Math Formula

Tuesday, September 25, 2012

Should I Eat That Apple Today Or Tomorrow? - Part I

Disclaimer: The study conducted is not at all scientific, and this is by purpose. I know it has several flaws.
Apart from that, there might be several other studies on that topic already. Still, here are my thoughts. You have been warned!

Imagine a basket of apples, which is magically re-filled every day with fresh apples. You have free access to that basket, you are not starving, and you are generally fond of apples.
Every day you can either take one apple, eat and enjoy it; or reject to do so.
Should you eat an apple every day, just because it is free, or can it make sense to constrain yourself on certain days, in order to enjoy it even more the next day?

Not too surprising, the answer is, similar to all questions that are worth being asked at all: It depends!
According to the first model I will present today, it depends on one factor only: On your individual saturation factor. If eating an apple today reduces your level of satisfaction tomorrow by more than a half, skip the apple today; otherwise, eat it.

I will try to explain my chain of thought, as easy and clearly as possible. That's for three reasons:
  • I want to show you that a micro-economic model is nothing that's for university graduates and PhD's only (alright I'll admit, that idea is credited to Karl Popper)
  • I want to show myself that this micro-economic model is nothing that's for university graduates and PhD's only
  • I know this theory is still very weak and probably has fundamental flaws. Probably even similar theories already exist, which I do not know about. Still, I want to fail fast, in order to improve it.
Basic idea
We are talking about the consumption of a freely available good.
This could be an apple, a glass of water, watching TV, or having sex (whereas arguably some of the assumptions made below do not hold).
Each period (say, a day), the consumer faces the decision whether to consume that good or not. Consumption provides some form of satisfaction, which I will further on refer to as utility. The good is assumed to be saturating. If it was consumed in previous periods, it keeps providing utility, but less than in previous periods - because the consumer gets saturated (the technical term is marginal utility).
The consumer wants to maximize her gross utility - the sum of the utility provided every day. How should she decide every day in order to maximize gross utility?

As this is the first version of the model, assumptions are very restrictive. I'll try to weaken some of these in the upcoming weeks; of course also your input and ideas are warmly welcome!

Assumption 1:
There is only one free good, which saturates the consumer.

Assumption 2:
The good provides some form of utility, but is not necessary to survive.

Assumption 3:
The consumption decision is to be made every period (e.g., a day). The amount consumed cannot be chosen, only whether to consume or not at all. Goods cannot be taken and donated, which might provide some utility, too. They can only be consumed or not.

Assumption 4:
If the good was already consumed in the directly precedent period, utility is reduced linearly by the saturation factor. Imagine watching TV every day. Clearly, the level of enjoyment in each period is not that high each time, as if you would watch only once a month.

Assumption 5:
Contrary to a typical spending function, the consumer is indifferent between consuming the apple today or tomorrow. The apple today provides exactly the same utility as the apple tomorrow (in accordance with A4, given no apple was consumed the day prior to that).

Assumption 6:
Consumption of the good in one period does NOT provide utility in the following periods. However, according to A4, if consumed again, utility is reduced.

Assumption 7:
The consumer seeks to optimize the overall utility gained; that is, the sum of all utilities (resulting from A5 and A6).

Alright, being well prepared with these assumptions, it gets slightly mathematical now. Don't worry, I'll try to keep it as short and easy as possible. I hear the critics among you already shouting about homo economicus misusage - and rightly so. Let me respond to this critique at the end.

The variables we'll use are as follows:
  • \(c(t)\) refers to the consumption of the good in the period t. In each period, it can be either 0 (no consumption) or 1 (consumption).
  • \(u(t)\) refers to the utility gained in period t. According to A2 and A4, this depends on the consumption in t, and also the previous period. That is: \[u(t) = f(c(t), c(t-1))\]
  • \(g\) is the gross utility. According to A5, this is the sum of all u(t) over all periods. This is the value to be maximized.
  • The utility factor \(a\). According to A2 and A5, this is the level of utility one single unit of the good (e.g., one apple) would provide if none was consumed in the previous period.
  • The saturation factor \(s\): How much the utility is reduced in period t if the good was consumed in the previous period already, and therefore the consumer is saturated a little bit already. This results from A4. This factor can be any value between 0 and 1. The higher it is, the less the additional utility gained in the period after consumption.
  • The utility function \(f\): How all of the aforementioned variables are related. Resulting from A4, A5 and A6, we can say: \[u(t) = a c(t) - a c(t) c(t-1) s = a c(t) (1 - c(t-1) s)\]
That was a little bit theoretical now, so let me give you an example.

Example 1
Let's look at the consumption of apples across three days.

On the first day, the consumer is totally into apples, so he'll eat the apple. For the sake of that example, let's also eat it on day 2 and 3. So: \[c_1 = 1, c_2 = 1, c_3 = 1\]
Choosing of factor \(a\) is arbitrary, so why not make it 10 (so \(a = 10\))?
Saturation factor \(s\) would be subject to empirical studies; however, I'll just as arbitrarily set it to 0.2 (\(s = 0.2\)).
Question: What is the utility u in each of the 3 periods? What is the gross utility?

Let's start with the utilities in each period.
Utility in first period \(u_1\) is straightforward, because there was no previous period and therefore no saturation to take into account. Thus \[u_1 = a c_1 (1 - c_0 s) = 10 ⋅ 1 (1 - 0 ⋅ 0.2) = 10\]

Utility in second period we get by simply filling into the utility function f:
\[u_2 = a c_2 (1 - c_1 s) = 10 ⋅  1 ⋅ (1 - 1 ⋅ 0.2) = 10 (1 - 0.2) = 8\]

The same is true for period 3:
\[u_3 = a c_3 (1 - c_2 s) = 10 ⋅ 1 ⋅ (1 - 1 ⋅ 0.2) = 10 (1 - 0.2) = 8\]

The gross utility g is the sum of those three:
\[g = u_1 + u_2  + u_3 = 10 + 8 + 8 = 26\]

We can sum up this example as follows:

Period 1 2 3
c(t) 1 1 1
u(t) 108 8
g 10 18 26

Table 1

Wasn't too hard, was it? So let's directly dive into a second example, which empirically comes close to our final answer already.

Example 2
Now, let's assume that the consumer consumed the good in period 1 (similar to example 1, \(c_1 = 1\)). There is no previous period, so the consumer is not at all saturated, so abstinence does not make sense. In period 2 however, the consumer abstains from consumption (\(c_2 = 0\)).
In period 3, he consumes again (\(c_3 = 1)\).
Question: What is the utility u in each of the 3 periods? What is the gross utility?

Similar to the method from above,
\(u_1 = a c_1 = 10\)
\(u_2 = a c_2 (1 - c_1 s) = 10 ⋅ 0 ⋅ (1 - 0.2) = 0\)
\(u_3 = a c_3 (1 - c_2 s) = 10 ⋅ 1 ⋅ (1 - 0 ⋅ 0.2) = 10\)
\(g = 20\)

... or in table representation:
Period 1 2 3
c(t) 1 0 1
u(t) 100 10
g 10 10 20

Table 2

\(g = 20\) is less that in example 1, where \(g = 26\)! That's an interesting finding, because now we know that given an utility factor \(a = 10\) and saturation factor \(s = 0.2\), it does NOT make sense to abstain from consumption. On the contrary, the good should always be consumed!
Let's repeat those two examples, but with another saturation factor s instead; say, \(s = 0.6\).

Example 3
Same setup as in example 1, the consumer always consumes, but \(s = 0.6\).
\(c_1 = 1\)
\(c_2 = 1\)
\(c_3 = 1\)


\(u_1 = a c _1 = 10\)
\(u_2 = a c_2(1 - c_1 s) = 10 ⋅ 1 ⋅ (1 - 0.6) = 4\)
\(u_3 = a c_3 (1 - c_2 s) = 10 ⋅ 1 ⋅ (1 - 1 ⋅ 0.6) = 4\)
\(g = 18\)

Period 1 2 3
c(t) 1 1 1
u(t) 104 4
g 10 14 18

Table 3

Example 4
Same setup as in example 2, the consumer abstains in period 2, but \(s = 0.6\)

\(c_1 = 1\)
\(c_2 = 0\)
\(c_3 = 1\)

\(u_1 = a c _1 = 10\)
\(u_2 = a c_2(1 - c_1 s) = 10 ⋅ 0 ⋅ (1 - 0.6) = 0\)
\(u_3 = a c_3 (1 - c_2 s) = 10 ⋅ 1 ⋅ (1 - 0 ⋅ 0.6) = 10\)
\(g = 20\)

Period 1 2 3
c(t) 1 0 1
u(t) 100 10
g 10 10 20

Table 4

Now the results are the other way around - it pays off now to abstain in period 2!
A modification in the utility factor would not make any difference, because it would simply result in a higher or lower overall utility.

Alright, we're almost there. I want to leave it up to the reader to draw his own conclusions, until I will offer mine during next week.

Should I Eat That Apple Today Or Tomorrow? - Part II can be found here

Wednesday, September 19, 2012

Electronic Communication Is Dead - Long Live Electronic Communication

In the past-PC-age we entered a couple of years ago, mobile devices and ubiquitous internet access have spread enormously.
Consequently, also electronic communication has increased significantly. For a variety of applications, electronic communication is not only a replacement, but even superior to face-to-face communication.

I will further on refer to that as real communication. That's not to say that writing an e-mail or Facebook status updates are unreal; of course they are not. Yet, from my point of view, it's just not as real as talking to somebody while sitting next to him or her.

Electronic communication is a great tool when time or geographical distances have to be overcome. Sometimes, it's also helpful to address a bigger audience.

However, I strongly feel that way too often electronic communication is also chosen even when real communication would easily be feasible. That's sad. Call me conservative, but I truly believe in the value and beauty of real communication. As much as modern platforms try to position themselves as 'social networks', in their very core they are not social at all. People sitting in front of their computers are NOT social; be it 10, 100, or 100 millions of them.

Among the major reasons why electronic communication is preferred over real communication are the aforementioned. Another one is that it's simply that much easier to find out about shared interests and topics to talk about, compared to real conversations, which might be time-consuming and maybe even boring until a topic of shared interest is discovered.

Enough of ranting, and time to offer an alternative.

Why not combine those too - the possibilities that modern devices and technologies offer, resulting in real talks and discussions? I think there is a chance that electronic communication does not have to replace real communication; it might support and facilitate it instead!

Expect more on that topic soon from my side.

If that caught your attention, please leave a comment below, and I'll make sure I'll keep you up to date.

Electronic communication is dead - long live electronic communication ... as a facilitator for real communication!

Tuesday, September 11, 2012

Buchrezension: Christian Felber - 50 Vorschläge für eine gerechtere Welt

Disclaimer: This is a review of Christian Felber's 50 Vorschläge für eine gerechtere Welt. As far as I know, this book is only available in German, which is why I'll also write the review in German. Sorry to my English-speaking fellows.


Wie schon der Klappentext von "50 Vorschläge für eine gerechtere Welt" nahelegt, wird in diesem Buch keine wissenschaftliche Analyse von Einkommensgerechtigkeit, Entwicklungshilfe, Staatsverschuldung und die Rolle von TNCs (Transnational Corporations) im globalen Wirtschaftsleben vorgenommen, sondern Christian Felber's subjektive Auffassung der Welt dargestellt. Ein Blick auf das Inhaltsverzeichnis ("Zinsen runter!", "Börsen auf euren Platz!", "Zähmung von Konzernen") spricht eine ebenso klare Sprache.

Weiters - und auch das muss man ihm zugute halten - erwartet er nicht,  dass sämtliche seiner 50 Vorschläge auf Zustimmung stoßen, sondern "... wichtig ist, dass das Nachdenken über Alternativen angeregt wird".

Die Erwartungen des Lesers von Vornherein derart zu kanalisieren zeugt von Authentizität, spricht mich an und veranlasst mich, auf den kommenden 330 Seiten stets wachsam vor blinder Zustimmung und kritisch zu sein.

Keine Frage, Christian Felber wählt seine Worte mit Bedacht und ist sehr geschickt darin, passende Zahlen und Statistiken seinem Standpunkt gemäß zu zitieren. Eine große Bandbreite von gesellschaftlichen und wirtschaftlichen Themen wird angesprochen - globale und nationale Steuern, die Rolle von Weltbank, IMF und WTO in einer globalisierten Wirtschaftswelt, Umweltverschmutzung, Mindestlohn und Grundeinkommen, Patente, Agrarwirtschaft, nachhaltige Entwicklung, ...
Leider ist mein Wissensstand in vielen von diesen Themen auf Binsenweisheiten beschränkt, sodass es mir schwer fällt, mir über den Wahrheitsgehalt der angegeben Hypothesen und die Sinnhaftigkeit der vorgeschlagenen Lösungen ein Urteil zu bilden.

Über mindestens zwei der Vorschläge meine ich aber, ein gewisses Verständnis zu haben. Diese beiden Vorschläge veranlassen mich zu Kritik nicht nur den Inhalt betreffend, sondern auch die Herangehensweise.

Vorschlag (1) Ein neues Bretton Woods
Um spekulativen Attacken auf Währungen Einhalt zu gebieten und Währungsstabilität zu gewährleisten, schlägt Felber ein System "fixer Wechselkurse" auf globaler Ebene vor, für das der Euro eine gute Vorstufe darstellen würde.
Er räumt zwar kurz ein, dass damit sämtliche Staaten ein äußerst wichtiges Instrument der Finanzpolitik aus der Hand geben würden, relativiert dies aber sogleich wieder, indem er sogar noch einen Schritt weiter geht und weltweit besser koordinierte oder sogar zentralisierte Wirtschaftspolitik fordert - die offenbar nicht einmal im Euroraum möglich noch von den EU-Bürgern gewünscht ist!

Denjenigen Lesern, die nicht zufällig Finanzpolitik studiert haben, eine Lösung derart in den Mund zu legen, ohne zumindest ausreichend auf die Risiken und Nebenwirkungen hinzuweisen, steht meiner Auffassung nach der von Felber selbst geforderten Transparenz, Toleranz und Offenheit diametral gegenüber.

Vorschlag (19) Globale einheitliche Konzernbesteuerung
Felber fordert hier global einheitliche Steuersätze für Konzerne und kritisiert Steuerflucht in Steueroasen.
Auf Seite 146 schreibt er: "Eine effektive Sofortmaßnahme gegen Steuerflucht wäre die Erhöhung der Zahl der BetriebsprüferInnen ... In Österreich ist die Zahl der BetriebsprüferInnen zwischen 2000 und 2004 um 13 Prozent auf 1554 gesunken ... Hinter dem Personalabbau kann nur das ideologische Motiv des Rückzugs des Staates stecken."

Auch hier wird nur eine Alternative - die freie Interpretation der Tatsachen durch Felber - dargestellt und als einzige Möglichkeit präsentiert. Kann es nicht auch sein, dass durch technologische Errungenschaften, verbesserte Computersysteme, bessere automatisierte Prüfungen, mehr Effizienz, ... der Personalabbau möglich wurde?

Wiederum zwingt Felber seinen Rückschluss auf, und lässt dem Leser keinen Spielraum, sich ein eigenes Bild des dargestellten Sachverhaltes zu bilden.

Natürlich ist es ein bisschen unfair von mir, aus über 300 Seiten, teilweise sicher gut durchdachten und recherchierten Materials, zwei Absätze herauszusuchen und auf diesen herumzuhacken. Jedoch, wenn sich mir derartige Fragen stellen, bei den beiden Sachgebieten, von denen ich meine etwas zu verstehen - wie mag es sich wohl mit den anderen verhalten, bei denen ich über weniger Vorwissen verfüge?

Für ebenfalls etwas unglücklich halte ich die inflationäre Verwendung des Wortes "Demokratie", die Felber vor, hinter, und neben alles stellt. Tatsachen sind in dieser dichotomen Darstellung entweder strikt demokratisch (= unbedingt gut und positiv) oder undemokratisch (= unbedingt böse, schlecht, negativ).

Auch wenn Felber Sprecher von Attac Österreich ist, macht ihn das nicht automatisch zum Sprachrohr der "globalen Zivilgesellschaft", die wohl mehrere Ausprägungen, Dimensionen und Strömungen hat. Ein Beispiel dazu (S. 187): " ... genau das wäre aber das Prinzip der 'Ernährungssouveränität', das von den sozialen Bewegungen des Südens und der globalen Zivilgesellschaft eingefordert wird."

Aller Kritik zum Trotz muss ich Felber ein großes Lob aussprechen. Es ist ihm gelungen, sein selbsternanntes Ziel zu erreichen - mich zum Nachdenken anzuregen. Vieles war mir komplett neu und werde ich künftig in einem anderen Licht betrachten und hinterfragen.
Einem Jeden, der offen für alternative Gedanken über Gesellschaft, Wirtschaft und Umwelt, und bereit ist, diesen mit einer gesunden Portion Skepsis und kritischem Denken zu begegnen, sei dieses Werk ans Herz gelegt.

Tuesday, September 4, 2012

A Typical Day ... In The Life Of An IT Project Leader

When talking with friends and relatives, a question that I'm asked quite frequently is "... and what exactly do you do at your job?". Answering that somebody decided to give my current job the title "IT project leader" wouldn't help too much.
First, because the majority of people don't work in IT and consequently don't have a clear picture about daily business.
Second, because I've come to realize that even within the IT industry there is a huge variety of possible "project leader" responsibilities and tasks.
And third, as you might know, job titles don't mean too much anyways.

Thus, I've decided to describe what a typical day in my current job looks like.


Some background information first: I'm currently working on a project in a Bosnian-Herzegovinian administration. The project is funded by the European Union and the main goal is to bring the country closer to EU standards in the field of VAT and customs legislation and procedures, and with regard to the IT systems used. I'm in charge of the IT part of that project.

So, my small team and I normally start working at 8.30. We are not particularly strict on the working hours, however we do not allow flexitime nor tele-working. I'm strongly convinced that there is no replacement for sitting next to each other and discussing face-to-face.

Mondays ...

On Mondays, we get the week started with a short review of the previous week's achievements, problems encountered, and questions arisen. We also discuss this week's main tasks, technical questions and make key decisions together.
Among other reasons, I think this is an important team building measure, helps to develop common knowledge, and represents a platform to encourage team members to share what they are proud of and improve their communication skills.
Apart from that, we call for a meeting spontaneously at need or simply discuss informally with each other anytime.


Daily Business

On other days, I might have meetings with representatives of the local administration. We talk about their exact requirements for certain IT programs we are about to develop, testing and training for these programs, knowledge transfer to local employees, hardware issues and administrative stuff.
Unfortunately, my local language skills are still far from sufficient to discuss important matters, so half of the time is lost in translation.

Depending on which stage we are in one of our sub-projects, I would typically spend some time on planning activities then. Which additional information do we need to make the next steps? Whom do I get this information from? Which technology should we use for that project? What should that program look like? How busy are my colleagues at the moment, and which of these planning or pre-development tasks should I delegate to them? Which sub-tasks should be done for that project, how are they related, and until when should they be done? On which hardware infrastructure will we install that system, and whom do we need for that? When are the meeting rooms for testing available, and whom should we invite to it?

A scrum board, similar to the one used by us. Source:

As we are that small a team, I do some programming too. Sometimes, that comes as a nice alternation to all these meetings and planning stuff, which are not always particularly amusing. Furthermore, it helps me to better understand what's going on beneath the surface of our programs.

Every now and then, I grab a chair and sit with members of my team directly to check their progress or problems encountered. Even though I try to avoid micro-managing as much as possible and sit with them only when they call me, I sometimes take the freedom and check spontaneously when I feel that circumstances demand it. For example, when we agreed that a certain user interface form should be provided within two days, and I haven't heard anything from him for four days.
Again, I want to give them the possibility to show what they are proud of, and establish and maintain trust between each other. In case somebody is stuck somewhere, I like to ask such basic questions until they have broken the problem to such small chunks that the solution comes inevitably to them (that is, I take the role of a rubber duck).

Since I'm responsible for the products that we deliver, I also test the software before any of our clients sees it. This is the moment when all the various parts that my colleagues worked on are connected, and potential design or usability issues show. Sometimes I have to turn colleagues down on their proposals, because they would not be do-able in reasonable time, or would not make sense to the final users, even though they might be nice from a technicians point of view.
Part of my job prior to delivering a product is to write guidelines and handbooks for the users. Not very entertaining, but necessary.


However, there are also some challenges that are out of our control. For example, sometimes expectations from the EU and the beneficiary are not quite in line with each other; we act as an intermediary between them and have to find some solution.

A huge obstacle for progress in Bosnia-Herzegovina as a whole is politics. No government for quite a while, no key-decisions made, budgetary problems, ... These impediments have a negative impact on our work, too, because by the end of the day, whatever we do and provide is subject to legal boundaries.

Personally, I strongly believe in all my colleagues' intrinsic motivation, and do everything I can to remove all potential barriers, in order to enable them to do their best job.

Working Environment

Our working environment is a little bit suboptimal. Our chairs might have been acceptable some 15 years ago, but are definitely not any more now; in our office, there is no real window to the outside world, and for weeks we have been suffering in the heat, because the one and only guy who would know how to fix the air condition is on vacation.

Well, at least our office is not in the basement. Source:

Once a quarter, I meet with representatives of the European Delegation and assistance directors of the local administration to discuss the overall progress of our project and obstacles encountered. Quality of and participation at these meetings varies.

Fridays ...

By the end of the week, I have to provide a report for the European Delegation in Sarajevo, which monitors the progress of our project against certain performance indicators.


For the non IT guys among you, I hope that I managed to create a rough picture of my work. For the IT guys, I hope that I made you smile at least once or twice when recognizing certain things from your workaday life ;-).

Generally speaking, it seems to me that most people (including me) have no clue what most other people are actually doing in their job. Some "typical days" I already found on the web include:
Still, more "typical days" would be totally interesting - so why not share yours in the comments below?

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