Loss leader item definition I've recently encountered the term "loss leader" for items. The definition is pricing an item at a discount for the purpose of increasing overall revenues.

One example is Sony selling the PS4 at a loss in order to take more market share, which gain more profits via game sales.

Another example is grocery stores selling items on sale so that customers have a reason to visit the store, and then hopefully buy other items.

My question is: can this definition be extended to businesses that deal with data? For example, selling an online service at a discount to customers for the purpose of collecting data, and then selling that data to marketing firms for a profit.

Is that also an example of a loss-leader item? Or is there a more accurate example?

"Loss leader" is a term primarily from marketing. It is occasionally used by economists, but not in a formal way because its definition is insufficiently precise.

To see why we have to be careful, it is useful to think about the economic principles underlying the three examples you mentioned. I do this below, but the ;tldr version is that the business model for selling data follows a totally different economic logic and even grocery stores vs playstations follows slightly different logic.

The grocery store example is probably the closest thing to what would commonly be understood as a loss-leader. The reason this strategy works is because consumers face some kind of friction that makes them disproportionately prefer one-stop shopping to visiting many stores (e.g. becoming informed about different stores is costly, switching stores in the middle of a shop is costly, etc.). The fact that consumers don't want to go to many stores means that once they are attracted into a store by a low price, they can be exploited with higher prices on other goods. To reiterate: note that this business model is driven by a feature of consumers' behaviour (search/shopping frictions).

The Playstation example follows a slightly different logic, similar to the razord and blades model mentioned by others. The key factors here are: (1) products are complements—we have two types of good (games consoles and games, or razors and blades) that only work if they are consumed together. (2) products are imperfectly compatible (I can't use Playstation games in an XBox).

Now, suppose I bought a Playstation and then decided the games were too expensive and I would prefer switch over to XBox. This would require that I buy a new games console, which is expensive—so I will tend to be unwilling to switch to a different platform. This is just like the grocery store example: we have a situation where consumers are unwilling to switch from one supplier to another. Just like that example, firms offer a low introductory price to initially attract consumers, only to later exploit them once they are locked-in.

But note here that the switching frictions are not an intrinsic property of consumer behavior like in the earlier examples, but rather are now driven by the properties of the products themselves (complementarity and incompatibility). We have therefore identified two distinct sets of conditions under which this kind of pricing strategy might be attractive to a firm: either consumers are intrinsically reluctant to switch or they can be made so through design and compatibility choices.

What about businesses that offer free services in return for data? Here the underlying economic logic is completely different to the other two cases. These are typically examples of so-called two-sided markets. A two-sided market is a market in which a central intermediary (called a "platform") matches people from two distinct groups. In this particular example the two sides will be consumers and marketing firms, and the job of the platform is to bring the two together so that new value can be unlocked through the exchange of data.

Two-sided platforms typically involve a chicken and egg type problem because in order for the platform to function it is necessary to make sure both groups are on board (a heterosecual dating site that attracts only men won't be very useful!). The usual solution to this problem is that one of the two groups is subsidised (e.g. allowed to join the platform for free or at reduced cost). Once that group joins, the platform becomes more attractive to the other group, who can be charged a higher price. A classic example of this is nightclubs, which would often run "ladies nights" (low price admission for females,) thus ensuring many females enter the club. Once the club is full of females, it becomes much easier for the club owner to charge a high admission fee to men. Similarly, firms like Facebook subsidise consumers (with a free service) to get as many consumers on board as possible, so that the firm is able to extract as much value as possible from the other side of the market (selling data to marketing firms).

Note that the underlying economic mechanism here is different from the other cases. Those examples were about creating frictions to lock-in consumers, so that those same consumers could be charged a high price. Two-sided pricing is about offering a low price to one group in order to get them on board so that a totally different group of consumers can be charged a high price.

Final note: games consoles are also two-sided markets (they serve both gamers and game developers and must get both on board to be successful). So a bit of the two-sided logic applies there too: Playstations are sold below cost to gamers to get lots of gamers onto the platform because this allows Sony to maximise revenues from the royalty fees paid by game developers, as well as revenues from selling games to consumers.


Nash Equilibrium and Pareto efficiency What is the difference between Nash equilibrium and Pareto Efficiency. Can you give me an example where Nash equilibrium is not Pareto Optimal?

Nash Equilibrium (N.E) is a general solution concept in Game Theory. N.E is a state of game when any player does not want to deviate from the strategy she is playing because she cannot do so profitably. So, no players wants to deviate from the strategy that they are playing given that others don't change their strategy. Thus, it is a mutually enforcing kind of strategy profile.

'Pareto optimality' is an efficiency concept. So no state will be Pareto Optimal if, at least one of the players can get more payoff without decreasing the payoff of any other player. There are many many examples of Nash Equilibria which are not pareto optimal. The most famous example could be the N.E in prisoner's dilemma.


What is the best example social norm effect economy? Here is my example.

I read the paper called "Social norms and Energy Conservation" (2010) by Hunt Allcott, about the energy conservation of households by providing them with the amount of energy individual household use and their average neighbor's energy usage. The first thing is this research discover at the first place that household did not use the best efficient method to conserve the energy. Interesting things are 1 ) the adding reference descriptive social norm for society to adjust 2 ) not only people decrease their energy usage toward that descriptive social norms but some who below average adjust toward social norm level.

So what are the another phenomena social norm affect individual decision ?

Well, it sounds like the paper is drawing a conclusion between behavioral responses towards energy consumption when they're shown public averages.

There's a problem with that paper -- unless it makes specific reference to this:
- How does he/she derive causation between variation in electricity and 'social norms'? I don't see social normality being the primary influence.

Separately there are psychological effects at play like:

• Bystander Effect, Social Loafing, Diffusion, and Moral disengagement

That very much could be at play, confounding the entire study. What if I chose to increase energy expenditures 'just' because I see that the averages aren't 'that bad.'

"Everyone else is saving well, so I can go heavy and not hurt the environment as much..."

This incentive and what I understand as the one described in the paper where people conform to a standard norm are different.

But if you're doing some homework and need some 'answer': there are many, cigarettes are very heavily advocated against right now. Someone would choose to change their habit of smoking because 'it's currently less acceptable.


Most common programs used by Economists I recently asked a professor if he was planning on hiring a research assistant for next semester. I thought I'd be a pretty good candidate since I have decent experience using STATA, SAS, SPSS, R Studio and Mathematica, but he started asking me about a couple programs I had never heard of before. That led me to wonder what are the most commonly used programs for Economics. A friend of mine suggested I also look into Matlab and Python.

There's three important dimensions for programs/languages:

Convention: Having a program that everyone uses helps you to get feedback/help, work with coauthors, use other people's codes
Ease of use: Since many uses in economics are routines, having the program doing these for you and making your implementation of the use easier is a big bonus
Adaptability: A program that allows you doing covering most of your needs and learning only one syntax versus having to work with different programs at the same time

In terms of frequency of usage among academic economists, here's my ranking:

Top tier

For econometrics, by far, STATA. Mostly because of convention and ease of use.
For dynamic programming, and to some extent monte carlo, by far, Matlab. Mostly because of convention and ease of use

Second tier

For time series econometrics, Eviews (ease of use)
For all kinds of econometrics, R (adaptability, somewhat convention)
The swiss knife of really anything, Python (adaptability)

Specialists

SAS, for huge data sets
Fortran, for efficient prebuilt routines and large scale computation

This list is of course my personal opinion, and for academic economists only. I believe that no one will dispute the top tier, but the second tier/specialists can be somewhat debated. And then there's some more who are even more specialist (for example, Octave as a open source Matlab alternative)


US unemployment data release date Using the CSV file provided by St. Louis Fed (which is based on the data series LNS14000000 from the Bureau of Labor Statistics) I noticed that the date is always the first day of each month for the unemployment rate, i.e. for May 1957 it is 1957-05-01 and so on. Because BLS currently will announce the data for June 2018 on the 6th of July, I doubt that the CSV file is correct. Where can I find the accurate historic release dates for the unemployment rates?

After some more intensive (4 mins) googling I found it on the BLS website.


Is it possible for disposable income to be lower than consumption expenditure? I have an issue dealing with dataset provided for my coursework.

Because of the fact that I've been failing to find time-series of the same or similar values anywhere from world bank to Office for National Statistics, I strongly doubt it.

The data series provided is shown below in a form of line chart. The brief provided says it's in constant prices, it unfortunately does not indicate the reference year. What it is supposed to describe is consumption and disposable income for the United Kingdom over the period of 03Q2 to 15Q4. I don't believe there would be negative savings for the whole period.

I have been looking around to find some hint that would prove this true, unfortunately the graph below shows the opposite. I can explain the jump in disposable income by change in reference year, however the consumption data does not make sense to me. At all.

the first graph is 1970-2003, the second is 2003-2015


Construct a game with only pure strategy nash equilibrium I'm trying to construct a $4 \times4$ Normal-Form Game with two players, where each player has four strategies and it satisfies:

1) The game has exactly 4 Nash Equilibria

2) All equilibria involve only pure strategies (meaning there's no mixed strategy Nash Equilibrium)

Could someone give an example of this kind of game, and explain briefly how you construct it? I'm not sure when a game has no MSNE but only the PSNE. Thanks a lot.

This was cross-posted. See my answer to this question here:

https://math.stackexchange.com/questions/1650075/construct-a-game-with-only-pure-strategy-nash-equilibrium


What is the proper term for "contraction economics?" By "contraction economics" I mean theories and work based on the assumption that the population of a country will decline over time.

An example might be a paper looking at the housing market for Japan over the next 50 years (if it assumed that population decline continued over that time).

It doesn't look like there's an established term. Combine "demographic decline", "population decline" or even "fertility decline" (although this doesn't imply population decline) with whatever you are interested in (markets, economic growth etc.)

These papers (if macro) usually get JEL-tagged "J11 Demographic Trends, Macroeconomic Effects, and Forecasts" in combination with whatever is getting modeled, e.g. "Scotland the Grey: A Linked Demographic–Computable General Equilibrium (CGE) Analysis of the Impact of Population Ageing and Decline" is tagged with J11 and a bunch of R1x codes, the latter for regional economics/models.


How much is currently invested in artificial general intelligence research and development? Glossary: Artificial general intelligence (AGI) is the name given to an upcoming technology that would be able to solve all sorts of problems, like a human, and unlike more specialized existing artificial intelligence (AI). In a sense, AGI is closer to depiction of AI in movies and in the public's mind.
Originally my question was about valuation but I was told this is not allowed here. So I am only asking about existing investments in artificial general intelligence.
Company or VC names are optional.
The main point is to get more information about artificial general intelligence economics.

I agree with @1muflon1's comment that this is quite broad, because AGI can be defined in many different ways. For instance, do we consider simple learning tasks as AGI or metacognition?
This is a brief survey of AGI startups, but another point to keep in mind is that few startups/firms are actually gunning for AGI because we generally have problems in other, "easier" subfields of machine learning. For example, there are still difficulties with reinforcement learning for robotics or few-shot learning, both of which are much more specific tasks than AGI.
In sum, it's hard to provide good estimates because 1) the sum of money is likely to be small and 2) AGI is often defined broadly and used more in pop culture than by technical researchers.


Random Utility interpretation Can someone explain intuitively, the Block-Marschack Polynomials that completely characterize random utility.

Given a universe of choices $X$, subsets of alternatives $A \subseteq X$, and choice probabilities $\Pi_{A}(x)$ for item $x \in A \subseteq X$, the Block-Marschak polynomials can be defined recursively as (see McFadden, Revealed stochastic preference:
a synthesis, 2005) as

$K_{x, \emptyset} = \Pi_{X}(x) \,, \quad K_{x, A} = \Pi_{X\setminus A}(x) - \sum_{C \subset A} K_{x, C}$

When the choice probabilities are the result of utility maximization, Barbara and Pattanaik (Falmagne and the rationalizability of stochastic choices in terms of random orderings, 1986) provide a useful and intuitive interpretation of $K_{x,A}$ as the probability of the event that $x$ is ranked behind the elements of $A$ and ahead of all the remaining elements in $X \setminus A$.


How and when is M0 money created? The Federal Reserve Coin and Currency Service Website
describes their currency order process thus:

The 7.2 billion notes included in the FY 2015 order reflect the Board’s estimate of net demand for currency from domestic and international customers.
The print order is determined, by denomination, based on historical
payments to and receipts from circulation, destruction rates, and also
to build inventories of new-design notes before issuance.
Historically, most of the notes that the Board orders each year
replace unfit currency that Reserve Banks receive from circulation.
The estimated number of notes that Reserve Banks will destroy accounts
for nearly 85 percent of the proposed FY 2015 print order and includes
both unfit currency, as well as all old-design $100 notes received
from circulation.  The expected growth of Reserve Bank net payments
(payments less receipts) to circulation primarily accounts for the
remainder of the notes in the FY 2015 print order.

From this description, it is unclear to me how and when M0 Money is created. It seems this is tied to 'Reserve Bank net payments'.
How and when is M0 money created?

First it is helpful to provide some definitions.

M0 includes all paper dollars (plus coins and US notes).  Regardless of whether or not they they are held in the banking system.

M0 is not a useful metric because it omits electronic dollars.  The two main liabilities to the Fed are electronic dollars (some refer to them as Fed Funds or deposits at the Fed which banks can hold) and paper dollars.

M0 + electronic dollars = MB.  MB is by far a much better metric for measuring what the government has created for money.

The Fed's balance sheet may be illustrative in showing how this works. Much of the Fed liabilities are MB, but only a much smaller part are M0. The difference between paper and electronic dollars is not significant.  If a bank asks the Fed to trade their electronic dollars for paper (or vice versa, the Fed will oblige.  If the Fed runs short on paper, they will have the treasury print more, but this doesn't expand MB.

Think of paper dollars as ice, electronic dollars as flowing water and MB as all the water in the system (frozen or flowing).  Whatever the form, it is not important as the total amount of water remains the same.

Let's try to answer our question specifically using a timeline and ledger entries.

Say the Fed buys some assets from a bank.  They acquire these assets (+Fed assets) and grant the bank new deposits (+liabilites aka bank deposits).  Now this is always done with electronic dollars to start.

Then say the bank has a lot of withdrawals and wishes to convert some of their federal despots assets into cash assets.  They ask the Fed to do this, which gladly obliges.  The Fed decreases their deposit liability and increases their paper note liability.  In this moment M0 was increased.  But it is not significant.  What was significant was when MB was increased after the Fed acquired the asset from the bank.


Where to find the latest statistics of brain drain in the world? Where to find the latest statistics of brain drain in the world?

I would appreciate your suggestions.

Well this is not easy to answer because there is no single measure of brain drain.

For example, many times brain drain is just measured as net immigration from a country (since it is reasonable to assume, and also supported by evidence, that its the smarter and more entrepreneurial people who leave). If you want to measure it by just immigration you could use the UN migration stock data.

Of course, the above approach is very crude. There are other approaches that look migration by education levels. These usually use census data that you can find for every particular country at their statistical office web page. There is also interesting dataset on this commissioned by European Commission, see here, but it only covers OECD countries and its recorded only in 5-year intervals.

There are also some 'fancy' ways how brain circulation can be measured such as by tracking author affiliations, like in this report, but I am not aware of any dataset on this that would be consistently kept up to date. However, nowadays many journals require authors to make their dataset public so you can just search in google scholar the recent articles on this and make data request to journal.


Why do we want MSB = MSC not MSB > MSC? Why do economists want Marginal Social Benefit to equal Marginal Social Cost not be greater than?

Remember that the M in MSB standard for marginal. In other words, the marginal social benefit is the extra benefit we would get by increasing the activity by one unit and the marginal social cost is the extra cost we would get by increasing the activity by one unit.

Suppose, at the status quo, the MSB is 5 and the MSC is 3 (so MSB > MSC). That means if we increased the activity by one unit we would get 5 units of extra benefit and 3 units of extra cost, so the net change in welfare is $5-3=+2$. Thus, the status quo can't be optimal because we could increase welfare by adding an extra unit of the activity.

Suppose, at the status quo, the MSB is 3 and the MSC is 5 (so MSB < MSC). That means if we reduce the activity by one unit we would loose 3 units of benefit but save 5 units of cost, so the net change in welfare is $-3+5=+2$. Thus, the status quo can't be optimal because we could increase welfare by reducing the activity by one unit.

Only if MSB=MSC is it the case that we can't increase welfare by either increasing or reducing the activity.


Can stimulus packages lead to hyperinflation? I have a limited understanding of economy, however, I've been trying to catch up from various resources. Recently, the news are all about the enormous stimuli bills debated/implemented by governments all around the world to counterbalance the negative effects of the coronavirus. My question has two parts:

First, where do those numbers come from? In the US they are talking about $2 trillion rescue plans, a number which I have no sense whatsoever for. In simple terms, which are the most important factors lawmakers consider when coming to this number (or, at least to the order of magnitude)?
Is it possible these stimuli will lead to hyperinflation? On the short run, the stimuli won't increase the productivity since businesses will still be closed. "Dumping" money on them will indeed help them from default, but with no underlying productivity I can't see how this extra liquidity won't boost inflation. In other words, the supplies are limited due to the reduced productivity, but now the demand will increase because everyone will have free cash in their hands.

No chance. The economy is heading for a deep recession, because of an exogenous fall in demand (think of a supply and demand graph, where demand falls drastically, and so Q and P falls). Recessions most of the time mean less inflation (firms sell less). Exceptions are called stagflation and are fairly uncommon, except in totally destroyed economies where inflation is a deep cause of the recession, like in Venezuela.

numbers are most likely calculated by looking at needs, size of market, etc. In most cases these stimulus are funds. They are money to be put in a box and taken as needed. Not all might be used.
a lot of funds are targeted and not given directly as cash to people. In any case, people won't be spending the money as crazy, partly because there is little on which to spend it (no eat out, no holidays). Plus all the uncertainty about how long this will last make people averse to spend it. Wage costs are low and partly subsidized too so firms won't increase prices.


Stochastic growth in continuous time Literature: See Chang (1988) for theoretical part and Achdou et
  al. (2015) for numerical part respectively.

Model

Consider the following stochastic optimal growth problem in per capita notation.
\begin{align}
&\max_{c}\int^\infty_0 e^{-\rho t}u(c)dt\\
\text{s.t.}~~~&  dk = [f(k) - (n-\sigma^2) k - c]dt - \sigma kdz\\
&c\in[0,f(k)]\\
&k(0) = k_0
\end{align}
everthing is standard except for $dz$ which is the increment of a standard Wiener process, i.e. $z(t)\sim\mathcal{N}(0,t)$. The population growth rate has mean $n$ and variance $\sigma^2$.

Analytical Solution

We presume Cobb-Douglas technology
\begin{align}
f(k) = k^\alpha,\quad \alpha\in(0,1)
\end{align}

and CRRA utility
\begin{align}
u(c) = \frac{c^{1-\gamma}}{1-\gamma},\quad \gamma > 1.
\end{align}
Set up the Hamilton-Jacobi-Bellman equation (HJB-e)
\begin{align}
\rho v(k) = \max_c\left\{\frac{c^{1-\gamma}}{1-\gamma} + v'(k)(k^\alpha - (n - \sigma^2)k - c) + v''(k)\frac{k^2\sigma^2}{2}\right\}
\end{align}

The first order condition (FOC) reads
\begin{align}
c = v'(k)^{-\frac{1}{\gamma}}=:\pi(k)
\end{align}
where $\pi(\cdot)$ denotes the policy function.

Resubstitute FOC into HJB-e
\begin{align}
\rho v(k) = \frac{v'(k)^{\frac{\gamma-1}{\gamma}}}{1-\gamma} + v'(k)k^\alpha - v'(k)(n - \sigma^2)k  -  v'(k)^{\frac{\gamma-1}{\gamma}} + v''(k)\frac{k^2\sigma^2}{2}.
\end{align}

We guess a functional form of $v(k)$ with (Posch (2009, eq. 41))
\begin{align}
v(k) = \Psi \frac{k^{1-\alpha\gamma}}{1-\alpha\gamma}
\end{align}

where $\Psi$ is some constant. The first and second order derivative of $v$ are given by
\begin{align}
v'(k) &= \Psi k^{-\alpha\gamma}\\
v''(k) &= -\alpha\gamma\Psi k^{-1-\alpha\gamma}.
\end{align}

The HJB-e then reads
\begin{align}
&\rho \Psi\frac{k^{1-\alpha\gamma}}{1-\alpha\gamma} = \frac{\Psi^{\frac{\gamma-1}{\gamma}}k^{\alpha(1-\gamma)}}{1-\gamma} + \Psi k^{\alpha(1-\gamma)} - (n-\sigma^2) \Psi k^{1-\alpha\gamma} -  \Psi^{\frac{\gamma-1}{\gamma}} k^{\alpha(1-\gamma)}  - \alpha\gamma\Psi k^{1-\alpha\gamma}\frac{\sigma^2}{2}\\[2mm]
\Longleftrightarrow \quad &
k^{1-\alpha\gamma}\left(\frac{\rho}{1-\alpha\gamma} + n - \sigma^2\left(1 - \frac{\alpha\gamma}{2}\right)\right) = k^{\alpha(1-\gamma)}\left[1+\Psi^{-\frac{1}{\gamma}}\frac{\gamma}{1-\gamma}\right]
\end{align}

The maximized HJB-e is true iff the following conditions hold
\begin{align}
\rho = \left(-n + \sigma^2\left(1 - \frac{\alpha\gamma}{2}\right)\right)(1-\alpha\gamma)\quad \wedge \quad \Psi = \left(\frac{\gamma-1}{\gamma}\right)^{-\gamma}
\end{align}

Resubstitute $\Psi$ into $v$ which finally gives the true value function
\begin{align}
v(k) = \left(\frac{\gamma-1}{\gamma}\right)^{-\gamma} \frac{k^{1-\alpha\gamma}}{1-\alpha\gamma}.
\end{align}

How come that $v$ does not depend on $\sigma$?

So the deterministic and stochastic value function must be the same. The policy function is then readily given by (use FOC and derivative of value function)

\begin{align}
\pi(k) = \left(1-\frac{1}{\gamma}\right)k^\alpha.
\end{align}

Note that this function does not depend on $\sigma$ either.

Numerical Approximation

I solved the HJB-e by an upwind scheme. Error tolerance $\epsilon=1e-10$. In the figure below I plot the policy function for varying $\sigma$. For $\sigma\to 0$ I arrive at the true solution (purple). But for $\sigma>0$ the approximated policy function deviates from the true one. Which should not be the case, since $\pi(k)$ does not depend on $\sigma$, right?

Can anyone confirm that the approximated policy functions should be the same for any $\sigma$, since the true one is independent of $\sigma$?

More of a comment:

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

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

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

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

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

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

the restriction can be written as

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

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

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


How does inflation impact the welfare of the economy? When the government causes inflation through printing money, the individuals who saved their money in the bank are poorer.
Is there a way to determine how different inflation rates impact the welfare of the economy?
I tried answering this question myself using the production function, and, though I was able to come up with some conjectures, I was unable to come to a definite conclusion.

First, there are direct negative effects from inflation, known as the shoe leather cost and menu costs of inflation. These are direct costs which come from price changes: People will carry less cash, need to update their knowledge about prices, firms need to update their prices and wages, and similar. These are usually small, but typically higher given higher inflation rates.

Second, there are direct redistributional effects, which come from the devaluation of money and everything denoted in nominal terms, including most importantly nominal bonds and debt (credits). Usually, we imagine borrowers to be less wealthy than lenders (1). Here (unexpected) inflation will redistribute wealth from the rich to the poor. Under most standard welfare functions, this will be a first-order welfare improvement.

Third, we typically think that poorer people have higher marginal propensity to consume (MPC). Assuming that we are in a situation with inefficiently high savings rates (for example in Keynesian traps), the aforementioned redistribution will improve allocations, but this is typically a second-order effect (but also this will depend on what you believe is true about the Keynesian multipliers).

Wage contracts belong into the second argument, but deserve a special mentioning due to their extensive treatment in the literature.

(1): This is sufficient, but not necessary. In order to get a higher MPC from borrowers than from lenders, it is sufficient that the borrowers are not optimally smoothing consumption over time (for example, because they are up against a borrowing constraint) - we call these types of consumers Hand-to-mouth, because they will typically consume all their disposable income. As long as the distance between the (aggregated) borrowers consumption and what they would like to consume in a frictionless environment is larger than the distance between the (aggregated) lenders' consumption and what they would like to consume in a frictionless environment (2), devaluing debt will increase consumption.

(2): It may sound surprising, but there is a significant mass of wealthy hand-to-mouth consumers. See Kaplan et al, 2014


Calculating Nash Equilibrium prices for Bertrand duopolists I am attempting to solve the following problem.

Suppose that firms' marginal and average costs are constant and equal to c and that inverse market demand is given by $P = a - bQ$ where $a,b > 0$.

Calculate the Nash Equilibrium prices for Bertrand duopolists, which choose prices for their identical products simultaneously.

Now I attempted to solve this problem and got $P_1 = P_2 = \frac{a+c}{2}$ where $P1, P2$ are prices.

My professor lists the answer as $P_1 = P_2 = c$.

Can someone please tell me where I messed up? Thanks!

The important thing to remember here is that Bertrand duopolists compete over price, not quantity. This means that in the game each player sets a price and the quantity sold is then determined by the demand curve. In this game the firm with the lowest price sells to the entire market and if both firms have the same price they each sell to half of the market. Now, we have to think about the logic that goes into determining equilibrium. It is easy to see that neither firm will ever set a price lower than $c$ because setting a price lower than marginal cost will give the firm negative profit. So we have to start that it must be the case that $p_1, p_2 > c$. Now, suppose that $p_1 > p_2 > c$. This cannot happen because firm 1 has an incentive to set a price below that of firm 2 and above $c$ so they will take the whole market. The same logic can be applied to the case where $p_2 > p_1 > c$. Now, consider the case where $p_1 > p_2 = c$. In this case firm 1 has the incentive to set there price equal to $c$ and split the market with firm 2, so this cannot be a Nash equilibrium. Again, we can apply the same logic to the case where $p_2 > p_1 = c$. So, the only candidate left for Nash equilibrium is scenario where $p_1 = p_2 = c$. This result is very interesting considering that with one firm we get a profit maximizing monopoly result but by adding just one additional firm we get the same pricing as perfect competition as long as the firms are playing the Bertrand price competition game.


Self-teaching 1st year PhD Microeconomic Theory How should one proceed if he wanted to master the microecon theory course typically taught in the 1st year of a PhD program on his own? Which text(s) and/or online course(s) should he follow? Suppose the guy has had a good training of econ up to the intermediate level and is familiar to the math topics the microecon course would typically demand.

Thanks in advance.

My prof is always telling us, if we want to pursue PhD level Econ in the future, we should master the full content of the following book:

Microeconomic Theory. Andreu Mas—Colell Michael D. Whinston and. Jerry R. Green. New York Oxford OXFORD UNIVERSITY PRESS 1995.

He also mentioned that there's main difference in viewpoint between graduate-level and top-level PhD Microeconomics. While in Grad School students calculate and theorize in the vector space, PhD students do mathematical operations using set theory almost all the time.


Is elasticity purely an aggregate concept or can it be individualized First question here.  I am not an economist by training, but I do quite a bit of econometric analysis in my job (my background is maths).  I often get asked about elasticity, and I am familiar with several different ways of calculating elasticity.  My question is this: in the price-volume relationship for elasticity, does it make sense to ask about elasticity for individual customers, or is elasticity properly understood to be an aggregate (market) concept.  Is it possible to build an elasticity model for individual customers.

For clarification, these customer typically purchase thousands of units every month (these are B2B sales, not B2C).  Or is there something fundamental about elasticity that makes it intrinsically aggregate.  I have seen some discussion in the literature about individual customer elasticity, but the literature seems to be fairly sparse, so I am not sure how much to trust it.

In theory, the elasticity quantifies in proportional terms the "reaction" of the dependent variable to a change of the independent variable, where the two are related through a functional relationship. So the concept is universal and mathematical -it applies to any univariate function, and not only in the field of Economics (when we have a multivariate function, then partial elasticities can be defined and used, but they face some constraints). So there is nothing "intrinsically aggregate" about the concept. In its theoretical conceptualization.

But in order to estimate/calculate the elasticity of any function, we must have the function in the first place. So the question boils down to "Can we obtain an individual demand function?"

It would appear that the matter is only one of data availability. If we somehow could have data on many transactions of the same individual related to the same good, then we could use these data points (price, quantity) =$\{(p_1,q_1),...,(p_n,q_n)\}$,  in order to approximate its demand function... and we would probably be mistaken.
And this is because these points do not necessarily represent movements along the individual demand schedule. They are equilibrium points, points reflecting not the preferences of the individual alone, but their "crossing" with the supplier's behavior. Only if we could be reasonably certain that for a given set of transaction data, the demand schedule have not shifted (due to say, income effects), we could then use these data to estimate the demand function (by the way at market level, this is the classic endogeneity problem: using market outcomes to estimate a relation we estimate neither market demand, nor market supply, but rather the locus of market equilibrium points).

So while realized transactions possess the strong element of "truth" (the individual did actually bought such quantity at such price), they do not necessarily reveal to us his demand function.

In your case, if you can have other data on the buyer, especially in order to assess any possible "income effects" (for the case you are examining, that would be turnover and/or profit data for a company), you could combine them with its purchases from you to arrive at an elasticity estimation (there are also possible issues with substitution effects, but for them you will have to have data on what your customer purchases from your competitors). Is it a listed company? If it is, I guess you can find quarterly Financial Statements over the web (meaning that you will have to transform the data on purchases to quarterly too).

This could take the form of a multiple regression model

$$E(\ln q_i) = \beta_0 + \beta_1\ln s_i + \beta_2\ln p_i, i=1,...,n$$

where $q_i=$ quantity purchased in period $i$ (month or quarter), $s_i$ would be the turnover of the customer (assumption = if the customer sells more to its customers, he purchases more from me), and $p_i=$ average price of $q_i$. One could also include Customer's profit data as an additional regressor, in order to control for their possible effect on purchases from us. And of course, any other regressor that you think can have an effect on the purchasing decisions of the customer.

The use of natural logarithms, means that

$$\hat \beta_2 = \frac {\partial E(\ln Q_i)}{\partial \ln P_i} \approx \eta_{q,p}$$

i.e. it is the estimate of the price elasticity of demand. The above model assumes a demand function that is characterized by a constant price elasticity. You can make it more complex or even non-linear, if you suspect that the elasticity of demand in your case may vary.


How does one derive the elasticity of substitution with implicit functions? I would like to derive the elasticity of substitution. I'm aware that such a thread with a very straightforward explanation already exists, but my case is slightly different and I'm not sure how to differentiate the functions involved.

But let me first introduce you to my problem. I have to derive the elasticity of substitution
$$\sigma = \frac{f_1 f_2(f_1z_1+f_2z_2)}{z_1z_2[2f_{1,2}f_1f_2-f_{11}(f_2)^2-f_{22}(f_1)^2]}$$
where I have the following production function $y^0 - f(z_1,rz_1)=0$ for which $r$ is defined the following: $r=\frac{z_2}{z_1}$.

As I have already mentioned this problem is already perfectly solved in this thread: How does one derive the elasticity of substitution?

But now comes the clue in my specification, where I do not now how to proceed: I have to express $z_1$ as function of $r$, such that $z_1=g(r)$. The marginal rate of substitution can thus be expressed as follows $$MRTS_{21}=\frac{f_1(g(r),rg(r))}{f_2(g(r),rg(r))}$$
How can I derive the differential of $f(g(r),rg(r))$, which is the first step in the derivation of the elasticity of substitution. I somehow should use the theorem of implicit functions, but I'm not sure how..

I hope someone can explain this differential to me!

Cheers

To derive the formula for the elasticity of substition I consider a function with two arguments $f(x_1,x_2)$. I then consider a level curve $f(x_1,x_2) = c$ assumed to define $x_2$ as a function of $x_1$. From this it follows that
$$\frac{\partial }{\partial x_1} f(x_1,x_2(x_1)) = c \Leftrightarrow \\[8pt]
f_1(x_1,x_2) + f_2(x_1,x_2) \frac{\partial x_2}{\partial x_1} = 0 \Leftrightarrow \\[8pt] \frac{\partial x_2}{\partial x_1} = - \frac{f_1(x_1,x_2) }{f_2(x_1,x_2) }$$
giving the slope of the level curve in terms of $f_i := \partial f/\partial x_i$ for $i=1,2$. Given the definition of MRS I conclude that
$$(1) \ \ MRS(x_1,x_2) := \frac{f_1(x_1,x_2) }{f_2(x_1,x_2) } = -\frac{\partial x_2}{\partial x_1}.$$
Then define the ratio function
$$r(x_1) = x_2(x_1)/x_1$$
again using that $x_2$ is a function of $x_1$. This function can be inverted to get $x_1 = r^{-1}(r)$ and using again that $x_2$ is a function of $x_1$ the MRS can be written as
$$MRS(r) := \frac{f_1(r^{-1}(r),x_2(r^{-1}(r)))}{f_2(r^{-1}(r),x_2(r^{-1}(r)))} $$
and differentiated with respect to $r$ to get
$$(2)\ \ \frac{\partial MRS(r)}{\partial r} = \left[\frac{\left(f_{11} + f_{12}\frac{\partial x_2}{\partial x_1}\right) f_2 - \left(f_{21} + f_{22}\frac{\partial x_2}{\partial x_1}\right)f_1}{f_2^2} \right]\frac{\partial r^{-1}(r)}{\partial r},$$
where the expression in square brackets is $\partial MRS(x_1,x_2(x_1))/\partial x_1$.
I then use that $r^{-1}(r) = x_1$ implying that $\partial r^{-1}(r)/\partial r = 1/\partial r(x_1)/\partial x_1$ and from the definition of $r(x_1)$ it follows that
$$(3) \ \ \frac{\partial r(x_1)}{\partial x_1} = \frac{\frac{\partial x_2}{\partial x_1} x_1 - x_2}{x_1^2} = \frac{}{}-\frac{f_1}{f_2}\frac{1}{x_1} - \frac{x_2}{x^2_1} = -f_1 r\left[ \frac{1}{f_2x_2} + \frac{1}{f_1x_1}\right],$$
using that $r =x_1/x_1$ and that $\frac{\partial x_2}{\partial x_1}  = - f_1/f_2$. Inserting the reciprocal value of (3) into (2) it follows that
$$(4)\ \ \frac{\partial MRS(r)}{\partial r} = -\left[\frac{\left(f_{11} + f_{12}\frac{\partial x_2}{\partial x_1}\right) f_2 - \left(f_{21} + f_{22}\frac{\partial x_2}{\partial x_1}\right)f_1}{f_2^2} \right] \left[ \frac{1}{f_1 r\left[ \frac{1}{f_2x_2} + \frac{1}{f_1x_1}\right]}\right].$$
What remains to be done is inserting this expression into the definition of the elasticity of substitution and cleaning it up. The Elasticity of substition is defined as the elasticity of $r = x_2/x_1$ as a function of $MRS$:
$$(5) \ \  \sigma := \frac{MRS}{r} \frac{\partial r}{\partial MRS} = \frac{1}{\frac{r}{MRS} \frac{\partial MRS(r)}{\partial r}}$$
being the reciprocal of the elasticity of MRS with respect to $r=x_2/x_1$. Inserting (4) into (5) it therefore follows that
$$1/\sigma =- \left[\frac{r}{f_1/f_2}\right]\left[\frac{\left(f_{11} + f_{12}\frac{\partial x_2}{\partial x_1}\right) f_2 - \left(f_{21} + f_{22}\frac{\partial x_2}{\partial x_1}\right)f_1}{f_2^2} \right] \left[ \frac{1}{f_1 r\left[ \frac{1}{f_2x_2} + \frac{1}{f_1x_1}\right]}\right],$$
which is reduced by removing the factor $r$ and using again that $\partial x_2/\partial x_2 = -f_1/f_2$ to get
$$1/\sigma =- \left[\frac{1}{f_1/f_2}\right]\left[\frac{\left(f_{11} - f_{12}\frac{f_1}{f_2}\right) f_2 - \left(f_{21} - f_{22}\frac{f_1}{f_2}\right)f_1}{f_2^2} \right] \left[ \frac{1}{f_1 \left[ \frac{1}{f_2x_2} + \frac{1}{f_1x_1}\right]}\right] \\[8pt]
= -\left[\frac{\left(\frac{f_{11}f_2}{f_1} - f_{12}\right) f_2 - \left(f_{21} \frac{f_2}{f_1}- f_{22}\right)f_1}{f_2^2} \right] \left[ \frac{1}{f_1 \left[ \frac{1}{f_2x_2} + \frac{1}{f_1x_1}\right]}\right]\\[8pt]
= -\left[\frac{\frac{f_{11}f^2_2}{f_1} - f_{12} f_2 - f_{21} f_2+ f_{22}f_1}{f_2^2} \right] \left[ \frac{1}{f_1 \left[ \frac{1}{f_2x_2} + \frac{1}{f_1x_1}\right]}\right]\\[8pt]
= -\left[\frac{f_{11}}{f^2_1} - \frac{f_{12}}{f_1f_2}  - \frac{f_{21}}{f_1f_2} + \frac{f_{22}}{f_2^2} \right] \left[ \frac{1}{\left[ \frac{1}{f_2x_2} + \frac{1}{f_1x_1}\right]}\right].$$
Taking the reciprocal and using that $f_{12} = f_{21}$ it follows that
$$ \sigma = - \frac{\frac{1}{f_2x_2} + \frac{1}{f_1x_1}}{\frac{f_{11}}{f^2_1} - \frac{2f_{12}}{f_1f_2}   + \frac{f_{22}}{f_2^2}} ,$$
which is the formula found in for example: Daniel McFadden Constant Elasticity of Substitution Production Functions
The Review of Economic Studies , Jun., 1963, Vol. 30, No. 2 (Jun., 1963), pp. 73-
83 [stated as equation (1)] or in
Knut Sydsæter, Arne Strøm, Peter Berck Economists’ Mathematical
Manual Fourth Edition  [stated as formula 5.21].
I leave it for you to show that this formula is equivalent to the one stated in the question (I however prefer this one because the way the indeces are written makes it easier to remember).


Why does a stronger currency have a tightening effect on economic conditions? http://www.economist.com/blogs/buttonwood/2015/12/central-bank-predictability

  Ever since 1987, banks have been willing to cut rates when markets
  have wobbled. Driving down bond yields has been an explicit aim of QE
  (and pushing up stockmarkets an implicit one). Currencies move in
  anticipation of interest rate divergence (hence the strength of the
  dollar this year) and a stronger/weaker currency has a
  tightening/easing effect on economic conditions.

A related question is what exactly is meant by tightening effect on economic conditions. This term is meant loosely in financial media and I do not know exactly what it means.

Tight monetary policy reduces the amount of money available in the economy and strengthens the currency. It is usually implemented by raising interest rates, increasing capital requirements for banks, or sometimes selling government bonds.

When there is less money and credit to go around, business activity slows down, economic growth slows down. Businesses that could have expanded by taking out loans do not do so; consumers who could have purchased more with their credit cards can't do so; investors who could have invested more money into businesses (equities) put the money into government bonds.


Practical advice for calculating optimal prices The company I work for is interested in making the pricing for its products more quantitative.  I researched the topic and I found some theory for calculating optimal pricing in Microeconomics texts and the "Pricing and Revenue Optimization" text by Phillips.
I have an engineering background and the theory makes sense to me, but I can't find any good material about how to implement these calculations in practice.
Here are some more specific questions

Calculating the optimal price requires a price-response function (seems very similar to a demand curve) associating price with demand.  The material I've read assumes that this function is known, but I can't find any good material about how to fit a price-response function in practice.  I've found some vague advice about using survey data, but it doesn't seem that practical or specific to me.  Are there some more specific and established methods for fitting a price-response function?  Maybe from historical transaction data?

Calculating the optimal price requires a cost function associating production quantity with cost.  I can imagine calculating this by accounting for raw material and labor costs in the manufacturing plant, but would appreciate if there's a more formal way to do this.  Maybe a complete tally of the costs I can sum up.

I imagine that any estimates of the price-response function and the cost function will have error.  Is there an established way to quantify the error and its impact on my pricing calculations?  This isn't addressed by the resources I've found.  Pricing of my company's products will have a large impact on revenue and I don't want to just fly by the seat of my pants.

Are there established methods for simultaneously optimizing the prices of a portfolio of products given a manufacturing quantity constraint?  The plants are constrained by the quantity of product they can produce.  The Phillips text has some theory on constrained pricing for one product, but not a portfolio of products.

Any advice is greatly appreciated!  Or even simply some insight as to whether optimal pricing theory is useful in practice, or sharing any war stories of actually implementing optimal pricing.

A price-response function differs from a demand curve. A price-response function appears in a model where prices are selected by the firm, instead of output. A demand function appears when firms are price takers and cannot influence the price of the product on the market. They will have to sell it at whatever the going rate is.
I will try to answer the questions but they will be very general answers, hopefully they are useful.

The price-response function can be estimated from historical data. I don't know what you mean by transaction data. But if your company is a manufacturer of stuff then transactions could mean the cost of your raw materials and intermediate goods purchases. Then it is possible to estimate a price-response function from this. But it is important to remember that the price-response you estimate is based on your own companies pricing strategy in the past. If your company has made mistakes in it's pricing before, how will estimating this price-response function help that? I think it is better to use a method that takes data from the entire industry instead and benchmark your company against that.

You don't need to do this in very much detail. Just setup your problem generally. Such as, Production Function = Y = F(x1, x2, ...) and cost function = C = G(x1, x2, x3, p1, p2, p3). Solve that problem, what do you end up with? Focus on estimating what is needed in that function in reduced form. I would think what you need is a good measure of your marginal costs.

Estimating the price-response function will certainly have error. But that depends on a lot of things: data availability, model specification, measurement error, etc. You can benchmark against other studies in your field or outside your field instead of trying to removing error completely. You can eventually compare the model's predictions against out-of-sample values.

Unless there is some interdependency between the production of these products within the factories, this should not be a problem I think. For instance, are these products made in the same factories? Does the production of one affect the other? If not, you can get probably get away with solving the problem for each product's price response separately.


Why the name for isoelastic utility? If $u(x)=\frac{x^{1-\mu}}{1-\mu}$, then the elasticity defined as $\frac{\partial u}{\partial x}\frac{x}{u}=1-\mu$.

However, when we define $u(x)=\frac{x^{1-\mu}-1}{1-\mu}$ (usual def. for isoelastic utility), we have $\frac{\partial u}{\partial x}\frac{x}{u}=(1-\mu)\frac{x^{1-\mu}}{x^{1-\mu}-1}$. And this doesn't seem to give a constant elasticity. So, why do we call this utility isoelastic?

Any help would be appreciated.

Iso-elastic utility is defined as a function $U(w)$ where for all $k \gt 0$ you have $$U(kw)=f(k)U(w)+g(k)$$ for some functions $f(k)$ and $g(k)$ independent of $w$, i.e. an affine transformation of the original utility function

This is iso- because this kind of utility function leads to identical (or at least proportionate) decisions: it means that the optimal risk/reward behaviour at given level of wealth $w$ is also optimal for another level of wealth $kw$ if you multiply all the original investments by $k$.  For example, if at some wealth level you would put a third of it into a particular risky investment and two-thirds into a particular safe investment, then with an iso-elastic utility function you would do the same with at any wealth level

Both your formulations are iso-elastic in this sense, since they only differ by a constant $\frac{1}{1-\mu}$ and so lead to identical distribution decisions.  The difference between them is that the first has $u(0)=0$ and $u(1)=\frac{1}{1-\mu}$ while the second has $u(1)=0$, and since that difference has no real-life implications it might be unreasonable to claim the two utility functions had different properties

Those who use the second formulation often associate it with a logarithmic utility function as the limit function as $\mu \to 1$.  This limit cannot be done without subtracting the $\frac{1}{1-\mu}$ (no longer a constant, since $\mu$ is changing), so they take the second formulation for arithmetical convenience


According to the U.S., what constitutes as fair subsidies? The U.S. asked China to do this during the trade negotiations:

  China immediately will cease providing market-distorting subsidies and
  other types of government support that can contribute to the creation
  or maintenance of excess capacity in the industries targeted by the
  Made in China 2025 industrial plan;

However, why does the U.S. think it's unfair? And also what would constitute fair subsidies since the U.S. is known to give massive subsidies to companies like Boeing and Ford? Is it me or were logic and fairness thrown completely out of the window during the U.S. trade negotiations?

One potential approach to this question would be to look at the agreements made under the WTO, of which both China and the US are members.

According to the WTO there are two different categories of non-allowable subsidies.

  Prohibited subsidies... require recipients to meet certain export targets, or to use domestic goods instead of imported goods. They are prohibited because they are specifically designed to distort international trade, and are therefore likely to hurt other countries’ trade.

There are also "Actionable subsidies" which are not permitted if the complaining country can show that these subsidies cause damage.

  The agreement defines three types of damage they can cause. One country’s subsidies can hurt a domestic industry in an importing country. They can hurt rival exporters from another country when the two compete in third markets. And domestic subsidies in one country can hurt exporters trying to compete in the subsidizing country’s domestic market.

Both the US and China have brought complaints about each other's subsidies to the WTO in the past. However the present US administration has expressed a lot of mistrust towards all forms of multilateral institutions including the WTO. By taking unilateral action instead, the US effectively dodges the question of defining fair versus unfair trading practices in a  clear and rational way.


Price-consumption curve Suppose a consumer whose income is $b$ has a utility function given by $U(x,y) = 2xy+y^2$ with the price of $x$ being $p_x$ and the price of $y$ being $p_y$.

Draw the price-consumption curve assuming $y$ is an inferior good (keep the price of $x$ constant).

If we set up the Lagrangian $$ L = 2xy+y^2 + \lambda \cdot (b - p_xx-p_yy) $$

and solve the maximization problem, we'll end up with

$$x(p_x,p_y,b) = \left( \frac{p_y-p_x}{2p_xp_y - p_x^2} \right) \cdot b, \,\,\,\, y(p_x,p_y,b) = \left( \frac{p_x}{2p_xp_y - p_x^2} \right) \cdot b $$

If $y$ is to be inferior, then we must have (considering income and prices to be strictly positive)

$$ \frac{\partial y(p_x,p_y,b)}{\partial b} < 0 \implies \left( \frac{p_x}{2p_xp_y - p_x^2} \right)  < 0 \Leftrightarrow 2p_xp_y - p_x^2 < 0  $$

However, in order for the amount consumed of $y$ to be non-negative, we must have

$$ \left( \frac{p_x}{2p_xp_y - p_x^2} \right) \cdot b \geq 0 \Leftrightarrow 2p_xp_y - p_x^2 \geq 0  $$

Thus, we can conclude that if the demand for $y$ is to be non-negative at strictly positive prices and income, then $y$ can't be an inferior good.

However, if we respect the condition given by the non-negativity of $y$, we can still plot the price-consumption curve. Taking the following pairs of prices

$$ (p_x,p_y) = \{ (1,1),(1,3),(1,5) \}$$

and letting $b = 48$, we'll have:

$$\begin{cases}
x(1,1,48) = 0, y(1,1,48) = 48 \\ x(1,3,48) = 9.60, y(1,3,48) = 9.60 \\ x(1,5,48) \approx 21.34, y(1,5,48) \approx 5.34
\end{cases}$$

Plotting these values on a graph, we have:

Is my answer correct?

Thanks!

It's true that given the utility function the $y$-good is a normal good, so the question is quite odd. Ignoring this, your calculations are correct, but you could simplify to $y(p_x,p_y,b)=\frac{b}{2p_y-p_x}$.

Your curve contains a mistake, since $x(1,3,48)=19.2$. Indeed by substituting your expressions for $x$ and $y$ you can show that $2x+y=\frac{b}{p_x}$ as long as $p_y\ge p_x$, so the price-consumption curve is piecewise linear.


Yield curve flattening- abstract question I just stopped and thought about the current economic state, and yield curve in particular.

As you can see here, the yield curve is starting to flatten, means longer bonds demand is high, while short term bonds demand are low.

This is happening due to the "fear" from the upcoming short term economics, so the investors are selling short bonds and buying long bonds.

In US, the chance for government default are very low, as they can print more money and never declare a default, which will cause inflation (something that affect both short term and long term).

So why does the investors are buying longer bonds, with the same yield as short term yield, while the risk is so low? What is the rational behind getting longer bonds?

Thanks.

If an investor has a fixed amount to invest for a given time horizon, then a longer-term bond locks in the current long-term bond interest rate, but a short-term bond only provides this rate for a short time. After that, the short-term interest rate may be more or less favourable. Apparently the investors expect that the short-term rate will become less favourable for them after the current short-term bonds mature.

Investment is mostly about expectations, which may or may not be correct. Where the expectations come from is a more complicated question.


Why did the pound sterling lose its reserve status to USD? Why did the pound sterling lose it reserve status to USD? Was this due to some agreement during the Bretton Woods negotiations?

As written, this question has an extremely wide scope, and an answer would be the length of a book. I will attempt a narrow answer.
People use “reserve currency” at present in a very loose manner. In the context of this question, it had a very specific meaning. Currencies were pegged, ultimately to gold. Currencies that had inadequate gold reserves used “strong” gold-backed currencies as extra backing for their pegs. Hence, the strong currencies were used as reserves.
Britain lost almost all of its gold reserves in World War II, in order to finance the war effort. (The process started earlier, with large losses in World War I.) Without adequate gold reserves of its own, the pound was not a credible backing for another country’s gold peg. Hence, it lost reserve status.
The Bretton Woods agreement enshrined the financial reality of the post-war system: the U.S. has accumulated almost all of the official gold reserves as a result of supplying the warring countries. The system was set so that the US dollar was gold-backed, and other currencies were backed by the USD.
Anything beyond this outline turns into a financial history of 1910-1950, for which there are many choices.


Confusion about the jack-knife Suppose that I am trying to use the jack-knife to estimate the variance of some estimator $E$. If I have $n$ data points, I begin by computing $n$ estimates (call them $B_1$, ..., $B_n$), each obtained from leaving one of the $n$ data points out of my sample. If I understand it correctly, the Wikipedia page then suggests that my estimate of the variance should be
$$\hat{Var(E)} = \frac{\sum_{i = 1}^n (B_i - \bar{B_i})^2}{n-1}$$
where $\bar{B_i}$ is the average of my $n$ estimates. The standard error is then $\sqrt(\hat{Var(E)})$.
On the other hand, the notes here seem to suggest
$$\hat{Var(E)} = \sum_{i = 1}^n (B_i - \bar{B_i})^2\left(\frac{n-1}{n}\right)$$
What am I missing here? And which formula should I use? Many thanks in advance!
Extra question: if the answer is indeed the second formula, will standard errors indeed get smaller (as one would expect) as $n$ gets large? I ask because $\sum_{i = 1}^n (B_i - \bar{B_i})^2/n \approx Var(B_i)$ for large $n$; so it appears that the second estimate is roughly $Var(B_i)(n-1)$. It is not clear to me that this is decreasing in $n$ (even if $Var(B_i)$ goes to zero as $n$ gets large).

I'm not a statistician... and this is the economics forum, so forgive me for the possible mistakes. I got most of this information from these slides.
Consider a statistic of interest  $\theta$ with a consistent but biased estimate $\hat \theta$. The Jacknife estimates $\hat \theta_{(i)}$ with is the same statistic, based on the sample that is obtained from removing observation $i$. Doing this for all $i$ and taking the mean over the values $\hat \theta_{(i)}$ gives:
$$
\hat \theta_{(.)} = \frac{1}{n} \sum_{i = 1}^n \hat \theta_{(i)}
$$
As stated above, the estimator $\hat \theta$ is biased, so let:
$$
\mathbb{E}(\hat \theta) = \theta + \frac{b}{n} + O\left(\frac{1}{n^2}\right)
$$
Where $b$ is the first order bias of the estimator $\hat \theta$. Then for the Jacknife estimates, we have a similar expression:
$$
\mathbb{E}(\hat \theta_{(i)}) = \theta + \frac{b}{n-1} + O\left(\frac{1}{n^2}\right).
$$
So, ignoring the higher order terms, we get:
$$
\mathbb{E}(\hat \theta_{(i)}) - \frac{b}{n-1} =  \mathbb{E}(\hat \theta) - \frac{b}{n},\\
\to (n-1)\mathbb{E}(\hat \theta_{(i)} - \hat \theta) = \frac{b}{n}
$$
This shows that: $(n-1) (\hat \theta_{(i)} - \hat \theta)$ is an `unbiased' estimator for $\dfrac{b}{n}$ (at least when we are ignoring all other higher order bias terms). Then using this correction, we have the following 'bias-corrected estimate':
$$
pv_{(i)} = \hat \theta + (n-1)(\hat \theta - \hat \theta_{(i)}) = n \hat \theta + (n-1) \hat \theta_{(i)}.
$$
This is called the pseudovalue.
Now, of course it would be stupid to only use $pv_{(i)}$ for one particular value of $i$ . So a better bias-corrected estimate is the one that averages over all these, the jacknife estimator:
$$
\hat \theta_{jack} = \frac{1}{n}\sum_{i = }^n pv_i =  n \hat \theta + (n-1) \hat \theta_{(.)}.
$$
The pseudovalues $pv_{(i)}$ are not necessarily i.i.d. but assume they are anyway. Then, their variance is given by:
$$
\begin{align*}
{\rm var}(pv_i) &= \frac{1}{n-1} \sum_{i = 1}^n (pv_i - \hat \theta_{jack})^2,\\
&= \frac{1}{n-1} \sum_{i = 1}^n (n \hat \theta - (n-1)\hat \theta_{(.)})^2,\\
&= \frac{1}{n-1} \sum_{i = 1}^n (n \hat \theta + (n-1) \hat \theta_{(i)} - n \hat \theta - (n-1) \hat \theta_{(.)} )^2,\\
&= \frac{(n-1)^2}{n-1} \sum_{i = 1}^n (\hat \theta_{(i)}- \hat \theta_{(.)})^2,\\
&= (n-1) \sum_{i = 1}^n (\hat \theta_{(i)} - \hat \theta_{(.)})^2
\end{align*}
$$
Assuming a central limit theorem holds for $\hat \theta_{jack}$, then:
$$
\frac{\theta_{jack} - \theta}{s_n} \to^d N(0,1)
$$
where $s_n$ is the variance of $pv_i$ divided by $n$.
$$
s_n^2 = \frac{n-1}{n} \sum_{i = 1}^n \left(\hat \theta_{(i)} - \hat \theta_{(.)}\right)^2.
$$
This 'variance', $s^2_n$, is the estimator that you give in your question.


How to use an instrumental variable to estimate the parameter? I have the following linear model of log wages (w) explained using years of schooling (S), years of experience and its square $(E,E^2)$ and 3 dummy variables indicating whether the individual was black (B), lived in the south (Sth), and lived in a metropolitan area (Sm).
$w_i=\alpha+\beta_1S_i+\beta_2E_i+\beta_3E_i^2+\beta_4B_i+\beta_5Sth_i+\beta_6Sm_i+\epsilon_i$ where $\epsilon_i$is an unobserved error term and $i$ indexes individuals.
A reduced form model for schooling is written as
$S_i=\delta+z_i'\pi+v_i$ where $z_i$ is a $L\times 1$vector including the instrument (lived near college) and all the exogenous variables in the first regression equation, $\pi$ is a $L\times 1$vector of unknown parameters, $\delta$ is an unknown scalar parameter, and $v_i$ is an error term.
Assuming that $S_i$ is endogenous, how can I use the reduced form equation in conjunction with the first regression equation to identify the parameter $\beta_1$? How does the use of instrumental variable differ from the use of OLS estimator in this case?

Reduced form is a regression of dependent variable  on instrument directly without using some two stage approach.

Consider the following example of endogenous system

Second Stage: $$Y = \alpha + \beta X + \epsilon$$

First Stage: $$X = \mu + \gamma Z+ \eta $$

Where $Y$ is dependent variable $X$ endogenous regressor and $Z$ is your instrument.

One option is to estimate this with some two stage approach as previous post suggests where you would first estimate predicted $\hat{X}$ and then use the $\hat{X}$ in second stage instead of actual $X$ - however, this is not reduced form.

A reduced form is when you use the instrument directly in stead of the endogenous variable so in this case reduced form would be:

$$Y= \kappa + \omega Z + \xi$$

You can work from this general case to your specific one.

I would recommend looking at the handbook Mostly Harmless Econometrics form Angrist and Pischke. They discuss reduced form in Ch4 instrumental variables in action.

The difference between OLS and IV estimator (in matrix notation) is as follows:

OLS: $\hat{\beta} = (\sum_i X_i X_i^{\prime} )^{-1}\sum_i X_i y_i$ - This estimator is biased in the presence of endogeneity

IV: $\hat{\beta}_{2SLS} = (x^{\prime} Z(Z^{\prime}Z)^{-1}x)^{-1}x'Z(Z^{\prime}Z)^{-1}y$ - (here $x$ is given by $x= Z \gamma + \eta$) this estimator has still bias but the bias declines if the first stage is strong - has high F-statistics as in approximation the bias term gets multiplied by $1/(F+1)$ where F is the test statistics so bias goes to zero as $F$ goes to infinity and in practice its very close to zero for $F>10$.


Where the money from QE goes So when QE is used (or something similar that results in printing mone), where does the newly created money go? Does some entity get free money? Why is that allowed?

[...] where does the newly created money go?

This money is used by central banks to "buy" commercial banks' bonds $\iff$ commercial banks are refinancing themselves $\iff$ this money goes to commercial banks.

  Does some entity get free money?

Yes, when central banks buy commercial banks' bonds for free, i.e. at a 0 interest rate.

  Why is that allowed?

The main reason is that as counter-cyclical agents, central banks have to change reference rates to stimulate their national economies, even if sometimes doing so implies to center them on 0, or even on a negative value. Note that in the case of negative interest rates, we are talking about entities that are paid to get money.

E.g. when refinancing themselves at a lower-than-previously cost, commercial banks are theoretically more prompt to be, say, flexible, and thus to stimulate demands (here and there) in the national economy by lending money (here and there). If supplies stay constant, markets will reach a new equilibrium via prices rising (inflation) due to these stimulated demands. Persistent inflation means new business opportunities, which in turn means growth if capacities to cut these opportunities exist domestically, or thanks to foreign direct investments.


A Cake Eating Problem in Continuous Time: Hamiltonian or HJB? Your standard continuous time cake eating problem is defined as follows:
$$\max_{c(t)}\int_0^\infty e^{-rt} \ln (c(t)) dt$$
subject to
$$f(k(t))=k(t)$$
$$\dot{k}(t)=-c(t)$$
Approaching this problem by using the Hamilton Jacobi Bellman Equation (the continuous time analogue of the discrete time bellman) with the appropriate drop of time parametrization we have:
$$rv(k)=ln(c)+v'(k)\dot{k}$$
However in the context of using the (present valued) Hamiltonian proper we have:
$$\mathcal{H}=e^{-rt} \ln(c(t))+\lambda(t)\dot{k}(t)$$
My question is, under what circumstances would one use the Hamiltonian over the HJB?
Note for more detail on this question see:
https://math.stackexchange.com/questions/3293825/transversality-condition-with-unbounded-value-function

The comment by user @MaartenPunt is accurate. I don't think that in general one can identify situations where one should have a clear preference over one formulation over the other. It is more of a case-specific issue (and maybe for some twisted problems where one of the two may fail for usually technical reasons). See this post for some related discussion, https://economics.stackexchange.com/a/14289/61.
...Or sometimes one may get a bit confused, for example, in the specific problem, one could momentarily stop and wonder "what is the derivative of the Hamiltonian with respect to the state variable?"
Well, it is what it appears to be: zero. Because
$$\frac{\partial \mathcal H}{\partial k}= \frac{\partial \lambda \dot k}{\partial k} = -\frac{\partial \lambda c}{\partial k} = 0,$$
because we do not differentiate the decision variable, or the multiplier, with respect to the state variable. Now, optimally, we have
$$\frac{\partial \mathcal H}{\partial k} = -\dot \lambda,$$
and so it follows that the multiplier is constant along the time axis, $\dot \lambda = 0$. Then for the other first-order condition, we have
$$\frac{\partial \mathcal H}{\partial c} = 0 \implies e^{-rt} \frac 1 c = \lambda.$$
Differentiating this with respect to time we get
$$-re^{-rt} \frac 1 c - e^{-rt} \frac{\dot c}{c^2} = 0 \implies \dot c = -rc,$$
which is what we get from HJB as "policy" function.
As for whether this is a maximum, it is, because the Hamiltonian is jointly concave in $c$ and $k$, see, https://economics.stackexchange.com/a/6063/61.


Looking for behavioral economics research about the redemption of gift cards This is a long shot! I was wondering if anyone could point me to any behavioral economics or other economics research on perceived value, specifically I'm looking at why some people don't redeem activity gift cards before they expire.

My hypothesis is that time doing something else they choose, is perceived as better used than time doing the activity that the gift card pays for.

For context, some of these gift cards are are worth \$100 - $500 and generally the activity they pay for is chosen by the gift giver who would know about the likes and dislikes of the receiver.

I know this is quite general, but I'm working as an analyst in a company that sells gift cards and I would like to have some background research before I look to draw any conclusions from the data, I know that some people use them, some people don't  and I can see some patterns in variables in the two groups, but I'd like to bring some theoretical rigor to the analysis.

A classical economic explanation for the phenomenon you describe is that the gift giver does not know the receivers preferences well enough. Prominently, Joel Waldfogel makes this point in his fun paper "The Deadweight Loss of Christmas":

  I find that holiday gift giving destroys between one-third and one-tenth of the value of gifts.

This article pops up in the public domain every year around the holidays (example in the NYT) and its idea of course also applies to all other gift-giving-and-receiving situations.
Of course many people (including economists) disagree with that notion and you find quite a lot of comments and replies on that paper in the AER, just type the title of the paper into google.scholar.


What happens to interest rates when they are already at (near) zero and the stock market crashes? Let's say the global stock market crashes in the coming months (it's currently at an all time high in the western world). What happens to interest rates?

"Usually", as I understand from my absolute layperson perspective, interest rates would be lowered as a counter measure. But what happens if interest rates are already (nearly) zero, as is the case in some countries?

They would be just pushed to their lowest possible level. Recent experience in Switzerland and Germany shows the interest rate can be slightly negative but that’s it. Once the interest rate hit (zero) lower bound it can’t be pushed further as long as there is cash that carries implied zero interest. At that point central bank would have to resort to other policy instruments such as QE, helicopter money, forward guidance etc.

However, if some western country would decide to go completely cashless it would be possible to have arbitrary negative interest rate. In that case the interest rate would just get pushed further down.


Can the money multiplier happen within a single bank / a single loan? Many tutorials explain the money multiplier effect by involving a chain of banks (e.g. khan academy)
So if reserve requirements are 10% and bank A owns 1000€ reserves, bank A can lend 900€ to bank B; now bank B has 900€ reserves so it can lend 810€ to bank C, and so on to infinity. Making it $M1 = \frac {1} {10\%} \times M0 = $ 1000€ reserves + 9000€ loans.
Is this chain really necessary, or can simply bank A with 1000€ reserves issue a single loan of 9000€?

From what I saw, the video confused various forms of monetary instruments.
If a customer gets a \$1000 transfer from the Federal Reserve, Bank A has a \$1000 deposit liability, and a new \$1000 balance at the Federal Reserve.
Under the assumption that the bank was at its reserve limit, it has \$900 in excess reserves.
It can eliminate those excess reserves by making a \$9000 loan, as that creates a deposit with \$900 of required reserves. The growth chain ends there.
In practice, the proceeds of a loan are typically spent quickly. As such, the bank would expect a need for an outflow of the size of the loan. It needs to hold liquid assets that can be liquidated to meet the outflow, or have the capacity to borrow in the inter-bank market.
Given the unpredictability of cash flows, in the pre-2008 era in the US (one of the few places with formal reserve requirements), banks made loans, and then borrowed in the Fed Funds markets to make up deficiencies. The Fed supplied the Fed Funds market the amount required to hit its policy interest rate target. (Currently, reserve requirements have been abolished, and there is a permanent excess of reserves.)
The presentater probably relied on out of date textbooks.  This paper by BoE staff explains how the “money multiplier” is a misconception: link to working paper.


How to show that the income elasticity of Marshallian demand is equal to unity? Suppose that the expenditure function is multiplicatively separable in $\textbf{p}$ and u so that
$$e(p,u) =k(u)g(\textbf{p}),$$
 where k(·) is some positive monotonic function of a single variable, and g: $\mathbb{R^n_{+}}$ $\rightarrow$ $\mathbb{R}_{+}$.

Thank you in advance.

Here's my attempt at a hint, though I appreciate feedback, as I am not sure how rigorous this is. As per the comment I gave with the resource, your question seems to require a previous question in order to do this.

So start by showing that the share of income spent on good $x_i$ can always be measured by the elasticity of expenditure function with respect to $p_i$ at $(p, u^*)$ where $u^* = v(p,w)$

$$\mid \eta^ {e_{x_i, p_i}}\mid \ = \frac{\frac{\Delta x_i}{x_i}}{\frac{\Delta p_i}{p_i}} = \frac{\Delta x_i}{\Delta p_i} \cdot \frac{p_i}{x_i} = \frac{\partial x_i}{\partial p_i} \cdot \frac{p_i}{x_i}$$

We know that,

$$e(p,u^*) = p \cdot \tilde x, \forall \ \tilde x ∈ x^h (p, u^*) = x(p, e(p, u^*))$$

by duality, where $x^h(p, u^*)$ denotes Hicksian demand. So,

$$\frac{\partial e(p_i,u^*)}{\partial p_i} = x_i$$
$$\frac{\partial x_i}{\partial e(p_i, u^*)} = \frac{x_i}{w}$$

$$\implies \frac{\partial x_i}{\partial p_i} \cdot \frac{p_i}{x_i} = \frac{\partial e}{\partial p_i} \cdot \frac{\partial x_i}{\partial e}\cdot \frac{p_i}{x_i} = \frac {x_i^2}{w} \cdot \frac{p_i}{x_i} = \frac{p_i x_i}{w}$$

Which is the share of income spent on good $x_i$


Is there some background/explanation why the Fed discontinued publishing their M3 indicator, circa 2006? As Wikipedia says and as it can be easily verified, since 2006, the Fed no longer publishes an M3 indicator (unlike the ECB which still hangs on to that notion). So is there some background or explanation to this 2006 Fed decision to abandon their M3?

https://www.federalreserve.gov/releases/h6/discm3.htm:

  M3 does not appear to convey any additional information about economic activity that is not already embodied in M2 and has not played a role in the monetary policy process for many years. Consequently, the Board judged that the costs of collecting the underlying data and publishing M3 outweigh the benefits.


Why can two functions represent the same preferences? I wonder why two functions can represent the same preferences?

Suppose I strictly prefer Apple ($A$) to Banana ($B$) and that these are the only two goods in existence.

Consider the following functions:†

The function $u$ with $u(A)=1$, $u(B)=0$.
The function $v$ with $v(A)=-99$, $v(B)=-100$.
The function $w$ with $w(A)=0.1$, $w(B)=0.01$.

Each of the above functions correctly represents my preference because in each case, the function's value at $A$ exceeds that at $B$.

A utility function (representation) is merely a (very) convenient way to numerically encode my preference. Here there are only two goods and I prefer $A$ to $B$. So, any function whose value at $A$ is greater than that at $B$ would correctly represent my preference.

In this example, we have only two goods, so a utility function isn't particularly useful or convenient.

But with more goods (and sometimes also more assumptions), utility functions can help to produce useful results that tell us something about the real world.

†Real-valued, with domain $\{A,B\}$.


Seemingly contradictory relationship between bond yields and economic growth? I have a few seemingly contradictory ways of viewing the relationship between economic growth and bond yields:

Reductions in FFR are largely induced by IOER. Since IOER and bonds are competing investments, a reduction in IOER increases demand for bonds and therefore increases bond prices and reduces yields. Main idea: lower interest rates cause lower bond yields.

Economic growth occurs in low interest environments, so number one's "main idea" should hold: lower interest rates cause lower bond yields.

Economic growth leads to rising bond yields. From CNBC article:

"Bulls like Tchir insist that, in this case, the rise in bond yields is not a negative for stocks: “This time the rise in yields is coming from economic growth, stimulus, and infrastructure.  All of that is good for stocks.  That’s why this rise doesn’t scare me too much.”"

During times of slowing economic growth, demand for money decreases leading to reduced demand for loans and a resulting decrease in interest rates. This environment makes investors nervous so bonds become more attractive, driving up demand and therefore increasing price and reducing yield.

I am very confused about the relationship between interest rates and bond yields. I thought they moved in the same direction, but the above is confusing me. Any clarity? Thanks!

(Note: there were similar questions in the past, but I did not see an exact match.)
As used in this question, “interest rates” are the rate of interest associated with a policy rate or a deposit. A “yield” is the the rate of return on a bond given its purchase price. For a bond, since the payments are fixed, the yield moves inversely with price.
If we simplify to the case of a zero coupon bond that matures at time T (starting at $t=0$), the price is given as:
$$
P(T) = e^{- \int_0^T f(t)dt},
$$
where $f(t)$ is the instantaneous forward rate. (Based on Rebanato’s “Interest-Rate Option Models”, page 6. Should be in any fixed income textbook.)
Put into words: the price of the bond is given by “averaging” the forward rates over the life of the bond. Higher forward rates implies a lower price (and hence, a higher yield).
The central bank “risk-free” rates for short maturities, and the instantaneous forward rate initially coincides with that rate. Further along the time axis, the forward rate is normally interpreted as the expected policy rate plus a term premium.
If economic growth is expected to be strong, market participants normally expect rate hikes. For example, that is the implied behaviour of “The Taylor Rule,” which the reader can easily find references for.
In a recession, it is entirely possible for the central bank to lower the policy rate, and market participants to expect a strong recovery, and forward rates rise. However, one can look at bond data to see that the policy rate and bond yields are roughly “correlated.”
As for the relationship to equity prices (which show up in the question), the situation is muddled and should be a separate question.


How are disaster effects calculated into GDP? Assuming no income was lost, only assets were destroyed (e.g. homes), how does disaster event impact GDP numbers?

Or otherwise, is losing and rebuilding wealth neutral to GDP (e.g. spending on construction instead of entertainment)?

Is GDP calculated so well that all subtle effects are reflected in the numbers (e.g. lost home might affect work opportunities in mid-term)?

GDP is just a partial measure of flow. There are lots of changes to the stock of a nation, its capital, that are not captured by GDP.

Destruction of assets in natural disasters isn't recognised as a loss in GDP. It gets worse: the rebuilding would actually be a positive on GDP. NB any loss in economic output from, say, destruction of factories, would appear as a negative on GDP - the loss of the factory's output.

Changes in natural capital aren't captured either.

GDP is just a measure of volume of transactions. It gets misused as a proxy for economic wellbeing. That's not the indicator's fault, it's the fault of those who misuse it.


Why would minimum rent under franchise arrangements for McDonald's decrease year by year? I am working on a project regarding the refranchising strategy of McDonald's and came across this piece of data in their 2014 annual report. My understanding of minimum rent is that its a fixed amount to be paid by franchisees to McDonald's as the franchisees are leasing a restaurant location from McDonald's. Hence, I have no idea why its decreasing.

Suppose McDonald's has 2 franchisees. Franchisee A under its current franchise arrangement has to pay \$100 a year of minimum rent until the current arrangement expires in 2025. Franchisee B, on the other hand, has to pay \$75 a year but its arrangement expires in 2019.

The future minimum rent due to McDonald's in 2018 is $\$100 + \$75 = \$175$. This continues until 2020, where the payments then drop to only \$100 a year after Franchisee B's arrangement expires. Although, we would expect a high renewal rate with McDonald's franchisees, the table only shows future cash flows under contracts existing today, or as they say in the annual report

  "The following table summarizes...future minimum rent payments due to the Company under existing franchise arrangements as of December 31, 2014."

Note that these values are not discounted. In our simple example, McDonald's is owed \$100 a year from 2021 to 2025 by Franchisee A and then gets $0 a year after 2025 since there are no more arrangements left. \$100 a year from 2021 to 2025 sums to \$500 for the thereafter row.

These tables of contractual obligations and future cash flows are helpful to analyze the future cash needs of a business. Often times companies may have a lot of debt due in a specific year when a bond issue matures. While companies often refinance ("rollover") that debt, it is helpful for investors to know that that debt maturity is coming up since if the company cannot refinance (say it is a lousy retailer or there is a financial crisis) and does not have enough cash on hand, the company could be forced into bankruptcy.

This future minimum rents table provided by McDonald's tells investors how much cash is contractually coming in the door, and also sheds light on the remaining life of McDonald's franchise arrangements.


What is the difference between Solow growth, classical growth, and neoclassical growth? My friends and I are taking some introductory macroeconomics courses and these terms keep getting thrown around without being clear how they are related.

Can someone provide brief definitions for each of these and how they are different?

Classical growth theory: we can put many authors in it but I'd say Ricardo (if we put Malthus aside) is the first one to have describe a real growth theory. For their defenders, growth should somehow end at a certain point in time and is also very unstable for various reasons: Ricardo thinks growth would end because of diminishing returns (cf. Ricardo's On the Principles of Political Economy and Taxation (1817)). In the classical growth theory, you can also include the theory of Harrod-Domar which basically explains that growth is unstable: there is either too much investment in comparaison to savings, or there is not enough investment (cf. Harrod's "An Essay in Dynamic Theory", The Economic Journal (1939)).
Neoclassical growth: Solow's model is a neoclassical model of growth. It comes in response to the Harrod-Domar model and tries to explain that in the long run, growth is stable (no growth of capital per head).. The only extra growth per head can only come through technological progress (cf. Solosw' "A contribution to the theory of economic growth", Quarterly Journal of Economics (1956)), which is exogeneous.

I encourage you also to look at two other models such as: the AK (accumulated knowledge), which is based on the theory of Solow but tries to make technological changes a endogenous variable in the model (in the Solow model technological change is not the consequence of specific policies); Schumpeterian model created by Aghion and Howitt (1998) which also describes the policies that would be best to stimulate innovation and therefore growth...


How to show that a homothetic utility function has demand functions which are linear in income A homothetic utility function is one which is a monotonic transformation of a homogeneous utility function.

I am asked to show that if a utility function is homothetic then the associated demand functions are linear in income.

In general if $H$ is monotonic and we compose it with a function $g$ which is homogeneous we get $H(g(x,y))$ which is homothetic and so the ratio of derivatives of $H$ with respect to $x$ and $y$ is the same as the ratio of the derivatives of $g$ with respect to $x$ and $y$ since the outer function cancels out. This means all income expansion paths are rays from the origin and the slope of indifference curves (level sets) have the same slope along the income expansion path.

My question is how does one show generally that the demand functions are linear in income? If you don't have the functional form of the utility function then what can you substitute into the budget constraint to solve for $x$ or $y$ as functions of prices and income only?

All you know is that the negative ratio of derivatives is equal to $p_1/p_2$ but you can't substitute anything into the budget constraint for $x$ or $y$ since you only have general partial derivatives.

The only way I can think to do that is take the inverse of the derivative of the inner (homogenous) function g in order to solve for $x$ (or $y$).

I think what you need is that if $U(x,y)$ is homothetic then
$$
\forall \alpha \in \mathbb{R}_{++}, \forall (x,y) : \hskip 6pt
\frac{\frac{\partial U(x,y)}{\partial x}}{\frac{\partial U(x,y)}{\partial y}} =
\frac{\frac{\partial U(\alpha \cdot x,\alpha \cdot y)}{\partial x}}{\frac{\partial U(\alpha \cdot x,\alpha \cdot y)}{\partial y}}
$$
and love.


Why does the answer not include increased negative unplanned stock investment? I will focus on the event "c":

The answer for "c" is following:

  A sharp increase in the rate of real GDP growth leads to
  a higher level of planned investment spending by producers, according to the accelerator principle, as they increase production capacity to meet higher demand.

I agree with the answer, but it seems to be incomplete. It was already established that growing negative change in unplanned inventory investment is a sign of a booming economy:

  In fact, economists who study
  macroeconomic variables in an attempt to determine the future path of the economy pay careful attention to changes in inventory levels. Rising inventories typically indicate positive unplanned inventory investment and a slowing economy, as sales are less than had been forecast. Falling inventories typically indicate negative unplanned inventory investment and a growing economy, as sales are greater than forecast.

So it would seem to be logical to expect that "A sharp increase in the economy's growth rate of real GDP" will cause increased negative unplanned inventory investments, AKA decreased inventory stocks. Does the answer omit this part without a good reason or do I misunderstand/miss something?

Scenario “C” does not specify “unexpected.” Since greater growth was expected, planned inventory investment would rise to meet higher expected demand.


Why do national governments not rent money from central banks directly? The central bank gives money to the business banks, who then give that money to people, companies and government agencies/units.

When a government controls the central bank, why doesn't the government lend money from it instead of business banks?

That way they would have:

a lower interest rate
control on their interest rate
theoritically no limit
etc.

EDIT:
My question is only about where the government gets the money. I'm not suggesting that the central bank should lend money directly to people or companies.

Note: This answer was posted 4 months before the OP clarified what it really wanted to ask (see comments below the answer).

I will accept @Ubiquitous view of the question, which in summary is:

Why not having a publicly owned monopoly in the banking sector? Instead of a, however regulated, private banking sector?

It would be naive to counter "then why not nationalize all production activities?". This is not a "socialism or capitalism?" socio-philosophico-ideological issue. Strictly from the point of view of how the Economics discipline analyzes things, we must recognize the critical and special role the banking system plays in modern economies (because it intermediates savings and investment, consumption smoothing and intertemporal allocation of resources), as well as its peculiarities.
And whenever the words "critical","special", "peculiar", arise in economic analysis, the merits of a private-market structure against a publicly controlled one must be carefully analyzed and assessed.

First let's define what is the main business-line of a bank, in the most basic, abstract sense: sublessor of perfectly liquid capital. It borrows capital from the savers and lends it to the debtors -for a fee, which is the interest, and which depends on the length of the lease. And as with any lease, the lessee must also return what has been lent.

Let's move now to some of the main reasons that have made societies produced a good/service through a state monopoly (obviously I won't go through all the taxonomy and intricacies of the various categories of public goods):

Non-excludability  pertains to public goods like national safety: we cannot exclude those citizens that don't pay for it. This creates disincentives to pay for it. But the society as a whole needs it. So everybody pays whether they want it or not (through taxes that are backed by the monopoly of violence that the state holds), and the service is offered to all by a state monopoly. Does non-excludability holds for what the banking sector offers? No, because the bank gets to decide who gets the service or not. And the "service" is then at the control of the debtor.  So this cannot be an argument in favor of a public monopoly in the banking sector.

Decreasing Average Costs with the scale of production, is what traditionally defines a "natural monopoly": it is in the nature of the production process to have decreasing average costs as quantity produced increases, and so the state steps in so that the benefits to the monopolist accrue to all society through the state. Is the business of a bank characterized by "automatically" decreasing average costs as credit expands?

What are the "production costs" here? Various administrative costs certainly (branches, overheads etc), which are unlikely to exhibit a downward trend through out -rather they are very well likely to have the familiar U-shape, falling for initial small levels of credit volume, then perhaps a stage of constant returns to scale, then decreasing returns to scale (and so increasing average costs). A distinct and peculiar cost here, is outright loss of the capital. Surely, when one lets an apartment, it may suffer various damages from the use of it by the tenant -but it won't disappear with him. These costs will almost certainly increase with the "scale of production" (credit expansion) as the bank expands to less trustworthy debtors. So no "decreasing average costs here" - the banking sector is not a natural monopoly.

A case of negative externalities can be made, that moreover cannot be reversed: the choices a bank makes as to where it will lend its capital, and for what purposes, may not satisfy the needs of the economy as a whole: the economy may need transportation infrastructure -but the banks may lend capital for building office space, which are less needed. But once capital is sunk into buildings, it cannot be transformed into roads (certainly not directly, while indirectly, it won't be timely and it will have dead burden costs). But externalities are regulated in other ways, not by imposing a state monopoly.

What about the various imperfections that inadvertently characterize all actual markets, banking sector included? Incomplete and asymmetric information, rigidities, straightforward inefficiency, etc? Here, the matter becomes quantitative, exactly in view of the criticality of the banking sector: a given level of imperfection and inefficiency would matter less for society if observed in another market, compared to the banking sector. So we have to measure it -and then compare this with the level of inefficiency and imperfection that we would observe if we had a public monopoly instead.

This is what I had to offer as food for thought. I close with some responses to the OP's specific projections:

(In case of a state monopoly, the businesses would have)
A lower interest rate
Why? The central bank would lend public money. To private businesses. It would also have to bear administrative costs. Also, it would be accountable for public money. This would introduce conservatism into the system, to avoid accusations for favoritism for example. Either higher interest rates, or much more stringent criteria to grant a loan. Would that be desirable, as there will be no-one else (officially) lending capital in the economy?) What about the possible increase in loan-shark activity?

Control on their interest rate
I do not understand what that means.

Theoretically no limit
No way. Either the OP has in mind that the central bank will have vastly larger amounts of capital to lend (it will, but will it lend it "easily"? -see previous remark), or he has in mind creation of capital out of thin air based on the "state's authority", which of course would have solved all humanity's materialistic issues, if it could happen.