Why has increased productivity over the last 100 years not affected how much people work? If we are generally richer and more productive due to better technology and other factors, why do we still work so much?

I understand that there are various incentives to work (e.g. implicit status awards) that aren't linked with productivity in the abstract. But in a very simple model, if we can do more with less input, why are we still doing as much as we can?

Let's work such a very simple model. We have a Robinson Crusoe island economy, an isolated individual that lives totally alone. In order to consume something Crusoe must work. Assume for even more simplicity that capital is not needed (say, fruit-gathering by hand). Crusoe does not like to work but he would rather sit relaxed and enjoy the good weather in his island. Apart from the biological necessity to eat something, Crusoe also likes the taste of fruits he gathers. Fruits cannot be stored.

So we have a, daily utility function of the form

$$U = U(c, \ell),  \;\; \ell + L = T$$

$$U_c >0,\;\; U_{\ell}>0,\;\; U_{cc} <0, \;\; U_{\ell \ell} <0,\;\; U_{c\ell} =U_{\ell c} \geq 0$$

The last assumption on the cross-partial seems like the more reasonable one.
$\ell$ is leisure and $L$ is amount of work, and $T$ the maximum amount of time that Crusoe can work (say, $16$ hours). We also have a  "fruit-gathering" function

$$Q = f(L) = AL^a$$

We can reasonably assume that we have decreasing marginal product of labor (due to the body getting tired going up and down all these trees), so $0<a<1$.

Since fruit cannot be stored and capital is absent, the only optimization problem that makes sense here is a static one, meaning $c=f(L)$.

Then we want to max over $L$ the function $U[f(L), T-L]$.

The f.o.c. is

$$\frac {\partial U[f(L), T-L]}{\partial L}\equiv G = U_c[f(L), T-L]\cdot f'(L) - U_{\ell}[f(L), T-L] = 0$$

and the s.o.c is

$$ \partial G/\partial L = U_{cc}\cdot f'(L) - U_{c\ell}\cdot f'(L) + U_c\cdot f''(L) - U_{\ell c}f'(L) +U_{\ell \ell} <0$$

Given our assumptions, this expression is everywhere negative, so we have our maximum.

We want to examine what happens as $A$ in the fruit-gathering function increases. Using the implicit function theorem we have, around the solution,

$$\frac {dL}{dA} = -\frac {\partial G/\partial A}{\partial G/\partial L}$$

We know that the denominator is negative, so together with the minus sign in front becomes positive. Therefore

$$\text{sign}\left\{\frac {dL}{dA}\right\} = \text{sign}\big\{\partial G/\partial A\big\}$$

$$= U_{cc}\cdot[ \partial f/\partial A ]\cdot f' +[\partial f'/\partial A]\cdot U_c  - U_{\ell c}\cdot [\partial f/\partial A] $$

This expression is of ambiguous sign, which is a first indication that things may not be that straightforward after all.

To validate the conjecture of the OP we would need to obtain,

$$\text{sign}\left\{\frac {dL}{dA}\right\} < 0 \implies U_{cc}\cdot[ \partial f/\partial A ]\cdot f' +[\partial f'/\partial A]\cdot U_c  - U_{\ell c}\cdot [\partial f/\partial A] < 0$$

$$\implies U_{\ell c}\cdot [\partial f/\partial A] >  U_{cc}\cdot[ \partial f/\partial A ]\cdot f' +[\partial f'/\partial A]\cdot U_c$$

$$\implies U_{\ell c} >  U_{cc}\cdot f' +\frac {\partial f'/\partial A}{\partial f/\partial A}\cdot U_c$$

Using the first order condition, we can substitute for $U_c = U_{\ell}/f'$, so

$$\text{sign}\left\{\frac {dL}{dA}\right\} < 0 \implies  U_{\ell c} >  U_{cc}\cdot f' +\frac {\partial f'/\partial A}{\partial f/\partial A}\cdot [U_{\ell}/f']$$

Now

$$\frac {\partial f'/\partial A}{\partial f/\partial A} \cdot \frac {1}{f'} = \frac {(a/L)L^a} { L^a} \cdot \frac {1}{(a/L)AL^a}$$

$$= \frac {1}{f} = \frac {1}{c}$$

So

$$\text{sign}\left\{\frac {dL}{dA}\right\} < 0 \implies  U_{\ell c} >  U_{cc} \cdot f'+ U_{\ell}/c$$

and re-arranging while multiplying throughout by $c/U_c$ and using the f.o.c. again, we get

$$\text{sign}\left\{\frac {dL}{dA}\right\} < 0 \implies  f'\cdot (RRA_c-1) > - U_{\ell c}\cdot c/ U_c$$

where $RRA_c$ is the coefficient of relative risk aversion related to consumption.

So we see that if $RRA_c\geq 1$, which is the usual assumption, this inequality is certain to hold and so indeed higher productivity will lead to less time spent working... so why reality does not conform with our theoretical results?

But it does. Historically, the amount of time spent working has been declining . The problem with the OP's question is that the phrase "we do as much as we can" is contaminated by framework effects: if what happens around me is people working, say, $10$ hours a day, $5$ days a week, and I work $11$ hours a day, $6$ days a week, I tend to think that, since I exceed the standard around me, "I do what I can", being oblivious to the fact that people used to work $16$ hours a day, $7$ days a week, with perhaps a few days per year off at best. So no, we do not really "do as much as we can".


Most profitable conversion of stock into money When Forbes-lists of top billionaires are published we are usually aghast of their riches and statements such as "the 8 richest people own as much as the poorer half" are disseminated.

I was wondering however, most of these top billionaires have a huge concentration of their wealth in the form of stocks/securities. Is this kind of wealth then calculated as "number of stocks possessed x latest stock price"? That would entail a subtle commitment/choice because of the reason that when a large shareholder such as a billionaire sells of his stake in a short period time (to consume the proceeds) this sudden excess of supply in shares deflates the stock-price thus rendering the total proceeds lower than the value previously proposed.

Q: is there a simple way to answer the question how large the proceedings can optimally be if a large shareholder wishes to liquidate his shares in a time-interval $T>0$ (assuming something like a rational-markets hypothesis applies to all other parties)?

Yes.  There is a good chapter on this general question in The Valuation Handbook book by Ashok Abbott.  It is a whole chapter so it is too long reproduce here.

Shortened down, he shows that there is a half-life effect given the amount of volume that a dealer normally carries and how long it normally takes them to liquidate a position.

ISBN-10: 0470385790


How do 'econometric' explanations differ from 'economic' ones? I am interpreting some coefficients of a regression model and have been asked to, first, give an 'economic' explanation and then an 'econometric' explanation as to why coefficients differ as more variables are added to the regression. I don't quite understand, however, how my answers should differ.

Econometric and economic explanations are not some standardized terminology so it is often best to clarify with the person asking you but generally speaking, when someone asks for economic explanation they are looking for explanation in terms of an economic theory or underlying economic relationships. If someone asks for econometric explanation they are likely looking for an statistical explanation.
An example related to changing coefficients lets suppose we have models:
$$ Wage = 0.5 + 5 EDU   $$
$$ Wage = 0.6 + 10 EDU + 6 EXP  $$
Where EDU is education and EXP experience and lets also say we know $cor(EDU,EXP) \neq 0$.
An economic explanation would be that from economic theory we know that wages depend on your marginal productivity which is some function of both education and experience. In the first regression we include only education and do not control for what the peoples actual experience is. Since people who have higher education might have less experience on average than people with less education (due to all that time spent in school) so we expect the coefficients to change when we actually control for the fact that not all people have the same experience.
An econometric explanation would be simply that we know from econometrics that in the more parsimonious model (assuming the more general model is true) the estimated beta coefficient in this case will be given by
$$E[\hat{\beta_1}]= \beta_1 + \beta_2 \frac{\sum  (EDU_{i}-\bar{EDU})(EXP_{i}-\bar{EXP})}{\sum (EDU_{i}-\bar{EDU_1})^2}$$
we know that $cor(EDU, EXP) \neq 0$ and that $\beta_2 \neq 0$ so we also know that coefficient $\beta_1$ must change between the regressions.
However, again note that your question is a soft-question depending on where you study teachers might have slightly different understanding of this so you should always ask. Furthermore, you should also inquire on how rigorous you have to be when providing both economic and econometric explanations. Depending on the level of your class and university overall simple textual economic explanation like I provided here would not suffice and the econometric one could be arguably done better. The above is just quick example in order to make it easier to understand differences between them.


Stackelberg Oligopoly 3 firms Imagine that there are 3 firms in a monopolistic market, F1, F2 and F3. Firms 1 and 2 are incumbent firms and act simultaneously whereas Firm 3 observes the actions of both firms before deciding whether to enter.

All firms face a market price of $P(Q) = 16-q_1-q_2-q_3$. Incumbent firms face a production cost of $C_i (q_i) = 4q_i$ for $i= 1,2$. Firm 3 faces a production cost of $C_3(q_3) = 4 + 4q_3$. Find both firm 3 and firm 1's payoff.

I understand that I need to take firm 3's best response function which is
$$0.5  (12-q_2-q_1)$$
but I am not sure where to go from there. Do I substitute this back into the price equation? I tried doing this but it wouldn't yield any definitive answers. Thanks!

You are right that you first have to find F3's best-response function. F1 and F2 take as given this reaction of F3 to whatever they produce.
Hence, you plug this best-response function into the incumbents' profit maximization problem. In that way, you take care of the fact that the incumbents anticipate F3's reaction, indirectly determining $q_3$.

You should also check if the resulting reaction quantity $q_3$ is non-negative! It can be optimal to deter the entry of F3 completely.


Does land value tax create an incentive to merge land ownerships? LVT is "a tax on the unimproved value of land", and "in theory, it does not distort decision making". But if I own land then improvements such as buildings on my neighbour's land can easily increase the value of mine.

It seems like the total LVT payable would therefore be reduced if I sold my land to my neighbour and they paid tax on the entire estate at the value it would have had not been improved. This seems like a major distortion of decision making.

Some people strongly disagree that LVT is not distortionary:

  George was right that other taxes may have stronger disincentives, but
  some economists now recognize that the single land tax is not
  innocent, either. Site values are created, not intrinsic. Why else
  would land in Tokyo be worth so much more than land in Mississippi? A
  tax on the value of a site is really a tax on productive potential,
  which is a result of improvements to land in the area. Henry George’s
  proposed tax on one piece of land is, in effect, based on the
  improvements made to the neighboring land.

  And what if you are your “neighbor”? What if you buy a large expanse
  of land and raise the value of one portion of it by improving the
  surrounding land. Then you are taxed based on your improvements. This
  is not far-fetched. It is precisely what the Disney Corporation did in
  Florida. Disney bought up large amounts of land around the area where
  it planned to build Disney World, and then made this surrounding land
  more valuable by building Disney World. Had George’s single tax on
  land been in existence, Disney might never have made the investment.
  So even a tax on unimproved land can reduce incentives.
  ... Zachary Gochenour and Bryan Caplan have pointed out that while the
  surface value of land is more apparent, especially for farming
  purposes, many lands have hidden natural resources, such as gold,
  water, and oil. These resources require investment on the part of
  owners to discover and produce. “Information about the land can be
  considered an improvement in its own right.” To tax the entire, or
  even a large, value of the mineral resources would create enormous
  disincentives for exploration and production

The Concise Encyclopedia of Economics: Henry George (1839-1897 )

To answer this more definitively we'd need to take a stand on how we think the tax assessor would measure unimproved value. We could then ask if combined plots would distort this measure. I read the quote above as saying that the assessor looks at the sale prices of undeveloped lots in the area. But the value of these lots is necessarily higher due to the improvements of others (or even your own). Combining plots, to the extent that it makes big, valuable projects possible, distorts this measure but in the wrong direction. Some other method that tried to strip out the indirect value of your own improvements on the unimproved value of your own land but left in the increase in value of the improvements of others would bias towards combining properties.


Why bankrupt firms continue to operate? Many firms in the United States file for bankruptcy every year, yet they still continue operating. Why would they do this instead of completely shutting down?
Well, obviously there's a reason behind this like it's less costly somehow. But I can't understand it completely, though.
Can anyone explain this, please?

Declaring bankruptcy is a way to prevent creditors from seizing assets and pursuing lawsuits to recover what they are owed in a piecemeal fashion. It forces all parties to wait for a judgement that determines in what fashion various classes of creditors will be repaid.

In the United States, there are two main ways a private firm goes bankrupt - known as Chapter 7 and Chapter 11 (chapters of the bankruptcy act).

In a Chapter 11 bankruptcy, the firm aims to reorganise its debts. The typical outcome is that the original equity holders lose almost all control of the firm as subordinated debtors have their claims converted into equity claims. Other debtors may get paid only a percentage of their claim, or they are given new debt. What happens is determined by negotiation among the major creditors and firm management, overseen by the bankruptcy judge. By lowering the debt burden of the firm (and possibly eliminating pension obligations that cannot be sustained), the firm is hoped to then be profitable, and able to pay back the remaining debts.

Chapter 7 bankruptcy is a liquididation. All assets are sold, and then the proceeds are used to pay off debtors. However, the liquidation value of most assets is far below their carrying cost on the balance sheet, and so the recovery values are extremely low. The exceptions might be things like real estate, which another firm might be able to use in a more profitable fashion. From the prospective of creditors, the recovery value is typically much lower in a liquidation (barring special cases) - look at the prices for clothing in liquidation sales versus normal retail price. Industrial equipment is specialised, and the buyers know that this is a liquidation, and so they will only bid if prices are extremely cheap versus new equipment. However, if a firm tried Chapter 11 and fails to recover, it is more likely to give up and liquidate the next time.


Does easy credit in a region cause property to be more expensive? Does easy credit (e.g. lower minimum down payment, lower interest rate) cause housing prices (purchase, rent) in that area to be more expensive? Intuitively, this seems to be the case, because the availability of credit means more people can be a potential buyer, which drives up demands, which should increase price. Has there been an empirical research that backed this up or refuted it?

Theoretically, multiperiod borrow and lend models I am familiar with suggest that an increase in ease of credit (increasing the credit supply) should increase demand. This in turn raises the price of housing. So I believe your intuition here is correct.

Empirically, I am only familiar with one paper analyzing this relationship, which finds the same thing.

  ...because of geographic diversification, treated banks expand credit: Housing demand increases, house prices rise, but to a lesser extent in areas with elastic housing supply, where the housing stock increases instead.

Credit Supply and the Price of Housing

Favara and Imbs (2014)

http://www.jeanimbs.com/papers2_files/Favara_Imbs_May2014.pdf


Bananas and oranges in communist countries This is a question I wanted to ask for a long time. If you check the GDP or East Germany in 1989 and compare it to that of banana-producing countries you can see:

GDP in billions USD (1989):
East Germany: $160
Ecuador: $13.89
India: $296
China: $347.8
Philippines: $42.58
Vietnam: $6.293

GDP per capita USD (1989):
East Germany: $9679
Ecuador: $1390.21
India: $346.11
China: $310.88
Philippines: $705.58
Vietnam: $94.56

With these numbers, trading something for a banana should have been possible. The East German was better off than an Indian or Chinese, not to mention other banana-producing nations like Ecuador. I know that foreign currency was in hot demand in communist countries to repay debt, so maybe an account-deficit is the reason why the East Germans could not buy tropical fruits (i.e. they lacked the means to trade, foreign currency)? Still, these numbers make me wonder. Deals could be made in the banana-producing nation's currency. Some banana producers were/are communist. Maybe the numbers are incorrect?

EDIT: Here is a relevant quote:

  Bananas had been rare in the GDR because the imports, coming mainly
  from Ecuador, were limited due to lack of convertible currency.

Obviously, I disagree, there is always a way to pay and Ecuador was not the only producer. Note how West German ads made a permanent impression on the East Germans:

  Today the consumption of bananas in East Germany is 20 percent higher
  than in West Germany.

Also, the all-important image from those days:

there actually were some bananas in communist countries. There was just shortage of bananas and other products as well such as toilet paper etc.

As this article from Financial Times shows, there actually were some bananas in East Germany.

  Near the queue, locals were doling out used toys and bananas (the West Germans believed the East Germans didn’t know what bananas were). “But we had bananas from Cuba,” Meinfelder says in exasperation.

So there were bananas in communist countries but there was a shortage of them, and as with other products their availability for you dependent on your contacts and what (political) class you were member of (shopkeepers would often set aside high in demand products for friends). Prominent members of party had access to things ordinary people not in special shops reserved for them and so on.

Why there was a shortage of bananas?

Because, centrally planned economies are very inefficient when it comes to aggregating the information about what consumers want compared to market economies which aggregate the information using price system. Moreover, price system provides not just information to market participants but also gives them incentives to behave in a way to avoid surpluses and shortages on the market, whereas in the centrally planed economies there are no efficient mechanisms to achieve that.

For example, central planners might decide that the quantity of bananas they want to import should be some $x$ based on their calculation of how much bananas an average person could eat in a year. Afterwards, the central planners decide on price not in a way which they think the supply equates the demand (and in fact central planners are even not able to get such information since market mechanism is absent - so they cant do that even if they would wanted), but in a way they believe it is appropriate by making guesses or following some political/ideological/moral criteria.

For example, if a demand for bananas is given by $D_{b} = 100- p $, where $p$ is the price,  and supply of bananas is given by $ S_b= -10 + p$ (lets say this is the supply at which Cubans are wiling to send bananas to East Germany) then at a market price $p=45$ there will not be any shortage of bananas. At price $\$55$ people will demand exactly $45= D_b$ bananas and supply of bananas will also be exactly $45 = S_b$.

But if someone just arbitrarily decides to set price to $\$20$ - maybe the political leadership wants to make bananas affordable to everyone, the demand for bananas at $\$20$ will be $80 = D_b(\$20)$ while the Cubans will only be willing to supply $10$ bananas $S_b(\$10) = 10$. Hence people will want to buy 80 bananas but stores will only have 10 and there will be shortage. During shortages goods are often being allocated through personal favors, or first come first served system, or goods might be reserved for members of 'upper class' (i.e. politburo) and so on. This is why many communist countries experienced long ques shortages and economic malaise in general.


Is Marginal Revenue not always equal to the price? Marginal Revenue is equal to the price in perfect competition, but MR is also defined as the revenue obtained by selling one extra unit of the good, so how is it not always the case that MR=P ?
Revenue from one unit of a good = Price of the good.

Or is that definition not true, namely MR should be seen as $\frac{\partial R}{\partial Q}$ (which deosn't really make sense for goods that are discrete things, but let's just admit it does?)

No, marginal revenue is not always equal to the price. It would be if marginal revenue were defined as only the amount paid for the last sold unit, which is equal to the price by definition. However, selling one more unit of a good might have  implications on the market price itself, thus impacting the revenue as a whole.

Consider a monopolist selling a quantity Q1 in a given period at a price of P1. It is a monopolist so it is selling the maximum amount demand can bear at this price. I.e. Qd(P1)=Q1.
Suppose he is now deciding whether or not to sell an additional unit and prices for all goods he sells have to be uniform (i.e. no price discrimination). Since at the current price P1 no additional unit can be sold, the price has to drop to P2 so that: Qd(P2)=Q1+1.

What is the marginal revenue of this decision? It is not equal to P2 since this would ignore the effects on the revenue overall. Instead, the effect is : MR=P2+(P2-P1)*Qd(P1). So on the one hand there is the price of the last unit sold, but on the other hand there is the effect on all other units sold because the price itself has changed.

You are right that a demand curve theoretically speaking is not a smooth function, and shouldn't have a slope but instead be some kind of step-function technically speaking. However if this step function for example implies that every increase of 1 in the price means a decrease of say 2 in quantity demanded, then nothing is lost in making it a linear function of the form Qd=a-2P.

So yes your last definition is correct.


Rigorously Defining Newcomb's "Paradox" I was surprised to find that we did not have a question on this Stack Exchange on this particular problem in decision theory. So I have chosen to add a question on Newcomb's Paradox, though I would like to limit the scope of it to its economic considerations more than its philosophical considerations.

For those unfamiliar with the problem, here is the usual formulation of the problem.

You are presented with two boxes.

Box A is clear and has \$1,000 in it.
Box B is opaque and either has \$0 or \$1,000,000 in it, which is decided by another player, let's say a machine here.

You can choose to take just Box B, or both Box A and B, but before you choose, a machine makes a decision about what is in Box B, based on what it thinks you will do. The machine has played this game many times before and empirically is almost always correct in predicting what the player will do.

If it thinks you are going to choose both boxes, the machine will place \$0 in Box B.
If it thinks you are going to choose just Box B, the machine will place \$1,000,000 in Box B.

Empirically, people are split on whether to play the one box or two box strategy. The intuition for both cases goes likes this.

For those who pick one box, the intuition is that if the machine is almost always right, then the expected value/utility of picking just Box B will be much much higher than picking both boxes. So obviously one should pick just Box B and not be greedy.

For those who pick two boxes, the intuition is that picking both boxes seems to be a dominant strategy. If the machine has already picked putting nothing in Box B, it doesn't hurt, and can only help, if you pick both boxes. If the machine has already picked putting \$1,000,000 in Box B, then...well you should still want both boxes!

So what's the rub? Philosophers like getting into the weeds with this question in discussing causality or free will. But perhaps one criticism of this thought experiment is that the scenario described here is not rigorously defined within the realm of game theory. The machine's only goal is to predict the player's move correctly, but it does not actually have a defined payoff for making the correct prediction. One can map the set of choices and player payoffs as a tree, where the player cannot observe the choice of the machine, but the information set needs more elaboration than this. How does the machine make its prediction exactly so that it is "almost always right"? Why does the machine get to completely preclude mixed strategies and just...know what the player will do most of the time? Essentially, the whole game, strategies and payoffs and information, seems all very hazy. Should it even be considered a game? Or is this just a weird decision theory question?

With paradoxes, trying to add in extra assumptions, or showing why an existing assumption is ill-defined, this can go a long way to providing a possible solution to a paradox. So my question(s) are:

  How could one alter the formulation of Newcomb's Paradox to make it decisively analyzable with game theory or decision theory, and what strategy/decision should the player make in that case?
  If you would choose not to alter the formulation of the paradox, what is the correct analysis of the problem?

Two ending points.

$^1$ I hope I have formulated my question so that there could be multiple correct answers that are objectively correct, and not just opinion based.

$^2$ If you think Newcomb's Paradox is just so incoherent that one can't really alter it without really altering what makes the paradox interesting, you can talk about that too. I am not asking that as a question because I think that would be too opinion based.

In order to start making this tractable, I'd start by stating in which order the two events – the player making their choice, and the machine deciding how much money to put into box B – happen. There's two options:

First, the machine deposits money into box B (based on a guess as to how the player will choose); the player chooses afterward.
First, the player chooses; the machine deposits money into box B afterward.

(Technically, there's a third option: both actions being performed at the same time. I'd consider this to be equivalent to the first, in that the machine cannot observe the player's actual choice, and the machine's choice is a given for the player.)

The first option is not interesting as a one-off game, as choosing both boxes is clearly a dominant strategy. However, it would be interesting as an iterated game where the player's goal is to maximize their total payout, while the machine's goal is to minimize it. Obviously the player's optimal strategy would depend on the strategy (programming) of the machine, and vice versa. In order to identify overall good strategies, one could perhaps come up with different strategies for both player and machine, pit them against each other over a certain number of rounds, and see which strategy is robust against a wide variety of adversary strategies, the way that Axelrod did for prisoner's dilemma strategies in the early 1980s.

For the second option, the machine's decision-making process needs to be clarified; what does it mean for the machine to be "almost always correct"? I'd implement this as follows: the machine has access to an oracle that will tell it the player's choice, but which, with probability $p > 0$, will give an incorrect answer. The machine always follows the oracle and puts \$1,000,000 into box B iff the oracle says the player did not choose both boxes. This scenario could then be analyzed using standard tools, and the player's optimal strategy determined for both one-off and iterated games, depending on the value of $p$.


Comparative cost of public transport Is there a good database comparing the cost of public transport? I found this one and this one but they cite no sources so have no idea how they were constructed. Also, it is for a given period. Ideally the database should have more years. I've searched in OECD and world bank without success. Help please! :)

The world bank group has a Urban Transport Data Analysis Tool (UT-DAT) located here: https://www.worldbank.org/en/topic/transport/publication/urban-transport-data-analysis-tool-ut-dat1

It has an excel file that has some data.  There is also Data.world  https://data.world/datasets/transportation

There is Global Mass Transit website but its a paid service with some free options:   https://www.globalmasstransit.net/index.php

This Wiki site here might be a better option for you on free public transportation data links:
https://www.transitwiki.org/TransitWiki/index.php/Publicly-accessible_public_transportation_data

The world bank has Public private partnerships investment in transport (current US$).
Which are contractual relationships typically between a state or local government, who are the owners of most transportation infrastructure, and a private company.

https://data.worldbank.org/indicator/IE.PPN.TRAN.CD

This looks like a hard find.


Do patents foster innovation? I'm looking for a good meta analysis which answers the question if patents are generally beneficial to economy or not. Some papers I've read claim they are indispensable, other say it depends on the field. I'm looking for a current state of the art meta analysis / review.

This article is from 2002, but it does a pretty good job of summarizing the pros and cons and has a section on normative decisions. Here is the abstract:

  In this paper, we review the economic effects of intellectual property rights and specifically address the economics of the patent system. The production and dissemination of new knowledge is fraught with market failures because knowledge is a public good. Patents provide a second-best solution to the resulting appropriability problem. We review the main benefits and costs of the patent system, focusing on the role that patents play in providing incentives for innovation, in promoting the dissemination of knowledge, and in helping technology transfer and commercialization of new technology. From a more normative perspective, we address the questions of what the features of an optimal patent system are and whether the patent system is socially desirable. We examine the problem of the optimal length and scope of patent protection, both for the case of a single innovation and for the richer case of cumulative innovations. Finally, we review the issues related to how the patent system influences the market structure and research and development investments.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1317&context=card_workingpapers


GMM - when a model is identified Suppose we are using GMM to estimate the model $y=m(x;\theta_0)+u$ (for some function $m$ and $\theta_0 \in\mathbb{R^p}$)  and we are using the moment condition: $\mathbb{E}[g(\theta_0)]=0$ where $g:\mathbb{R^p}\rightarrow\mathbb{R^p}$ so the model is just identified. My question is how do we know that our estimator $\hat\theta$ is not dependent on the weight matrix?

Thanks!

In the exactly identified case, it is natural to assume that a unique $\theta$ satisfies $\bar{g}(\theta) = 0$, because the number of parameters is equal to the number of equations. Let $\hat\theta$ denote such $\theta$ value.

When $W$ is positive definite, $\bar{g}(\theta)' W \bar{g}(\theta) \ge 0$ (because $W$ is positive definite), and $\bar{g}(\theta)' W \bar{g}(\theta)$ attains zero if and only if $\bar{g}(\theta)=0$. That is, the global minimizer of $\bar{g}(\theta)' W \bar{g}(\theta)$ equals the solution to $\bar{g}(\theta)=0$, which is $\hat\theta$, for whatever positive definite $W$ matrix. Thus, $W$ is irrelevant.

Note that this argument does not hold if $W$ is not positive definite. For example, if $W$ is positive semi-definite but not positive definite, then the GMM estimator may not be unique.


CES: Production function: Elasticity of substitution $\sigma = 1/(1 + \rho)$ I have to prove that $\sigma = 1/(1 + \rho)$ for the CES production function:

\begin{align}
q = (l^\rho + k^\rho)^\frac{1}{\rho}
\end{align}

I found out that I need to solve the following equation:
\begin{align}
\sigma = \frac{\frac{d(k/l)}{k/l}}{\frac{dRTS}{RTS}} = \frac{d(k/l)}{dRTS}\frac{RTS}{k/l} = \frac{d(k/l)}{d((k/l)^{1-\rho})}\frac{(k/l)^{1-\rho}}{k/l}
\end{align}

But i just don't know how to rewrite this expression to $\sigma = 1/(1 + \rho)$

The production function is:
$$q = (l^\rho + k^\rho)^\frac{1}{\rho}$$
The MPL and MPK are respectively:
$$q_l = \frac{\partial q}{\partial l} = \frac{1}{\rho} \cdot (l^\rho + k^\rho)^{\frac{1}{\rho}-1} \cdot \rho\cdot l^{\rho-1}$$
$$q_k = \frac{\partial q}{\partial k} = \frac{1}{\rho} \cdot (l^\rho
+ k^\rho)^{\frac{1}{\rho}-1} \cdot \rho\cdot k^{\rho-1}$$
What is the rate that l can be substituted for k?

Where $f$ is a differentiable real-valued function of a single variable, we define the elasticity of f(x) with respect to x (at the point x) to be
$$\sigma(x) =  \frac{x f'(x)}{f(x)}\equiv \frac{\frac{df(x)}{f(x)}}{\frac{dx}{x}}$$

Do a change of variables such that $u = ln(x)$ ($\rightarrow x = e^u$) and $v=ln(f(x))$ ($\rightarrow f(x) = e^v$)
Note that $v' = f'(x) / f(x)$ and $u'=\frac{1}{x}$ so that
$$\frac{v'}{u'}=\frac{\frac{f'(x)}{f(x)}}{\frac{1}{x}} = \sigma(x)$$
Note that this is also the result you get by solving for $ \frac{d ln f(x)}{d ln(x)}$ because  $ \frac{d ln f(x)}{d ln(x)} = \frac{d v}{d u}$ which we solve via the chain rule:
$$ \frac{d v}{d u} = \frac{d v}{d x} \cdot \frac{d x}{d u} = \frac{f'(x)}{f(x)} \cdot x $$
which happens to be exactly the definition of $\sigma(x)$.

Now let's tackle your elasticity problem.

$$ ln(\frac{q_k}{q_l})= log(\frac{\frac{1}{\rho} \cdot (l^\rho + k^\rho)^{\frac{1}{\rho}-1} \cdot \rho\cdot l^{\rho-1}}{\frac{1}{\rho} \cdot (l^\rho
+ k^\rho)^{\frac{1}{\rho}-1} \cdot \rho\cdot k^{\rho-1}}) = ln (\frac{l}{k})^{\rho-1} = (\rho-1) ln (l/k) = (1 - \rho) ln (k/l)$$
$$ \Rightarrow ln (k/l) = \frac{1}{1-\rho} \cdot ln(\frac{q_k}{q_l})$$

So $\sigma = \frac{1}{1-\rho}$


Find the optimal demand functions for capital and labour for this firm I'm trying to solve this question which states:

Suppose that a profit maximizing producer has a production function described by Q = K^3/4 L^1/4 and faces the general isocost line (TC = rK + wL).

Find the optimal demand functions for capital and labor for this firm.

Here's what I've done and know:

I've solved for the MP1(labor) and MP2(capital):
MP1 = 1/4 (K^3/4 * L^-3/4 )
MP2 = 3/4 (K^-1/4 * L^1/4 )

I also know that MP1 / MP2 = w / r.

Can someone point out a suggestion to solve for K and L, the optimal demand functions?

Thanks

A firm requieres capital $K\in\mathbb{R}_+$ and labor $L\in\mathbb{R}_+$ to produce the final good $Q$. The technology is of Cobb-Douglas type $Q:(K,L)\mapsto K^{\alpha}L^{1-\alpha}$, here $\alpha=0.75$. Denote the capital rent by $r$ and the worker's wage by $w$. Production costs are then given by $C:(K,L)\mapsto rK+wL$. Instead of maximizing profits, the firm wants to minimize costs to produce a given quantity $\bar{Q}>0$ (look up the duality of $\min-\max$ problems in producer theory). We end up with the following programm
\begin{align}
\min_{K,L}~C(K,L)\quad\text{s.t.}~~Q(K,L)\geq\bar{Q}.
\end{align}
Which is
\begin{align}
\min_{K,L}~(rK+wL)\quad\text{s.t.}~~K^{.75}L^{.25}\geq\bar{Q}.
\end{align}
Set up the lagragian
\begin{align}
\mathcal{L}=rK+wL+\lambda(\bar{Q}-K^{.75}L^{.25}).
\end{align}
Note that the constraint is binding (Why? Look that up too!) The FOCs are given by
\begin{align}
\frac{\partial \mathcal{L}}{\partial K}=0\\
\frac{\partial \mathcal{L}}{\partial L}=0\\
\frac{\partial \mathcal{L}}{\partial\lambda}=0
\end{align}
Solve for $K$ and $L$.


Price optimization with demand forecast I have one year sales data of a retail company and lets say I am forecasting the next month sales for the product. I have got the sales using time series in R. Now I want to forecast the price as well. I want to build a model using both the demand and price. My function should be f(DP) where D is demand and P is price. I want to maximize Revenue or Profit where Revenue=DP.

As of now, I forecasted sales and did a linear programming on Price itself to get optimal price of a single product. I want my model to be robust but this is chicken - egg theory where demand forecast is dependent on the price and price is dependent on demand. Please help by sharing some theories which would better fit for this or some R models.

First, You may model the sale or demand as a function of price. You can use a regression model to control for controls. This regression will provide you with price elasticity of demand which show how your demand is sensitive to a change in price.
Then, you may use the above relationship to plug in for sale in the optimization step. This way you only solve for the optimum price.


What is the probability of an unemployed worker receiving no job offer during a time period? we are currently covering one sided search models and I had a question for you all. I kind of understand the raw calculus behind finding the probability of a job offer over a time interval h, but what about the reverse. Suppose we have a time interval h, what would the probability for an unemployed worker to receive no job offer during said time interval h? Would it just be 0?

Unless I misunderstand the question these seem to be complementing events with probabilities $p$ and $1-p$.


Why regulate the financial world rather than take over some of the services? The government regulates some of the behavior of financial markets. Understandably, especially considering the crisis.

But would it not be easier if the government overtook some of the aspects of the financial markets? In that case, regulation would not be necessary, since the government was in charge of that particular aspect.

For example, say the government overtook the business of giving out mortgages to house buyers. In this case, the government would not have to worry about banks giving out subprime mortgages, securitizing them, and selling them off, the government would be in charge of the entire process and since the government does not seek profit-maximization, it would make sure to do it right.

Governments do offer financial services. It varies from country to country, and changes over time. The political drift has been to reduce the role of government since the 1980s, so this role has generally shrunken.

For example, some countries had postal banking - citizens had basic banking functions offered at post offices.

I will just use some Canadian examples; other countries have similar programmes.

The Canadian government has a Business Development Bank, which helps new firms develop (website). It is taking on risks that commercial banks would be reluctant to take.

The Canada Mortgage and Housing Corporation (CMHC - website) has a programme of mortgage insurance that is compulsory for all high loan-to-value mortgages in Canada (“subprime”). The loans have to meet minimum risk standards, but the loan guarantee means that the private banks are not exposed to the risk of the mortgages. The Canadian housing market slowed down during the Financial Crisis, but fared better than the United States. The fact that the Canadian banks were insulated from the credit risk of risky mortgages was certainly a factor.

Returning to your question - why not expand the programme, and have the government completely take over the mortgage lending role? One obvious advantage for the government is that it is not forced to justify lending decisions to citizens - that is being done in the private sector. People could easily be concerned about favouritism in lending decisions if the government controlled all mortgage lending. For example, if the child of a politician gets a big mortgage when other people are being refused, it could easily turn into a political scandal. On top of this, there is the ongoing political argument between government control versus free markets. The objective of this website is to avoid opinion-based answers, so I will not dwell on that political debate.


Why doesn't the price of gold drop as mining occurs that produces more gold? According to my common knowledge, the price should drop when supply increases. Why doesn't the price of gold drop slowly as more gold is produced from mining?

You cannot reason directly from a price change. Prices may increase because supply has fallen or demand has changed. In general we can't distinguish between the two unless we know something about the demand and supply curve in particular and not just prices and quantities.

For example, when demand increases (the demand curve shifts to the right but supply curves are held fixed) this increases demand for gold at all prices. Which means that equilibrium quantity increases (more gold is produced) as well.

.

But that gold doesn't decrease prices. The only reason more gold was produced was because prices were higher. If prices fell in response to higher quantity produced the producers (who have the same supply function by assumption) would not produce more. So in response to a demand shock for gold prices increase in order to clear the market for gold. Otherwise there is not enough gold at the old prices.


Can somebody explain to me why exactly people necessarily had to starve under "communist rule"? So, all my life, I've been told certain things. One of the least controversial is the "truth" that if you pick communism for a country, people will automatically starve. Allegedly, this is because the rulers will (I frankly have no idea if this is even really part of communism) insist on having centralized factories producing food, and then ship this out to every corner of the country so that everyone gets fed, but due to human flaws (or something), the food never ends up where it should?

I've always been confused about this. If that does happen, surely they would not keep doing it for long? Surely their plan isn't to starve their own people to death? Why is it so important to have huge centralized factories and then ship out all the food/goods?

And I don't understand why "the human factor" applies here but not in a capitalist system (or other). And why can't they just have a bunch of local sub-factories which operate according to the same principles, for practical purposes?

I cannot imagine that all the factory workers and food truck drivers just sit around with their hands in their pockets and whistle all day while their fellow men starve, just because they are in a communist country. As lazy and stupid as people tend to be in general, it doesn't go to that extreme... does it?

Surely they have managers/bosses even in a communist factory/food distribution system?

I really hope that somebody will finally clear this up for me, because I'm clearly missing some crucial detail about all this, which people never want to tell me when they say that communism is so bad.

PS: I'm not a communist.

I would like to just add to +1 answer of @fizz.
It is completely true that dictators often are self interested but the problem with communism is not only this but the fact that many ideas that are according to self proclaimed communists at the core of communism are are inherently inefficient.
For example, many communists want to get rid of private property (See the history of economic thought by Grant and Brue).
But a problem is that private property is an irreplaceable institution necessary for economy to prosper (see any economics textbook for example Mankiws Principles of Economics). In fact the famine in communist Russia is often attributed to farm collectivization which took the ownership of the farms from farmers and put them into hands of state where people had little incentive to take well care of them. This being said some level of economic output is attainable even without property rights, pre-historic hunter-gatherer societies existed without them, but it is generally agreed that they are necessary precondition for sustained economic development (See Acemoglu & Robinson Why Nations Fail). Also, lack of property rights is actually the most cited cause of our current environmental problems i.e. over-pollution, over-fishing etc  (again see Mankiw's Principles of Economics) as absence of property rights creates the tragedy of commons.
There reason why lack of property rights leads to loss of output and efficiency is that without secure property rights people cant be sure they will be able to use their output in any way. A farmer would not produce any output if all crops are expropriated.  Furthermore, due to tragedy of commons in absence of property rights people are locked in prisoner dilemma where everyone is incentivised to overuse resources before anyone else has chance to already collect them.  There are also other issues and this is only short and surface level exploration of importance of property rights as full explanation would be way beyond the scope of this answer but I encourage you to explore it more fully in the sources I provided and works cited therein.
Moreover, communists often believe in radical egalitarianism (Again see Grant & Brue). As Marx himself wrote “from each according to his ability, to each according to his needs.” Now there is nothing wrong with believing inequality is bad and trying to reduce it but what many self proclaimed communist fail to grasp is that inequality is what gives people incentive to put in extra effort, and hence any society that wants to increase its standards of living has to have some inequality. If someone works hard and gets the same pay as someone who slacks of then what’s the point? People soon learn it’s better not to put extra effort - and consequently many communist countries eventually result to some sort of forced labor which is again much less efficient than free labor where people are properly incentivized. This does not mean that every single action in an economy needs economic incentives (narrowly defined) there can obviously be instances of altruism because peoples' utility can take into account the well-being of others (as famously alluded to already by Adam Smith in his Theory of Moral Sentiments). Moreover, people also can intrinsically value some work in itself - if you have any hobby where you produce something that would be an example of that.  But it is generally agreed upon by profession that no large economic system can function without a system that provides an economic incentives for people to produce goods and services optimally.
Even the goal of the proletariat dictatorship, in the Marxist-Leninist tradition is supposed to be true communism that is property-less, moneyless (i.e. based on barter and communal exchanges), classless (i.e. there are no workers no owners no classes at all) and stateless (Marxism is in its hart anarchist movement as state is only seen as temporary apparatus that dies out once the true communism is achieved).
However, as already mentioned above property, inequality (which implies some sort of class) are important. Money is also important in economics as it provides a solution the issue of double coincidence of wants which otherwise wastes precious time and other resources, and economists agree state is necessary for provision of public goods and very helpful in solution to many problems that are based on externalities. So even if we could achieve the true communism it would probably fail to deliver high material welfare standards.
In fact the only time in human history where the sort of society that Marx thought communism would be was actually in existence, was in prehistoric hunter-gatherer societies which were always living at subsistence level.
Hence often unappreciated fact about communist regimes is that they would often not work even if their leaders would be angels. To give you analogy, no matter how a good person you are if you want to cure people using homeopathy you won’t help them.
However, you should also note that communism as mentioned by Giskards +1 comment is badly defined. In economics communism does not even have a definition - you won’t find the term in many modern economic textbooks. The term communism is so often used and misused that it is meaningless. Trying to define it is as trying to define a deity - nobody will probably ever agree on single definition. Here I use the term communism as a system that would describe the ideologies and economic goals of Soviet Union or Maoist China.


Majority Rule and Single Peakedness Majority Rule will induce non empty choice set if individual preferences are single peaked

Is this statement true? I have some trouble in understanding the meaning of 'single peakedness' in context of this statement. Does choice set here imply that we need to find the, say, favorite alternative amongst the given ones? I understannd that Majority Voting is riddled with intransitivity. What does 'non empty' choice set imply ?

What I understand is that for single peaked alternatives, individual has a particular alternative of his choice and the alternatives that are away from the peak would be preferred less.
My concepts seem to be quite shaky. Please bear with me.

Suppose that A={a,b,c,....,z} is a finite set of social alternatives, and let P={>1,>2,....,>N} be a profile of strict preference orders on $A$ (where the set {1,2,...,N} indexes the voters).    We say that the profile P is single-peaked if there is some way to order the alternatives in A (e.g. in alphabetical order) such that, for each of the preference orders >n in P, there is some "ideal point" (say, h) such that

a<n b <n c <n ... <n g <n h >n i >n j >n .... >n  y >n z.

Note that the condition does not impose any particular preferences between, say, g and i, or indeed between any element of {a,b,...,g} and any element of {i,j,..,z}.  Note also that different voters could have different ideal points.  (So voter n has ideal point h in the above exampe, but maybe voter m has ideal point d....)  Note also that the question here is not whether a single preference ordering >n is "single-peaked" ---the question is that entire the profile P is single-peaked, meaning that we can find a single ordering of A such that all the preferences in P are single-peaked with respect to this ordering.  (In the above example, I used alphabetical order, but this was just for simplicity.  The question is only whether some order exists.)

Why is this condition useful?  Suppose you try to construct a social preference order >0 by determining the comparison between each pair of alternatives through a simple majority vote (as recommended by Condorcet).   So for example, for alternatives b and g, we will stipulate that b >0 g if and only if  b >n g for a majority of the voters {1,2,...,N}.  (For simplicity, suppose N is odd, so that majority vote never results in a tie.) We know that in general, this method does not result in a transitive preference relation.  (This is Condorcet's Paradox.)  However, if the profile P is single-peaked, then this method of "pairwise majority vote" always yields a transitive social preference order.  (This was discovered by Duncan Black.)   Furthermore, the "maximal" element of the resulting social preference order is the median of the ideal points of the voters.  (This is the famous Median voter theorem.)

In summary, if the profile P is single-peaked, then not only does majority rule induce a non-empty choice set (as you said), but this choice set is rationalized by a complete and transitive social preference order (obtained by pairwise majority votes), and furthermore we can say exactly what the choice set is (it is the median of the ideal points of the voters).


Interpretation of dummy variable : Random Effects Model I am running a RE regression and I have export similarity index between two countries as the dependent variable and have a dummy variable such as share a border(=1 if countries share border, 0 otherwise). This is, of course, time invariant.

My question is: how do I interpret the coefficient of this dummy variable? For example, if the coefficient is 0.15, how would I interpret it? I have gone through multiple papers but failed to find the interpretation. Please help!

Help will be greatly appreciated!

Thank you!

As a first pass, I would interpret as with any other dummy variable's coefficient. Assuming a linear model, when two countries share a border, their export similarity index rises, on average, by 0.15 when all other variables are held fixed.

If you're writing a report on this model, you'll obviously need to discuss at length what this actually means.  The result seems intuitive: countries that share a border likely share other similarities that would lead to their portfolio of exports having more in common than if the two countries were separated by some larger geological or political distance.


Differences between GMM and MSM? In wikipedia, the main difference between GMM and MSM(Method of simulated Moments) is in the former the moment/orthogonality conditions can be evaluated analytically, while in the latter they cannot and we have to use sample analogues.

However, in wikipedia and other texts, with GMM we also use sample analogues.

So, what is the difference between both methods?

Any help would be appreciated.

While in GMM one uses theoretical analytical moments, in MSM one uses simulated theoretical moments instead.

For GMM,

  [t]he method requires that a certain number of moment conditions were specified for the model. These moment conditions are functions of the model parameters and the data, such that their expectation is zero at the true values of the parameters. The GMM method then minimizes a certain norm of the sample averages of the moment conditions. (Wikipedia)

Crucially,

  In order to apply GMM, we need to have "moment conditions", i.e. we need to know a vector-valued function $g(Y,\theta)$ such that $m(\theta_{0})\equiv \mathbb{E}[\,g(Y_{t},\theta _{0})\,]=0$.

For SMM, values of functions of the data and the parameters are too difficult to calculate analytically. Essentially, we cannot calculate what the moments of the data are given the parameters; for example, we cannot calculate $\mathbb{E}(XY)$. Instead we simulate a large sample of $X$s and $Y$s and calculate $\frac{1}{n}\sum_{i=1}^{n}X_i Y_i$ (simulated sample, not the actual sample) to replace the theoretical $\mathbb{E}(XY)$. The rest is the same.


How to tell the difference between consumer and capital goods As a first year macroeconomics student I'm unable to understand if in rudimentary macroeconomic analysis that categorizes goods either as consumer or capital goods, with the latter being defined as "high-value , durable-use producer goods that undergo depreciation with employment in production process", the assets that a company posseses for use by its employees (like staff fridge) should be considered as a capital good or consumer good.

As in, should the comfort that these facilities extend to labour force be seen as an indirect contribution to the production process or not.

Any help would be greatly appreciated!

(Apologies if it's a basic question but I just couldn't find an answer elsewhere and exams are approaching.)

The only difference between consumer and capital goods is whether or not the good in question is purchased by a firm or a consumer.

The practical implications of this is whether or not this expenditure is included in $I$ or $C$ of the GDP equation.

Investopedia defines $I$ as: "the sum of all the country's investment, including businesses capital expenditures"

Going into detail on "capital expenditure":

  What is 'Capital Expenditure (CAPEX)'

  Capital expenditure, or CapEx, are funds used by a company to acquire or upgrade physical assets such as property, industrial buildings or equipment. It is often used to undertake new projects or investments by the firm. This type of outlay is also made by companies to maintain or increase the scope of their operations. These expenditures can include everything from repairing a roof to building, to purchasing a piece of equipment, or building a brand new factory.

It would appear that a staff fridge is a capital expenditure based on the above criteria because it contributes to maintaining the firms scope of operations.


Decision to make one side of a multisided platform the subsidy side I'm reading Matchmakers: The New Economics of Multisided Platforms by economists David S. Evans and Richard Schmalensee.

They describe how businesses often make a rational choice to allow one side of their "matchmaking" business to be the "subsidy side", i.e. the side paying a negative price, and the other side to be the "money side", as in the side that pays fees to the business. Here "matchmaking" means serving as an intermediary that lowers the transaction cost of connecting 2 or more populations, such as Visa connecting shoppers and retailers.

For example, PayPal pays (or used to pay) consumers for signing up for the service, so they're the subsidy side. Businesses typically pay the fees and are thus the "money side".

Is there an equation, formula, or inequality that describes how the business chooses which side to treat as the subsidy or money side?

Yes. For example, in Armstrong (2006), a monopoly platform sets the price for side 1, $p_1$, such that

$$\frac{p_1-f_1+n_2\alpha_2}{p_1}=\frac{1}{\eta_1}$$

where $f_1$ is the unit cost on side 1, $n_2$ is the number of consumers on side 2, $\alpha_2$ is the cross-side externality created by each side 1 consumer, and $\eta_1$ is the conditional price elasticity of demand on side 1.

Thus, side 1 consumers get subsidised (i.e. $p_1<f_1$) if

their demand is very elastic
they create a big externality for the other side.

That's the basic principle. Subsidise the guys who create a lot of value and who would run away if the price were high.

Thus, for example, nightclubs offer free entry to females rather than males if the owners believe that females are more price sensitive and that men care more than women about meeting members of the opposite sex (I let you decide for yourself whether that's true or not).

By the way, we can compere this equation to the one a normal monopolist would use:

$$\frac{p-f}{p}=\frac{1}{\eta}.$$

The reduction in price to internalise the network externality can clearly be seen.


Is a hedonic regression a reduced-form? If house prices are a function of location, physical characteristics and an error term i.e.

house_price = f (location, physical, e)

And I estimate a regression with the log of house price as my dependent variable, and a range of location characteristics (e.g. distance to CBD/coast/roads etc) and physical characteristics (e.g. no. bedrooms/bathrooms/garage etc) as regressors.

Can I call this my house price model? or is it a reduced-form estimation?

I think I can call it my model, because I am modelling how house prices are explained, but I am unsure.

In the benchmark hedonic price analysis, we assume a utility function of the general form

$$U = U(x, z_1,...,z_n)$$

where "$x$" stands for the composite good, and $(z_1,...,z_n)$ are the characteristics of good $y$ that are valued by the consumer. Assume for simplicity (as is usually done in the literature, and as is the OP case), that the consumer will only purchase just one unit of good $y$ (one house). The budget constraint in this case is

$$x+p(z_1,...,z_n) = M$$

where $M$ is the available income and $p(z_1,...,z_n)$ is the price of the good, expressed as a function of those same characteristics. This is an important departure from the standard consumer theory, because here, $p$ is not market price, but it is the "willingness to pay" of the consumer, decomposed into a function of many characteristics.

The lagrangean here is

$$\Lambda = U(x, z_1,...,z_n) + \lambda[M-x-p(z_1,...,z_n)]$$ and the f.o.c's are

$$\partial U / \partial x = \lambda$$

$$\partial U / \partial z_i = \lambda \partial p / \partial z_i, \;\;\; \forall i$$

So

$$\partial p / \partial z_i = \frac {\partial U / \partial z_i}{\partial U / \partial x}$$

Note that we have differentiated the price also, since again, this is not "the market price faced by the consumer" but his/her willingness-to-pay.

The hedonic-price econometric estimation is based on actual transactions, and so on data related to prices that consumers have actually agreed to pay.
So the specification

$$p = f(z_1,...,z_n, e)$$

estimates $$\partial p / \partial z_i$$ (and/or their binary-characteristic analogues), which is seen to be the ratio of the marginal utility of the characteristic scaled by the marginal utility of income.

If one assumes quasi-linear preferences of the form

$$U = v( z_1,...,z_n) +x$$

then $\lambda =1$ and so the marginal utility of the characteristic is the same as the marginal monetary willingness-to-pay for that characteristic.

On the basis of these remarks, I think you can conclude whether the econometric specification is a "reduced form" or not.


Predicting GDP contribution from market share I want to find the GDP share of several companies, but I have their market share.
Now we know that these two are not equal, and the market share to GDP ratio represents general overvaluation or undervaluation of shares.

Is it fair to assume that they are proportional though? That if a company has a high market share, it will also have a high GDP contribution?

What are the general trends regarding this?

They are not necessarily proportional.

GDP contribution is the value added by a company. You need to deduct the cost of inputs that are either imported or bought from another entity that is included in the GDP.

Even if two companies seem similar the value added can differ.

Let's compare two imaginary sneaker companies.

CheaperSneaker buys/manufactures sneakers from Asia for \$10 and sell them to department stores for \$20. \$3 are spent on labor and \$5 are used to buy various services from domestic companies. Profit is \$2.

Sales: 20
GDP contribution: 5  (25% of sales)

FancySneaker also buys/manufactures sneakers from Asia. The cost is \$12 per pair. \$5 are spent on labor and \$20 are spent on domestic services (mostly ad campaigns and PR firms). The sneakers are sold to stores for \$50. Profit is \$13.

Sales: 50
GDP contribution: 18  (36% of sales)

The GDP contribution is not the same.

As a general rule of thumb, highly profitable companies and companies with high domestic labor costs contribute a higher proportion of revenue to GDP.


Could low interest rates encourage savings? We normally assume that a lower interest rate will induce less saving as the returns on saving are lower. However, if a central bank committed itself to a low or even negative interest rate for a long period of time, could citizens come to anticipate that they will need to save more for their future/retirement as they won't be able to rely on interest payments anymore? Before 2007, when interest rates in the UK for example were often around 5%, people with a pension large enough would have been able to live off of the interest they earnt. Today, however, interest rates are closer to 0% so retirees would only be able to fund themselves by withdrawing their savings or risking their funds in investments elsewhere, something which many people either lack the knowledge to do or are too risk-averse to consider. Anticipating this, a rational person would likely save a great deal more, knowing that they'll be without any significant interest earnings during their retirement. So, could low interest rates lead to more savings in the long run?
Adair Turner briefly mentions this phenomenon in Chapter 8 of his book Between Debt and the Devil, describing how it occurred during the rapid growth periods in Japan, Korea and Taiwan where the governments followed policies of financial repression to increase loans to businesses and thus investment, with funds provided by households saving more.

tl;dr Yes it is possible, in fact it is possible even under the most basic macroeconomic consumption models (see chapter 8 in Romer's Advanced Macroeconomics textbook). This is because price change at any market (and interest rate is just price for savings) will always cause two effects. A substitution  effect and income effect.
Lower interest rate creates an intertemporal  substitution effect which diverts consumption from future to present causing people to save less.
The income effect depends on whether a person is net lender (saver) or net borrower. For net lender lower interest rate has negative income effect which indeed causes them to  consume less and save more. Opposite holds for net borrower though.
This being said empirically in most cases substitution effect dominates the income effect (see discussion in Romer Advanced Macroeconomics) and as mentioned in the above paragraph the income effect will lead to increase in savings only for net lenders. However, in those rare cases where income effect dominates it is possible to observe increase in savings after interest rate decreases.
Full answer:
The intuition mentioned above  can be seen from any standard consumption model. For example, consider simple two period model with bond market. In first period consumer budget constraint is given as:
$$C_1 + S_1 = Y_1 \tag{1}$$
where $C_1$, $S_1$ and $Y_1$ are consumption, savings and income respectively in period 1. Saving is done by purchasing a simple bond that carriers real interest $r$. Consequently in second period we will have budget constraint given by:
$$ C_2 = (1+r)S_1+ Y_2 \tag{2}$$
We can merge the two budget constraints through rearranging the first period budget constraint for savings $S_1=Y_1 - C_1$, which gives us the intertemporal budget constraint:
$$C_1 + \frac{C_2}{1-r} = Y_1 + \frac{Y_2}{1-r} \tag{3}$$
The equation 3 already showcases the income effect since if we can see that if interest rate decreases the right hand side of an equation 3 $Y_1 + \frac{Y_2}{1-r} $ which is the person's lifetime wealth also becomes lower.
Next the person will try to maximize their lifetime utility $U(C_1,C_2)$ and hence we have the following problem:
$$ \max U(C_1,C_2) \quad s.t. C_1 + \frac{C_2}{1-r} = Y_1 + \frac{Y_2}{1-r} \tag{4}$$
Now I will skip some derivation steps but we can solve the above problem with Lagrangian where from FOCs we will be able to find that marginal rate of substitution between future and present consumption is equal to:
$$ \frac{U'_{C_2}}{U'_{C_1}} = 1+r \tag{5}$$
And hence the marginal rate of substitution depends on interest rate $r$ where higher $r$ leads us to consume more in the future. Since saving $S_1=Y_1-C_1$, lower consumption today means we save more.
Now the optimum consumption will be found at the point where marginal rate of substitution is tangent to the budget constraint. Now in this can be seen from figure 8.2 in Romer's macroeconomics posted below where

Panel (a), the individual is initially at the point ($Y_1,Y_2$); that is, saving is
initially zero. In this case the increase in r has no income effect—the individual’s initial consumption bundle continues to be on the budget constraint.
Thus first-period consumption necessarily falls, and so saving necessarily
rises.
In Panel (b), $C_1$ is initially less than $Y_1$, and thus saving is positive. In
this case the increase in r has a positive income effect—the individual can now afford strictly more than his or her initial bundle. The income effect
acts to decrease saving, whereas the substitution effect acts to increase it.
The overall effect is ambiguous; in the case shown in the figure, saving does
not change.
Finally, in Panel (c) the individual is initially borrowing. In this case both
the substitution and income effects reduce first-period consumption, and
so saving necessarily rises.

Consequently it is theoretically possible that decrease in real interest will reduce the amount of saving provided that person is a net lender in their first period and provided that income effect dominates the substitution effect.  The case (b) is also the most relevant one since on net the wealth in any real life economy is positive so people must be on average savers rather than lenders, however even despite of that empirically substitution effect usually dominates the income effect on savings market. This why its very hard to find any evidence for lower interest rates leading to more savings with Japan, Korea and Taiwan perhaps being exceptions as argued in the source you provided.


How do economists explain why people contribute to Wikipedia? What incentives do contributors have?
I believe they earn no money. And usually, they earn no reputation either, because most of the contributions are anonymous.
I believe this is a public goods game. Have economists studied this "Wikipedia puzzle"? How might they explain it? To what extent would economists consider this a "puzzle"?

By "contributors", I mean those who edit Wikipedia pages, not those who contribute in other ways (e.g. donations).

I wouldn't underestimate the role of learning by answering.
Drafting a significant text typically forces a person to put their thoughts in order, to engage in research, and then to structure the information for the purpose of recording and conveying it. It is not unusual that further insights or questions emerge during this process, the answerer certainly becomes more familiar with the subject, and good communication is itself a skill that requires significant attention and practice to develop.
Moreover, publicising one's thinking (even to a very small audience) typically invites challenge and puts it to the test of what others think of it, which again tends to flush out all kinds of faults and oversights - either faults in the thinking itself, or faults in the way it has been articulated and formulated into words.
Clearly, the assumption embedded in this question is that communication is done purely for the benefit of the listener, and that knowledge transfer is done in a "jug and mug" style, but there is more truth than you might think in that hoary old claim that academics have much to learn from their students.
So part of the answer to why people freely labour to communicate on sites like Wikipedia (not to mention here at StackExchange) is therefore bound up in the question of what stake they have, not just in developing the knowledge they appear to possess, but also in developing and rehearsing all the broadly intellectual skills associated with the development, retention, and communication of knowledge.


Math in Melitz and Ottaviano (2008) I am reading Melitz and Ottaviano (2008), but I find it hard to understand some math in the model.

The preference is given by :

, which implies a demand function:

Then the paper says the "inverse demand function can then be inverted to yield the linear market demand system for these varieties":

But what operations do they take in getting the function $q_i$?

I am very confused on dealing with the $Q_c$ variable, which is defined to be :

Thanks.

hint:
sum equation (2) for all i and use the definition of $Q^c$, we get an expression for $Q^c$. then, substitute this expression into (2) and solve for $q^c$.


Price setting firms with cost reduction technology As part of my undergraduate studies in Industrial Economics, I am trying to solve the following question:

  Two price-setting firms are competing in a market for a homogeneous product. There are 10,000 people in the population, each of whom is willing to pay at most 10 for one unit of the good. Initially, both firms have a marginal cost of 5. Assume that the firms are not capacity constrained and cannot collude. What is the equilibrium in this market and what are the firms’ profits?

  Suppose now that a new technology becomes available that lowers the marginal cost to 3. The cost to a firm of purchasing this technology is 10,000. The firms must now simultaneously decide whether to adopt the new technology or not, and following this decision, they simultaneously set prices. Each firm can observe whether its rival acquired the new technology or not before setting its price. What is (are) the equilibrium (equilibria) in the market now?

I am struggling with both parts of the question but I think I got the answer to the first part more or less correct. It comes down to a Bertrand equilibrium where both firms get a fraction of the total market share, charge price equal to marginal cost (i.e. 5) and make 0 profit. Thoughts?

Now the second part is more tricky since the per unit cost will depend on the total output of the firm so it can spread the 10,000 investment over the number of units manufactured. Some loose thoughts:

I can see that if both firms decide to invest in the cost reduction technology and they split the market in equal parts, i.e. each produce 5,000 units, then they will need to charge 5 to not incur loses, i.e. there is no point in investing.
I also get that if a firm were to supply all the market, its average cost would be 4.

The above two points make me think that the possible equilibria are:

Both firms invest in the cost reduction technology and upon seeing that the other firm has also invested, decide to split the market into equal parts so as not to incur losses.
One firm decides to invest and the other doesn't, upon seeing that the other has invested, the non-investing firms decides to not compete since it knows the other firm will supply all the market at a cost slightly below its own marginal cost of 5. The investing firm supplies all the market and makes monopoly profit.

Option 2 doesn't look like a Nash equilibrium to me since both firms know they can get monopoly profit if they invest and the other doesn't and 0 profit if they both invest and split the market so they both decide to invest and the only Nash equilibrium is option 1.

Do I make any sense? Help appreciated.

Your reasoning for the 1st part is correct.

The 2nd part is a 2-period game. You should try to solve it by backward induction. First you go through all the 2nd period subgames. Then you can use the payoffs of the subgames and write up the investment decision subgame as a bimatrix game. However, the question is poorly written and as stated  this game has no Nash equilibria in pure continous strategies. Let's go through the reasoning as to why.

First, let's find the NE for all possible cases in the 2nd period.

Both firms have adopted the technology and have marginal cost 3. They will engage in a Bertrand game, set their prices to 3 and make 0 profit.
No firm has invested, both charge a price of 5 and make zero profit.
Now on to tricky case. What if one firm 1 has invested and firm 2 hasn't? It is crucial to know how firms split the market if they both charge the same price in this case. Since this is not given in the question, it is not really possible give a definite answer. I will go through two cases.

First, let's assume there's a 50:50 split with identical prices. Any equilibrium price above 5 can be ruled out by the usual Bertrand game argeuments. Firm 2 will never charge a price below 5, since it will make a loss. Firm 1 will never charge a price below 5, because given $p_2 \geq 5$ it could always increase it's profits by raising the price. So really the only candidate for an equilibrium is that both firms charge 5. However, if we assume a 50:50 split in this case, then firm 1 could increase it's profit by slightly decreasing the price and gaining the whole market. As a result, there is no equilibrium in this subgame, and hence no equilibrium for the overall game.

Second, let's assume arbitrarily that if both firms charge the same price, then all customers will buy from firm 1. In this case $p_1 = p_2 = 5$ is a Nash equilibrium.

You could then go on to find the NE of the whole game for different assumptions on the payoff split.


Economic Metrics (ROI, PP, NPW) So I am doing this project, which includes in calculating the Economic Metrics for a profitability analysis. I have calculated Return on Investment (ROI), Net Present Worth (NPW) and Payback Period (PP). But the problem is that the values for my project are not 'textbook like', if you can call that. I have the following.

ROI = -60 %/yr

PP = -4 years

NPV = -200 Million

I am having trouble in understanding what the above actually mean in terms of investment. The way I have understood is the following:

For ROI, since it is negative, therefore the cost of the investment is way higher than the current value investment. Looking at the formula, it should mean that the we have a 60% loss every year, with regard to the actual value of the investment.

For PP, this I don't fully understand. If the payback period is negative, does it mean that the investment is never reached, but instead 3 years worth of investment is also lost? Or that the investment period should be increased by 3 years in order to get profit?

For NPV, does it mean that the outflow is 200 million higher than the inflow? Is this based on inflation or something else.

I am not fully sure about the 'analysis' of these for an investment and their 'meaning'.

If anyone can help or give a hint, it will be highly appreciated.

Based on the first and second number it seems that your investment has more costs than benefits, so if all those flows were to be brought to present value, the project will lose 200 Million. This is consistent with the fact that it has a negative return of $60\%$ on average. However, the pay-back period makes no sense. I think that you probably just applied a formula and since on average you are losing money every period ($60\%$), being in this situation one less year is considered by the formula as making that money (instead of loosing it), hence "the time that will take you to pay-back the investment" is -4 years. You probably don't want to present that number, since this is not its natural interpretation, and instead say that the project is never paid back.


In a context of globalisation and high wage inequality, why should governments help unskilled workers? With globalisation, wage inequality continues to be a strong issue for many developed nations.

What I seek to find out here is, why should we even do anything to help the unskilled workers?

From what I understand, having minimum wage laws and various skills training policies are put in place to help the unskilled. However, we should know that unskilled workers generally do not know economics. The main issue they are having is that they know the "poor is getting poorer, while the rich is getting richer." Given that, they do not understand that unskilled workers are gaining less from trade in comparison to skilled workers, and therefore are not helping themselves to "upgrade" and join the skilled force labour.

I know that there are countless manual, unskilled labour required and if the whole labour force is skilled, some would have to be forced into unskilled labour jobs. However when our society can reach that point in time, I assume the the wages of the unskilled labour would have also increased to a point where the wage gap is insignificant enough to draw some of the labour force towards unskilled jobs. But this is only possible if the country is closed off to foreign labour.

As a developed country, most of the labour force are already skilled workers. The reason why wages of the unskilled labour have not increased, in my opinion, is due to foreign labour. Labour from emerging markets i.e. China/Myanmar/Phillipines etc. are suppressing the wage growth of the unskilled labour force.

So as long as there are countries with large labour force that are "under-developed", wouldn't that mean no matter how much you try to help the unskilled workers, the influx of unskilled labour from emerging market eventually wipes those efforts away.

On the other hand, if we do nothing to help, the growth of an emerging market eventually catches up to that of a developed nation as growth plateaus progressively. We eventually reach a point in time where there are no longer any "undeveloped" countries. The unskilled foreign labour would much rather work in their respective countries then and the resultant would be more unskilled workers becoming skilled which increases wages for unskilled jobs, pulling wage inequality together.

What am I misunderstanding here?

After the exchange in comments, the OP appears to ask "why government intervention if the market will take care of the situation?"

Well we know that government intervention is advised when markets "fail" or, more accurately, are not characterized, at least to a respectable degree, by the ideal conditions required by theory in order for them to function efficiently.

But I will not discuss what could be the "market failures" in the specific case the OP discusses, and whether government intervention could actually improve things.

Instead I will give an extra reason why in principle, government intervention may be required: the speed by which market forces operate. This matters a lot from a socio-political point of view, and it should also matter from a strict economic point of view, because, the slower the pace of adjustment, the longer the period of inefficiencies. So even if market forces will eventually tend to reduce the skills-and-wage gap, it is important how long it will take. And if it takes, say, decades, government intervention could in principle be argued in favor in order to speed up the process.


What is an equilibrium generated by replication? Sorry this might be a little too rudimentary for you, but I'm not an Econ background. When I was doing exercises for MGW chapter 17 "Positive Existence of Equilibrium" I came across the following statement

  The consumers preferences are strictly convex, this implies that there is no equilibrium in the overall economy generated by replication.

What doe equilibrium generated by replication mean? I couldn't find it in the text.

Thanks in advance.

For each agent in the economy, create n agents with the same endowment and preferences. The result is the replication economy. Sometimes n is taken to infinity in proofs.
Chapter 17.I in Mas-Colell explains in detail. Related material is the regularizing effects of aggregation, appendix of Chapter 4.


Rival and non excludable products I learnt that if the service provided is of non-rival and non-excludable in nature, the problem of free riding occurs and the provider may not get a profit. I can understand how non-excludability results in free riding but I couldn't uderstand the effect of
  non-rivalry. In the book I read, street performance was cited as an example for non-rival and non-excludable service. The following is an excerpt from the book 'Day to day economics' by  Satish Y. Deodhar

  at a given market price, the relative buying power of different consumers might exclude some of them from buying the car or the toothpaste. In the case of the street-performing couple, this ‘excludability’ feature is missing, because they cannot prevent individuals—either physically or by charging an appropriate price—from viewing the performance. Thus, due to the non-rivalry and the non-excludability of the service which they provide, the problem of free riding occurs, and the market fails to deliver—ergo, the street performers cannot run a profitable business.

Is there any service that is rival and non-excludable? If so, how is it different from the previous case with regard to free riding?

To continue the example of the street performer:

Suppose there are two people offering the performer money, but in exchange they want her to perform different songs. Person A prefers song A while person B prefers song B. Whoever offers the higher sum gets their wish. In this case there is rivalry between the consumers. Yet there is also non-excludability: Even if someone loses the bidding war, they can listen to the song chosen by the other person.

Note that the rivalry results in higher profits than if both people preferred song A played, because then they would have had no incentive to bid against each other due to non-excludability.


Technical Analysts and Econometricians: A Question on Methods I've been reading the book Technical Analysis Explained by Martin J. Pring as a result of a conversation with one of my friends who said he did technical analysis but didn't apply the types of models employed by econometrician when forecasting (i.e ARIMA, VAR ect).

as I progressed through the book, I noticed though the methods were simple and required little knowledge of statistics but they worked very well. They call these methods as a part of trend analysis.

My Question: why are such methods not employed by more frequently by economists/econometricians?

Note: an example of such methods can be seen in the presentation by Martin Pring: Technical Analysis for Short Term Traders

why are such methods not employed by more frequently by
  economists/econometricians?

Because the so-called technical analysis ("TA") is overly simplistic and devoid of mathematical (or at least rational) basis.

The application of algebra, probability, time series, and other tools & disciplines does not guarantee accuracy of forecast, but at least that application provides a more robust framework with which to model financial data than what is achievable through TA. Just to mention one example, TA does not address arbitrage opportunities, which is a useful and consistent approach to pricing financial instruments.

  I noticed though the methods were simple and required little knowledge
  of statistics, they worked very well. They call these methods as a
  part of trend analysis.

There is a false sense of accuracy surrounding TA. Materials that teach or promote TA obviously will present instances where --in hindsight-- the method appears to work. But nothing in TA predicts, models, or at least explains the price trajectory of a financial instrument (let alone its timing).

I think that if/when TA supposedly "works", it is only because of a kind of self-reinforcing feedback: TA "indoctrination" inadvertently prompts TA adepts to reinforce that, say, a price-band (or however it is called) is about to be broken because the price of the stock has touched its limit twice. Thus, TA-based traders react by performing certain transactions expecting to profit from the supposedly imminent direction of the stock.


ARIMA modelling and Economic interpretation ARIMA models, from what I know, are atheoretical models in the sense that they don't provide us with meaningful economic interpretation of a process.
However in population forecasting, can ARIMA models be interpreted in a meaningful way?
i.e.

can $AR(1)$ process can be interpreted as:

population growth in period $t$ is a function of population in period $t-1$

can $MA(1)$ process can be interpreted as:

population in period $t$ is a function of a policy or ongoing event (like immigration or emigration) which has occured in $t-1$.

So we can think of an AR(1) process as:

$y_t = a*y_{t-1} +e_t$

where $e_t$ is some shock / noise process that we can't explain. Note that we can rewrite an AR process as an MA process where by tracing through we get

$y_t = a^2*y_{t-2}+a*e_{t-1}+e_t\approx \sum_{i=0}^{t-1}a^i*e_{t-i}$

So that an AR process is just the weighted sum of all previous shocks where $a$ is what determines the persistence of past shocks.

So then what does it mean to say we have an AR(1) process? Well it means that the outcome today is to some extent dependent on the outcome yesterday (as you yourself suggested). In an extreme case we can set $a=1$ so that we have a random walk process where

$\Delta y_t=y_t-y_{t-1}=e_t$

This implies that the outcome today depends entirely on the outcome yesterday and any additional change in the series is purely due to random noise. Alternatively if $a\geq1$ we would say the process is non-stationary or explosive while if $a<1$ then the process is stationary around the mean of the process or of the shocks themselves.

An MA process has a similar interpretation except we think of it more in terms of unexplainable shocks or noise with some degree of persistence. The important thing is that it is not really something we have a variable for in the MA case but rather this notion that the the process just depends on this noise component. It is more common to find these types of models for forecasting in finance where there's alot of movement but a less clear sense of what might be driving it.

In terms of population forecasting, the AR component could definitely be interpreted as you suggested, while the MA component is less easy to interpret. It's really just a sum of shocks that are otherwise unexplained. If you had an explanation for it (i.e. immigration etc.) then you would likely want to include that as an explanatory variable to model it explicitly rather than approximately through the MA process.


what percentage of a banks money do they lend Say a bank has 1 billion dollars deposited by individuals with bank accounts. How much of this does the banks lend/invest? Obviously it can't lend all of it or when I go to the bank there would be no money for me to take out. I realize this probably varies between institutions but in general about how much.

Also, what factors would contribute to the percentage they lend relative to the amount the bank has. For example, interest rates, inflation etc.

I'll put my comment as an answer and add one or two things. To see how much a bank lends in comparison to deposits, you can look at what is called the loan-to-deposit (LTD)ratio of banks in their annual reports. Usually it is between 60% and 90% but as you mentioned this can vary upon institutions .. And geographic areas as well ! For instance, in 2015 in the EU the average LTD ratio was 108% whereas in the US the average is about 79%. You can check per state the LTD ratio from data gathered by the Fed and the FDIC.

As to factors that determine this amount, I would probably put regulation as the first point. If I had to think about other macro points that could affect the LTD I would probably mention interest rate and in particular LIBOR rates as they tend to give an idea about the financial stress on the banking level and therefore to a certain extend the willingness for a bank to lend money and/or to require more liabilities.


What does increase or decrease in marginal utility mean in terms of quantity demanded? According to the definition of marginal utility " it is the utility or satisfaction derived from the consumption of an additional unit of any commodity."
So, the question is what does increase or decrease in Marginal Utility of a good, let's say X, will mean and how we can relate it to quantity demanded?
This whole thing came while I was going through Edgeworth-Pareto definition of Complementary and Substitute goods. Thanks in advance.

Typically, we have concave, increasing utility functions. So that means, the more you consume of a good x the more utility you have. However, the marginal utility (the first derivative of the utility function) is decreasing in consumption. So each additional unit of consumption has less additional value than the one before.
A simple example would be food. If you're starving, that first bite of food has the highest utility. But one you get full, additional bites will only have a little additional utility. So the more you consume, the less satisfaction from each additional bite.
In this sense, a higher marginal utility, means a lower level of consumption. That could mean a higher demand.


Are there internationally published sources of trade sanctions? How to implement embargoes with respect to a trading company?

Let's assume i am a small trading agent which assists and guides small exporters and importers while keeping embargoes and light sanctions under considerations. My source of info regarding sanctions are workers of other big players. I usually get help from them in order to declare a trade clear.

I know that United Nations publishes Sanctions Lists of banned Individuals and Companies, I also know that Banks and Exchange companies have software solutions to screen a name against these lists.

These lists are not enough for Trading as an embargo usually includes source, destination and product being traded.

Are there any Internationally published sources of embargoes which can be consulted? Is there an automated software solution (free or cheap) to screening a trade?

The following site might help you out: https://www.globaltradealert.org


The Case for Basic Income in developed and underdeveloped countries From what I can tell, the idea of the basic income guarantee is very popular in some circles as an excellent alternative to a lot of modern welfare systems.

Has anybody developed a theoretic or empirical model in which minimum income is tested? In this model, what are the necessary and sufficient conditions for such a model to be preferred to a more traditional alternative?

If anyone has suggested readings on the topic, that would be appreciated as well.

Thanks to densp for identifying this paper.

It refers to a major pilot project undertaken in Namibia

Background:

The Basic Income Grant (BIG) pilot project took place in the Otjivero-Omitara area, about 100 kilometres east of Windhoek. All residents below the age of 60 years receive a Basic Income Grant of N$100 per person per month, without any conditions being attached. The grant is being given to every person registered as living there in July 2007, whatever their social and economic status.

Before the pilot project, the area was characterised by unemployment, hunger and poverty.

Conclusions:

Since the introduction of the Basic Income Guarantee (BIG), household poverty has dropped significantly. Using the food poverty line, 76% of residents fell below this line in November 2007. This was reduced to 37% within one year of the BIG.
There was a dramatic increase in economic activity. The rate of those engaged in income generating activities (above the age of 15) increased from 44% to 55%. Thus the BIG enabled recipients to increase their work both for pay, profit or family gain as well as self-employment. The grant enabled recipients to increase their productive income earned, particularly through starting their own small business, including brick-making, baking of bread and dress-making. The BIG contributed to the creation of a local market by increasing households' buying power. This finding contradicts critics' claims that the BIG would lead to laziness and dependency.
Huge reduction in child malnutrition from 42% to 17% in 6 months.
Increase in school attendances (non attendance due to financial reasons dropped 42%)
Drop in crime (theft down 42%)
Estimated cost for a nationwide program in Namibia would be 2-3% of GDP. Not cheap, not unaffordable either.

All thing considered, the author of this report seemed pretty happy with the outcome. There were some issues impacting the data. Since it was a localised study, there was a fair bit of migration towards the treatment area. The long term impacts are not yet known as well.

Additional resources:

Haarmann, Claudia; Haarmann, Dirk; Jauch, Herbert; Mote Hilma et al 2008. Towards a Basic Income Grant for all. Basic Income Grant Pilot Project. First Assessment Report, September 2008. Windhoek

Kameeta, Zephania; Haarmann, Claudia; Haarmann, Dirk; Jauch, Herbert 2007. Promoting employment and decent work for all - Towards a good practice model in Namibia. - Research Paper - Presentation to the United Nations Commission for Social Development. Windhoek

Haarmann, Claudia; Haarmann, Dirk (ed.) 2005. The Basic Income Grant in Namibia. Resource Book. Windhoek


Marginal Rate of Substitution for perfect complements I have come across the following problem:
Determine the marginal rate of substitution MRS(x1, x2) at point (x1, x2) = (5,1) for the following function:
u(x1, x2) = min(x1, x2).
The solution is that the MRS is undefined at that point.
However, I don't understand why that is. With this utility function, we get an income expansion path that goes exactly 45 degrees from the origin, because the two goods are alway consumed in equal quantities.
And as far as I know, the MRS of such a function (u(x1, x2) = min(αx1, βx2)) is only undefined at the exact angles of these curves, i.e. where x2 = (α/β)x1. In the problem at hand, however, we have x2 < (α/β)x1, i.e. 1 < 5.
Shouldn't this mean that the MRS at the point (5, 1) is actually 0 and not undefined?

I think this is sort of a trick question.
First, you are completely right MRS is undefined at the kink - this is trivial MRS is the slope of indifference curve, which in this case is L shaped, and derivatives are not defined on the kink.
So this leaves us with two other parts of L shaped function. The vertical part and the horizontal part.
Over the horizontal portion of the indifference curve $\alpha x_1 > \beta x_2$ the MRS is given as:
$$MRS= \frac{U'_{x_1}}{U'_{x_2}} = \frac{0}{\beta}= 0 $$
So here the MRS is clearly defined.
However, at the vertical portion where $\alpha x_1<\beta x_2$ we will have a problem since:
$$MRS = \frac{U'_{x_1}}{U'_{x_2}} = \frac{\alpha}{0} = \infty | x_1 \wedge x_2 \geq 0 $$
but here on account of division by $0$ some people still say that the MRS is not defined.
However, the tricky part here is that choice of which good goes on $x$-axis and which good goes on $y$-axis is arbitrary. Usually people would put $x_1$ on $x$-axis and $x_2$ on $y$-axis but it is completely fine in principle to put $x_1$ on $y$-axis and $x_2$ on $x$-axis.  In that case the result above would be exactly reversed.
If this is for an exam often people who draft exercises just make some simple answer key that might not cover all possible solutions and maybe the answer key included option where their role was reversed.