argued that there were good reasons not to expect to observe Giffen goods in real life. Those reasons do not apply to the backward-bending supply curve for labor.
One of the reasons was that while we expect consumption of most goods to go up when income goes up, a Giffen good must be a good whose consumption goes down with increasing income--an inferior good. Indeed, it must be so strongly inferior that the income effect of an increase in its price (which, since we are buying it, is equivalent to a decrease in real income) outweighs the substitution effect. Our labor is something we are selling, not buying; an increase in its price (the wage rate) makes us richer not poorer, and so inclined to buy more leisure. So the backward-bending supply curve for labor only requires leisure to be a normal good.

Argument and diagram by unknown:
http://people.bath.ac.uk/ak220/teaching/labor%20supply.pdf
EDIT
From the link:

Suppose now that the wage someone receives goes up, (Diagram II). Obviously, this also increases the cost of leisure since the opportunity cost for not working is the wage you don’t get. So, since leisure has become more expensive, the worker increases his working time. This is the (negative) substitution effect. At the same time, there is also an income effect coming from the fact that since your wage increased, your whole wage income increased$^2$.Thus, the income effect will tempt the
worker to increase his/her leisure. Be careful here: Leisure became more expensive
but the income effect is positive. Remember that when we were talking about a
normal good X, an increase in price would have caused both effects to be negative.
I’ll explain this contradiction later.
An increase in the wage will cause the budget line to pivot upwards to the new
position MoM1. The consumer now is on the new indifferent curve $I_1$. As you can see,
he has both increased his leisure and his consumption! Let’s decompose this effect.
The substitution effect will make the worker work more, $Q_0$ to $Q_2$. However, the
income effect will push in the opposite direction, $Q_2$ to $Q_1$. Since the I.E. over weights
the S.E., the consumer will increase his leisure.

This worker’s reaction was actually determined by the IE, since the SE would always
motivate the worker to work more. For a different worker, the IE could have acted in
the same direction as the S.E. Clearly, this depends on where the indifference curves
lie on the diagram, their shape (preferences) and the level of non wage income. Suppose a worker possesses a very significant source of non wage income. Obviously,
he would react more smoothly in a wage increase than someone who relies solely on
his wage income.
For a particular level of wage, a worker would be indifferent between working and
not working at all. This wage is called reservation wage and depends on the level of
the non wage income, keeping preferences constant.
Finally, few comments on the contradiction I mentioned before:
Suppose we have good X which is normal and its price increases. There is a decrease
in the consumption of the good since the good became more expensive in relation to
other goods. (Substitution effect). There is also a decrease in the consumption of the
good because of the income effect, since the real income decreased and the good is
normal. Consequently the one effect adds to the other and the total effect is negative.
Now in X’s position we have Leisure, assuming that leisure is a normal good. If its
price increases (increase in wage) then leisure becomes more expensive so the worker
would want to consume less of it (work more). On the other hand the income effect motivates the worker to increase his/her leisure instead of reducing it (as it was the
case with good X). Who is wrong here?
Apparently none! In the conventional model of goods X and Y we are concerned with
people who consume the goods and do not sell those goods. In contrast, an individual
not only consumes leisure but also “sells” it to an employer (in which case it is called
work time). Thus when the price of leisure increases, it may become more expensive
to consume but at the same time the consumer benefits from selling it at a higher
price! Thus, the income effect can be either positive or negative depending on
consumer’s preferences and particularly on how much leisure he sells in relation to
how much he consumes.

In (2)[Diagram II] it seems that IE>SE but optimal choice of leisure is increasing. Seems that leisure is normal here.


How yield rates influence the "cost of borrowing" for borrowers I am currently learning about quantitative easing, and I am having trouble understanding yield rates and how that influences the "cost of borrowing".

This is the resource I am using.

The lecturer says something along the lines of "the yield of bonds reflects the cost of borrowing for the issuer. If the yield for these bonds reduces it means accessing finance is cheaper. They can raise finance but now at a lower cost to them" (he is referring to both government and corporate bonds).

I am a bit confused about some things here. When he says that "the yield of [corporate] bonds reflects the cost of borrowing for the issuer, so for banks who issue corporate bonds, if the yield on the bonds decreases it is cheaper to access finance", is this simply referring to how much the company has to pay back  for the bond or is it referring to how much it costs banks to borrow from the central bank - and are corporate bonds only referring to banks or are they referring to all corporations? And when they say "the yield of these bonds reduces ... they can raise finance at a lower cost to them", is that referring banks borrowing from other banks or something?

Sorry if this is confusing I'm just having trouble piecing this together.

Thank you

This question is too long. To be useful for this website, questions need to be questions, without filler text. You should also try to avoid suggesting answers, as if your suggestion is wrong (as happened here), it makes it harder to answer the question.

You have questions about the notion of “corporation” versus “bank.” A bank is just a type of corporation, and both banks and non-banks issue corporate bonds.

  The yield of [corporate] bonds reflects the cost of borrowing for the issuer, so for banks who issue corporate bonds, if the yield on the bonds decreases it is cheaper to access finance", is this simply referring to how much the company has to pay back for the bond or is it referring to how much it costs banks to borrow from the central bank?

Neither of your suggestions.

A bond is a loan that has been structured in a fashion to allow it to be bought and sold in a market. The standard structure is to repay the principal at maturity, and the interest paid in the form of coupons on a fixed schedule (depending on the market, typically either every 6 or 12 months). The initial sale of the bond by the issuer is the loan operation, after that, the issuer just pays the coupons and principal, and is not directly affected by later transactions.

Unless the bond is callable, the issuer has no right to pay back the loan early, and so there is no notion of “paying back” the bond - it is always repaid on a fixed schedule.

Meanwhile, borrowing from the central bank has nothing to do with this.

Instead, what the speaker is referring to is the cost of issuing new bonds. Most issuers will have existing bonds, and their price in the secondary market implies a certain rate of return for investors. Investors will only buy newly issued bonds if the interest on them is comparable to those existing bonds. So if the central bank does actions to lower bond yields in the secondary corporate bond markets, corporations can issue new bonds at a lower interest rate.


Proof that the diff-in-diff (wrt sample size) of the expectation of a first-order statistic is positive (Stigler 1961) I'm trying to prove a claim made in Stigler (1961), "The Economics of Information." This claim has to do with showing that the marginal benefit
of making an additional search (e.g., searching an additional store for a lower price) is decreasing in the number of searches.

Let $F$ be the distribution of prices $p$. Then, the expected value of the minimum price after $n$ searches is
$$
E(n) \equiv n \int_0^\infty p (1-F)^{n-1} F' \mathrm d p.
$$
In the paper, the claim is that
$$
[E(n+2) - E(n+1)] - [E(n+1) - E(n)] > 0.
$$

I have found a related question here. However,
this linked question considers the max of arbitrary $n_1 < n_2 < n_3$. Here, I'm
considered only with the statement as it appears in Stigler's article.
Does anybody know how to prove this?

Notes:

I'm note sure if "convex" is the right term here. The linked question and its answer raise some doubts that it is convex in the strict sense of the word. I suppose what I'm after is just the differences in the differences (a weaker condition that convexity?).

Well, you cannot take the derivative of $E(n)$ with respect to $n$, because $n$ is an integer variable.

More generally, you want to prove a property with respect to $n$. The problem you have is that the corresponding domain is not a convex set: say, for $n$ and $n+1$, $0<\lambda <1$, the value $\lambda n + (1-\lambda) (n+1) = n+1-\lambda$ does not belong to the domain since it is not an integer. But if the domain of the function, with respect to the variable you are interested in, is not a convex set, the concept of convexity/concavity is not even defined (perhaps in higher mathematics they have some more nuanced concept to accommodate that).

To determine whether the inequality you want holds, a brute-force algebraic approach is to examine its sign directly: we have

$$[E(n+2) - E(n+1)] - [E(n+1) - E(n)] =\\= (n+2) \int_0^\infty p (1-F)^{n+2-1} F' \mathrm d p \\- 2 (n+1) \int_0^\infty p (1-F)^{n+1-1} F' \mathrm d p\\ +n \int_0^\infty p (1-F)^{n-1} F' \mathrm d p$$

$$= \int_0^\infty p (1-F)^{n-1} F'\cdot\Big[(n+2)(1-F)^2 - 2(n+1)(1-F)+n\Big] \mathrm d p $$

Doing the algebra

$$(n+2)(1-F)^2 - 2(n+1)(1-F)+n  \\= n(1-F)^2 + 2(1-F)^2 - 2n(1-F) - 2(1-F) +n \\
= n\Big[(1-F)^2 - 2(1-F) +1\Big]  - 2(1-F)F \\
= n [(1-F) -1]^2 - 2(1-F)F = nF^2 -  2(1-F)F = F\Big[nF-2+2F\Big]\\
=F\cdot \Big[(n+2)F-2\big]$$

So we have arrived at

$$[E(n+2) - E(n+1)] - [E(n+1) - E(n)] = \int_0^\infty p (1-F)^n F'\cdot\Big[(n+2)F-2\Big] \mathrm d p$$

Breaking up and manipulating,

$$[E(n+2) - E(n+1)] - [E(n+1) - E(n)] = \\=(n+2)\int_0^\infty p (1-F)^{n+1} F' \mathrm d p \\- \left(\frac{2}{n+1}\right)(n+1)\int_0^\infty p (1-F)^n F'\mathrm d p$$

$$\implies [E(n+2) - E(n+1)] - [E(n+1) - E(n)] = E(n+2)-\frac{2}{n+1}E(n+1)$$

Simplifying $E(n+2)$ from both sides we get

$$-2E(n+1) + E(n) = -\frac{2}{n+1}E(n+1)$$

$$\implies E(n) = \frac {2n}{n+1}E(n+1)$$

and by induction

$$\implies E(n+1) = \frac {2(n+1)}{n+2}E(n+2) \implies E(n+2) = \frac {n+2}{2(n+1)}E(n+1)$$

Therefore

$$[E(n+2) - E(n+1)] - [E(n+1) - E(n)] = $$
$$= \left(\frac {n+2}{2(n+1)} -1\right)E(n+1) - \left( 1- \frac {2n}{n+1}\right)E(n+1) $$
$$= \left(\frac {n+2}{2(n+1)} -1 -  1+ \frac {2n}{n+1}\right)E(n+1)$$

$$=\frac {n+2 - 4(n+1) + 4n}{2(n+1)}E(n+1) = \frac {n-2}{2(n+1)}E(n+1)$$

So $n=1$ is not a search, for $n=2$ we have equality, and for $n\geq 3$ the inequality holds.


What is the difference between identification, calibration and estimation? In fitting theoretical models to data, what is the difference between identification, calibration and estimation?

Identification and estimation are often used interchangeably (at least that’s my observation from attending conferences and reading papers) but according to econometric literature there is a subtle difference.
For example, in the John Stachurski "A Primer in Econometric Theory" the identification is a process of finding out if the parameters are identifiable and identifiability is defined as

“Identifiability means that the parameter vector associated with the unknown distribution can eventually be distinguished from the data.”

I will omit all the other formalism that follows but in essence we can say that parameter is identified if the map from the parameter space to the space of probability distributions of observables can be inverted.
The estimation is actually the process of calculating what the actual parameter $\hat{\beta}$ is.
When it comes to calibration in forecasting it is the comparison of model estimates to actual data with an aim to improve the model fit.
In macroeconomics it is a strategy for finding numerical values for the parameters of artificial economic worlds. A model is calibrated when its parameters are quantified from casual empiricism or unrelated economic studies or are chosen to guarantee that the model mimics some particular feature of the historical data. In other fields it might have different uses as well.


What Happened in 2008? Some say "housing crash" but I suspect the existing global banking system imploded.  Am I off-base, or ...?

In my experience, CME S&P futures, for example, require a performance bond of something less than 10% of the market value of the underlying asset(s) to open a position, i.e. healthy leverage is baked into the product.  As I calculated back then, TARP and TARPII literally provided enough capital to purchase the entire US stock market via futures contracts.

Today, a decade later, the run on global banking seems to continue.  "Buy gold bcs you can't trust governments or banks" commercials come on TV about every 15 minutes. Also, inflation continues to outpace return on bank deposits, i.e. negative real interest rates.  Punishment for holding cash; and we see several Nations outlawing large denominations of cash.  Gold has been repatriated out of NYNY in masse.

Did the global banking system collapse in 2008, or was it simply a housing/mortgage issue?  Lastly, if it did, my understanding is that like 99% of $100 bills notes are held outside of the USA.  Why didn't the Fed simply declare bankruptcy, void all those notes (and all those complex derivative contracts), and start over with new money?  Why the fake?  The sun's going to come up tomorrow regardless...?

To sum up the 2008 crisis in a few bullets:

Loose lending policies by government and private institution caused regular (and poor) folk to become real estate speculators.
Housing prices declined rapidly, causing foreclosures.  This caused banks and investors to lose money and put the housing/construction industry on hold, causing unemployment.
Many mortgage-backed securities were based on the value of real estate and their risks had not been taken into account by investors, who were unprepared for losses.
Financial institutions were highly levered and tightly connected with each other by contracts and derivatives that lacked transparency, causing a crisis of faith in these institutions.
Government bailouts were reasonably successful in keeping the problem contained but at great cost and setting a questionable precedent.
Since then the financial system has recovered and done very well.

The low real interest rates you mention isn't a problem with the banking system, it's a simple problem with too many parties (globally) wanting to save and not enough wanting or being able to borrow.  The latter effect is partly because of government and bank reluctance repeat the same mistakes with loose lending and partly because we don't have a lot of good real investments available to us.

  Some say "housing crash" but I suspect the existing global banking system imploded. Am I off-base, or ...?

Yes, you are off base.  The banking system, and financial system in general, temporarily lost a lot of value and suffered from a credit crunch but have since recovered and are doing very well.

  As I calculated back then, TARP and TARPII literally provided enough capital to purchase the entire US stock market via futures contracts.

Posting margin to take a large position in futures contracts is very different from "purchasing" the stock market. I don't understand how this is related to your question, though.  Using bailout funds to speculate on the market seems like an odd idea.  Note that TARP funds were loans, which have been repaid and made the government a tidy profit.

  Did the global banking system collapse in 2008, or was it simply a housing/mortgage issue?

Again, it didn't collapse, but it did suffer.  The housing situation was the precipitating event but there were a number of problems that came to fruition at the same time.

  Lastly, if it did, my understanding is that like 99% of $100 bills notes are held outside of the USA. Why didn't the Fed simply declare bankruptcy, void all those notes (and all those complex derivative contracts), and start over with new money? Why the fake? The sun's going to come up tomorrow regardless...?

Why would the fed want to declare bankruptcy? If it tried to void our currency there would be negative global economic and political repercussions the likes of which we have never seen.  I cannot imagine this happening nor why you would think it would be a good thing.

Is there a reason you think voiding derivative contracts would be a good thing?  Those are contracts parties voluntarily engaged in, many of which are necessary to provide stability to both or at least one participant.  During the crisis the fact that big banks were involved in so many derivatives undermined their credit-worthiness because people couldn't be certain how much risk they had.  But that is a very, very far cry from saying that it would be a good idea to void derivatives, or even certain classes of derivatives.


Deriving and explaining the weighted cost of capital The Wikipedia article for the "weighted cost of capital" (WACC) defines the WACC
as "the rate that a company is expected to pay on average to all its security holders to finance its assets." What exactly does this mean? Does this mean that this is supposed to be the expected returns on the company's stocks as well as the expected return on the company's bonds? Also, how are the two equations, given in the Wikipedia article, derived? For convenience, the two equations are the following. The first is
$$
\text{WACC} = \frac{\sum_{i=1}^N r_i \cdot MV_{i}}{\sum_{i=1}^N MV_i}, \tag{1}
$$
where $N$ is the number of sources of capital (securities, types of liabilities); $r_i$ is the required reate of return for security $i$; and $MV_i$ is the market value of all outstanding securities $i$. The second is
$$
\text{WACC}  = \frac{D}{D+E}K_d + \frac{E}{D+E}K_e \tag{2},
$$
where $D$ is the total debt, $E$ is the total shareholder’s equity, $Ke$ is the cost of equity, and $Kd$ is the cost of debt.

EDIT:
Thanks for the answers below. "Derivation" was too strong of a word to use, which was clear after the explanations given. It was just a little unclear what the objects were in practice. The discussions below clarified things. Also, I found this paragraph from a website linked in one of the answers helpful:

  To understand WACC, think of a company as a bag of money. The money in the bag comes from two sources: debt and equity. Money from business operations is not a third source because, after paying for debt, any cash left over that is not returned to shareholders in the form of dividends is kept in the bag on behalf of shareholders. If debt holders require a 10% return on their investment and shareholders require a 20% return, then, on average, projects funded by the bag of money will have to return 15% to satisfy debt and equity holders. The 15% is the WACC.

If you are asking "Is the WACC the amount that the company expects to earn on the stocks and bonds that it holds.." then the answer is no.

The WACC, in very simple terms, is the amount of money a company pays to obtain financing for projects. These types of financing are clearly listed in the wikipedia article and clearly extend beyond stocks and bonds issued by the company.

A company can calculate the WACC to determine whether or not undertaking a project will be profitable. That is, a company can determine that it must earn some minimum return on a project before that project becomes profitable.

You, as a consumer, possibly have experience with cost of capital. Consider the interest paid on a car loan. That interest is the cost you incur for financing the purchase of your vehicle by borrowing funds from a financial intermediary.

As far as derivation goes - I'm not sure how to simplify these formulas much more. However, you can think simply about the first as the ratio of the interest paid out on sources of financing and the total market value of those sources of financing (so...some ration < 1) and the second is a more simple case of the first.

http://www.investopedia.com/walkthrough/corporate-finance/5/cost-capital/wacc.aspx

I think this website gives a decent walkthrough of the concept. Hope this helps some.


Are newspaper articles more liberal than their readership? This question was posted on a forum (see here), and I thought it was interesting, especially in light of the recent spotlight on Matthew Gentzkow's work. So, I'm re-posting it here.

  Some studies claim that newspaper articles are usually more liberal than their readership. Since the news market is competitive, should we doubt this claim?

This strikes me as a straightforward industrial organization anomaly question. Like, why do hot dogs and buns come in different counts to a package or why are the finest apples shipped out of apple producing regions?

Gentzkow and Shapiro (2010) that this paradox is only an apparent contradiction. They find slant is mostly a product of readership bias.

  By contrast, we find much less evidence for a role of newspaper owners
  in determining slant. While slant is somewhat correlated across
  co-owned papers, this effect is driven by the geographic clustering of
  ownership groups. After controlling for the geographic location of
  newspapers, we find no evidence that the variation in slant has an
  owner-specific component. We also find no evidence that pressure from
  incumbent politicians or the tastes of reporters are important drivers
  of slant.

But jmbejara already mentions knowing about Gentzkow so it isn't obvious what he's looking for beyond this insight.

Timothy Taylor,  Managing Editor of the JEP and blogger at CONVERSABLE ECONOMIST also has an article on this subject that may be of interest,
The Economics of Media Bias.